Subgroups — C₃×#61075 #10679682

Order 768.

2740 conjugacy classes of subgroups.

The subgroup lattice has 1412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#577	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3488	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#3486	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#3285	C₂	1	2	yes	maximal, complemented
6	C₃×D₄×SD₁₆	C₂	1	2	yes	maximal, complemented
7	C₃×#3278	C₂	1	2	yes	maximal, complemented
8	C₃×#3275	C₂	1	2	yes	maximal, complemented
9	C₃×#3271	C₂	1	2	yes	maximal, complemented
10	C₃×#3270	C₂	1	2	yes	maximal, complemented
11	C₃×#3266	C₂	1	2	yes	maximal, complemented
12	C₃×#3265	C₂	1	2	yes	maximal, complemented
13	C₃×#3154	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3055	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3046	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#3043	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#3009	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2947	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2933	C₂	1	1	yes	maximal, characteristic, complemented
24	#61075	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
27	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
28	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₃×#577	—	2	8	no	—
30	C₂×C₃×#137	—	2	8	no	—
31	C₂×C₃×#137	C₂²	1	1	yes	characteristic
32	C₂×C₃×#137	C₂²	1	1	yes	characteristic
33	C₂×C₃×#137	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₃×#137	C₂²	1	2	yes	complemented
35	C₂×C₃×#137	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×#137	C₂²	1	2	yes	complemented
37	C₂×C₃×#137	C₂²	1	2	yes	complemented
38	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
40	C₂×C₃×#135	C₂²	1	1	yes	characteristic
41	C₂×C₃×#135	C₂²	1	2	yes	complemented
42	C₂×C₃×#135	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₃×Q₁₆	C₂²	1	2	yes	complemented
44	C₂²×C₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₃×SD₁₆	C₂²	1	2	yes	complemented
46	C₂²×C₃×SD₁₆	C₂²	1	2	yes	complemented
47	C₂²×C₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₃×#131	C₂²	1	1	yes	characteristic, complemented
49	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
50	C₃×#550	C₂²	1	2	yes	—
51	C₃×D₄×Q₈	—	2	1	no	—
52	C₃×D₄×Q₈	—	2	1	no	—
53	C₃×D₄×Q₈	C₂²	1	2	yes	complemented
54	C₃×D₄×Q₈	C₂²	1	2	yes	complemented
55	C₃×#548	—	2	1	no	—
56	C₃×#548	—	2	1	no	—
57	C₃×#548	C₂²	1	2	yes	—
58	C₃×#548	C₂²	1	2	yes	complemented
59	C₃×#548	C₂²	1	2	yes	complemented
60	C₃×#546	—	2	2	no	—
61	C₃×#546	C₂²	1	2	yes	—
62	C₃×D₄²	—	2	2	no	—
63	C₃×D₄²	C₂²	1	2	yes	—
64	C₃×#537	—	2	1	no	—
65	C₃×#537	C₂²	1	1	yes	characteristic
66	C₃×#536	—	2	2	no	—
67	C₃×#536	C₂²	1	1	yes	characteristic, complemented
68	C₃×#536	C₂²	1	1	yes	characteristic, complemented
69	C₃×#535	—	2	1	no	—
70	C₃×#535	C₂²	1	1	yes	characteristic
71	C₃×#525	—	2	1	no	—
72	C₃×#525	—	2	2	no	—
73	C₃×#525	C₂²	1	1	yes	characteristic
74	C₃×#525	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₃×#121	—	2	1	no	—
76	C₂×C₃×#121	C₂²	1	1	yes	characteristic
77	C₃×#520	C₂²	1	1	yes	characteristic
78	C₃×#519	C₂²	1	1	yes	characteristic, complemented
79	C₃×#497	C₂²	1	2	yes	complemented
80	C₃×#496	C₂²	1	2	yes	complemented
81	C₃×#495	C₂²	1	2	yes	complemented
82	C₃×#492	C₂²	1	2	yes	complemented
83	C₃×#470	C₂²	1	2	yes	complemented
84	C₃×#469	C₂²	1	2	yes	complemented
85	C₃×#468	C₂²	1	2	yes	complemented
86	C₃×#468	C₂²	1	2	yes	complemented
87	C₃×#467	C₂²	1	2	yes	complemented
88	C₃×#466	C₂²	1	2	yes	complemented
89	C₃×#465	C₂²	1	2	yes	complemented
90	C₃×#465	C₂²	1	2	yes	complemented
91	C₃×#464	C₂²	1	2	yes	complemented
92	C₃×#464	C₂²	1	2	yes	complemented
93	C₃×#464	C₂²	1	2	yes	complemented
94	C₃×#463	C₂²	1	2	yes	complemented
95	C₃×#462	C₂²	1	2	yes	complemented
96	C₃×#461	C₂²	1	2	yes	complemented
97	C₃×#460	C₂²	1	2	yes	complemented
98	C₃×#460	C₂²	1	2	yes	complemented
99	C₃×#452	C₂²	1	1	yes	characteristic, complemented
100	C₃×#452	C₂²	1	1	yes	characteristic, complemented
101	C₃×#452	C₂²	1	2	yes	complemented
102	C₃×#452	C₂²	1	2	yes	complemented
103	C₃×#452	C₂²	1	2	yes	complemented
104	C₃×#451	C₂²	1	1	yes	characteristic, complemented
105	C₃×#451	C₂²	1	2	yes	complemented
106	C₃×#450	C₂²	1	1	yes	characteristic, complemented
107	C₃×#450	C₂²	1	2	yes	complemented
108	C₃×#450	C₂²	1	2	yes	complemented
109	C₃×#449	C₂²	1	1	yes	characteristic, complemented
110	C₃×#449	C₂²	1	1	yes	characteristic, complemented
111	C₃×#449	C₂²	1	2	yes	complemented
112	C₃×#448	C₂²	1	2	yes	complemented
113	C₃×#448	C₂²	1	2	yes	complemented
114	C₃×#448	C₂²	1	2	yes	complemented
115	C₃×#448	C₂²	1	2	yes	complemented
116	C₃×#448	C₂²	1	1	yes	characteristic, complemented
117	C₃×#448	C₂²	1	2	yes	complemented
118	C₃×#447	C₂²	1	1	yes	characteristic, complemented
119	C₃×#441	C₂²	1	2	yes	complemented
120	C₃×#440	C₂²	1	2	yes	complemented
121	C₃×C₄×Q₁₆	C₂²	1	2	yes	complemented
122	C₃×C₄×SD₁₆	C₂²	1	2	yes	complemented
123	C₃×#436	C₂²	1	2	yes	complemented
124	C₃×#435	C₂²	1	2	yes	complemented
125	C₃×#435	C₂²	1	2	yes	complemented
126	C₃×C₈×D₄	C₂²	1	2	yes	complemented
127	C₃×#428	C₂²	1	1	yes	characteristic, complemented
128	C₃×#424	C₂²	1	1	yes	characteristic, complemented
129	C₃×#418	C₂²	1	1	yes	characteristic, complemented
130	C₃×#417	C₂²	1	1	yes	characteristic, complemented
131	C₃×#416	C₂²	1	1	yes	characteristic
132	C₃×#416	C₂²	1	1	yes	characteristic, complemented
133	C₂×C₃×#103	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₃×#103	C₂²	1	1	yes	characteristic, complemented
135	C₃×#408	C₂²	1	1	yes	characteristic, complemented
136	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
137	C₃×#405	C₂²	1	1	yes	characteristic, complemented
138	C₂×#577	C₂×C₃	1	1	yes	characteristic, complemented
139	C₂²×#137	C₂×C₃	1	1	yes	characteristic, complemented
140	#3488	C₂×C₃	1	1	yes	characteristic, complemented
141	#3486	C₂×C₃	1	1	yes	characteristic, complemented
142	#3285	C₂×C₃	1	2	yes	complemented
143	D₄×SD₁₆	C₂×C₃	1	2	yes	complemented
144	#3278	C₂×C₃	1	2	yes	complemented
145	#3275	C₂×C₃	1	2	yes	complemented
146	#3271	C₂×C₃	1	2	yes	complemented
147	#3270	C₂×C₃	1	2	yes	complemented
148	#3266	C₂×C₃	1	2	yes	complemented
149	#3265	C₂×C₃	1	2	yes	complemented
150	#3154	C₂×C₃	1	1	yes	characteristic, complemented
151	#3063	C₂×C₃	1	1	yes	characteristic, complemented
152	#3055	C₂×C₃	1	1	yes	characteristic, complemented
153	#3046	C₂×C₃	1	1	yes	characteristic, complemented
154	#3043	C₂×C₃	1	1	yes	characteristic, complemented
155	#3013	C₂×C₃	1	1	yes	characteristic, complemented
156	#3009	C₂×C₃	1	1	yes	characteristic, complemented
