Subgroups — C₃×#61095 #10679702

Order 768.

2790 conjugacy classes of subgroups.

The subgroup lattice has 942 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	2	yes	maximal, complemented
2	C₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#3287	C₂	1	2	yes	maximal, complemented
5	C₃×D₄×SD₁₆	C₂	1	2	yes	maximal, complemented
6	C₃×#3278	C₂	1	2	yes	maximal, complemented
7	C₃×#3274	C₂	1	2	yes	maximal, complemented
8	C₃×#3271	C₂	1	4	yes	maximal, complemented
9	C₃×#3265	C₂	1	4	yes	maximal, complemented
10	C₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#3062	C₂	1	2	yes	maximal, complemented
12	C₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3012	C₂	1	2	yes	maximal, complemented
15	C₃×#3010	C₂	1	2	yes	maximal, complemented
16	C₃×C₄×#137	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2935	C₂	1	1	yes	maximal, characteristic, complemented
18	#61095	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
20	C₂×C₃×H(5,𝔽₂)	C₂²	1	2	yes	—
21	C₃×#577	—	2	16	no	—
22	C₂×C₃×#137	C₂²	1	1	yes	characteristic
23	C₂×C₃×#137	C₂²	1	4	yes	complemented
24	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
25	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
26	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
27	C₂×C₃×#135	C₂²	1	2	yes	—
28	C₂×C₃×#135	C₂²	1	4	yes	complemented
29	C₂²×C₃×SD₁₆	C₂²	1	4	yes	complemented
30	C₂²×C₃×SD₁₆	C₂²	1	2	yes	complemented
31	C₂×C₃×#131	C₂²	1	2	yes	complemented
32	C₃×#550	—	2	1	no	—
33	C₃×#550	C₂²	1	2	yes	—
34	C₃×#550	C₂²	1	2	yes	—
35	C₃×#550	C₂²	1	2	yes	complemented
36	C₃×D₄×Q₈	—	2	1	no	—
37	C₃×D₄×Q₈	C₂²	1	2	yes	complemented
38	C₃×#548	—	2	2	no	—
39	C₃×#548	C₂²	1	4	yes	complemented
40	C₃×D₄²	—	2	2	no	—
41	C₃×D₄²	—	2	2	no	—
42	C₃×D₄²	C₂²	1	2	yes	—
43	C₃×D₄²	C₂²	1	2	yes	—
44	C₃×#537	—	2	2	no	—
45	C₃×#537	C₂²	1	2	yes	complemented
46	C₃×#535	—	2	2	no	—
47	C₃×#535	C₂²	1	2	yes	—
48	C₃×#532	—	2	1	no	—
49	C₃×#532	—	2	2	no	—
50	C₃×#532	C₂²	1	1	yes	characteristic
51	C₃×#532	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₃×#127	—	2	1	no	—
53	C₂×C₃×#127	C₂²	1	1	yes	characteristic
54	C₃×C₄×#41	C₂²	1	1	yes	characteristic
55	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
56	C₃×#496	C₂²	1	4	yes	complemented
57	C₃×#493	C₂²	1	2	yes	complemented
58	C₃×#492	C₂²	1	2	yes	complemented
59	C₃×#469	C₂²	1	4	yes	complemented
60	C₃×#468	C₂²	1	4	yes	complemented
61	C₃×#466	C₂²	1	4	yes	complemented
62	C₃×#465	C₂²	1	4	yes	complemented
63	C₃×#464	C₂²	1	2	yes	complemented
64	C₃×#463	C₂²	1	2	yes	complemented
