Subgroups — C₃×#60772 #10679379

Order 768.

2186 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3489	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3488	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3203	C₂	1	2	yes	maximal, complemented
4	C₃×#3201	C₂	1	2	yes	maximal, complemented
5	C₃×#3200	C₂	1	2	yes	maximal, complemented
6	C₃×#3198	C₂	1	2	yes	maximal, complemented
7	C₃×#3197	C₂	1	2	yes	maximal, complemented
8	C₃×#3196	C₂	1	2	yes	maximal, complemented
9	C₃×#3194	C₂	1	2	yes	maximal, complemented
10	C₃×#3193	C₂	1	2	yes	maximal, complemented
11	C₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3096	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3056	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3055	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#3054	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#3013	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#3012	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#3010	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#3009	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2879	C₂	1	1	yes	maximal, characteristic, complemented
24	#60772	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	C₂×C₃×#137	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×#135	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
34	C₃×#550	—	2	1	no	—
35	C₃×D₄×Q₈	—	2	1	no	—
36	C₃×#548	—	2	1	no	—
37	C₃×#548	—	2	1	no	—
38	C₃×#547	—	2	2	no	—
39	C₃×#547	—	2	1	no	—
40	C₃×#546	—	2	2	no	—
41	C₃×#546	—	2	1	no	—
42	C₃×#546	—	2	2	no	—
43	C₃×#546	—	2	1	no	—
44	C₃×D₄²	—	2	2	no	—
45	C₃×D₄²	—	2	1	no	—
46	C₃×#537	C₂²	1	2	yes	—
47	C₃×#537	C₂²	1	1	yes	characteristic
48	C₃×#537	C₂²	1	1	yes	characteristic
49	C₃×#537	C₂²	1	2	yes	complemented
50	C₃×#536	C₂²	1	1	yes	characteristic
51	C₃×#536	C₂²	1	2	yes	complemented
52	C₃×#535	C₂²	1	2	yes	—
53	C₃×#535	C₂²	1	1	yes	characteristic
54	C₃×#525	C₂²	1	2	yes	—
55	C₃×#525	C₂²	1	1	yes	characteristic
56	C₃×#525	C₂²	1	2	yes	complemented
57	C₃×#525	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
59	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₃×#121	C₂²	1	2	yes	—
61	C₂×C₃×#121	C₂²	1	1	yes	characteristic
62	C₃×#520	C₂²	1	1	yes	characteristic
63	C₃×#520	C₂²	1	1	yes	characteristic, complemented
64	C₃×#485	C₂²	1	2	yes	complemented
65	C₃×#485	C₂²	1	2	yes	complemented
66	C₃×#485	C₂²	1	2	yes	complemented
67	C₃×#485	C₂²	1	2	yes	complemented
68	C₃×#484	C₂²	1	2	yes	complemented
69	C₃×#484	C₂²	1	2	yes	complemented
70	C₃×#484	C₂²	1	2	yes	complemented
71	C₃×#483	C₂²	1	2	yes	complemented
72	C₃×#482	C₂²	1	2	yes	complemented
73	C₃×#482	C₂²	1	2	yes	complemented
74	C₃×#482	C₂²	1	2	yes	complemented
75	C₃×#482	C₂²	1	2	yes	complemented
76	C₃×#481	C₂²	1	2	yes	complemented
77	C₃×#480	C₂²	1	2	yes	complemented
78	C₃×#480	C₂²	1	2	yes	complemented
79	C₃×#480	C₂²	1	2	yes	complemented
80	C₃×#470	C₂²	1	1	yes	characteristic, complemented
81	C₃×#470	C₂²	1	2	yes	complemented
82	C₃×#470	C₂²	1	1	yes	characteristic, complemented
83	C₃×#469	C₂²	1	1	yes	characteristic, complemented
84	C₃×#469	C₂²	1	2	yes	complemented
85	C₃×#469	C₂²	1	1	yes	characteristic, complemented
86	C₃×#468	C₂²	1	1	yes	characteristic, complemented
87	C₃×#468	C₂²	1	2	yes	complemented
88	C₃×#468	C₂²	1	2	yes	complemented
89	C₃×#468	C₂²	1	2	yes	complemented
90	C₃×#468	C₂²	1	2	yes	complemented
91	C₃×#468	C₂²	1	1	yes	characteristic, complemented
92	C₃×#468	C₂²	1	2	yes	complemented
93	C₃×#468	C₂²	1	1	yes	characteristic, complemented
94	C₃×#468	C₂²	1	2	yes	complemented
95	C₃×#468	C₂²	1	1	yes	characteristic, complemented
96	C₃×#467	C₂²	1	2	yes	complemented
97	C₃×#466	C₂²	1	2	yes	complemented
98	C₃×#465	C₂²	1	2	yes	complemented
99	C₃×#465	C₂²	1	2	yes	complemented
100	C₃×#452	C₂²	1	2	yes	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	2	yes	complemented
105	C₃×#450	C₂²	1	2	yes	complemented
106	C₃×#450	C₂²	1	2	yes	complemented
107	C₃×#450	C₂²	1	2	yes	complemented
108	C₃×#449	C₂²	1	2	yes	complemented
109	C₃×#449	C₂²	1	2	yes	complemented
110	C₃×#449	C₂²	1	2	yes	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×#447	C₂²	1	2	yes	complemented
116	C₃×#428	C₂²	1	1	yes	characteristic, complemented
117	C₃×#428	C₂²	1	1	yes	characteristic, complemented
118	C₃×#427	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₃×#107	C₂²	1	1	yes	characteristic, complemented
120	C₃×#419	C₂²	1	1	yes	characteristic, complemented
121	C₃×#418	C₂²	1	1	yes	characteristic, complemented
122	C₃×#417	C₂²	1	1	yes	characteristic, complemented
123	C₃×#417	C₂²	1	1	yes	characteristic, complemented
124	C₃×#416	C₂²	1	1	yes	characteristic, complemented
125	C₃×#416	C₂²	1	1	yes	characteristic, complemented
126	C₂×C₃×#103	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₃×#102	C₂²	1	1	yes	characteristic, complemented
128	C₃×#408	C₂²	1	1	yes	characteristic
129	C₃×#408	C₂²	1	1	yes	characteristic
130	C₃×#408	C₂²	1	2	yes	complemented
131	C₃×#408	C₂²	1	2	yes	complemented
132	C₃×#408	C₂²	1	1	yes	characteristic, complemented
133	C₃×#408	C₂²	1	1	yes	characteristic, complemented
134	C₃×#407	C₂²	1	2	yes	complemented
135	C₃×#407	C₂²	1	2	yes	complemented
136	#3489	C₂×C₃	1	1	yes	characteristic, complemented
137	#3488	C₂×C₃	1	1	yes	characteristic, complemented
138	#3203	C₂×C₃	1	2	yes	complemented
139	#3201	C₂×C₃	1	2	yes	complemented
140	#3200	C₂×C₃	1	2	yes	complemented
141	#3198	C₂×C₃	1	2	yes	complemented
142	#3197	C₂×C₃	1	2	yes	complemented
143	#3196	C₂×C₃	1	2	yes	complemented
144	#3194	C₂×C₃	1	2	yes	complemented
145	#3193	C₂×C₃	1	2	yes	complemented
146	#3098	C₂×C₃	1	1	yes	characteristic, complemented
147	#3098	C₂×C₃	1	1	yes	characteristic, complemented
148	#3097	C₂×C₃	1	1	yes	characteristic, complemented
149	#3096	C₂×C₃	1	1	yes	characteristic, complemented
150	#3056	C₂×C₃	1	1	yes	characteristic, complemented
151	#3055	C₂×C₃	1	1	yes	characteristic, complemented
152	#3054	C₂×C₃	1	1	yes	characteristic, complemented
153	C₂×#468	C₂×C₃	1	1	yes	characteristic, complemented
154	#3013	C₂×C₃	1	1	yes	characteristic, complemented
155	#3012	C₂×C₃	1	1	yes	characteristic, complemented
156	#3010	C₂×C₃	1	1	yes	characteristic, complemented