157	#3002	C₂×C₃	1	1	yes	characteristic, complemented
158	C₂×#448	C₂×C₃	1	1	yes	characteristic, complemented
159	#2947	C₂×C₃	1	1	yes	characteristic, complemented
160	#2933	C₂×C₃	1	1	yes	characteristic, complemented
161	C₃×2₋¹⁺⁴	—	2	4	no	—
162	C₃×2₋¹⁺⁴	—	4	2	no	—
163	C₃×H(5,𝔽₂)	—	2	4	no	—
164	C₃×H(5,𝔽₂)	—	4	2	no	—
165	C₂×C₃×#41	—	2	1	no	—
166	C₂×C₃×#41	—	2	2	no	—
167	C₂×C₃×#41	—	2	1	no	—
168	C₂×C₃×#41	—	2	1	no	—
169	C₂×C₃×#41	—	2	1	no	—
170	C₂×C₃×#41	—	2	4	no	—
171	C₂×C₃×#41	—	4	2	no	—
172	C₂×C₃×#41	C₂³	1	1	yes	characteristic
173	C₂×C₃×#41	C₂³	1	1	yes	characteristic
174	C₂×C₃×#41	C₂³	1	2	yes	—
175	C₂×C₃×#41	C₂³	1	2	yes	—
176	C₂×C₃×#41	C₂³	1	1	yes	characteristic
177	C₂×C₃×#41	C₂³	1	1	yes	characteristic
178	C₂×C₃×#41	C₂³	1	1	yes	characteristic
179	C₂×C₃×#41	C₂³	1	1	yes	characteristic
180	C₂²×C₃×Q₈	—	2	1	no	—
181	C₂²×C₃×Q₈	—	2	1	no	—
182	C₂²×C₃×Q₈	—	2	1	no	—
183	C₂²×C₃×Q₈	—	2	1	no	—
184	C₂²×C₃×Q₈	—	2	4	no	—
185	C₂²×C₃×Q₈	—	4	2	no	—
186	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
187	C₂²×C₃×Q₈	C₂³	1	2	yes	—
188	C₂²×C₃×Q₈	C₂³	1	2	yes	—
189	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
190	C₂²×C₃×Q₈	C₂³	1	2	yes	—
191	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
192	C₂²×C₃×D₄	—	2	1	no	—
193	C₂²×C₃×D₄	—	2	1	no	—
194	C₂²×C₃×D₄	—	2	1	no	—
195	C₂²×C₃×D₄	—	2	2	no	—
196	C₂²×C₃×D₄	—	2	2	no	—
197	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
198	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
199	C₂²×C₃×D₄	C₂³	1	2	yes	—
200	C₂³×C₃×C₄	—	2	1	no	—
201	C₂³×C₃×C₄	—	2	1	no	—
202	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
203	C₃×#137	—	2	4	no	—
204	C₃×#137	—	2	4	no	—
205	C₃×#137	—	2	8	no	—
206	C₃×#137	—	2	8	no	—
207	C₃×#137	—	2	8	no	—
208	C₃×#137	—	2	4	no	—
209	C₃×#137	D₄	1	8	yes	complemented
210	C₃×AGL(1,ℤ/8)	—	2	8	no	—
211	C₃×AGL(1,ℤ/8)	—	2	4	no	—
212	C₃×#135	—	2	4	no	—
213	C₃×#135	—	2	8	no	—
214	C₃×#135	—	4	2	no	—
215	C₂×C₃×Q₁₆	—	2	8	no	—
216	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
217	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
218	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
219	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
220	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
221	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
222	C₂×C₃×SD₁₆	—	2	4	no	—
223	C₂×C₃×SD₁₆	—	2	8	no	—
224	C₂×C₃×SD₁₆	—	2	8	no	—
225	C₂×C₃×SD₁₆	—	4	2	no	—
226	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
227	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
228	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
229	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
230	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
231	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
232	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
233	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
234	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
235	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
236	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
237	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
238	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
239	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
240	C₂×C₃×D₈	C₂³	1	2	yes	—
241	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
242	C₃×#131	—	2	4	no	—
243	C₂×C₃×M₁₆	—	2	4	no	—
244	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
245	C₂×C₃×M₁₆	C₂³	1	2	yes	—
246	C₂×C₃×M₁₆	C₂³	1	2	yes	—
247	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
248	C₂²×C₃×C₈	C₂³	1	2	yes	—
249	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
250	C₂²×C₃×C₈	C₂³	1	2	yes	—
251	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
252	C₃×C₄⋊Q₈	—	2	1	no	—
253	C₃×C₄⋊Q₈	—	2	2	no	—
254	C₃×C₄⋊Q₈	—	2	2	no	—
255	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
256	C₃×#127	—	2	2	no	—
257	C₃×#127	C₂³	1	2	yes	—
258	C₃×#124	—	2	1	no	—
259	C₃×#124	—	2	2	no	—
260	C₃×#124	—	2	2	no	—
261	C₃×#124	—	2	2	no	—
262	C₃×#124	C₂³	1	2	yes	—
263	C₃×#124	C₂³	1	2	yes	—
264	C₃×#123	—	2	2	no	—
265	C₃×#123	—	2	1	no	—
266	C₃×#123	—	2	2	no	—
267	C₃×#123	—	2	2	no	—
268	C₃×#123	D₄	1	2	yes	—
269	C₃×C₂²⋊Q₈	—	2	1	no	—
270	C₃×C₂²⋊Q₈	—	2	2	no	—
271	C₃×C₂²⋊Q₈	—	2	2	no	—
272	C₃×C₂²⋊Q₈	—	2	1	no	—
273	C₃×C₂²⋊Q₈	—	2	1	no	—
274	C₃×C₂²⋊Q₈	—	2	2	no	—
275	C₃×C₂²⋊Q₈	—	2	2	no	—
276	C₃×C₂²⋊Q₈	—	2	2	no	—
277	C₃×C₂²⋊Q₈	—	2	2	no	—
278	C₃×C₂²⋊Q₈	—	2	2	no	—
279	C₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
280	C₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
281	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
282	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
283	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
284	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
285	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
286	C₃×#121	—	2	1	no	—
287	C₃×#121	—	2	2	no	—
288	C₃×#121	—	2	2	no	—
289	C₃×#121	—	2	2	no	—
290	C₃×#121	—	2	2	no	—
291	C₃×#121	—	2	1	no	—
292	C₃×#121	—	2	1	no	—
293	C₃×#121	—	2	1	no	—
294	C₃×#121	—	2	1	no	—
295	C₃×#121	—	2	2	no	—
296	C₃×#121	—	2	2	no	—
297	C₃×#121	—	2	2	no	—
298	C₃×#121	—	2	2	no	—
299	C₃×#121	D₄	1	1	yes	characteristic
300	C₃×#121	D₄	1	1	yes	characteristic
301	C₃×#121	C₂³	1	1	yes	characteristic
302	C₃×#121	C₂³	1	2	yes	—
303	C₃×#121	C₂³	1	2	yes	—
304	C₃×#121	C₂³	1	2	yes	—
305	C₃×#121	C₂³	1	1	yes	characteristic
306	C₃×#120	—	2	1	no	—
307	C₃×#120	—	2	2	no	—
308	C₃×#120	—	2	2	no	—
309	C₃×#120	—	2	2	no	—
310	C₃×#120	—	2	2	no	—
311	C₃×#120	D₄	1	2	yes	—
312	C₃×C₄×Q₈	—	2	1	no	—
313	C₃×C₄×Q₈	—	2	1	no	—
314	C₃×C₄×Q₈	C₂³	1	2	yes	—
315	C₃×C₄×Q₈	C₂³	1	2	yes	—
316	C₃×C₄×Q₈	C₂³	1	2	yes	—
317	C₃×C₄×D₄	—	2	2	no	—
318	C₃×C₄×D₄	—	2	2	no	—
319	C₃×C₄×D₄	—	2	1	no	—
320	C₃×C₄×D₄	—	2	1	no	—
321	C₃×C₄×D₄	—	2	2	no	—
322	C₃×C₄×D₄	—	2	2	no	—
323	C₃×C₄×D₄	—	2	2	no	—
324	C₃×C₄×D₄	—	2	2	no	—
325	C₃×C₄×D₄	—	2	2	no	—
326	C₃×C₄×D₄	C₂³	1	2	yes	—
327	C₃×C₄×D₄	C₂³	1	2	yes	—
328	C₃×C₄×D₄	C₂³	1	2	yes	—
329	C₃×#117	—	2	1	no	—
330	C₃×#117	—	2	2	no	—
331	C₃×#117	C₂³	1	1	yes	characteristic
332	C₃×#117	C₂³	1	1	yes	characteristic
333	C₂×C₃×C₄⋊C₄	—	2	1	no	—
334	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
335	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
336	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
337	C₃×#107	C₂³	1	2	yes	—
338	C₃×#106	C₂³	1	2	yes	—
339	C₃×C₄⋊C₈	C₂³	1	2	yes	—
340	C₃×C₄⋊C₈	C₂³	1	2	yes	—
341	C₃×#103	C₂³	1	2	yes	—
342	C₃×#103	C₂³	1	2	yes	—
343	C₃×#103	C₂³	1	2	yes	—
344	C₃×#103	C₂³	1	2	yes	—
345	C₃×#103	C₂³	1	1	yes	characteristic
346	C₃×#103	C₂³	1	1	yes	characteristic
347	C₃×#103	C₂³	1	1	yes	characteristic