65	C₃×#462	C₂²	1	1	yes	characteristic, complemented
66	C₃×#461	C₂²	1	1	yes	characteristic, complemented
67	C₃×#460	C₂²	1	4	yes	complemented
68	C₃×#460	C₂²	1	2	yes	complemented
69	C₃×#460	C₂²	1	2	yes	complemented
70	C₃×#460	C₂²	1	1	yes	characteristic, complemented
71	C₃×#459	C₂²	1	1	yes	characteristic, complemented
72	C₃×#452	C₂²	1	4	yes	complemented
73	C₃×#450	C₂²	1	4	yes	complemented
74	C₃×#449	C₂²	1	4	yes	complemented
75	C₃×#449	C₂²	1	4	yes	complemented
76	C₃×#449	C₂²	1	4	yes	complemented
77	C₃×#448	C₂²	1	4	yes	complemented
78	C₃×#448	C₂²	1	4	yes	complemented
79	C₃×#447	C₂²	1	4	yes	complemented
80	C₃×#441	C₂²	1	2	yes	complemented
81	C₃×#440	C₂²	1	2	yes	complemented
82	C₃×C₄×Q₁₆	C₂²	1	2	yes	complemented
83	C₃×C₄×SD₁₆	C₂²	1	2	yes	complemented
84	C₃×#436	C₂²	1	2	yes	complemented
85	C₃×#435	C₂²	1	4	yes	complemented
86	C₃×C₈×D₄	C₂²	1	2	yes	complemented
87	C₃×#428	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
89	C₃×#419	C₂²	1	1	yes	characteristic, complemented
90	C₃×#417	C₂²	1	1	yes	characteristic
91	C₃×#416	C₂²	1	2	yes	complemented
92	C₂×C₃×#102	C₂²	1	2	yes	complemented
93	C₃×#408	C₂²	1	2	yes	complemented
94	C₃×C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
95	C₂×#577	C₂×C₃	1	2	yes	complemented
96	#3498	C₂×C₃	1	1	yes	characteristic, complemented
97	#3497	C₂×C₃	1	1	yes	characteristic, complemented
98	#3287	C₂×C₃	1	2	yes	complemented
99	D₄×SD₁₆	C₂×C₃	1	2	yes	complemented
100	#3278	C₂×C₃	1	2	yes	complemented
101	#3274	C₂×C₃	1	2	yes	complemented
102	#3271	C₂×C₃	1	4	yes	complemented
103	#3265	C₂×C₃	1	4	yes	complemented
104	#3151	C₂×C₃	1	1	yes	characteristic, complemented
105	#3062	C₂×C₃	1	2	yes	complemented
106	#3035	C₂×C₃	1	1	yes	characteristic, complemented
107	C₂×#460	C₂×C₃	1	1	yes	characteristic, complemented
108	#3012	C₂×C₃	1	2	yes	complemented
109	#3010	C₂×C₃	1	2	yes	complemented
110	C₄×#137	C₂×C₃	1	1	yes	characteristic, complemented
111	#2935	C₂×C₃	1	1	yes	characteristic, complemented
112	C₃×2₋¹⁺⁴	—	2	8	no	—
113	C₃×2₋¹⁺⁴	—	4	4	no	—
114	C₃×H(5,𝔽₂)	—	2	8	no	—
115	C₃×H(5,𝔽₂)	—	4	4	no	—
116	C₂×C₃×#41	—	2	2	no	—
117	C₂×C₃×#41	—	2	4	no	—
118	C₂×C₃×#41	—	2	2	no	—
119	C₂×C₃×#41	C₂³	1	2	yes	—
120	C₂×C₃×#41	C₂³	1	4	yes	—
121	C₂×C₃×#41	C₂³	1	4	yes	—
122	C₂×C₃×#41	C₂³	1	1	yes	characteristic
123	C₂×C₃×#41	C₂³	1	2	yes	—
124	C₂²×C₃×Q₈	—	2	2	no	—
125	C₂²×C₃×Q₈	C₂³	1	4	yes	—
126	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
127	C₂²×C₃×D₄	—	2	2	no	—
128	C₂²×C₃×D₄	—	2	4	no	—
129	C₂²×C₃×D₄	—	2	2	no	—
130	C₂²×C₃×D₄	—	2	2	no	—