157	#3009	C₂×C₃	1	1	yes	characteristic, complemented
158	#2879	C₂×C₃	1	1	yes	characteristic, complemented
159	C₃×2₋¹⁺⁴	—	4	2	no	—
160	C₃×2₋¹⁺⁴	—	4	2	no	—
161	C₃×H(5,𝔽₂)	—	4	2	no	—
162	C₃×H(5,𝔽₂)	—	4	2	no	—
163	C₂×C₃×#41	—	2	1	no	—
164	C₂×C₃×#41	—	2	2	no	—
165	C₂×C₃×#41	—	2	1	no	—
166	C₂×C₃×#41	—	4	2	no	—
167	C₂×C₃×#41	—	4	2	no	—
168	C₂×C₃×#41	D₄	1	2	yes	—
169	C₂×C₃×#41	D₄	1	1	yes	characteristic
170	C₂×C₃×#41	D₄	1	1	yes	characteristic
171	C₂×C₃×#41	C₂³	1	1	yes	characteristic
172	C₂×C₃×#41	C₂³	1	1	yes	characteristic
173	C₂×C₃×#41	C₂³	1	2	yes	—
174	C₂×C₃×#41	C₂³	1	2	yes	—
175	C₂×C₃×#41	C₂³	1	1	yes	characteristic
176	C₂×C₃×#41	C₂³	1	1	yes	characteristic
177	C₂×C₃×#41	C₂³	1	2	yes	—
178	C₂²×C₃×Q₈	—	2	1	no	—
179	C₂²×C₃×Q₈	D₄	1	1	yes	characteristic
180	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
181	C₂²×C₃×Q₈	C₂³	1	2	yes	—
182	C₂²×C₃×D₄	—	2	1	no	—
183	C₂²×C₃×D₄	—	2	2	no	—
184	C₂²×C₃×D₄	—	2	2	no	—
185	C₂²×C₃×D₄	—	2	1	no	—
186	C₂²×C₃×D₄	D₄	1	1	yes	characteristic
187	C₂²×C₃×D₄	D₄	1	2	yes	—
188	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
189	C₂²×C₃×D₄	C₂³	1	2	yes	—
190	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
191	C₂³×C₃×C₄	C₂³	1	2	yes	—
192	C₃×#137	—	4	2	no	—
193	C₃×AGL(1,ℤ/8)	—	4	2	no	—
194	C₃×#135	—	4	2	no	—
195	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
196	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
197	C₂×C₃×SD₁₆	—	4	2	no	—
198	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
199	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
200	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
201	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
202	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
203	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
204	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
205	C₂×C₃×D₈	C₂³	1	2	yes	—
206	C₂×C₃×M₁₆	—	4	2	no	—
207	C₂×C₃×M₁₆	—	4	2	no	—
208	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
209	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
210	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
211	C₂×C₃×M₁₆	C₂³	1	2	yes	—
212	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
213	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
214	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
215	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
216	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
217	C₂²×C₃×C₈	C₂³	1	2	yes	—
218	C₃×C₄⋊Q₈	—	2	1	no	—
219	C₃×C₄⋊Q₈	—	2	2	no	—
220	C₃×#127	—	2	1	no	—
221	C₃×#127	—	2	2	no	—
222	C₃×#124	—	2	1	no	—
223	C₃×#124	—	2	2	no	—
224	C₃×#124	—	2	1	no	—
225	C₃×#124	—	2	2	no	—
226	C₃×#123	—	2	2	no	—
227	C₃×#123	—	2	2	no	—
228	C₃×#123	—	2	2	no	—
229	C₃×#123	—	2	1	no	—
230	C₃×#123	—	2	2	no	—
231	C₃×#123	—	2	1	no	—
232	C₃×#123	—	2	2	no	—
233	C₃×C₂²⋊Q₈	—	2	1	no	—
234	C₃×C₂²⋊Q₈	—	2	2	no	—
235	C₃×C₂²⋊Q₈	—	2	1	no	—
236	C₃×C₂²⋊Q₈	—	2	2	no	—
237	C₃×C₂²⋊Q₈	—	2	1	no	—
238	C₃×C₂²⋊Q₈	—	2	2	no	—
239	C₃×C₂²⋊Q₈	—	2	1	no	—
240	C₃×C₂²⋊Q₈	—	2	2	no	—
241	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
242	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
243	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
244	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
245	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
246	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
247	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
248	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
249	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
250	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
251	C₃×#121	—	2	2	no	—
252	C₃×#121	—	2	2	no	—
253	C₃×#121	—	2	2	no	—
254	C₃×#121	—	2	1	no	—
255	C₃×#121	—	2	2	no	—
256	C₃×#121	—	2	2	no	—
257	C₃×#121	—	2	1	no	—
258	C₃×#121	—	2	2	no	—
259	C₃×#121	—	2	2	no	—
260	C₃×#121	—	2	2	no	—
261	C₃×#121	—	2	1	no	—
262	C₃×#121	—	2	2	no	—
263	C₃×#121	—	2	1	no	—
264	C₃×#121	—	2	2	no	—
265	C₃×#121	C₂³	1	2	yes	—
266	C₃×#121	C₂³	1	2	yes	—
267	C₃×#121	C₂³	1	2	yes	—
268	C₃×#121	C₂³	1	2	yes	—
269	C₃×#121	C₂³	1	1	yes	characteristic
270	C₃×#121	C₂³	1	2	yes	—
271	C₃×#121	C₂³	1	1	yes	characteristic
272	C₃×#121	C₂³	1	1	yes	characteristic
273	C₃×#121	C₂³	1	2	yes	—
274	C₃×#121	C₂³	1	1	yes	characteristic
275	C₃×#120	—	2	1	no	—
276	C₃×#120	—	2	2	no	—
277	C₃×#120	—	2	1	no	—
278	C₃×#120	—	2	2	no	—
279	C₃×#120	—	2	2	no	—
280	C₃×#120	—	2	2	no	—
281	C₃×#120	—	2	2	no	—
282	C₃×C₄×Q₈	—	2	1	no	—
283	C₃×C₄×Q₈	—	2	1	no	—
284	C₃×C₄×D₄	—	2	2	no	—
285	C₃×C₄×D₄	—	2	1	no	—
286	C₃×C₄×D₄	—	2	2	no	—
287	C₃×C₄×D₄	—	2	1	no	—
288	C₃×C₄×D₄	—	2	1	no	—
289	C₃×C₄×D₄	—	2	2	no	—
290	C₃×C₄×D₄	—	2	1	no	—
291	C₃×C₄×D₄	—	2	2	no	—
292	C₃×C₄×D₄	—	2	1	no	—
293	C₃×C₄×D₄	—	2	2	no	—
294	C₃×C₄×D₄	—	2	1	no	—
295	C₃×C₄×D₄	—	2	2	no	—
296	C₃×#117	C₂³	1	1	yes	characteristic
297	C₃×#117	C₂³	1	1	yes	characteristic
298	C₃×#117	C₂³	1	2	yes	—
299	C₃×#117	C₂³	1	2	yes	—
300	C₂×C₃×C₄⋊C₄	—	2	1	no	—
301	C₂×C₃×C₄⋊C₄	—	2	2	no	—
302	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
303	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
304	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
305	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
306	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
310	C₃×#107	C₂³	1	2	yes	—
311	C₃×#107	C₂³	1	2	yes	—
312	C₃×#107	C₂³	1	1	yes	characteristic
313	C₃×#107	C₂³	1	1	yes	characteristic
314	C₃×#107	C₂³	1	2	yes	—
315	C₃×#107	C₂³	1	2	yes	—
316	C₃×#106	C₂³	1	1	yes	characteristic
317	C₃×#106	C₂³	1	1	yes	characteristic
318	C₃×#106	C₂³	1	2	yes	—
319	C₃×#106	C₂³	1	2	yes	—
320	C₃×#103	C₂³	1	2	yes	—
321	C₃×#103	C₂³	1	2	yes	—
322	C₃×#103	C₂³	1	1	yes	characteristic
323	C₃×#103	C₂³	1	1	yes	characteristic
324	C₃×#103	C₂³	1	1	yes	characteristic
325	C₃×#103	C₂³	1	1	yes	characteristic
326	C₃×#103	C₂³	1	2	yes	—
327	C₃×#103	C₂³	1	2	yes	—
328	C₃×#103	C₂³	1	2	yes	—
329	C₃×#103	C₂³	1	2	yes	—
330	C₃×#102	C₂³	1	2	yes	—
331	C₃×#102	C₂³	1	2	yes	—
332	C₃×#102	C₂³	1	1	yes	characteristic
333	C₃×#102	C₂³	1	1	yes	characteristic
334	C₃×#102	C₂³	1	1	yes	characteristic
335	C₃×#102	C₂³	1	1	yes	characteristic
336	C₃×#102	C₂³	1	2	yes	—