348	C₃×#103	C₂³	1	1	yes	characteristic
349	C₃×#103	C₂³	1	2	yes	—
350	C₃×#102	C₂³	1	1	yes	characteristic
351	C₃×#102	C₂³	1	1	yes	characteristic
352	C₃×#102	C₂³	1	1	yes	characteristic
353	C₃×#102	C₂³	1	1	yes	characteristic
354	C₃×#102	C₂³	1	2	yes	—
355	C₃×#102	C₂³	1	2	yes	—
356	C₃×#102	C₂³	1	2	yes	—
357	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
358	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
359	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
360	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
361	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
362	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
363	C₃×#97	C₂³	1	2	yes	—
364	C₃×C₄×C₈	C₂³	1	2	yes	—
365	C₂×2₋¹⁺⁴	C₂²×C₃	1	1	yes	characteristic, complemented
366	C₂×H(5,𝔽₂)	C₂²×C₃	1	1	yes	characteristic
367	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
368	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
369	#577	—	2	8	no	—
370	C₂×#137	—	2	8	no	—
371	C₂×#137	C₂²×C₃	1	1	yes	characteristic
372	C₂×#137	C₂²×C₃	1	1	yes	characteristic
373	C₂×#137	C₂²×C₃	1	1	yes	characteristic, complemented
374	C₂×#137	C₂²×C₃	1	2	yes	complemented
375	C₂×#137	C₂²×C₃	1	1	yes	characteristic, complemented
376	C₂×#137	C₂²×C₃	1	2	yes	complemented
377	C₂×#137	C₂²×C₃	1	2	yes	complemented
378	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	1	yes	characteristic, complemented
379	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	complemented
380	C₂×#135	C₂²×C₃	1	1	yes	characteristic
381	C₂×#135	C₂²×C₃	1	2	yes	complemented
382	C₂×#135	C₂²×C₃	1	1	yes	characteristic, complemented
383	C₂²×Q₁₆	C₂²×C₃	1	2	yes	complemented
384	C₂²×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
385	C₂²×SD₁₆	C₂²×C₃	1	2	yes	complemented
386	C₂²×SD₁₆	C₂²×C₃	1	2	yes	complemented
387	C₂²×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
388	C₂×#131	C₂²×C₃	1	1	yes	characteristic, complemented
389	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
390	#550	C₂²×C₃	1	2	yes	—
391	D₄×Q₈	—	2	1	no	—
392	D₄×Q₈	—	2	1	no	—
393	D₄×Q₈	C₂²×C₃	1	2	yes	complemented
394	D₄×Q₈	C₂²×C₃	1	2	yes	complemented
395	#548	—	2	1	no	—
396	#548	—	2	1	no	—
397	#548	C₂²×C₃	1	2	yes	—
398	#548	C₂²×C₃	1	2	yes	complemented
399	#548	C₂²×C₃	1	2	yes	complemented
400	#546	—	2	2	no	—
401	#546	C₂²×C₃	1	2	yes	—
402	D₄²	—	2	2	no	—
403	D₄²	C₂²×C₃	1	2	yes	—
404	#537	—	2	1	no	—
405	#537	C₂²×C₃	1	1	yes	characteristic
406	#536	—	2	2	no	—
407	#536	C₂²×C₃	1	1	yes	characteristic, complemented
408	#536	C₂²×C₃	1	1	yes	characteristic, complemented
409	#535	—	2	1	no	—
410	#535	C₂²×C₃	1	1	yes	characteristic
411	#525	—	2	1	no	—
412	#525	—	2	2	no	—
413	#525	C₂²×C₃	1	1	yes	characteristic
414	#525	C₂²×C₃	1	1	yes	characteristic, complemented
415	C₂×#121	—	2	1	no	—
416	C₂×#121	C₂²×C₃	1	1	yes	characteristic
417	#520	C₂²×C₃	1	1	yes	characteristic
418	#519	C₂²×C₃	1	1	yes	characteristic, complemented
419	#497	C₂²×C₃	1	2	yes	complemented
420	#496	C₂²×C₃	1	2	yes	complemented
421	#495	C₂²×C₃	1	2	yes	complemented
422	#492	C₂²×C₃	1	2	yes	complemented
423	#470	C₂²×C₃	1	2	yes	complemented
424	#469	C₂²×C₃	1	2	yes	complemented
425	#468	C₂²×C₃	1	2	yes	complemented
426	#468	C₂²×C₃	1	2	yes	complemented
427	#467	C₂²×C₃	1	2	yes	complemented
428	#466	C₂²×C₃	1	2	yes	complemented
429	#465	C₂²×C₃	1	2	yes	complemented
430	#465	C₂²×C₃	1	2	yes	complemented
431	#464	C₂²×C₃	1	2	yes	complemented
432	#464	C₂²×C₃	1	2	yes	complemented
433	#464	C₂²×C₃	1	2	yes	complemented
434	#463	C₂²×C₃	1	2	yes	complemented
435	#462	C₂²×C₃	1	2	yes	complemented
436	#461	C₂²×C₃	1	2	yes	complemented
437	#460	C₂²×C₃	1	2	yes	complemented
438	#460	C₂²×C₃	1	2	yes	complemented
439	#452	C₂²×C₃	1	1	yes	characteristic, complemented
440	#452	C₂²×C₃	1	1	yes	characteristic, complemented
441	#452	C₂²×C₃	1	2	yes	complemented
442	#452	C₂²×C₃	1	2	yes	complemented
443	#452	C₂²×C₃	1	2	yes	complemented
444	#451	C₂²×C₃	1	1	yes	characteristic, complemented
445	#451	C₂²×C₃	1	2	yes	complemented
446	#450	C₂²×C₃	1	1	yes	characteristic, complemented
447	#450	C₂²×C₃	1	2	yes	complemented
448	#450	C₂²×C₃	1	2	yes	complemented
449	#449	C₂²×C₃	1	1	yes	characteristic, complemented
450	#449	C₂²×C₃	1	1	yes	characteristic, complemented
451	#449	C₂²×C₃	1	2	yes	complemented
452	#448	C₂²×C₃	1	2	yes	complemented
453	#448	C₂²×C₃	1	2	yes	complemented
454	#448	C₂²×C₃	1	2	yes	complemented
455	#448	C₂²×C₃	1	2	yes	complemented
456	#448	C₂²×C₃	1	1	yes	characteristic, complemented
457	#448	C₂²×C₃	1	2	yes	complemented
458	#447	C₂²×C₃	1	1	yes	characteristic, complemented
459	#441	C₂²×C₃	1	2	yes	complemented
460	#440	C₂²×C₃	1	2	yes	complemented
461	C₄×Q₁₆	C₂²×C₃	1	2	yes	complemented
462	C₄×SD₁₆	C₂²×C₃	1	2	yes	complemented
463	#436	C₂²×C₃	1	2	yes	complemented
464	#435	C₂²×C₃	1	2	yes	complemented
465	#435	C₂²×C₃	1	2	yes	complemented
466	C₈×D₄	C₂²×C₃	1	2	yes	complemented
467	#428	C₂²×C₃	1	1	yes	characteristic, complemented
468	#424	C₂²×C₃	1	1	yes	characteristic, complemented
469	#418	C₂²×C₃	1	1	yes	characteristic, complemented
470	#417	C₂²×C₃	1	1	yes	characteristic, complemented
471	#416	C₂²×C₃	1	1	yes	characteristic
472	#416	C₂²×C₃	1	1	yes	characteristic, complemented
473	C₂×#103	C₂²×C₃	1	1	yes	characteristic, complemented
474	C₂×#103	C₂²×C₃	1	1	yes	characteristic, complemented
475	#408	C₂²×C₃	1	1	yes	characteristic, complemented
476	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
477	#405	C₂²×C₃	1	1	yes	characteristic, complemented
478	C₂⁴×C₃	—	2	1	no	—
479	C₂⁴×C₃	—	2	2	no	—
480	C₂⁴×C₃	—	2	1	no	—
481	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
482	C₃×#41	—	2	2	no	—
483	C₃×#41	—	2	2	no	—
484	C₃×#41	—	2	2	no	—
485	C₃×#41	—	2	4	no	—
486	C₃×#41	—	2	4	no	—
487	C₃×#41	—	2	2	no	—
488	C₃×#41	—	2	2	no	—
489	C₃×#41	—	2	2	no	—
490	C₃×#41	—	2	2	no	—
491	C₃×#41	—	2	2	no	—
492	C₃×#41	—	2	2	no	—
493	C₃×#41	—	4	4	no	—
494	C₃×#41	—	4	1	no	—
495	C₃×#41	—	4	1	no	—
496	C₃×#41	—	4	2	no	—
497	C₃×#41	—	4	2	no	—
498	C₃×#41	—	4	4	no	—
499	C₃×#41	—	4	8	no	—
500	C₃×#41	—	4	4	no	—
501	C₃×#41	—	4	4	no	—
502	C₃×#41	C₂×D₄	1	4	yes	—
503	C₂×C₃×Q₈	—	2	1	no	—
504	C₂×C₃×Q₈	—	2	1	no	—
505	C₂×C₃×Q₈	—	2	2	no	—
506	C₂×C₃×Q₈	—	2	2	no	—
507	C₂×C₃×Q₈	—	2	1	no	—
508	C₂×C₃×Q₈	—	2	2	no	—
509	C₂×C₃×Q₈	—	2	2	no	—
510	C₂×C₃×Q₈	—	2	4	no	—
511	C₂×C₃×Q₈	—	2	4	no	—
512	C₂×C₃×Q₈	—	2	2	no	—
513	C₂×C₃×Q₈	—	2	4	no	—
514	C₂×C₃×Q₈	—	2	2	no	—
515	C₂×C₃×Q₈	—	2	2	no	—
516	C₂×C₃×Q₈	—	4	4	no	—
517	C₂×C₃×Q₈	—	4	2	no	—
518	C₂×C₃×Q₈	—	4	2	no	—
519	C₂×C₃×Q₈	—	4	1	no	—
520	C₂×C₃×Q₈	—	4	2	no	—
521	C₂×C₃×Q₈	—	4	4	no	—
522	C₂×C₃×Q₈	—	4	4	no	—
523	C₂×C₃×Q₈	—	4	4	no	—
524	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