131	C₂²×C₃×D₄	—	2	1	no	—
132	C₂²×C₃×D₄	—	2	1	no	—
133	C₂²×C₃×D₄	C₂³	1	2	yes	—
134	C₂²×C₃×D₄	C₂³	1	4	yes	—
135	C₃×#137	—	2	16	no	—
136	C₃×#137	D₄	1	8	yes	complemented
137	C₃×AGL(1,ℤ/8)	—	2	16	no	—
138	C₃×AGL(1,ℤ/8)	—	2	8	no	—
139	C₃×AGL(1,ℤ/8)	—	4	4	no	—
140	C₃×#135	—	2	8	no	—
141	C₃×#135	—	2	16	no	—
142	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
143	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
144	C₂×C₃×SD₁₆	—	2	8	no	—
145	C₂×C₃×SD₁₆	—	2	16	no	—
146	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
147	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
148	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
149	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
150	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
151	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
152	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
153	C₂×C₃×D₈	C₂³	1	2	yes	—
154	C₂×C₃×D₈	C₂³	1	4	yes	—
155	C₂×C₃×D₈	C₂³	1	4	yes	—
156	C₃×#131	—	2	8	no	—
157	C₂×C₃×M₁₆	C₂³	1	4	yes	—
158	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
159	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
160	C₂²×C₃×C₈	C₂³	1	2	yes	—
161	C₂²×C₃×C₈	C₂³	1	4	yes	—
162	C₃×C₄⋊Q₈	—	2	2	no	—
163	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
164	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₃×#127	—	2	2	no	—
166	C₃×#127	—	2	2	no	—
167	C₃×#127	—	2	2	no	—
168	C₃×#127	—	2	2	no	—
169	C₃×#127	—	2	1	no	—
170	C₃×#127	—	2	1	no	—
171	C₃×#127	D₄	1	1	yes	characteristic
172	C₃×#127	C₂³	1	1	yes	characteristic
173	C₃×#127	C₂³	1	2	yes	—
174	C₃×#127	C₂³	1	2	yes	—
175	C₃×#124	—	2	2	no	—
176	C₃×#124	—	2	4	no	—
177	C₃×#124	D₄	1	2	yes	—
178	C₃×#124	C₂³	1	2	yes	—
179	C₃×C₂²⋊Q₈	—	2	2	no	—
180	C₃×C₂²⋊Q₈	—	2	4	no	—
181	C₃×C₂²⋊Q₈	—	2	4	no	—
182	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
183	C₃×#121	—	2	4	no	—
184	C₃×#121	—	2	4	no	—
185	C₃×#121	—	2	2	no	—
186	C₃×#121	—	2	1	no	—
187	C₃×#121	—	2	1	no	—
188	C₃×#121	—	2	2	no	—
189	C₃×#121	—	2	2	no	—
190	C₃×#121	—	2	4	no	—
191	C₃×#121	—	2	4	no	—
192	C₃×#121	—	2	4	no	—
193	C₃×#121	D₄	1	2	yes	—
194	C₃×#121	D₄	1	2	yes	—
195	C₃×#121	C₂³	1	4	yes	—
196	C₃×#121	C₂³	1	4	yes	—
197	C₃×#121	C₂³	1	4	yes	—
198	C₃×#120	—	2	4	no	—
199	C₃×#120	—	2	4	no	—
200	C₃×#120	—	2	4	no	—
201	C₃×C₄×Q₈	—	2	1	no	—
202	C₃×C₄×Q₈	—	2	1	no	—
203	C₃×C₄×Q₈	C₂³	1	2	yes	—
204	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
205	C₃×C₄×Q₈	C₂³	1	2	yes	—
206	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
207	C₃×C₄×D₄	—	2	2	no	—