337	C₃×#102	C₂³	1	2	yes	—
338	C₃×#102	C₂³	1	2	yes	—
339	C₃×#102	C₂³	1	2	yes	—
340	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
341	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
342	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
343	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
344	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
345	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
346	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
347	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
348	C₂×2₋¹⁺⁴	C₂²×C₃	1	1	yes	characteristic, complemented
349	C₂×H(5,𝔽₂)	C₂²×C₃	1	1	yes	characteristic
350	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
351	C₂×#137	C₂²×C₃	1	1	yes	characteristic, complemented
352	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	1	yes	characteristic, complemented
353	C₂×#135	C₂²×C₃	1	1	yes	characteristic, complemented
354	C₂²×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
355	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
356	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
357	#550	—	2	1	no	—
358	D₄×Q₈	—	2	1	no	—
359	#548	—	2	1	no	—
360	#548	—	2	1	no	—
361	#547	—	2	2	no	—
362	#547	—	2	1	no	—
363	#546	—	2	2	no	—
364	#546	—	2	1	no	—
365	#546	—	2	2	no	—
366	#546	—	2	1	no	—
367	D₄²	—	2	2	no	—
368	D₄²	—	2	1	no	—
369	#537	C₂²×C₃	1	1	yes	characteristic
370	#537	C₂²×C₃	1	1	yes	characteristic
371	#537	C₂²×C₃	1	2	yes	—
372	#537	C₂²×C₃	1	2	yes	complemented
373	#536	C₂²×C₃	1	1	yes	characteristic
374	#536	C₂²×C₃	1	2	yes	complemented
375	#535	C₂²×C₃	1	1	yes	characteristic
376	#535	C₂²×C₃	1	2	yes	—
377	#525	C₂²×C₃	1	2	yes	—
378	#525	C₂²×C₃	1	1	yes	characteristic
379	#525	C₂²×C₃	1	2	yes	complemented
380	#525	C₂²×C₃	1	1	yes	characteristic, complemented
381	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
382	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
383	C₂×#121	C₂²×C₃	1	2	yes	—
384	C₂×#121	C₂²×C₃	1	1	yes	characteristic
385	#520	C₂²×C₃	1	1	yes	characteristic
386	#520	C₂²×C₃	1	1	yes	characteristic, complemented
387	#485	C₂²×C₃	1	2	yes	complemented
388	#485	C₂²×C₃	1	2	yes	complemented
389	#485	C₂²×C₃	1	2	yes	complemented
390	#485	C₂²×C₃	1	2	yes	complemented
391	#484	C₂²×C₃	1	2	yes	complemented
392	#484	C₂²×C₃	1	2	yes	complemented
393	#484	C₂²×C₃	1	2	yes	complemented
394	#483	C₂²×C₃	1	2	yes	complemented
395	#482	C₂²×C₃	1	2	yes	complemented
396	#482	C₂²×C₃	1	2	yes	complemented
397	#482	C₂²×C₃	1	2	yes	complemented
398	#482	C₂²×C₃	1	2	yes	complemented
399	#481	C₂²×C₃	1	2	yes	complemented
400	#480	C₂²×C₃	1	2	yes	complemented
401	#480	C₂²×C₃	1	2	yes	complemented
402	#480	C₂²×C₃	1	2	yes	complemented
403	#470	C₂²×C₃	1	1	yes	characteristic, complemented
404	#470	C₂²×C₃	1	2	yes	complemented
405	#470	C₂²×C₃	1	1	yes	characteristic, complemented
406	#469	C₂²×C₃	1	1	yes	characteristic, complemented
407	#469	C₂²×C₃	1	2	yes	complemented
408	#469	C₂²×C₃	1	1	yes	characteristic, complemented
409	#468	C₂²×C₃	1	1	yes	characteristic, complemented
410	#468	C₂²×C₃	1	2	yes	complemented
411	#468	C₂²×C₃	1	2	yes	complemented
412	#468	C₂²×C₃	1	2	yes	complemented
413	#468	C₂²×C₃	1	2	yes	complemented
414	#468	C₂²×C₃	1	1	yes	characteristic, complemented
415	#468	C₂²×C₃	1	2	yes	complemented
416	#468	C₂²×C₃	1	1	yes	characteristic, complemented
417	#468	C₂²×C₃	1	2	yes	complemented
418	#468	C₂²×C₃	1	1	yes	characteristic, complemented
419	#467	C₂²×C₃	1	2	yes	complemented
420	#466	C₂²×C₃	1	2	yes	complemented
421	#465	C₂²×C₃	1	2	yes	complemented
422	#465	C₂²×C₃	1	2	yes	complemented
423	#452	C₂²×C₃	1	2	yes	complemented
424	#452	C₂²×C₃	1	2	yes	complemented
425	#452	C₂²×C₃	1	2	yes	complemented
426	#452	C₂²×C₃	1	2	yes	complemented
427	#451	C₂²×C₃	1	2	yes	complemented
428	#450	C₂²×C₃	1	2	yes	complemented
429	#450	C₂²×C₃	1	2	yes	complemented
430	#450	C₂²×C₃	1	2	yes	complemented
431	#449	C₂²×C₃	1	2	yes	complemented
432	#449	C₂²×C₃	1	2	yes	complemented
433	#449	C₂²×C₃	1	2	yes	complemented
434	#449	C₂²×C₃	1	2	yes	complemented
435	#448	C₂²×C₃	1	2	yes	complemented
436	#448	C₂²×C₃	1	2	yes	complemented
437	#448	C₂²×C₃	1	2	yes	complemented
438	#447	C₂²×C₃	1	2	yes	complemented
439	#428	C₂²×C₃	1	1	yes	characteristic, complemented
440	#428	C₂²×C₃	1	1	yes	characteristic, complemented
441	#427	C₂²×C₃	1	1	yes	characteristic, complemented
442	C₂×#107	C₂²×C₃	1	1	yes	characteristic, complemented
443	#419	C₂²×C₃	1	1	yes	characteristic, complemented
444	#418	C₂²×C₃	1	1	yes	characteristic, complemented
445	#417	C₂²×C₃	1	1	yes	characteristic, complemented
446	#417	C₂²×C₃	1	1	yes	characteristic, complemented
447	#416	C₂²×C₃	1	1	yes	characteristic, complemented
448	#416	C₂²×C₃	1	1	yes	characteristic, complemented
449	C₂×#103	C₂²×C₃	1	1	yes	characteristic, complemented
450	C₂×#102	C₂²×C₃	1	1	yes	characteristic, complemented
451	#408	C₂²×C₃	1	1	yes	characteristic
452	#408	C₂²×C₃	1	1	yes	characteristic
453	#408	C₂²×C₃	1	1	yes	characteristic, complemented
454	#408	C₂²×C₃	1	1	yes	characteristic, complemented
455	#408	C₂²×C₃	1	2	yes	complemented
456	#408	C₂²×C₃	1	2	yes	complemented
457	#407	C₂²×C₃	1	2	yes	complemented
458	#407	C₂²×C₃	1	2	yes	complemented
459	C₂⁴×C₃	—	2	2	no	—
460	C₂⁴×C₃	—	2	1	no	—
461	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
462	C₂⁴×C₃	C₂×D₄	1	2	yes	—
463	C₃×#41	—	2	2	no	—
464	C₃×#41	—	2	2	no	—
465	C₃×#41	—	2	2	no	—
466	C₃×#41	—	2	2	no	—
467	C₃×#41	—	2	2	no	—
468	C₃×#41	—	2	2	no	—
469	C₃×#41	—	2	2	no	—
470	C₃×#41	—	2	2	no	—
471	C₃×#41	—	4	2	no	—
472	C₃×#41	—	4	2	no	—
473	C₃×#41	—	4	4	no	—
474	C₃×#41	—	4	2	no	—
475	C₃×#41	—	4	2	no	—
476	C₃×#41	—	4	2	no	—
477	C₃×#41	—	4	2	no	—
478	C₃×#41	—	4	2	no	—
479	C₃×#41	—	4	2	no	—
480	C₃×#41	—	4	8	no	—
481	C₃×#41	—	4	4	no	—
482	C₃×#41	—	4	4	no	—
483	C₂×C₃×Q₈	—	2	2	no	—
484	C₂×C₃×Q₈	—	2	1	no	—
485	C₂×C₃×Q₈	—	2	2	no	—
486	C₂×C₃×Q₈	—	2	2	no	—
487	C₂×C₃×Q₈	—	4	2	no	—
488	C₂×C₃×Q₈	—	4	2	no	—
489	C₂×C₃×Q₈	—	4	2	no	—
490	C₂×C₃×Q₈	—	4	4	no	—
491	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
492	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
493	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