525	C₂×C₃×Q₈	C₂×D₄	1	4	yes	complemented
526	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
527	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
528	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
529	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
530	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
531	C₂×C₃×D₄	—	2	1	no	—
532	C₂×C₃×D₄	—	2	2	no	—
533	C₂×C₃×D₄	—	2	4	no	—
534	C₂×C₃×D₄	—	2	1	no	—
535	C₂×C₃×D₄	—	2	1	no	—
536	C₂×C₃×D₄	—	2	2	no	—
537	C₂×C₃×D₄	—	2	1	no	—
538	C₂×C₃×D₄	—	2	1	no	—
539	C₂×C₃×D₄	—	2	1	no	—
540	C₂×C₃×D₄	—	2	2	no	—
541	C₂×C₃×D₄	—	2	2	no	—
542	C₂×C₃×D₄	—	2	1	no	—
543	C₂×C₃×D₄	—	2	2	no	—
544	C₂×C₃×D₄	—	2	2	no	—
545	C₂×C₃×D₄	—	2	2	no	—
546	C₂×C₃×D₄	—	2	1	no	—
547	C₂×C₃×D₄	—	2	2	no	—
548	C₂×C₃×D₄	—	2	1	no	—
549	C₂×C₃×D₄	—	2	2	no	—
550	C₂×C₃×D₄	—	2	2	no	—
551	C₂×C₃×D₄	—	2	2	no	—
552	C₂×C₃×D₄	—	4	1	no	—
553	C₂×C₃×D₄	—	4	2	no	—
554	C₂×C₃×D₄	—	4	4	no	—
555	C₂×C₃×D₄	—	4	8	no	—
556	C₂×C₃×D₄	—	4	4	no	—
557	C₂×C₃×D₄	—	8	4	no	—
558	C₂×C₃×D₄	—	8	2	no	—
559	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
560	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
561	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
562	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
563	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
564	C₂×C₃×D₄	C₂⁴	1	2	yes	—
565	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
566	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
567	C₂²×C₃×C₄	—	2	1	no	—
568	C₂²×C₃×C₄	—	2	1	no	—
569	C₂²×C₃×C₄	—	2	2	no	—
570	C₂²×C₃×C₄	—	2	2	no	—
571	C₂²×C₃×C₄	—	2	1	no	—
572	C₂²×C₃×C₄	—	2	2	no	—
573	C₂²×C₃×C₄	—	2	2	no	—
574	C₂²×C₃×C₄	—	2	2	no	—
575	C₂²×C₃×C₄	—	2	1	no	—
576	C₂²×C₃×C₄	—	2	1	no	—
577	C₂²×C₃×C₄	—	2	1	no	—
578	C₂²×C₃×C₄	—	2	1	no	—
579	C₂²×C₃×C₄	—	2	2	no	—
580	C₂²×C₃×C₄	—	2	2	no	—
581	C₂²×C₃×C₄	—	2	1	no	—
582	C₂²×C₃×C₄	—	2	1	no	—
583	C₂²×C₃×C₄	—	2	2	no	—
584	C₂²×C₃×C₄	—	4	4	no	—
585	C₂²×C₃×C₄	—	4	4	no	—
586	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
587	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
588	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
589	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
590	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
591	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
592	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
593	C₃×Q₁₆	—	2	4	no	—
594	C₃×Q₁₆	—	2	4	no	—
595	C₃×Q₁₆	—	2	2	no	—
596	C₃×Q₁₆	—	2	4	no	—
597	C₃×Q₁₆	—	4	1	no	—
598	C₃×Q₁₆	C₂×D₄	1	8	yes	complemented
599	C₃×SD₁₆	—	2	4	no	—
600	C₃×SD₁₆	—	2	4	no	—
601	C₃×SD₁₆	—	2	4	no	—
602	C₃×SD₁₆	—	2	2	no	—
603	C₃×SD₁₆	—	2	2	no	—
604	C₃×SD₁₆	—	2	4	no	—
605	C₃×SD₁₆	—	2	4	no	—
606	C₃×SD₁₆	—	2	4	no	—
607	C₃×SD₁₆	—	4	2	no	—
608	C₃×SD₁₆	—	4	2	no	—
609	C₃×SD₁₆	—	4	1	no	—
610	C₃×SD₁₆	—	4	1	no	—
611	C₃×SD₁₆	C₂×D₄	1	8	yes	complemented
612	C₃×D₈	—	2	2	no	—
613	C₃×D₈	—	2	4	no	—
614	C₃×D₈	—	4	1	no	—
615	C₃×M₁₆	—	2	2	no	—
616	C₃×M₁₆	—	2	4	no	—
617	C₃×M₁₆	—	2	4	no	—
618	C₃×M₁₆	C₂×D₄	1	4	yes	complemented
619	C₂×C₃×C₈	—	2	2	no	—
620	C₂×C₃×C₈	—	2	2	no	—
621	C₂×C₃×C₈	—	2	4	no	—
622	C₂×C₃×C₈	—	2	4	no	—
623	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
624	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
625	C₂×C₃×C₈	C₂⁴	1	2	yes	—
626	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
627	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
628	C₂×C₃×C₈	C₂⁴	1	2	yes	—
629	C₃×C₄⋊C₄	—	2	1	no	—
630	C₃×C₄⋊C₄	—	2	2	no	—
631	C₃×C₄⋊C₄	—	2	2	no	—
632	C₃×C₄⋊C₄	—	2	2	no	—
633	C₃×C₄⋊C₄	—	2	2	no	—
634	C₃×C₄⋊C₄	—	2	2	no	—
635	C₃×C₄⋊C₄	—	2	2	no	—
636	C₃×C₄⋊C₄	—	2	2	no	—
637	C₃×C₄⋊C₄	—	2	2	no	—
638	C₃×C₄⋊C₄	—	2	1	no	—
639	C₃×C₄⋊C₄	—	2	1	no	—
640	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
641	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
642	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
643	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
644	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
645	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
646	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
647	C₃×C₂²⋊C₄	—	2	2	no	—
648	C₃×C₂²⋊C₄	—	2	1	no	—
649	C₃×C₂²⋊C₄	—	2	1	no	—
650	C₃×C₂²⋊C₄	—	2	1	no	—
651	C₃×C₂²⋊C₄	—	2	2	no	—
652	C₃×C₂²⋊C₄	—	2	2	no	—
653	C₃×C₂²⋊C₄	—	2	2	no	—
654	C₃×C₂²⋊C₄	—	2	2	no	—
655	C₃×C₂²⋊C₄	—	2	2	no	—
656	C₃×C₂²⋊C₄	—	2	2	no	—
657	C₃×C₂²⋊C₄	—	2	2	no	—
658	C₃×C₂²⋊C₄	—	2	2	no	—
659	C₃×C₂²⋊C₄	—	2	2	no	—
660	C₃×C₂²⋊C₄	—	2	2	no	—
661	C₃×C₂²⋊C₄	—	2	1	no	—
662	C₃×C₂²⋊C₄	—	2	1	no	—
663	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
664	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
665	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
666	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
667	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
668	C₃×C₄²	—	2	2	no	—
669	C₃×C₄²	—	2	2	no	—
670	C₃×C₄²	—	2	2	no	—
671	C₃×C₄²	—	2	1	no	—
672	C₃×C₄²	C₂⁴	1	2	yes	—
673	2₋¹⁺⁴	—	2	4	no	—
674	2₋¹⁺⁴	—	4	2	no	—
675	H(5,𝔽₂)	—	2	4	no	—
676	H(5,𝔽₂)	—	4	2	no	—
677	C₂×#41	—	2	1	no	—
678	C₂×#41	—	2	2	no	—
679	C₂×#41	—	2	1	no	—
680	C₂×#41	—	2	1	no	—
681	C₂×#41	—	2	1	no	—
682	C₂×#41	—	2	4	no	—
683	C₂×#41	—	4	2	no	—
684	C₂×#41	C₂³×C₃	1	1	yes	characteristic
685	C₂×#41	C₂³×C₃	1	1	yes	characteristic
686	C₂×#41	C₂³×C₃	1	1	yes	characteristic
687	C₂×#41	C₂³×C₃	1	2	yes	—
688	C₂×#41	C₂³×C₃	1	2	yes	—
689	C₂×#41	C₂³×C₃	1	1	yes	characteristic
690	C₂×#41	C₂³×C₃	1	1	yes	characteristic
691	C₂×#41	C₂³×C₃	1	1	yes	characteristic
692	C₂²×Q₈	—	2	1	no	—
693	C₂²×Q₈	—	2	1	no	—
694	C₂²×Q₈	—	2	1	no	—
695	C₂²×Q₈	—	2	1	no	—
696	C₂²×Q₈	—	2	4	no	—
697	C₂²×Q₈	—	4	2	no	—
698	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
699	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
700	C₂²×Q₈	C₂³×C₃	1	2	yes	—
701	C₂²×Q₈	C₂³×C₃	1	2	yes	—
702	C₂²×Q₈	C₂³×C₃	1	2	yes	—
703	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
704	C₂²×D₄	—	2	1	no	—
705	C₂²×D₄	—	2	1	no	—
706	C₂²×D₄	—	2	1	no	—
707	C₂²×D₄	—	2	2	no	—
708	C₂²×D₄	—	2	2	no	—
709	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
710	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
711	C₂²×D₄	C₂³×C₃	1	2	yes	—
712	C₂³×C₄	—	2	1	no	—
713	C₂³×C₄	—	2	1	no	—
714	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
715	#137	—	2	4	no	—
716	#137	—	2	4	no	—
717	#137	—	2	8	no	—
718	#137	—	2	8	no	—
719	#137	—	2	8	no	—
720	#137	—	2	4	no	—
721	#137	C₃×D₄	1	8	yes	complemented
722	AGL(1,ℤ/8)	—	2	8	no	—
723	AGL(1,ℤ/8)	—	2	4	no	—
724	#135	—	2	4	no	—
725	#135	—	2	8	no	—
726	#135	—	4	2	no	—
727	C₂×Q₁₆	—	2	8	no	—
728	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