208	C₃×C₄×D₄	—	2	1	no	—
209	C₃×C₄×D₄	—	2	1	no	—
210	C₃×C₄×D₄	—	2	2	no	—
211	C₃×C₄×D₄	—	2	2	no	—
212	C₃×C₄×D₄	—	2	2	no	—
213	C₃×C₄×D₄	—	2	4	no	—
214	C₃×C₄×D₄	—	2	1	no	—
215	C₃×C₄×D₄	—	2	1	no	—
216	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
217	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
218	C₃×C₄×D₄	C₂³	1	2	yes	—
219	C₃×C₄×D₄	C₂³	1	2	yes	—
220	C₃×#117	—	2	1	no	—
221	C₃×#117	C₂³	1	1	yes	characteristic
222	C₂×C₃×C₄⋊C₄	—	2	1	no	—
223	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₄²	—	2	1	no	—
225	C₂×C₃×C₄²	—	2	1	no	—
226	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
227	C₃×#107	C₂³	1	2	yes	—
228	C₃×#106	C₂³	1	2	yes	—
229	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
230	C₃×C₄⋊C₈	C₂³	1	2	yes	—
231	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
232	C₃×#103	C₂³	1	2	yes	—
233	C₃×#103	C₂³	1	2	yes	—
234	C₃×#103	C₂³	1	2	yes	—
235	C₃×#103	C₂³	1	2	yes	—
236	C₃×#103	C₂³	1	2	yes	—
237	C₃×#102	C₂³	1	4	yes	—
238	C₃×#102	C₂³	1	4	yes	—
239	C₃×#102	C₂³	1	2	yes	—
240	C₃×#102	C₂³	1	2	yes	—
241	C₃×#102	C₂³	1	2	yes	—
242	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
243	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
244	C₃×#97	C₂³	1	2	yes	—
245	C₃×C₄×C₈	C₂³	1	2	yes	—
246	C₂×2₋¹⁺⁴	C₂²×C₃	1	2	yes	complemented
247	C₂×H(5,𝔽₂)	C₂²×C₃	1	2	yes	—
248	#577	—	2	16	no	—
249	C₂×#137	C₂²×C₃	1	1	yes	characteristic
250	C₂×#137	C₂²×C₃	1	4	yes	complemented
251	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	complemented
252	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	4	yes	complemented
253	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	complemented
254	C₂×#135	C₂²×C₃	1	2	yes	—
255	C₂×#135	C₂²×C₃	1	4	yes	complemented
256	C₂²×SD₁₆	C₂²×C₃	1	4	yes	complemented
257	C₂²×SD₁₆	C₂²×C₃	1	2	yes	complemented
258	C₂×#131	C₂²×C₃	1	2	yes	complemented
259	#550	—	2	1	no	—
260	#550	C₂²×C₃	1	2	yes	—
261	#550	C₂²×C₃	1	2	yes	—
262	#550	C₂²×C₃	1	2	yes	complemented
263	D₄×Q₈	—	2	1	no	—
264	D₄×Q₈	C₂²×C₃	1	2	yes	complemented
265	#548	—	2	2	no	—
266	#548	C₂²×C₃	1	4	yes	complemented
267	D₄²	—	2	2	no	—
268	D₄²	—	2	2	no	—
269	D₄²	C₂²×C₃	1	2	yes	—
270	D₄²	C₂²×C₃	1	2	yes	—
271	#537	—	2	2	no	—
272	#537	C₂²×C₃	1	2	yes	complemented
273	#535	—	2	2	no	—
274	#535	C₂²×C₃	1	2	yes	—
275	#532	—	2	1	no	—
276	#532	—	2	2	no	—
277	#532	C₂²×C₃	1	1	yes	characteristic
278	#532	C₂²×C₃	1	1	yes	characteristic, complemented
279	C₂×#127	—	2	1	no	—
280	C₂×#127	C₂²×C₃	1	1	yes	characteristic
281	C₄×#41	C₂²×C₃	1	1	yes	characteristic