494	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
495	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
496	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
497	C₂×C₃×D₄	—	2	1	no	—
498	C₂×C₃×D₄	—	2	1	no	—
499	C₂×C₃×D₄	—	2	2	no	—
500	C₂×C₃×D₄	—	2	2	no	—
501	C₂×C₃×D₄	—	2	1	no	—
502	C₂×C₃×D₄	—	2	2	no	—
503	C₂×C₃×D₄	—	2	1	no	—
504	C₂×C₃×D₄	—	2	1	no	—
505	C₂×C₃×D₄	—	2	2	no	—
506	C₂×C₃×D₄	—	2	2	no	—
507	C₂×C₃×D₄	—	2	1	no	—
508	C₂×C₃×D₄	—	2	2	no	—
509	C₂×C₃×D₄	—	2	2	no	—
510	C₂×C₃×D₄	—	2	2	no	—
511	C₂×C₃×D₄	—	2	2	no	—
512	C₂×C₃×D₄	—	2	1	no	—
513	C₂×C₃×D₄	—	2	2	no	—
514	C₂×C₃×D₄	—	2	2	no	—
515	C₂×C₃×D₄	—	4	2	no	—
516	C₂×C₃×D₄	—	4	2	no	—
517	C₂×C₃×D₄	—	4	2	no	—
518	C₂×C₃×D₄	—	4	4	no	—
519	C₂×C₃×D₄	—	4	8	no	—
520	C₂×C₃×D₄	—	4	4	no	—
521	C₂×C₃×D₄	—	8	2	no	—
522	C₂×C₃×D₄	—	8	4	no	—
523	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
524	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
525	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
526	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
527	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
528	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
529	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
530	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
531	C₂×C₃×D₄	C₂⁴	1	2	yes	—
532	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
533	C₂²×C₃×C₄	—	2	2	no	—
534	C₂²×C₃×C₄	—	2	2	no	—
535	C₂²×C₃×C₄	—	2	2	no	—
536	C₂²×C₃×C₄	—	2	1	no	—
537	C₂²×C₃×C₄	—	2	2	no	—
538	C₂²×C₃×C₄	—	2	1	no	—
539	C₂²×C₃×C₄	—	2	2	no	—
540	C₂²×C₃×C₄	—	2	1	no	—
541	C₂²×C₃×C₄	—	2	2	no	—
542	C₂²×C₃×C₄	—	2	1	no	—
543	C₂²×C₃×C₄	—	2	2	no	—
544	C₂²×C₃×C₄	—	2	1	no	—
545	C₂²×C₃×C₄	—	4	2	no	—
546	C₂²×C₃×C₄	—	4	2	no	—
547	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
548	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
549	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
550	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
551	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
552	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
553	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
554	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
555	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
556	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
557	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
558	C₃×Q₁₆	—	4	1	no	—
559	C₃×Q₁₆	—	4	2	no	—
560	C₃×SD₁₆	—	4	2	no	—
561	C₃×SD₁₆	—	4	2	no	—
562	C₃×SD₁₆	—	4	1	no	—
563	C₃×SD₁₆	—	4	1	no	—
564	C₃×SD₁₆	—	4	2	no	—
565	C₃×SD₁₆	—	4	2	no	—
566	C₃×D₈	—	4	1	no	—
567	C₃×D₈	—	4	2	no	—
568	C₃×M₁₆	—	2	2	no	—
569	C₃×M₁₆	—	2	2	no	—
570	C₃×M₁₆	—	4	1	no	—
571	C₃×M₁₆	—	4	1	no	—
572	C₃×M₁₆	—	4	1	no	—
573	C₃×M₁₆	—	4	1	no	—
574	C₃×M₁₆	—	4	2	no	—
575	C₂×C₃×C₈	—	2	2	no	—
576	C₂×C₃×C₈	—	2	2	no	—
577	C₂×C₃×C₈	—	4	2	no	—
578	C₂×C₃×C₈	C₂⁴	1	2	yes	—
579	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
580	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
581	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
582	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
583	C₂×C₃×C₈	C₂⁴	1	2	yes	—
584	C₃×C₄⋊C₄	—	2	2	no	—
585	C₃×C₄⋊C₄	—	2	1	no	—
586	C₃×C₄⋊C₄	—	2	2	no	—
587	C₃×C₄⋊C₄	—	2	2	no	—
588	C₃×C₄⋊C₄	—	2	2	no	—
589	C₃×C₄⋊C₄	—	2	2	no	—
590	C₃×C₄⋊C₄	—	2	1	no	—
591	C₃×C₄⋊C₄	—	2	2	no	—
592	C₃×C₄⋊C₄	—	2	1	no	—
593	C₃×C₄⋊C₄	—	2	1	no	—
594	C₃×C₄⋊C₄	—	2	2	no	—
595	C₃×C₄⋊C₄	—	2	1	no	—
596	C₃×C₄⋊C₄	—	2	2	no	—
597	C₃×C₄⋊C₄	—	2	1	no	—
598	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
599	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
600	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
601	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
602	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
603	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
604	C₃×C₂²⋊C₄	—	2	2	no	—
605	C₃×C₂²⋊C₄	—	2	1	no	—
606	C₃×C₂²⋊C₄	—	2	2	no	—
607	C₃×C₂²⋊C₄	—	2	2	no	—
608	C₃×C₂²⋊C₄	—	2	2	no	—
609	C₃×C₂²⋊C₄	—	2	2	no	—
610	C₃×C₂²⋊C₄	—	2	1	no	—
611	C₃×C₂²⋊C₄	—	2	2	no	—
612	C₃×C₂²⋊C₄	—	2	1	no	—
613	C₃×C₂²⋊C₄	—	2	1	no	—
614	C₃×C₂²⋊C₄	—	2	1	no	—
615	C₃×C₂²⋊C₄	—	2	2	no	—
616	C₃×C₂²⋊C₄	—	2	2	no	—
617	C₃×C₂²⋊C₄	—	2	1	no	—
618	C₃×C₂²⋊C₄	—	2	2	no	—
619	C₃×C₂²⋊C₄	—	2	1	no	—
620	C₃×C₂²⋊C₄	—	2	2	no	—
621	C₃×C₂²⋊C₄	—	2	2	no	—
622	C₃×C₂²⋊C₄	—	2	2	no	—
623	C₃×C₂²⋊C₄	—	2	1	no	—
624	C₃×C₂²⋊C₄	—	2	2	no	—
625	C₃×C₂²⋊C₄	—	2	1	no	—
626	C₃×C₂²⋊C₄	—	2	2	no	—
627	C₃×C₂²⋊C₄	—	2	1	no	—
628	C₃×C₄²	—	2	2	no	—
629	C₃×C₄²	—	2	1	no	—
630	C₃×C₄²	—	2	2	no	—
631	C₃×C₄²	—	2	1	no	—
632	2₋¹⁺⁴	—	4	2	no	—
633	2₋¹⁺⁴	—	4	2	no	—
634	H(5,𝔽₂)	—	4	2	no	—
635	H(5,𝔽₂)	—	4	2	no	—
636	C₂×#41	—	2	1	no	—
637	C₂×#41	—	2	2	no	—
638	C₂×#41	—	2	1	no	—
639	C₂×#41	—	4	2	no	—
640	C₂×#41	—	4	2	no	—
641	C₂×#41	C₃×D₄	1	2	yes	—
642	C₂×#41	C₃×D₄	1	1	yes	characteristic
643	C₂×#41	C₃×D₄	1	1	yes	characteristic
644	C₂×#41	C₂³×C₃	1	1	yes	characteristic
645	C₂×#41	C₂³×C₃	1	1	yes	characteristic
646	C₂×#41	C₂³×C₃	1	2	yes	—
647	C₂×#41	C₂³×C₃	1	2	yes	—
648	C₂×#41	C₂³×C₃	1	1	yes	characteristic
649	C₂×#41	C₂³×C₃	1	1	yes	characteristic
650	C₂×#41	C₂³×C₃	1	2	yes	—
651	C₂²×Q₈	—	2	1	no	—
652	C₂²×Q₈	C₃×D₄	1	1	yes	characteristic
653	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
654	C₂²×Q₈	C₂³×C₃	1	2	yes	—
655	C₂²×D₄	—	2	1	no	—
656	C₂²×D₄	—	2	2	no	—
657	C₂²×D₄	—	2	2	no	—
658	C₂²×D₄	—	2	1	no	—
659	C₂²×D₄	C₃×D₄	1	1	yes	characteristic
660	C₂²×D₄	C₃×D₄	1	2	yes	—
661	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
662	C₂²×D₄	C₂³×C₃	1	2	yes	—
663	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
664	C₂³×C₄	C₂³×C₃	1	2	yes	—
665	#137	—	4	2	no	—
666	AGL(1,ℤ/8)	—	4	2	no	—
667	#135	—	4	2	no	—
668	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
669	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
670	C₂×SD₁₆	—	4	2	no	—
671	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
672	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
673	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
674	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
675	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
676	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