729	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
730	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
731	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
732	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
733	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
734	C₂×SD₁₆	—	2	4	no	—
735	C₂×SD₁₆	—	2	8	no	—
736	C₂×SD₁₆	—	2	8	no	—
737	C₂×SD₁₆	—	4	2	no	—
738	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
739	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
740	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
741	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
742	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
743	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
744	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
745	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
746	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
747	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
748	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
749	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
750	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
751	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
752	C₂×D₈	C₂³×C₃	1	2	yes	—
753	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
754	#131	—	2	4	no	—
755	C₂×M₁₆	—	2	4	no	—
756	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
757	C₂×M₁₆	C₂³×C₃	1	2	yes	—
758	C₂×M₁₆	C₂³×C₃	1	2	yes	—
759	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
760	C₂²×C₈	C₂³×C₃	1	2	yes	—
761	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
762	C₂²×C₈	C₂³×C₃	1	2	yes	—
763	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
764	C₄⋊Q₈	—	2	1	no	—
765	C₄⋊Q₈	—	2	2	no	—
766	C₄⋊Q₈	—	2	2	no	—
767	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
768	#127	—	2	2	no	—
769	#127	C₂³×C₃	1	2	yes	—
770	#124	—	2	1	no	—
771	#124	—	2	2	no	—
772	#124	—	2	2	no	—
773	#124	—	2	2	no	—
774	#124	C₂³×C₃	1	2	yes	—
775	#124	C₂³×C₃	1	2	yes	—
776	#123	—	2	2	no	—
777	#123	—	2	1	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	C₃×D₄	1	2	yes	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	1	no	—
785	C₂²⋊Q₈	—	2	1	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	C₃×D₄	1	1	yes	characteristic
792	C₂²⋊Q₈	C₃×D₄	1	1	yes	characteristic
793	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
794	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
795	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
796	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
797	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
798	#121	—	2	1	no	—
799	#121	—	2	2	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	1	no	—
804	#121	—	2	1	no	—
805	#121	—	2	1	no	—
806	#121	—	2	1	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	C₃×D₄	1	1	yes	characteristic
812	#121	C₃×D₄	1	1	yes	characteristic
813	#121	C₂³×C₃	1	2	yes	—
814	#121	C₂³×C₃	1	2	yes	—
815	#121	C₂³×C₃	1	1	yes	characteristic
816	#121	C₂³×C₃	1	1	yes	characteristic
817	#121	C₂³×C₃	1	2	yes	—
818	#120	—	2	1	no	—
819	#120	—	2	2	no	—
820	#120	—	2	2	no	—
821	#120	—	2	2	no	—
822	#120	—	2	2	no	—
823	#120	C₃×D₄	1	2	yes	—
824	C₄×Q₈	—	2	1	no	—
825	C₄×Q₈	—	2	1	no	—
826	C₄×Q₈	C₂³×C₃	1	2	yes	—
827	C₄×Q₈	C₂³×C₃	1	2	yes	—
828	C₄×Q₈	C₂³×C₃	1	2	yes	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	2	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	—	2	2	no	—
838	C₄×D₄	C₂³×C₃	1	2	yes	—
839	C₄×D₄	C₂³×C₃	1	2	yes	—
840	C₄×D₄	C₂³×C₃	1	2	yes	—
841	#117	—	2	1	no	—
842	#117	—	2	2	no	—
843	#117	C₂³×C₃	1	1	yes	characteristic
844	#117	C₂³×C₃	1	1	yes	characteristic
845	C₂×C₄⋊C₄	—	2	1	no	—
846	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
847	C₂×C₂²⋊C₄	—	2	1	no	—
848	C₂×C₂²⋊C₄	—	2	2	no	—
849	#107	C₂³×C₃	1	2	yes	—
850	#106	C₂³×C₃	1	2	yes	—
851	C₄⋊C₈	C₂³×C₃	1	2	yes	—
852	C₄⋊C₈	C₂³×C₃	1	2	yes	—
853	#103	C₂³×C₃	1	2	yes	—
854	#103	C₂³×C₃	1	2	yes	—
855	#103	C₂³×C₃	1	2	yes	—
856	#103	C₂³×C₃	1	2	yes	—
857	#103	C₂³×C₃	1	1	yes	characteristic
858	#103	C₂³×C₃	1	1	yes	characteristic
859	#103	C₂³×C₃	1	1	yes	characteristic
860	#103	C₂³×C₃	1	1	yes	characteristic
861	#103	C₂³×C₃	1	2	yes	—
862	#102	C₂³×C₃	1	1	yes	characteristic
863	#102	C₂³×C₃	1	1	yes	characteristic
864	#102	C₂³×C₃	1	1	yes	characteristic
865	#102	C₂³×C₃	1	1	yes	characteristic
866	#102	C₂³×C₃	1	2	yes	—
867	#102	C₂³×C₃	1	2	yes	—
868	#102	C₂³×C₃	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
870	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
871	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
872	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
873	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
874	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
875	#97	C₂³×C₃	1	2	yes	—
876	C₄×C₈	C₂³×C₃	1	2	yes	—
877	C₂³×C₃	—	2	2	no	—
878	C₂³×C₃	—	2	2	no	—
879	C₂³×C₃	—	2	1	no	—
880	C₂³×C₃	—	2	1	no	—
881	C₂³×C₃	—	2	2	no	—
882	C₂³×C₃	—	2	1	no	—
883	C₂³×C₃	—	4	1	no	—
884	C₂³×C₃	—	4	2	no	—
885	C₂³×C₃	—	4	4	no	—
886	C₂³×C₃	—	4	2	no	—
887	C₂³×C₃	—	4	2	no	—
888	C₂³×C₃	—	8	1	no	—
889	C₂³×C₃	—	8	1	no	—
890	C₂³×C₃	—	8	2	no	—
891	C₂³×C₃	—	8	1	no	—
892	C₂³×C₃	—	8	2	no	—
893	C₂³×C₃	C₂²×D₄	1	2	yes	—
894	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
895	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
896	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
897	C₃×Q₈	—	2	4	no	—
898	C₃×Q₈	—	2	2	no	—
899	C₃×Q₈	—	2	2	no	—
900	C₃×Q₈	—	2	1	no	—
901	C₃×Q₈	—	2	1	no	—
902	C₃×Q₈	—	2	2	no	—
903	C₃×Q₈	—	2	1	no	—
904	C₃×Q₈	—	2	2	no	—
905	C₃×Q₈	—	2	1	no	—
906	C₃×Q₈	—	2	1	no	—
907	C₃×Q₈	—	4	4	no	—
908	C₃×Q₈	—	4	4	no	—
909	C₃×Q₈	—	4	4	no	—
910	C₃×Q₈	—	4	2	no	—
911	C₃×Q₈	—	4	2	no	—
912	C₃×Q₈	C₂²×D₄	1	4	yes	—
913	C₃×Q₈	C₂²×D₄	1	2	yes	—
914	C₃×D₄	—	2	4	no	—
915	C₃×D₄	—	2	4	no	—
916	C₃×D₄	—	2	4	no	—
917	C₃×D₄	—	2	2	no	—
918	C₃×D₄	—	2	1	no	—
919	C₃×D₄	—	2	2	no	—
920	C₃×D₄	—	2	1	no	—
921	C₃×D₄	—	2	1	no	—
922	C₃×D₄	—	2	1	no	—
923	C₃×D₄	—	2	1	no	—
924	C₃×D₄	—	2	2	no	—
925	C₃×D₄	—	4	2	no	—
926	C₃×D₄	—	4	4	no	—
927	C₃×D₄	—	4	2	no	—
928	C₃×D₄	—	4	4	no	—
929	C₃×D₄	—	4	2	no	—
930	C₃×D₄	—	4	4	no	—
931	C₃×D₄	—	4	2	no	—
932	C₃×D₄	—	4	2	no	—
933	C₃×D₄	—	4	2	no	—
934	C₃×D₄	—	4	2	no	—
935	C₃×D₄	—	4	2	no	—
936	C₃×D₄	—	4	4	no	—
937	C₃×D₄	—	4	2	no	—
938	C₃×D₄	—	8	2	no	—
939	C₃×D₄	—	8	2	no	—
940	C₃×D₄	—	8	2	no	—
941	C₃×D₄	—	8	2	no	—
942	C₃×D₄	C₂²×D₄	1	2	yes	—
943	C₂×C₃×C₄	—	2	2	no	—
944	C₂×C₃×C₄	—	2	4	no	—
945	C₂×C₃×C₄	—	2	1	no	—
946	C₂×C₃×C₄	—	2	2	no	—
947	C₂×C₃×C₄	—	2	2	no	—
948	C₂×C₃×C₄	—	2	2	no	—
949	C₂×C₃×C₄	—	2	4	no	—
950	C₂×C₃×C₄	—	2	1	no	—
951	C₂×C₃×C₄	—	2	2	no	—
952	C₂×C₃×C₄	—	2	1	no	—
953	C₂×C₃×C₄	—	2	1	no	—