282	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
283	#496	C₂²×C₃	1	4	yes	complemented
284	#493	C₂²×C₃	1	2	yes	complemented
285	#492	C₂²×C₃	1	2	yes	complemented
286	#469	C₂²×C₃	1	4	yes	complemented
287	#468	C₂²×C₃	1	4	yes	complemented
288	#466	C₂²×C₃	1	4	yes	complemented
289	#465	C₂²×C₃	1	4	yes	complemented
290	#464	C₂²×C₃	1	2	yes	complemented
291	#463	C₂²×C₃	1	2	yes	complemented
292	#462	C₂²×C₃	1	1	yes	characteristic, complemented
293	#461	C₂²×C₃	1	1	yes	characteristic, complemented
294	#460	C₂²×C₃	1	4	yes	complemented
295	#460	C₂²×C₃	1	2	yes	complemented
296	#460	C₂²×C₃	1	2	yes	complemented
297	#460	C₂²×C₃	1	1	yes	characteristic, complemented
298	#459	C₂²×C₃	1	1	yes	characteristic, complemented
299	#452	C₂²×C₃	1	4	yes	complemented
300	#450	C₂²×C₃	1	4	yes	complemented
301	#449	C₂²×C₃	1	4	yes	complemented
302	#449	C₂²×C₃	1	4	yes	complemented
303	#449	C₂²×C₃	1	4	yes	complemented
304	#448	C₂²×C₃	1	4	yes	complemented
305	#448	C₂²×C₃	1	4	yes	complemented
306	#447	C₂²×C₃	1	4	yes	complemented
307	#441	C₂²×C₃	1	2	yes	complemented
308	#440	C₂²×C₃	1	2	yes	complemented
309	C₄×Q₁₆	C₂²×C₃	1	2	yes	complemented
310	C₄×SD₁₆	C₂²×C₃	1	2	yes	complemented
311	#436	C₂²×C₃	1	2	yes	complemented
312	#435	C₂²×C₃	1	4	yes	complemented
313	C₈×D₄	C₂²×C₃	1	2	yes	complemented
314	#428	C₂²×C₃	1	1	yes	characteristic, complemented
315	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
316	#419	C₂²×C₃	1	1	yes	characteristic, complemented
317	#417	C₂²×C₃	1	1	yes	characteristic
318	#416	C₂²×C₃	1	2	yes	complemented
319	C₂×#102	C₂²×C₃	1	2	yes	complemented
320	#408	C₂²×C₃	1	2	yes	complemented
321	C₄×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
322	C₂⁴×C₃	—	2	4	no	—
323	C₂⁴×C₃	—	2	2	no	—
324	C₃×#41	—	2	4	no	—
325	C₃×#41	—	2	2	no	—
326	C₃×#41	—	2	4	no	—
327	C₃×#41	—	2	8	no	—
328	C₃×#41	—	2	8	no	—
329	C₃×#41	—	2	4	no	—
330	C₃×#41	—	2	4	no	—
331	C₃×#41	—	4	4	no	—
332	C₃×#41	—	4	4	no	—
333	C₃×#41	—	4	16	no	—
334	C₃×#41	—	4	8	no	—
335	C₃×#41	—	4	8	no	—
336	C₃×#41	C₂×D₄	1	4	yes	—
337	C₂×C₃×Q₈	—	2	1	no	—
338	C₂×C₃×Q₈	—	2	4	no	—
339	C₂×C₃×Q₈	—	2	2	no	—
340	C₂×C₃×Q₈	—	2	8	no	—
341	C₂×C₃×Q₈	—	4	4	no	—
342	C₂×C₃×Q₈	—	4	8	no	—
343	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
344	C₂×C₃×Q₈	C₂×D₄	1	4	yes	complemented
345	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
346	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
347	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
348	C₂×C₃×D₄	—	2	1	no	—
349	C₂×C₃×D₄	—	2	8	no	—
350	C₂×C₃×D₄	—	2	2	no	—