677	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
678	C₂×D₈	C₂³×C₃	1	2	yes	—
679	C₂×M₁₆	—	4	2	no	—
680	C₂×M₁₆	—	4	2	no	—
681	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
682	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
683	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
684	C₂×M₁₆	C₂³×C₃	1	2	yes	—
685	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
686	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
687	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
688	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
689	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
690	C₂²×C₈	C₂³×C₃	1	2	yes	—
691	C₄⋊Q₈	—	2	1	no	—
692	C₄⋊Q₈	—	2	2	no	—
693	#127	—	2	1	no	—
694	#127	—	2	2	no	—
695	#124	—	2	1	no	—
696	#124	—	2	2	no	—
697	#124	—	2	1	no	—
698	#124	—	2	2	no	—
699	#123	—	2	2	no	—
700	#123	—	2	2	no	—
701	#123	—	2	2	no	—
702	#123	—	2	1	no	—
703	#123	—	2	2	no	—
704	#123	—	2	1	no	—
705	#123	—	2	2	no	—
706	C₂²⋊Q₈	—	2	1	no	—
707	C₂²⋊Q₈	—	2	2	no	—
708	C₂²⋊Q₈	—	2	1	no	—
709	C₂²⋊Q₈	—	2	2	no	—
710	C₂²⋊Q₈	—	2	1	no	—
711	C₂²⋊Q₈	—	2	2	no	—
712	C₂²⋊Q₈	—	2	1	no	—
713	C₂²⋊Q₈	—	2	2	no	—
714	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
715	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
716	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
717	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
718	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
719	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
720	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
721	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
722	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
723	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
724	#121	—	2	2	no	—
725	#121	—	2	2	no	—
726	#121	—	2	2	no	—
727	#121	—	2	1	no	—
728	#121	—	2	2	no	—
729	#121	—	2	2	no	—
730	#121	—	2	1	no	—
731	#121	—	2	2	no	—
732	#121	—	2	2	no	—
733	#121	—	2	2	no	—
734	#121	—	2	1	no	—
735	#121	—	2	2	no	—
736	#121	—	2	1	no	—
737	#121	—	2	2	no	—
738	#121	C₂³×C₃	1	1	yes	characteristic
739	#121	C₂³×C₃	1	2	yes	—
740	#121	C₂³×C₃	1	2	yes	—
741	#121	C₂³×C₃	1	2	yes	—
742	#121	C₂³×C₃	1	2	yes	—
743	#121	C₂³×C₃	1	2	yes	—
744	#121	C₂³×C₃	1	1	yes	characteristic
745	#121	C₂³×C₃	1	1	yes	characteristic
746	#121	C₂³×C₃	1	2	yes	—
747	#121	C₂³×C₃	1	1	yes	characteristic
748	#120	—	2	1	no	—
749	#120	—	2	2	no	—
750	#120	—	2	1	no	—
751	#120	—	2	2	no	—
752	#120	—	2	2	no	—
753	#120	—	2	2	no	—
754	#120	—	2	2	no	—
755	C₄×Q₈	—	2	1	no	—
756	C₄×Q₈	—	2	1	no	—
757	C₄×D₄	—	2	2	no	—
758	C₄×D₄	—	2	1	no	—
759	C₄×D₄	—	2	2	no	—
760	C₄×D₄	—	2	1	no	—
761	C₄×D₄	—	2	1	no	—
762	C₄×D₄	—	2	2	no	—
763	C₄×D₄	—	2	1	no	—
764	C₄×D₄	—	2	2	no	—
765	C₄×D₄	—	2	1	no	—
766	C₄×D₄	—	2	2	no	—
767	C₄×D₄	—	2	1	no	—
768	C₄×D₄	—	2	2	no	—
769	#117	C₂³×C₃	1	1	yes	characteristic
770	#117	C₂³×C₃	1	2	yes	—
771	#117	C₂³×C₃	1	1	yes	characteristic
772	#117	C₂³×C₃	1	2	yes	—
773	C₂×C₄⋊C₄	—	2	1	no	—
774	C₂×C₄⋊C₄	—	2	2	no	—
775	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
776	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
777	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
778	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
779	C₂×C₂²⋊C₄	—	2	1	no	—
780	C₂×C₂²⋊C₄	—	2	2	no	—
781	C₂×C₂²⋊C₄	—	2	1	no	—
782	C₂×C₂²⋊C₄	—	2	2	no	—
783	#107	C₂³×C₃	1	2	yes	—
784	#107	C₂³×C₃	1	2	yes	—
785	#107	C₂³×C₃	1	1	yes	characteristic
786	#107	C₂³×C₃	1	1	yes	characteristic
787	#107	C₂³×C₃	1	2	yes	—
788	#107	C₂³×C₃	1	2	yes	—
789	#106	C₂³×C₃	1	1	yes	characteristic
790	#106	C₂³×C₃	1	1	yes	characteristic
791	#106	C₂³×C₃	1	2	yes	—
792	#106	C₂³×C₃	1	2	yes	—
793	#103	C₂³×C₃	1	2	yes	—
794	#103	C₂³×C₃	1	2	yes	—
795	#103	C₂³×C₃	1	1	yes	characteristic
796	#103	C₂³×C₃	1	1	yes	characteristic
797	#103	C₂³×C₃	1	1	yes	characteristic
798	#103	C₂³×C₃	1	1	yes	characteristic
799	#103	C₂³×C₃	1	2	yes	—
800	#103	C₂³×C₃	1	2	yes	—
801	#103	C₂³×C₃	1	2	yes	—
802	#103	C₂³×C₃	1	2	yes	—
803	#102	C₂³×C₃	1	2	yes	—
804	#102	C₂³×C₃	1	2	yes	—
805	#102	C₂³×C₃	1	1	yes	characteristic
806	#102	C₂³×C₃	1	1	yes	characteristic
807	#102	C₂³×C₃	1	1	yes	characteristic
808	#102	C₂³×C₃	1	1	yes	characteristic
809	#102	C₂³×C₃	1	2	yes	—
810	#102	C₂³×C₃	1	2	yes	—
811	#102	C₂³×C₃	1	2	yes	—
812	#102	C₂³×C₃	1	2	yes	—
813	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
814	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
815	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
816	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
817	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
818	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
819	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
820	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
821	C₂³×C₃	—	2	2	no	—
822	C₂³×C₃	—	2	1	no	—
823	C₂³×C₃	—	2	2	no	—
824	C₂³×C₃	—	2	1	no	—
825	C₂³×C₃	—	4	2	no	—
826	C₂³×C₃	—	4	1	no	—
827	C₂³×C₃	—	4	2	no	—
828	C₂³×C₃	—	4	1	no	—
829	C₂³×C₃	—	4	2	no	—
830	C₂³×C₃	—	4	4	no	—
831	C₂³×C₃	—	4	2	no	—
832	C₂³×C₃	—	8	1	no	—
833	C₂³×C₃	—	8	2	no	—
834	C₂³×C₃	—	8	1	no	—
835	C₂³×C₃	—	8	2	no	—
836	C₂³×C₃	C₂²×D₄	1	2	yes	—
837	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
838	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
839	C₂³×C₃	C₂²×D₄	1	2	yes	—
840	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
841	C₃×Q₈	—	2	2	no	—
842	C₃×Q₈	—	2	2	no	—
843	C₃×Q₈	—	2	2	no	—
844	C₃×Q₈	—	2	1	no	—
845	C₃×Q₈	—	2	2	no	—
846	C₃×Q₈	—	2	1	no	—
847	C₃×Q₈	—	2	1	no	—
848	C₃×Q₈	—	2	1	no	—
849	C₃×Q₈	—	4	2	no	—
850	C₃×Q₈	—	4	4	no	—
851	C₃×Q₈	—	4	2	no	—
852	C₃×D₄	—	2	4	no	—
853	C₃×D₄	—	2	4	no	—
854	C₃×D₄	—	2	2	no	—
855	C₃×D₄	—	2	2	no	—
856	C₃×D₄	—	2	1	no	—
857	C₃×D₄	—	2	2	no	—
858	C₃×D₄	—	2	1	no	—
859	C₃×D₄	—	2	1	no	—
860	C₃×D₄	—	2	2	no	—
861	C₃×D₄	—	2	1	no	—
862	C₃×D₄	—	4	2	no	—
863	C₃×D₄	—	4	2	no	—
864	C₃×D₄	—	4	2	no	—
865	C₃×D₄	—	4	4	no	—
866	C₃×D₄	—	4	2	no	—
867	C₃×D₄	—	4	4	no	—
868	C₃×D₄	—	4	4	no	—
869	C₃×D₄	—	4	2	no	—
870	C₃×D₄	—	4	4	no	—
871	C₃×D₄	—	4	2	no	—
872	C₃×D₄	—	4	2	no	—
873	C₃×D₄	—	4	2	no	—
874	C₃×D₄	—	8	2	no	—
875	C₃×D₄	—	8	1	no	—
876	C₃×D₄	—	8	1	no	—
877	C₃×D₄	—	8	2	no	—
878	C₃×D₄	—	8	2	no	—