954	C₂×C₃×C₄	—	2	1	no	—
955	C₂×C₃×C₄	—	2	2	no	—
956	C₂×C₃×C₄	—	2	1	no	—
957	C₂×C₃×C₄	—	2	1	no	—
958	C₂×C₃×C₄	—	2	2	no	—
959	C₂×C₃×C₄	—	2	1	no	—
960	C₂×C₃×C₄	—	2	2	no	—
961	C₂×C₃×C₄	—	2	1	no	—
962	C₂×C₃×C₄	—	4	2	no	—
963	C₂×C₃×C₄	—	4	4	no	—
964	C₂×C₃×C₄	—	4	4	no	—
965	C₂×C₃×C₄	—	4	2	no	—
966	C₂×C₃×C₄	—	4	4	no	—
967	C₂×C₃×C₄	—	4	4	no	—
968	C₂×C₃×C₄	—	4	2	no	—
969	C₂×C₃×C₄	—	4	4	no	—
970	C₂×C₃×C₄	—	4	2	no	—
971	C₂×C₃×C₄	—	4	2	no	—
972	C₂×C₃×C₄	—	4	2	no	—
973	C₂×C₃×C₄	—	8	2	no	—
974	C₂×C₃×C₄	—	8	1	no	—
975	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
976	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
977	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
978	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
979	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
980	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
981	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
982	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
983	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
984	C₃×C₈	—	2	1	no	—
985	C₃×C₈	—	2	1	no	—
986	C₃×C₈	—	2	2	no	—
987	C₃×C₈	—	2	1	no	—
988	C₃×C₈	—	2	1	no	—
989	C₃×C₈	C₂²×D₄	1	4	yes	—
990	C₂⁴	—	2	1	no	—
991	C₂⁴	—	2	2	no	—
992	C₂⁴	—	2	1	no	—
993	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
994	#41	—	2	2	no	—
995	#41	—	2	2	no	—
996	#41	—	2	2	no	—
997	#41	—	2	4	no	—
998	#41	—	2	4	no	—
999	#41	—	2	2	no	—
1000	#41	—	2	2	no	—
1001	#41	—	2	2	no	—
1002	#41	—	2	2	no	—
1003	#41	—	2	2	no	—
1004	#41	—	2	2	no	—
1005	#41	—	4	4	no	—
1006	#41	—	4	1	no	—
1007	#41	—	4	1	no	—
1008	#41	—	4	2	no	—
1009	#41	—	4	2	no	—
1010	#41	—	4	4	no	—
1011	#41	—	4	8	no	—
1012	#41	—	4	4	no	—
1013	#41	—	4	4	no	—
1014	#41	C₂×C₃×D₄	1	4	yes	—
1015	C₂×Q₈	—	2	1	no	—
1016	C₂×Q₈	—	2	1	no	—
1017	C₂×Q₈	—	2	2	no	—
1018	C₂×Q₈	—	2	2	no	—
1019	C₂×Q₈	—	2	1	no	—
1020	C₂×Q₈	—	2	2	no	—
1021	C₂×Q₈	—	2	2	no	—
1022	C₂×Q₈	—	2	4	no	—
1023	C₂×Q₈	—	2	4	no	—
1024	C₂×Q₈	—	2	2	no	—
1025	C₂×Q₈	—	2	4	no	—
1026	C₂×Q₈	—	2	2	no	—
1027	C₂×Q₈	—	2	2	no	—
1028	C₂×Q₈	—	4	4	no	—
1029	C₂×Q₈	—	4	2	no	—
1030	C₂×Q₈	—	4	2	no	—
1031	C₂×Q₈	—	4	1	no	—
1032	C₂×Q₈	—	4	2	no	—
1033	C₂×Q₈	—	4	4	no	—
1034	C₂×Q₈	—	4	4	no	—
1035	C₂×Q₈	—	4	4	no	—
1036	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
1037	C₂×Q₈	C₂×C₃×D₄	1	4	yes	complemented
1038	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
1039	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
1040	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
1041	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
1042	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
1043	C₂×D₄	—	2	1	no	—
1044	C₂×D₄	—	2	2	no	—
1045	C₂×D₄	—	2	4	no	—
1046	C₂×D₄	—	2	1	no	—
1047	C₂×D₄	—	2	1	no	—
1048	C₂×D₄	—	2	2	no	—
1049	C₂×D₄	—	2	1	no	—
1050	C₂×D₄	—	2	1	no	—
1051	C₂×D₄	—	2	1	no	—
1052	C₂×D₄	—	2	2	no	—
1053	C₂×D₄	—	2	2	no	—
1054	C₂×D₄	—	2	1	no	—
1055	C₂×D₄	—	2	2	no	—
1056	C₂×D₄	—	2	2	no	—
1057	C₂×D₄	—	2	2	no	—
1058	C₂×D₄	—	2	1	no	—
1059	C₂×D₄	—	2	2	no	—
1060	C₂×D₄	—	2	1	no	—
1061	C₂×D₄	—	2	2	no	—
1062	C₂×D₄	—	2	2	no	—
1063	C₂×D₄	—	2	2	no	—
1064	C₂×D₄	—	4	1	no	—
1065	C₂×D₄	—	4	2	no	—
1066	C₂×D₄	—	4	4	no	—
1067	C₂×D₄	—	4	8	no	—
1068	C₂×D₄	—	4	4	no	—
1069	C₂×D₄	—	8	4	no	—
1070	C₂×D₄	—	8	2	no	—
1071	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
1072	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
1073	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
1074	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
1075	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
1076	C₂×D₄	C₂⁴×C₃	1	2	yes	—
1077	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
1078	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
1079	C₂²×C₄	—	2	1	no	—
1080	C₂²×C₄	—	2	1	no	—
1081	C₂²×C₄	—	2	2	no	—
1082	C₂²×C₄	—	2	2	no	—
1083	C₂²×C₄	—	2	1	no	—
1084	C₂²×C₄	—	2	2	no	—
1085	C₂²×C₄	—	2	2	no	—
1086	C₂²×C₄	—	2	2	no	—
1087	C₂²×C₄	—	2	1	no	—
1088	C₂²×C₄	—	2	1	no	—
1089	C₂²×C₄	—	2	1	no	—
1090	C₂²×C₄	—	2	1	no	—
1091	C₂²×C₄	—	2	2	no	—
1092	C₂²×C₄	—	2	2	no	—
1093	C₂²×C₄	—	2	1	no	—
1094	C₂²×C₄	—	2	1	no	—
1095	C₂²×C₄	—	2	2	no	—
1096	C₂²×C₄	—	4	4	no	—
1097	C₂²×C₄	—	4	4	no	—
1098	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
1099	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
1100	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
1101	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
1102	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
1103	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
1104	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
1105	Q₁₆	—	2	4	no	—
1106	Q₁₆	—	2	4	no	—
1107	Q₁₆	—	2	2	no	—
1108	Q₁₆	—	2	4	no	—
1109	Q₁₆	—	4	1	no	—
1110	Q₁₆	C₂×C₃×D₄	1	8	yes	complemented
1111	SD₁₆	—	2	4	no	—
1112	SD₁₆	—	2	4	no	—
1113	SD₁₆	—	2	4	no	—
1114	SD₁₆	—	2	2	no	—
1115	SD₁₆	—	2	2	no	—
1116	SD₁₆	—	2	4	no	—
1117	SD₁₆	—	2	4	no	—
1118	SD₁₆	—	2	4	no	—
1119	SD₁₆	—	4	2	no	—
1120	SD₁₆	—	4	2	no	—
1121	SD₁₆	—	4	1	no	—
1122	SD₁₆	—	4	1	no	—
1123	SD₁₆	C₂×C₃×D₄	1	8	yes	complemented
1124	D₈	—	2	2	no	—
1125	D₈	—	2	4	no	—
1126	D₈	—	4	1	no	—
1127	M₁₆	—	2	2	no	—
1128	M₁₆	—	2	4	no	—
1129	M₁₆	—	2	4	no	—
1130	M₁₆	C₂×C₃×D₄	1	4	yes	complemented
1131	C₂×C₈	—	2	2	no	—
1132	C₂×C₈	—	2	2	no	—
1133	C₂×C₈	—	2	4	no	—
1134	C₂×C₈	—	2	4	no	—
1135	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
1136	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
1137	C₂×C₈	C₂⁴×C₃	1	2	yes	—
1138	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
1139	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
1140	C₂×C₈	C₂⁴×C₃	1	2	yes	—
1141	C₄⋊C₄	—	2	1	no	—
1142	C₄⋊C₄	—	2	2	no	—
1143	C₄⋊C₄	—	2	2	no	—
1144	C₄⋊C₄	—	2	2	no	—
1145	C₄⋊C₄	—	2	2	no	—
1146	C₄⋊C₄	—	2	2	no	—
1147	C₄⋊C₄	—	2	2	no	—
1148	C₄⋊C₄	—	2	2	no	—
1149	C₄⋊C₄	—	2	2	no	—
1150	C₄⋊C₄	—	2	1	no	—
1151	C₄⋊C₄	—	2	1	no	—
1152	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
1153	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
1154	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
1155	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
1156	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
1157	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
1158	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
1159	C₂²⋊C₄	—	2	2	no	—
1160	C₂²⋊C₄	—	2	1	no	—
1161	C₂²⋊C₄	—	2	1	no	—
1162	C₂²⋊C₄	—	2	1	no	—
1163	C₂²⋊C₄	—	2	2	no	—
1164	C₂²⋊C₄	—	2	2	no	—
1165	C₂²⋊C₄	—	2	2	no	—
1166	C₂²⋊C₄	—	2	2	no	—
1167	C₂²⋊C₄	—	2	2	no	—
1168	C₂²⋊C₄	—	2	2	no	—
1169	C₂²⋊C₄	—	2	2	no	—
1170	C₂²⋊C₄	—	2	2	no	—
1171	C₂²⋊C₄	—	2	2	no	—
1172	C₂²⋊C₄	—	2	2	no	—
1173	C₂²⋊C₄	—	2	1	no	—
1174	C₂²⋊C₄	—	2	1	no	—