351	C₂×C₃×D₄	—	2	4	no	—
352	C₂×C₃×D₄	—	2	4	no	—
353	C₂×C₃×D₄	—	2	4	no	—
354	C₂×C₃×D₄	—	2	4	no	—
355	C₂×C₃×D₄	—	2	4	no	—
356	C₂×C₃×D₄	—	2	4	no	—
357	C₂×C₃×D₄	—	2	1	no	—
358	C₂×C₃×D₄	—	2	2	no	—
359	C₂×C₃×D₄	—	2	2	no	—
360	C₂×C₃×D₄	—	2	4	no	—
361	C₂×C₃×D₄	—	2	2	no	—
362	C₂×C₃×D₄	—	2	1	no	—
363	C₂×C₃×D₄	—	2	2	no	—
364	C₂×C₃×D₄	—	2	2	no	—
365	C₂×C₃×D₄	—	2	4	no	—
366	C₂×C₃×D₄	—	4	4	no	—
367	C₂×C₃×D₄	—	4	8	no	—
368	C₂×C₃×D₄	—	4	16	no	—
369	C₂×C₃×D₄	—	8	2	no	—
370	C₂×C₃×D₄	—	8	4	no	—
371	C₂×C₃×D₄	—	8	2	no	—
372	C₂×C₃×D₄	—	8	4	no	—
373	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
374	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
375	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
376	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
377	C₂×C₃×D₄	C₂⁴	1	2	yes	—
378	C₂×C₃×D₄	C₂⁴	1	4	yes	—
379	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
380	C₂²×C₃×C₄	—	2	1	no	—
381	C₂²×C₃×C₄	—	2	1	no	—
382	C₂²×C₃×C₄	—	2	4	no	—
383	C₂²×C₃×C₄	—	2	1	no	—
384	C₂²×C₃×C₄	—	2	1	no	—
385	C₂²×C₃×C₄	—	2	1	no	—
386	C₂²×C₃×C₄	—	2	4	no	—
387	C₂²×C₃×C₄	—	2	4	no	—
388	C₂²×C₃×C₄	—	2	2	no	—
389	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
392	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
393	C₃×Q₁₆	—	2	4	no	—
394	C₃×Q₁₆	C₂×D₄	1	8	yes	complemented
395	C₃×SD₁₆	—	2	8	no	—
396	C₃×SD₁₆	—	2	8	no	—
397	C₃×SD₁₆	—	2	4	no	—
398	C₃×SD₁₆	—	2	4	no	—
399	C₃×SD₁₆	—	2	8	no	—
400	C₃×SD₁₆	—	4	4	no	—
401	C₃×SD₁₆	C₂×D₄	1	8	yes	complemented
402	C₃×D₈	—	2	4	no	—
403	C₃×D₈	—	2	8	no	—
404	C₃×D₈	—	4	4	no	—
405	C₃×M₁₆	—	2	2	no	—
406	C₃×M₁₆	—	2	8	no	—
407	C₃×M₁₆	C₂×D₄	1	4	yes	complemented
408	C₂×C₃×C₈	—	2	4	no	—
409	C₂×C₃×C₈	—	2	8	no	—
410	C₂×C₃×C₈	C₂⁴	1	2	yes	—
411	C₂×C₃×C₈	C₂⁴	1	2	yes	—
412	C₂×C₃×C₈	C₂⁴	1	2	yes	—
413	C₂×C₃×C₈	C₂⁴	1	2	yes	—
414	C₃×C₄⋊C₄	—	2	2	no	—
415	C₃×C₄⋊C₄	—	2	2	no	—
416	C₃×C₄⋊C₄	—	2	1	no	—
417	C₃×C₄⋊C₄	—	2	1	no	—
418	C₃×C₄⋊C₄	—	2	1	no	—
419	C₃×C₄⋊C₄	—	2	1	no	—
420	C₃×C₄⋊C₄	—	2	1	no	—
421	C₃×C₄⋊C₄	—	2	4	no	—
422	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
423	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
424	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
425	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
426	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
427	C₃×C₂²⋊C₄	—	2	1	no	—
428	C₃×C₂²⋊C₄	—	2	4	no	—
429	C₃×C₂²⋊C₄	—	2	1	no	—
430	C₃×C₂²⋊C₄	—	2	1	no	—
431	C₃×C₂²⋊C₄	—	2	2	no	—
432	C₃×C₂²⋊C₄	—	2	4	no	—
433	C₃×C₂²⋊C₄	—	2	4	no	—
434	C₃×C₂²⋊C₄	—	2	2	no	—
435	C₃×C₂²⋊C₄	—	2	4	no	—