879	C₃×D₄	—	8	2	no	—
880	C₃×D₄	—	8	2	no	—
881	C₂×C₃×C₄	—	2	2	no	—
882	C₂×C₃×C₄	—	2	2	no	—
883	C₂×C₃×C₄	—	2	2	no	—
884	C₂×C₃×C₄	—	2	1	no	—
885	C₂×C₃×C₄	—	2	1	no	—
886	C₂×C₃×C₄	—	2	1	no	—
887	C₂×C₃×C₄	—	2	1	no	—
888	C₂×C₃×C₄	—	2	2	no	—
889	C₂×C₃×C₄	—	2	2	no	—
890	C₂×C₃×C₄	—	2	2	no	—
891	C₂×C₃×C₄	—	2	2	no	—
892	C₂×C₃×C₄	—	2	1	no	—
893	C₂×C₃×C₄	—	2	1	no	—
894	C₂×C₃×C₄	—	2	2	no	—
895	C₂×C₃×C₄	—	2	1	no	—
896	C₂×C₃×C₄	—	2	2	no	—
897	C₂×C₃×C₄	—	2	1	no	—
898	C₂×C₃×C₄	—	2	1	no	—
899	C₂×C₃×C₄	—	2	2	no	—
900	C₂×C₃×C₄	—	2	1	no	—
901	C₂×C₃×C₄	—	4	2	no	—
902	C₂×C₃×C₄	—	4	2	no	—
903	C₂×C₃×C₄	—	4	2	no	—
904	C₂×C₃×C₄	—	4	4	no	—
905	C₂×C₃×C₄	—	4	4	no	—
906	C₂×C₃×C₄	—	4	4	no	—
907	C₂×C₃×C₄	—	4	2	no	—
908	C₂×C₃×C₄	—	4	2	no	—
909	C₂×C₃×C₄	—	4	2	no	—
910	C₂×C₃×C₄	—	8	1	no	—
911	C₂×C₃×C₄	—	8	2	no	—
912	C₂×C₃×C₄	—	8	1	no	—
913	C₂×C₃×C₄	—	8	2	no	—
914	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
915	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
916	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
917	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
918	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
919	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
920	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
921	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
922	C₃×C₈	—	2	1	no	—
923	C₃×C₈	—	2	1	no	—
924	C₃×C₈	—	2	1	no	—
925	C₃×C₈	—	2	1	no	—
926	C₃×C₈	—	2	2	no	—
927	C₃×C₈	—	2	2	no	—
928	C₂⁴	—	2	2	no	—
929	C₂⁴	—	2	1	no	—
930	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
931	C₂⁴	C₂×C₃×D₄	1	2	yes	—
932	#41	—	2	2	no	—
933	#41	—	2	2	no	—
934	#41	—	2	2	no	—
935	#41	—	2	2	no	—
936	#41	—	2	2	no	—
937	#41	—	2	2	no	—
938	#41	—	2	2	no	—
939	#41	—	2	2	no	—
940	#41	—	4	2	no	—
941	#41	—	4	2	no	—
942	#41	—	4	4	no	—
943	#41	—	4	2	no	—
944	#41	—	4	2	no	—
945	#41	—	4	2	no	—
946	#41	—	4	2	no	—
947	#41	—	4	2	no	—
948	#41	—	4	2	no	—
949	#41	—	4	8	no	—
950	#41	—	4	4	no	—
951	#41	—	4	4	no	—
952	C₂×Q₈	—	2	2	no	—
953	C₂×Q₈	—	2	1	no	—
954	C₂×Q₈	—	2	2	no	—
955	C₂×Q₈	—	2	2	no	—
956	C₂×Q₈	—	4	2	no	—
957	C₂×Q₈	—	4	2	no	—
958	C₂×Q₈	—	4	2	no	—
959	C₂×Q₈	—	4	4	no	—
960	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
961	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
962	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
963	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
964	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
965	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
966	C₂×D₄	—	2	1	no	—
967	C₂×D₄	—	2	1	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	1	no	—
971	C₂×D₄	—	2	2	no	—
972	C₂×D₄	—	2	1	no	—
973	C₂×D₄	—	2	1	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	1	no	—
977	C₂×D₄	—	2	2	no	—
978	C₂×D₄	—	2	2	no	—
979	C₂×D₄	—	2	2	no	—
980	C₂×D₄	—	2	2	no	—
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	2	no	—
983	C₂×D₄	—	2	2	no	—
984	C₂×D₄	—	4	2	no	—
985	C₂×D₄	—	4	2	no	—
986	C₂×D₄	—	4	2	no	—
987	C₂×D₄	—	4	4	no	—
988	C₂×D₄	—	4	8	no	—
989	C₂×D₄	—	4	4	no	—
990	C₂×D₄	—	8	2	no	—
991	C₂×D₄	—	8	4	no	—
992	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
993	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
994	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
995	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
996	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
997	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
998	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
999	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
1000	C₂×D₄	C₂⁴×C₃	1	2	yes	—
1001	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	2	no	—
1004	C₂²×C₄	—	2	2	no	—
1005	C₂²×C₄	—	2	1	no	—
1006	C₂²×C₄	—	2	2	no	—
1007	C₂²×C₄	—	2	1	no	—
1008	C₂²×C₄	—	2	2	no	—
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	2	no	—
1011	C₂²×C₄	—	2	1	no	—
1012	C₂²×C₄	—	2	2	no	—
1013	C₂²×C₄	—	2	1	no	—
1014	C₂²×C₄	—	4	2	no	—
1015	C₂²×C₄	—	4	2	no	—
1016	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
1017	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
1018	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
1019	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
1020	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
1021	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
1022	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
1023	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
1024	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
1025	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
1026	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
1027	Q₁₆	—	4	1	no	—
1028	Q₁₆	—	4	2	no	—
1029	SD₁₆	—	4	2	no	—
1030	SD₁₆	—	4	2	no	—
1031	SD₁₆	—	4	1	no	—
1032	SD₁₆	—	4	1	no	—
1033	SD₁₆	—	4	2	no	—
1034	SD₁₆	—	4	2	no	—
1035	D₈	—	4	1	no	—
1036	D₈	—	4	2	no	—
1037	M₁₆	—	2	2	no	—
1038	M₁₆	—	2	2	no	—
1039	M₁₆	—	4	1	no	—
1040	M₁₆	—	4	1	no	—
1041	M₁₆	—	4	1	no	—
1042	M₁₆	—	4	1	no	—
1043	M₁₆	—	4	2	no	—
1044	C₂×C₈	—	2	2	no	—
1045	C₂×C₈	—	2	2	no	—
1046	C₂×C₈	—	4	2	no	—
1047	C₂×C₈	C₂⁴×C₃	1	2	yes	—
1048	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
1049	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
1050	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
1051	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
1052	C₂×C₈	C₂⁴×C₃	1	2	yes	—
1053	C₄⋊C₄	—	2	2	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	1	no	—
1060	C₄⋊C₄	—	2	2	no	—
1061	C₄⋊C₄	—	2	1	no	—
1062	C₄⋊C₄	—	2	1	no	—
1063	C₄⋊C₄	—	2	2	no	—
1064	C₄⋊C₄	—	2	1	no	—
1065	C₄⋊C₄	—	2	2	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
1068	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
1069	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
1070	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
1071	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
1072	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	2	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	2	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	1	no	—
1087	C₂²⋊C₄	—	2	2	no	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	2	no	—
1090	C₂²⋊C₄	—	2	2	no	—
1091	C₂²⋊C₄	—	2	2	no	—