1175	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
1176	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
1177	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
1178	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
1179	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
1180	C₄²	—	2	2	no	—
1181	C₄²	—	2	2	no	—
1182	C₄²	—	2	2	no	—
1183	C₄²	—	2	1	no	—
1184	C₄²	C₂⁴×C₃	1	2	yes	—
1185	C₂²×C₃	—	2	1	no	—
1186	C₂²×C₃	—	2	1	no	—
1187	C₂²×C₃	—	2	1	no	—
1188	C₂²×C₃	—	2	1	no	—
1189	C₂²×C₃	—	2	1	no	—
1190	C₂²×C₃	—	2	2	no	—
1191	C₂²×C₃	—	2	1	no	—
1192	C₂²×C₃	—	2	2	no	—
1193	C₂²×C₃	—	2	2	no	—
1194	C₂²×C₃	—	2	2	no	—
1195	C₂²×C₃	—	2	1	no	—
1196	C₂²×C₃	—	4	4	no	—
1197	C₂²×C₃	—	4	1	no	—
1198	C₂²×C₃	—	4	1	no	—
1199	C₂²×C₃	—	4	1	no	—
1200	C₂²×C₃	—	4	1	no	—
1201	C₂²×C₃	—	4	2	no	—
1202	C₂²×C₃	—	4	1	no	—
1203	C₂²×C₃	—	4	1	no	—
1204	C₂²×C₃	—	4	2	no	—
1205	C₂²×C₃	—	4	2	no	—
1206	C₂²×C₃	—	4	1	no	—
1207	C₂²×C₃	—	4	1	no	—
1208	C₂²×C₃	—	8	4	no	—
1209	C₂²×C₃	—	16	2	no	—
1210	C₂²×C₃	—	16	4	no	—
1211	C₂²×C₃	D₄²	1	2	yes	—
1212	C₂²×C₃	#577	1	2	yes	complemented
1213	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
1214	C₃×C₄	—	2	2	no	—
1215	C₃×C₄	—	2	1	no	—
1216	C₃×C₄	—	2	1	no	—
1217	C₃×C₄	—	2	2	no	—
1218	C₃×C₄	—	2	4	no	—
1219	C₃×C₄	—	2	2	no	—
1220	C₃×C₄	—	2	2	no	—
1221	C₃×C₄	—	4	1	no	—
1222	C₃×C₄	—	4	1	no	—
1223	C₃×C₄	—	4	1	no	—
1224	C₃×C₄	—	4	2	no	—
1225	C₃×C₄	—	4	2	no	—
1226	C₃×C₄	—	4	1	no	—
1227	C₃×C₄	D₄²	1	2	yes	—
1228	C₃×C₄	C₂³×D₄	1	1	yes	characteristic
1229	C₃×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1230	C₂³	—	2	2	no	—
1231	C₂³	—	2	1	no	—
1232	C₂³	—	2	2	no	—
1233	C₂³	—	2	1	no	—
1234	C₂³	—	2	2	no	—
1235	C₂³	—	2	1	no	—
1236	C₂³	—	4	1	no	—
1237	C₂³	—	4	2	no	—
1238	C₂³	—	4	4	no	—
1239	C₂³	—	4	2	no	—
1240	C₂³	—	4	2	no	—
1241	C₂³	—	8	1	no	—
1242	C₂³	—	8	1	no	—
1243	C₂³	—	8	2	no	—
1244	C₂³	—	8	1	no	—
1245	C₂³	—	8	2	no	—
1246	C₂³	C₂²×C₃×D₄	1	2	yes	—
1247	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
1248	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
1249	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
1250	Q₈	—	2	2	no	—
1251	Q₈	—	2	1	no	—
1252	Q₈	—	2	4	no	—
1253	Q₈	—	2	2	no	—
1254	Q₈	—	2	1	no	—
1255	Q₈	—	2	2	no	—
1256	Q₈	—	2	1	no	—
1257	Q₈	—	2	2	no	—
1258	Q₈	—	2	1	no	—
1259	Q₈	—	2	1	no	—
1260	Q₈	—	4	4	no	—
1261	Q₈	—	4	4	no	—
1262	Q₈	—	4	4	no	—
1263	Q₈	—	4	2	no	—
1264	Q₈	—	4	2	no	—
1265	Q₈	C₂²×C₃×D₄	1	4	yes	—
1266	Q₈	C₂²×C₃×D₄	1	2	yes	—
1267	D₄	—	2	4	no	—
1268	D₄	—	2	4	no	—
1269	D₄	—	2	4	no	—
1270	D₄	—	2	1	no	—
1271	D₄	—	2	2	no	—
1272	D₄	—	2	1	no	—
1273	D₄	—	2	1	no	—
1274	D₄	—	2	1	no	—
1275	D₄	—	2	1	no	—
1276	D₄	—	2	2	no	—
1277	D₄	—	2	2	no	—
1278	D₄	—	4	2	no	—
1279	D₄	—	4	4	no	—
1280	D₄	—	4	2	no	—
1281	D₄	—	4	4	no	—
1282	D₄	—	4	2	no	—
1283	D₄	—	4	4	no	—
1284	D₄	—	4	2	no	—
1285	D₄	—	4	2	no	—
1286	D₄	—	4	4	no	—
1287	D₄	—	4	2	no	—
1288	D₄	—	4	2	no	—
1289	D₄	—	4	2	no	—
1290	D₄	—	4	2	no	—
1291	D₄	—	8	2	no	—
1292	D₄	—	8	2	no	—
1293	D₄	—	8	2	no	—
1294	D₄	—	8	2	no	—
1295	D₄	C₂²×C₃×D₄	1	2	yes	—
1296	C₂×C₄	—	2	1	no	—
1297	C₂×C₄	—	2	2	no	—
1298	C₂×C₄	—	2	2	no	—
1299	C₂×C₄	—	2	4	no	—
1300	C₂×C₄	—	2	1	no	—
1301	C₂×C₄	—	2	2	no	—
1302	C₂×C₄	—	2	1	no	—
1303	C₂×C₄	—	2	1	no	—
1304	C₂×C₄	—	2	1	no	—
1305	C₂×C₄	—	2	2	no	—
1306	C₂×C₄	—	2	2	no	—
1307	C₂×C₄	—	2	2	no	—
1308	C₂×C₄	—	2	4	no	—
1309	C₂×C₄	—	2	1	no	—
1310	C₂×C₄	—	2	1	no	—
1311	C₂×C₄	—	2	2	no	—
1312	C₂×C₄	—	2	1	no	—
1313	C₂×C₄	—	2	2	no	—
1314	C₂×C₄	—	2	1	no	—
1315	C₂×C₄	—	4	2	no	—
1316	C₂×C₄	—	4	4	no	—
1317	C₂×C₄	—	4	4	no	—
1318	C₂×C₄	—	4	2	no	—
1319	C₂×C₄	—	4	4	no	—
1320	C₂×C₄	—	4	4	no	—
1321	C₂×C₄	—	4	2	no	—
1322	C₂×C₄	—	4	4	no	—
1323	C₂×C₄	—	4	2	no	—
1324	C₂×C₄	—	4	2	no	—
1325	C₂×C₄	—	4	2	no	—
1326	C₂×C₄	—	8	2	no	—
1327	C₂×C₄	—	8	1	no	—
1328	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1329	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1330	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1331	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1332	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1333	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1334	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1335	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1336	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
1337	C₈	—	2	1	no	—
1338	C₈	—	2	1	no	—
1339	C₈	—	2	2	no	—
1340	C₈	—	2	1	no	—
1341	C₈	—	2	1	no	—
1342	C₈	C₂²×C₃×D₄	1	4	yes	—
1343	C₂×C₃	—	2	2	no	—
1344	C₂×C₃	—	2	2	no	—
1345	C₂×C₃	—	4	1	no	—
1346	C₂×C₃	—	4	2	no	—
1347	C₂×C₃	—	4	2	no	—
1348	C₂×C₃	—	8	1	no	—
1349	C₂×C₃	—	8	1	no	—
1350	C₂×C₃	—	8	2	no	—
1351	C₂×C₃	C₂×D₄²	1	1	yes	characteristic
1352	C₂×C₃	C₂×#577	1	1	yes	characteristic
1353	C₂×C₃	#3586	1	1	yes	characteristic
1354	C₂²	—	2	1	no	—
1355	C₂²	—	2	1	no	—
1356	C₂²	—	2	1	no	—
1357	C₂²	—	2	1	no	—
1358	C₂²	—	2	1	no	—
1359	C₂²	—	2	2	no	—
1360	C₂²	—	2	2	no	—
1361	C₂²	—	2	2	no	—
1362	C₂²	—	2	1	no	—
1363	C₂²	—	2	1	no	—
1364	C₂²	—	2	2	no	—
1365	C₂²	—	4	4	no	—
1366	C₂²	—	4	1	no	—
1367	C₂²	—	4	1	no	—
1368	C₂²	—	4	1	no	—
1369	C₂²	—	4	1	no	—
1370	C₂²	—	4	2	no	—
1371	C₂²	—	4	2	no	—
1372	C₂²	—	4	1	no	—
1373	C₂²	—	4	1	no	—
1374	C₂²	—	4	1	no	—
1375	C₂²	—	4	1	no	—
1376	C₂²	—	4	2	no	—
1377	C₂²	—	8	4	no	—
1378	C₂²	—	16	2	no	—
1379	C₂²	—	16	4	no	—
1380	C₂²	C₃×D₄²	1	2	yes	—
1381	C₂²	C₃×#577	1	2	yes	complemented
1382	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1383	C₄	—	2	1	no	—
1384	C₄	—	2	1	no	—
1385	C₄	—	2	2	no	—
1386	C₄	—	2	4	no	—
1387	C₄	—	2	2	no	—
1388	C₄	—	2	2	no	—
1389	C₄	—	2	2	no	—
1390	C₄	—	4	1	no	—
1391	C₄	—	4	1	no	—
1392	C₄	—	4	2	no	—
1393	C₄	—	4	2	no	—
1394	C₄	—	4	1	no	—
1395	C₄	—	4	1	no	—
1396	C₄	C₃×D₄²	1	2	yes	—
1397	C₄	C₂³×C₃×D₄	1	1	yes	characteristic
1398	C₄	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1399	C₃	#61075	1	1	yes	characteristic, direct product factor, Sylow
1400	C₂	—	2	2	no	—
1401	C₂	—	2	2	no	—
1402	C₂	—	4	1	no	—
1403	C₂	—	4	2	no	—
1404	C₂	—	4	2	no	—
1405	C₂	—	8	1	no	—
1406	C₂	—	8	2	no	—
1407	C₂	—	8	1	no	—
1408	C₂	C₂×C₃×D₄²	1	1	yes	characteristic
1409	C₂	C₂×C₃×#577	1	1	yes	characteristic
1410	C₂	C₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#525 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₃×#577	C₂	semidirect
2. C₂²×C₃×#137	C₂	semidirect
3. C₃×#3488	C₂	semidirect
4. C₃×#3486	C₂	semidirect
5. C₃×#3285	C₂	semidirect
6. C₃×D₄×SD₁₆	C₂	semidirect
7. C₃×#3278	C₂	semidirect
8. C₃×#3275	C₂	semidirect
9. C₃×#3271	C₂	semidirect
10. C₃×#3270	C₂	semidirect
11. C₃×#3266	C₂	semidirect
12. C₃×#3265	C₂	semidirect
13. C₃×#3154	C₂	semidirect
14. C₃×#3063	C₂	semidirect
15. C₃×#3055	C₂	semidirect
16. C₃×#3046	C₂	semidirect
17. C₃×#3043	C₂	semidirect