436	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
437	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
438	C₃×C₄²	—	2	1	no	—
439	C₃×C₄²	—	2	1	no	—
440	C₃×C₄²	—	2	1	no	—
441	C₃×C₄²	—	2	2	no	—
442	C₃×C₄²	—	2	2	no	—
443	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
444	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
445	C₃×C₄²	C₂⁴	1	1	yes	characteristic
446	C₃×C₄²	C₂⁴	1	1	yes	characteristic
447	2₋¹⁺⁴	—	2	8	no	—
448	2₋¹⁺⁴	—	4	4	no	—
449	H(5,𝔽₂)	—	2	8	no	—
450	H(5,𝔽₂)	—	4	4	no	—
451	C₂×#41	—	2	2	no	—
452	C₂×#41	—	2	4	no	—
453	C₂×#41	—	2	2	no	—
454	C₂×#41	C₂³×C₃	1	2	yes	—
455	C₂×#41	C₂³×C₃	1	4	yes	—
456	C₂×#41	C₂³×C₃	1	4	yes	—
457	C₂×#41	C₂³×C₃	1	1	yes	characteristic
458	C₂×#41	C₂³×C₃	1	2	yes	—
459	C₂²×Q₈	—	2	2	no	—
460	C₂²×Q₈	C₂³×C₃	1	4	yes	—
461	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
462	C₂²×D₄	—	2	2	no	—
463	C₂²×D₄	—	2	4	no	—
464	C₂²×D₄	—	2	2	no	—
465	C₂²×D₄	—	2	2	no	—
466	C₂²×D₄	—	2	1	no	—
467	C₂²×D₄	—	2	1	no	—
468	C₂²×D₄	C₂³×C₃	1	2	yes	—
469	C₂²×D₄	C₂³×C₃	1	4	yes	—
470	#137	—	2	16	no	—
471	#137	C₃×D₄	1	8	yes	complemented
472	AGL(1,ℤ/8)	—	2	16	no	—
473	AGL(1,ℤ/8)	—	2	8	no	—
474	AGL(1,ℤ/8)	—	4	4	no	—
475	#135	—	2	8	no	—
476	#135	—	2	16	no	—
477	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
478	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
479	C₂×SD₁₆	—	2	8	no	—
480	C₂×SD₁₆	—	2	16	no	—
481	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
482	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
483	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
484	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
485	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
486	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
487	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
488	C₂×D₈	C₂³×C₃	1	2	yes	—
489	C₂×D₈	C₂³×C₃	1	4	yes	—
490	C₂×D₈	C₂³×C₃	1	4	yes	—
491	#131	—	2	8	no	—
492	C₂×M₁₆	C₂³×C₃	1	4	yes	—
493	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
494	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₃	1	2	yes	—
496	C₂²×C₈	C₂³×C₃	1	4	yes	—
497	C₄⋊Q₈	—	2	2	no	—
498	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
499	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
500	#127	—	2	2	no	—
501	#127	—	2	2	no	—
502	#127	—	2	2	no	—
503	#127	—	2	2	no	—
504	#127	—	2	1	no	—
505	#127	—	2	1	no	—
506	#127	C₃×D₄	1	1	yes	characteristic
507	#127	C₂³×C₃	1	2	yes	—
508	#127	C₂³×C₃	1	2	yes	—
509	#127	C₂³×C₃	1	1	yes	characteristic
510	#124	—	2	2	no	—
511	#124	—	2	4	no	—