1092	C₂²⋊C₄	—	2	1	no	—
1093	C₂²⋊C₄	—	2	2	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	2	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₄²	—	2	2	no	—
1098	C₄²	—	2	1	no	—
1099	C₄²	—	2	2	no	—
1100	C₄²	—	2	1	no	—
1101	C₂²×C₃	—	2	1	no	—
1102	C₂²×C₃	—	2	1	no	—
1103	C₂²×C₃	—	2	2	no	—
1104	C₂²×C₃	—	2	2	no	—
1105	C₂²×C₃	—	2	1	no	—
1106	C₂²×C₃	—	2	1	no	—
1107	C₂²×C₃	—	2	1	no	—
1108	C₂²×C₃	—	2	1	no	—
1109	C₂²×C₃	—	2	2	no	—
1110	C₂²×C₃	—	2	2	no	—
1111	C₂²×C₃	—	2	1	no	—
1112	C₂²×C₃	—	2	1	no	—
1113	C₂²×C₃	—	2	2	no	—
1114	C₂²×C₃	—	2	2	no	—
1115	C₂²×C₃	—	4	2	no	—
1116	C₂²×C₃	—	4	1	no	—
1117	C₂²×C₃	—	4	1	no	—
1118	C₂²×C₃	—	4	1	no	—
1119	C₂²×C₃	—	4	2	no	—
1120	C₂²×C₃	—	4	1	no	—
1121	C₂²×C₃	—	4	1	no	—
1122	C₂²×C₃	—	4	2	no	—
1123	C₂²×C₃	—	4	1	no	—
1124	C₂²×C₃	—	8	2	no	—
1125	C₂²×C₃	—	8	4	no	—
1126	C₂²×C₃	—	16	2	no	—
1127	C₂²×C₃	—	16	4	no	—
1128	C₂²×C₃	#534	1	2	yes	—
1129	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
1130	C₃×C₄	—	2	1	no	—
1131	C₃×C₄	—	2	1	no	—
1132	C₃×C₄	—	2	2	no	—
1133	C₃×C₄	—	2	2	no	—
1134	C₃×C₄	—	4	2	no	—
1135	C₃×C₄	—	4	1	no	—
1136	C₃×C₄	—	4	2	no	—
1137	C₃×C₄	—	4	1	no	—
1138	C₃×C₄	—	4	1	no	—
1139	C₃×C₄	—	4	1	no	—
1140	C₃×C₄	—	4	1	no	—
1141	C₃×C₄	—	4	2	no	—
1142	C₃×C₄	—	4	1	no	—
1143	C₃×C₄	#534	1	2	yes	—
1144	C₃×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1145	C₃×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1146	C₂³	—	2	2	no	—
1147	C₂³	—	2	1	no	—
1148	C₂³	—	2	2	no	—
1149	C₂³	—	2	1	no	—
1150	C₂³	—	4	2	no	—
1151	C₂³	—	4	1	no	—
1152	C₂³	—	4	2	no	—
1153	C₂³	—	4	1	no	—
1154	C₂³	—	4	2	no	—
1155	C₂³	—	4	4	no	—
1156	C₂³	—	4	2	no	—
1157	C₂³	—	8	1	no	—
1158	C₂³	—	8	2	no	—
1159	C₂³	—	8	1	no	—
1160	C₂³	—	8	2	no	—
1161	C₂³	C₂²×C₃×D₄	1	2	yes	—
1162	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
1163	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
1164	C₂³	C₂²×C₃×D₄	1	2	yes	—
1165	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
1166	Q₈	—	2	2	no	—
1167	Q₈	—	2	2	no	—
1168	Q₈	—	2	2	no	—
1169	Q₈	—	2	1	no	—
1170	Q₈	—	2	2	no	—
1171	Q₈	—	2	1	no	—
1172	Q₈	—	2	1	no	—
1173	Q₈	—	2	1	no	—
1174	Q₈	—	4	2	no	—
1175	Q₈	—	4	4	no	—
1176	Q₈	—	4	2	no	—
1177	D₄	—	2	4	no	—
1178	D₄	—	2	4	no	—
1179	D₄	—	2	1	no	—
1180	D₄	—	2	2	no	—
1181	D₄	—	2	1	no	—
1182	D₄	—	2	1	no	—
1183	D₄	—	2	2	no	—
1184	D₄	—	2	1	no	—
1185	D₄	—	2	2	no	—
1186	D₄	—	2	2	no	—
1187	D₄	—	4	2	no	—
1188	D₄	—	4	2	no	—
1189	D₄	—	4	2	no	—
1190	D₄	—	4	4	no	—
1191	D₄	—	4	4	no	—
1192	D₄	—	4	4	no	—
1193	D₄	—	4	2	no	—
1194	D₄	—	4	4	no	—
1195	D₄	—	4	2	no	—
1196	D₄	—	4	2	no	—
1197	D₄	—	4	2	no	—
1198	D₄	—	4	2	no	—
1199	D₄	—	8	2	no	—
1200	D₄	—	8	2	no	—
1201	D₄	—	8	2	no	—
1202	D₄	—	8	2	no	—
1203	D₄	—	8	1	no	—
1204	D₄	—	8	1	no	—
1205	D₄	—	8	2	no	—
1206	C₂×C₄	—	2	2	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	2	1	no	—
1210	C₂×C₄	—	2	1	no	—
1211	C₂×C₄	—	2	2	no	—
1212	C₂×C₄	—	2	2	no	—
1213	C₂×C₄	—	2	2	no	—
1214	C₂×C₄	—	2	2	no	—
1215	C₂×C₄	—	2	2	no	—
1216	C₂×C₄	—	2	2	no	—
1217	C₂×C₄	—	2	1	no	—
1218	C₂×C₄	—	2	1	no	—
1219	C₂×C₄	—	2	2	no	—
1220	C₂×C₄	—	2	1	no	—
1221	C₂×C₄	—	2	2	no	—
1222	C₂×C₄	—	2	1	no	—
1223	C₂×C₄	—	2	1	no	—
1224	C₂×C₄	—	2	2	no	—
1225	C₂×C₄	—	2	1	no	—
1226	C₂×C₄	—	4	2	no	—
1227	C₂×C₄	—	4	2	no	—
1228	C₂×C₄	—	4	2	no	—
1229	C₂×C₄	—	4	4	no	—
1230	C₂×C₄	—	4	4	no	—
1231	C₂×C₄	—	4	4	no	—
1232	C₂×C₄	—	4	2	no	—
1233	C₂×C₄	—	4	2	no	—
1234	C₂×C₄	—	4	2	no	—
1235	C₂×C₄	—	8	1	no	—
1236	C₂×C₄	—	8	2	no	—
1237	C₂×C₄	—	8	1	no	—
1238	C₂×C₄	—	8	2	no	—
1239	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1240	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1241	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1242	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1243	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1244	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1245	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1246	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
1247	C₈	—	2	1	no	—
1248	C₈	—	2	1	no	—
1249	C₈	—	2	1	no	—
1250	C₈	—	2	1	no	—
1251	C₈	—	2	2	no	—
1252	C₈	—	2	2	no	—
1253	C₂×C₃	—	2	2	no	—
1254	C₂×C₃	—	4	2	no	—
1255	C₂×C₃	—	4	1	no	—
1256	C₂×C₃	—	4	1	no	—
1257	C₂×C₃	—	4	2	no	—
1258	C₂×C₃	—	8	1	no	—
1259	C₂×C₃	—	8	2	no	—
1260	C₂×C₃	—	8	1	no	—
1261	C₂×C₃	C₂×#534	1	1	yes	characteristic
1262	C₂×C₃	#3585	1	1	yes	characteristic
1263	C₂×C₃	#3586	1	1	yes	characteristic
1264	C₂²	—	2	1	no	—
1265	C₂²	—	2	1	no	—
1266	C₂²	—	2	1	no	—
1267	C₂²	—	2	1	no	—
1268	C₂²	—	2	2	no	—
1269	C₂²	—	2	2	no	—
1270	C₂²	—	2	2	no	—
1271	C₂²	—	2	2	no	—
1272	C₂²	—	2	1	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	2	1	no	—
1275	C₂²	—	2	1	no	—
1276	C₂²	—	2	2	no	—
1277	C₂²	—	2	2	no	—
1278	C₂²	—	4	1	no	—
1279	C₂²	—	4	2	no	—
1280	C₂²	—	4	1	no	—
1281	C₂²	—	4	2	no	—
1282	C₂²	—	4	1	no	—
1283	C₂²	—	4	1	no	—
1284	C₂²	—	4	1	no	—
1285	C₂²	—	4	2	no	—
1286	C₂²	—	4	1	no	—
1287	C₂²	—	8	2	no	—
1288	C₂²	—	8	4	no	—
1289	C₂²	—	16	2	no	—
1290	C₂²	—	16	4	no	—
1291	C₂²	C₃×#534	1	2	yes	—
1292	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1293	C₄	—	2	1	no	—
1294	C₄	—	2	1	no	—
1295	C₄	—	2	2	no	—
1296	C₄	—	2	2	no	—
1297	C₄	—	4	1	no	—
1298	C₄	—	4	2	no	—
1299	C₄	—	4	1	no	—
1300	C₄	—	4	2	no	—
1301	C₄	—	4	1	no	—
1302	C₄	—	4	2	no	—
1303	C₄	—	4	1	no	—
1304	C₄	—	4	1	no	—
1305	C₄	—	4	1	no	—
1306	C₄	C₃×#534	1	2	yes	—
1307	C₄	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1308	C₄	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1309	C₃	#60772	1	1	yes	characteristic, direct product factor, Sylow
1310	C₂	—	2	2	no	—
1311	C₂	—	4	1	no	—
1312	C₂	—	4	2	no	—
1313	C₂	—	4	1	no	—
1314	C₂	—	4	2	no	—
1315	C₂	—	8	2	no	—
1316	C₂	—	8	1	no	—
1317	C₂	—	8	1	no	—
1318	C₂	C₂×C₃×#534	1	1	yes	characteristic
1319	C₂	C₃×#3585	1	1	yes	characteristic
1320	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 ◁ C₂²×C₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3489	C₂	semidirect
2. C₃×#3488	C₂	semidirect
3. C₃×#3203	C₂	semidirect
4. C₃×#3201	C₂	semidirect
5. C₃×#3200	C₂	semidirect
6. C₃×#3198	C₂	semidirect
7. C₃×#3197	C₂	semidirect
8. C₃×#3196	C₂	semidirect
9. C₃×#3194	C₂	semidirect
10. C₃×#3193	C₂	semidirect
11. C₃×#3098	C₂	semidirect
12. C₃×#3098	C₂	semidirect