18. C₃×#3013	C₂	semidirect
19. C₃×#3009	C₂	semidirect
20. C₃×#3002	C₂	semidirect
21. C₂×C₃×#448	C₂	semidirect
22. C₃×#2947	C₂	semidirect
23. C₃×#2933	C₂	semidirect
24. #61075	C₃	direct (N × H)
25. C₂×C₃×2₋¹⁺⁴	C₂²	semidirect
28. C₂³×C₃×Q₈	C₂²	semidirect
33. C₂×C₃×#137	C₂²	semidirect
34. C₂×C₃×#137	C₂²	semidirect
35. C₂×C₃×#137	C₂²	semidirect
36. C₂×C₃×#137	C₂²	semidirect
37. C₂×C₃×#137	C₂²	semidirect
38. C₂×C₃×AGL(1,ℤ/8)	C₂²	semidirect
39. C₂×C₃×AGL(1,ℤ/8)	C₂²	semidirect
41. C₂×C₃×#135	C₂²	semidirect
42. C₂×C₃×#135	C₂²	semidirect
43. C₂²×C₃×Q₁₆	C₂²	semidirect
44. C₂²×C₃×SD₁₆	C₂²	semidirect
45. C₂²×C₃×SD₁₆	C₂²	semidirect
46. C₂²×C₃×SD₁₆	C₂²	semidirect
47. C₂²×C₃×SD₁₆	C₂²	semidirect
48. C₂×C₃×#131	C₂²	semidirect
49. C₂²×C₃×M₁₆	C₂²	semidirect
53. C₃×D₄×Q₈	C₂²	semidirect
54. C₃×D₄×Q₈	C₂²	semidirect
58. C₃×#548	C₂²	semidirect
59. C₃×#548	C₂²	semidirect
67. C₃×#536	C₂²	semidirect
68. C₃×#536	C₂²	semidirect
74. C₃×#525	C₂²	semidirect
78. C₃×#519	C₂²	semidirect
79. C₃×#497	C₂²	semidirect
80. C₃×#496	C₂²	semidirect
81. C₃×#495	C₂²	semidirect
82. C₃×#492	C₂²	semidirect
83. C₃×#470	C₂²	semidirect
84. C₃×#469	C₂²	semidirect
85. C₃×#468	C₂²	semidirect
86. C₃×#468	C₂²	semidirect
87. C₃×#467	C₂²	semidirect
88. C₃×#466	C₂²	semidirect
89. C₃×#465	C₂²	semidirect
90. C₃×#465	C₂²	semidirect
91. C₃×#464	C₂²	semidirect
92. C₃×#464	C₂²	semidirect
93. C₃×#464	C₂²	semidirect
94. C₃×#463	C₂²	semidirect
95. C₃×#462	C₂²	semidirect
96. C₃×#461	C₂²	semidirect
97. C₃×#460	C₂²	semidirect
98. C₃×#460	C₂²	semidirect
99. C₃×#452	C₂²	semidirect
100. C₃×#452	C₂²	semidirect
101. C₃×#452	C₂²	semidirect
102. C₃×#452	C₂²	semidirect
103. C₃×#452	C₂²	semidirect
104. C₃×#451	C₂²	semidirect
105. C₃×#451	C₂²	semidirect
106. C₃×#450	C₂²	semidirect
107. C₃×#450	C₂²	semidirect
108. C₃×#450	C₂²	semidirect
109. C₃×#449	C₂²	semidirect
110. C₃×#449	C₂²	semidirect
111. C₃×#449	C₂²	semidirect
112. C₃×#448	C₂²	semidirect
113. C₃×#448	C₂²	semidirect
114. C₃×#448	C₂²	semidirect
115. C₃×#448	C₂²	semidirect
116. C₃×#448	C₂²	semidirect
117. C₃×#448	C₂²	semidirect
118. C₃×#447	C₂²	semidirect
119. C₃×#441	C₂²	semidirect
120. C₃×#440	C₂²	semidirect
121. C₃×C₄×Q₁₆	C₂²	semidirect
122. C₃×C₄×SD₁₆	C₂²	semidirect
123. C₃×#436	C₂²	semidirect
124. C₃×#435	C₂²	semidirect
125. C₃×#435	C₂²	semidirect
126. C₃×C₈×D₄	C₂²	semidirect
127. C₃×#428	C₂²	semidirect
128. C₃×#424	C₂²	semidirect
129. C₃×#418	C₂²	semidirect
130. C₃×#417	C₂²	semidirect
132. C₃×#416	C₂²	semidirect
133. C₂×C₃×#103	C₂²	semidirect
134. C₂×C₃×#103	C₂²	semidirect
135. C₃×#408	C₂²	semidirect
136. C₂×C₃×C₂²⋊C₈	C₂²	semidirect
137. C₃×#405	C₂²	semidirect
138. C₂×#577	C₂×C₃	semidirect
139. C₂²×#137	C₂×C₃	semidirect
140. #3488	C₂×C₃	semidirect
141. #3486	C₂×C₃	semidirect
142. #3285	C₂×C₃	semidirect
143. D₄×SD₁₆	C₂×C₃	semidirect
144. #3278	C₂×C₃	semidirect
145. #3275	C₂×C₃	semidirect
146. #3271	C₂×C₃	semidirect
147. #3270	C₂×C₃	semidirect
148. #3266	C₂×C₃	semidirect
149. #3265	C₂×C₃	semidirect
150. #3154	C₂×C₃	semidirect
151. #3063	C₂×C₃	semidirect
152. #3055	C₂×C₃	semidirect
153. #3046	C₂×C₃	semidirect
154. #3043	C₂×C₃	semidirect
155. #3013	C₂×C₃	semidirect
156. #3009	C₂×C₃	semidirect
157. #3002	C₂×C₃	semidirect
158. C₂×#448	C₂×C₃	semidirect
159. #2947	C₂×C₃	semidirect
160. #2933	C₂×C₃	semidirect
209. C₃×#137	D₄	semidirect
365. C₂×2₋¹⁺⁴	C₂²×C₃	semidirect
368. C₂³×Q₈	C₂²×C₃	semidirect
373. C₂×#137	C₂²×C₃	semidirect
374. C₂×#137	C₂²×C₃	semidirect
375. C₂×#137	C₂²×C₃	semidirect
376. C₂×#137	C₂²×C₃	semidirect
377. C₂×#137	C₂²×C₃	semidirect
378. C₂×AGL(1,ℤ/8)	C₂²×C₃	semidirect
379. C₂×AGL(1,ℤ/8)	C₂²×C₃	semidirect
381. C₂×#135	C₂²×C₃	semidirect
382. C₂×#135	C₂²×C₃	semidirect
383. C₂²×Q₁₆	C₂²×C₃	semidirect
384. C₂²×SD₁₆	C₂²×C₃	semidirect
385. C₂²×SD₁₆	C₂²×C₃	semidirect
386. C₂²×SD₁₆	C₂²×C₃	semidirect
387. C₂²×SD₁₆	C₂²×C₃	semidirect
388. C₂×#131	C₂²×C₃	semidirect
389. C₂²×M₁₆	C₂²×C₃	semidirect
393. D₄×Q₈	C₂²×C₃	semidirect
394. D₄×Q₈	C₂²×C₃	semidirect
398. #548	C₂²×C₃	semidirect
399. #548	C₂²×C₃	semidirect
407. #536	C₂²×C₃	semidirect
408. #536	C₂²×C₃	semidirect
414. #525	C₂²×C₃	semidirect
418. #519	C₂²×C₃	semidirect
419. #497	C₂²×C₃	semidirect
420. #496	C₂²×C₃	semidirect
421. #495	C₂²×C₃	semidirect
422. #492	C₂²×C₃	semidirect
423. #470	C₂²×C₃	semidirect
424. #469	C₂²×C₃	semidirect
425. #468	C₂²×C₃	semidirect
426. #468	C₂²×C₃	semidirect
427. #467	C₂²×C₃	semidirect
428. #466	C₂²×C₃	semidirect
429. #465	C₂²×C₃	semidirect
430. #465	C₂²×C₃	semidirect
431. #464	C₂²×C₃	semidirect
432. #464	C₂²×C₃	semidirect
433. #464	C₂²×C₃	semidirect
434. #463	C₂²×C₃	semidirect
435. #462	C₂²×C₃	semidirect
436. #461	C₂²×C₃	semidirect
437. #460	C₂²×C₃	semidirect
438. #460	C₂²×C₃	semidirect
439. #452	C₂²×C₃	semidirect
440. #452	C₂²×C₃	semidirect
441. #452	C₂²×C₃	semidirect
442. #452	C₂²×C₃	semidirect
443. #452	C₂²×C₃	semidirect
444. #451	C₂²×C₃	semidirect
445. #451	C₂²×C₃	semidirect
446. #450	C₂²×C₃	semidirect
447. #450	C₂²×C₃	semidirect
448. #450	C₂²×C₃	semidirect
449. #449	C₂²×C₃	semidirect
450. #449	C₂²×C₃	semidirect
451. #449	C₂²×C₃	semidirect
452. #448	C₂²×C₃	semidirect
453. #448	C₂²×C₃	semidirect
454. #448	C₂²×C₃	semidirect
455. #448	C₂²×C₃	semidirect
456. #448	C₂²×C₃	semidirect
457. #448	C₂²×C₃	semidirect
458. #447	C₂²×C₃	semidirect
459. #441	C₂²×C₃	semidirect
460. #440	C₂²×C₃	semidirect
461. C₄×Q₁₆	C₂²×C₃	semidirect
462. C₄×SD₁₆	C₂²×C₃	semidirect
463. #436	C₂²×C₃	semidirect
464. #435	C₂²×C₃	semidirect
465. #435	C₂²×C₃	semidirect
466. C₈×D₄	C₂²×C₃	semidirect
467. #428	C₂²×C₃	semidirect
468. #424	C₂²×C₃	semidirect
469. #418	C₂²×C₃	semidirect
470. #417	C₂²×C₃	semidirect
472. #416	C₂²×C₃	semidirect
473. C₂×#103	C₂²×C₃	semidirect
474. C₂×#103	C₂²×C₃	semidirect
475. #408	C₂²×C₃	semidirect
476. C₂×C₂²⋊C₈	C₂²×C₃	semidirect
477. #405	C₂²×C₃	semidirect
525. C₂×C₃×Q₈	C₂×D₄	semidirect
598. C₃×Q₁₆	C₂×D₄	semidirect
611. C₃×SD₁₆	C₂×D₄	semidirect
618. C₃×M₁₆	C₂×D₄	semidirect
721. #137	C₃×D₄	semidirect
1037. C₂×Q₈	C₂×C₃×D₄	semidirect
1110. Q₁₆	C₂×C₃×D₄	semidirect
1123. SD₁₆	C₂×C₃×D₄	semidirect
1130. M₁₆	C₂×C₃×D₄	semidirect
1212. C₂²×C₃	#577	semidirect
1381. C₂²	C₃×#577	semidirect
1399. C₃	#61075	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×#577	2
C₂²×C₃×#137	2
C₃×#3488	2
C₃×#3486	2
C₃×#3285	2
C₃×D₄×SD₁₆	2
C₃×#3278	2
C₃×#3275	2
C₃×#3271	2
C₃×#3270	2
C₃×#3266	2
C₃×#3265	2
C₃×#3154	2
C₃×#3063	2
C₃×#3055	2
C₃×#3046	2
C₃×#3043	2
C₃×#3013	2
C₃×#3009	2
C₃×#3002	2
C₂×C₃×#448	2
C₃×#2947	2
C₃×#2933	2
#61075	3

Subgroups — C3×#61075 #10679682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61075 #10679682