13. C₃×#3097	C₂	semidirect
14. C₃×#3096	C₂	semidirect
15. C₃×#3056	C₂	semidirect
16. C₃×#3055	C₂	semidirect
17. C₃×#3054	C₂	semidirect
18. C₂×C₃×#468	C₂	semidirect
19. C₃×#3013	C₂	semidirect
20. C₃×#3012	C₂	semidirect
21. C₃×#3010	C₂	semidirect
22. C₃×#3009	C₂	semidirect
23. C₃×#2879	C₂	semidirect
24. #60772	C₃	direct (N × H)
25. C₂×C₃×2₋¹⁺⁴	C₂²	semidirect
28. C₂×C₃×#137	C₂²	semidirect
29. C₂×C₃×AGL(1,ℤ/8)	C₂²	semidirect
30. C₂×C₃×#135	C₂²	semidirect
31. C₂²×C₃×SD₁₆	C₂²	semidirect
32. C₂²×C₃×M₁₆	C₂²	semidirect
33. C₂²×C₃×M₁₆	C₂²	semidirect
49. C₃×#537	C₂²	semidirect
51. C₃×#536	C₂²	semidirect
56. C₃×#525	C₂²	semidirect
57. C₃×#525	C₂²	semidirect
58. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
59. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
63. C₃×#520	C₂²	semidirect
64. C₃×#485	C₂²	semidirect
65. C₃×#485	C₂²	semidirect
66. C₃×#485	C₂²	semidirect
67. C₃×#485	C₂²	semidirect
68. C₃×#484	C₂²	semidirect
69. C₃×#484	C₂²	semidirect
70. C₃×#484	C₂²	semidirect
71. C₃×#483	C₂²	semidirect
72. C₃×#482	C₂²	semidirect
73. C₃×#482	C₂²	semidirect
74. C₃×#482	C₂²	semidirect
75. C₃×#482	C₂²	semidirect
76. C₃×#481	C₂²	semidirect
77. C₃×#480	C₂²	semidirect
78. C₃×#480	C₂²	semidirect
79. C₃×#480	C₂²	semidirect
80. C₃×#470	C₂²	semidirect
81. C₃×#470	C₂²	semidirect
82. C₃×#470	C₂²	semidirect
83. C₃×#469	C₂²	semidirect
84. C₃×#469	C₂²	semidirect
85. C₃×#469	C₂²	semidirect
86. C₃×#468	C₂²	semidirect
87. C₃×#468	C₂²	semidirect
88. C₃×#468	C₂²	semidirect
89. C₃×#468	C₂²	semidirect
90. C₃×#468	C₂²	semidirect
91. C₃×#468	C₂²	semidirect
92. C₃×#468	C₂²	semidirect
93. C₃×#468	C₂²	semidirect
94. C₃×#468	C₂²	semidirect
95. C₃×#468	C₂²	semidirect
96. C₃×#467	C₂²	semidirect
97. C₃×#466	C₂²	semidirect
98. C₃×#465	C₂²	semidirect
99. C₃×#465	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×#450	C₂²	semidirect
106. C₃×#450	C₂²	semidirect
107. C₃×#450	C₂²	semidirect
108. C₃×#449	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×#447	C₂²	semidirect
116. C₃×#428	C₂²	semidirect
117. C₃×#428	C₂²	semidirect
118. C₃×#427	C₂²	semidirect
119. C₂×C₃×#107	C₂²	semidirect
120. C₃×#419	C₂²	semidirect
121. C₃×#418	C₂²	semidirect
122. C₃×#417	C₂²	semidirect
123. C₃×#417	C₂²	semidirect
124. C₃×#416	C₂²	semidirect
125. C₃×#416	C₂²	semidirect
126. C₂×C₃×#103	C₂²	semidirect
127. C₂×C₃×#102	C₂²	semidirect
130. C₃×#408	C₂²	semidirect
131. C₃×#408	C₂²	semidirect
132. C₃×#408	C₂²	semidirect
133. C₃×#408	C₂²	semidirect
134. C₃×#407	C₂²	semidirect
135. C₃×#407	C₂²	semidirect
136. #3489	C₂×C₃	semidirect
137. #3488	C₂×C₃	semidirect
138. #3203	C₂×C₃	semidirect
139. #3201	C₂×C₃	semidirect
140. #3200	C₂×C₃	semidirect
141. #3198	C₂×C₃	semidirect
142. #3197	C₂×C₃	semidirect
143. #3196	C₂×C₃	semidirect
144. #3194	C₂×C₃	semidirect
145. #3193	C₂×C₃	semidirect
146. #3098	C₂×C₃	semidirect
147. #3098	C₂×C₃	semidirect
148. #3097	C₂×C₃	semidirect
149. #3096	C₂×C₃	semidirect
150. #3056	C₂×C₃	semidirect
151. #3055	C₂×C₃	semidirect
152. #3054	C₂×C₃	semidirect
153. C₂×#468	C₂×C₃	semidirect
154. #3013	C₂×C₃	semidirect
155. #3012	C₂×C₃	semidirect
156. #3010	C₂×C₃	semidirect
157. #3009	C₂×C₃	semidirect
158. #2879	C₂×C₃	semidirect
348. C₂×2₋¹⁺⁴	C₂²×C₃	semidirect
351. C₂×#137	C₂²×C₃	semidirect
352. C₂×AGL(1,ℤ/8)	C₂²×C₃	semidirect
353. C₂×#135	C₂²×C₃	semidirect
354. C₂²×SD₁₆	C₂²×C₃	semidirect
355. C₂²×M₁₆	C₂²×C₃	semidirect
356. C₂²×M₁₆	C₂²×C₃	semidirect
372. #537	C₂²×C₃	semidirect
374. #536	C₂²×C₃	semidirect
379. #525	C₂²×C₃	semidirect
380. #525	C₂²×C₃	semidirect
381. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
382. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
386. #520	C₂²×C₃	semidirect
387. #485	C₂²×C₃	semidirect
388. #485	C₂²×C₃	semidirect
389. #485	C₂²×C₃	semidirect
390. #485	C₂²×C₃	semidirect
391. #484	C₂²×C₃	semidirect
392. #484	C₂²×C₃	semidirect
393. #484	C₂²×C₃	semidirect
394. #483	C₂²×C₃	semidirect
395. #482	C₂²×C₃	semidirect
396. #482	C₂²×C₃	semidirect
397. #482	C₂²×C₃	semidirect
398. #482	C₂²×C₃	semidirect
399. #481	C₂²×C₃	semidirect
400. #480	C₂²×C₃	semidirect
401. #480	C₂²×C₃	semidirect
402. #480	C₂²×C₃	semidirect
403. #470	C₂²×C₃	semidirect
404. #470	C₂²×C₃	semidirect
405. #470	C₂²×C₃	semidirect
406. #469	C₂²×C₃	semidirect
407. #469	C₂²×C₃	semidirect
408. #469	C₂²×C₃	semidirect
409. #468	C₂²×C₃	semidirect
410. #468	C₂²×C₃	semidirect
411. #468	C₂²×C₃	semidirect
412. #468	C₂²×C₃	semidirect
413. #468	C₂²×C₃	semidirect
414. #468	C₂²×C₃	semidirect
415. #468	C₂²×C₃	semidirect
416. #468	C₂²×C₃	semidirect
417. #468	C₂²×C₃	semidirect
418. #468	C₂²×C₃	semidirect
419. #467	C₂²×C₃	semidirect
420. #466	C₂²×C₃	semidirect
421. #465	C₂²×C₃	semidirect
422. #465	C₂²×C₃	semidirect
423. #452	C₂²×C₃	semidirect
424. #452	C₂²×C₃	semidirect
425. #452	C₂²×C₃	semidirect
426. #452	C₂²×C₃	semidirect
427. #451	C₂²×C₃	semidirect
428. #450	C₂²×C₃	semidirect
429. #450	C₂²×C₃	semidirect
430. #450	C₂²×C₃	semidirect
431. #449	C₂²×C₃	semidirect
432. #449	C₂²×C₃	semidirect
433. #449	C₂²×C₃	semidirect
434. #449	C₂²×C₃	semidirect
435. #448	C₂²×C₃	semidirect
436. #448	C₂²×C₃	semidirect
437. #448	C₂²×C₃	semidirect
438. #447	C₂²×C₃	semidirect
439. #428	C₂²×C₃	semidirect
440. #428	C₂²×C₃	semidirect
441. #427	C₂²×C₃	semidirect
442. C₂×#107	C₂²×C₃	semidirect
443. #419	C₂²×C₃	semidirect
444. #418	C₂²×C₃	semidirect
445. #417	C₂²×C₃	semidirect
446. #417	C₂²×C₃	semidirect
447. #416	C₂²×C₃	semidirect
448. #416	C₂²×C₃	semidirect
449. C₂×#103	C₂²×C₃	semidirect
450. C₂×#102	C₂²×C₃	semidirect
453. #408	C₂²×C₃	semidirect
454. #408	C₂²×C₃	semidirect
455. #408	C₂²×C₃	semidirect
456. #408	C₂²×C₃	semidirect
457. #407	C₂²×C₃	semidirect
458. #407	C₂²×C₃	semidirect
1309. C₃	#60772	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#3489	2
C₃×#3488	2
C₃×#3203	2
C₃×#3201	2
C₃×#3200	2
C₃×#3198	2
C₃×#3197	2
C₃×#3196	2
C₃×#3194	2
C₃×#3193	2
C₃×#3098	2
C₃×#3097	2
C₃×#3096	2
C₃×#3056	2
C₃×#3055	2
C₃×#3054	2
C₂×C₃×#468	2
C₃×#3013	2
C₃×#3012	2
C₃×#3010	2
C₃×#3009	2
C₃×#2879	2
#60772	3

Subgroups — C3×#60772 #10679379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60772 #10679379