512	#124	C₃×D₄	1	2	yes	—
513	#124	C₂³×C₃	1	2	yes	—
514	C₂²⋊Q₈	—	2	2	no	—
515	C₂²⋊Q₈	—	2	4	no	—
516	C₂²⋊Q₈	—	2	4	no	—
517	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
518	#121	—	2	4	no	—
519	#121	—	2	4	no	—
520	#121	—	2	2	no	—
521	#121	—	2	1	no	—
522	#121	—	2	1	no	—
523	#121	—	2	2	no	—
524	#121	—	2	2	no	—
525	#121	—	2	4	no	—
526	#121	—	2	4	no	—
527	#121	—	2	4	no	—
528	#121	C₃×D₄	1	2	yes	—
529	#121	C₃×D₄	1	2	yes	—
530	#121	C₂³×C₃	1	4	yes	—
531	#121	C₂³×C₃	1	4	yes	—
532	#121	C₂³×C₃	1	4	yes	—
533	#120	—	2	4	no	—
534	#120	—	2	4	no	—
535	#120	—	2	4	no	—
536	C₄×Q₈	—	2	1	no	—
537	C₄×Q₈	—	2	1	no	—
538	C₄×Q₈	C₂³×C₃	1	2	yes	—
539	C₄×Q₈	C₂³×C₃	1	2	yes	—
540	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
541	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
542	C₄×D₄	—	2	2	no	—
543	C₄×D₄	—	2	1	no	—
544	C₄×D₄	—	2	1	no	—
545	C₄×D₄	—	2	2	no	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	2	2	no	—
548	C₄×D₄	—	2	4	no	—
549	C₄×D₄	—	2	1	no	—
550	C₄×D₄	—	2	1	no	—
551	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
552	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
553	C₄×D₄	C₂³×C₃	1	2	yes	—
554	C₄×D₄	C₂³×C₃	1	2	yes	—
555	#117	—	2	1	no	—
556	#117	C₂³×C₃	1	1	yes	characteristic
557	C₂×C₄⋊C₄	—	2	1	no	—
558	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
559	C₂×C₄²	—	2	1	no	—
560	C₂×C₄²	—	2	1	no	—
561	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
562	#107	C₂³×C₃	1	2	yes	—
563	#106	C₂³×C₃	1	2	yes	—
564	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
565	C₄⋊C₈	C₂³×C₃	1	2	yes	—
566	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
567	#103	C₂³×C₃	1	2	yes	—
568	#103	C₂³×C₃	1	2	yes	—
569	#103	C₂³×C₃	1	2	yes	—
570	#103	C₂³×C₃	1	2	yes	—
571	#103	C₂³×C₃	1	2	yes	—
572	#102	C₂³×C₃	1	4	yes	—
573	#102	C₂³×C₃	1	4	yes	—
574	#102	C₂³×C₃	1	2	yes	—
575	#102	C₂³×C₃	1	2	yes	—
576	#102	C₂³×C₃	1	2	yes	—
577	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
578	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
579	#97	C₂³×C₃	1	2	yes	—
580	C₄×C₈	C₂³×C₃	1	2	yes	—
581	C₂³×C₃	—	2	1	no	—
582	C₂³×C₃	—	2	2	no	—
583	C₂³×C₃	—	2	4	no	—
584	C₂³×C₃	—	4	8	no	—
585	C₂³×C₃	—	4	4	no	—
586	C₂³×C₃	—	8	2	no	—
587	C₂³×C₃	—	8	2	no	—
588	C₂³×C₃	—	8	4	no	—
589	C₂³×C₃	—	8	4	no	—
590	C₂³×C₃	C₂²×D₄	1	4	yes	—
591	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
592	C₃×Q₈	—	2	4	no	—
593	C₃×Q₈	—	2	4	no	—
594	C₃×Q₈	—	2	2	no	—
595	C₃×Q₈	—	2	1	no	—
596	C₃×Q₈	—	2	2	no	—
597	C₃×Q₈	—	2	2	no	—
598	C₃×Q₈	—	4	8	no	—
599	C₃×Q₈	C₂²×D₄	1	4	yes	—
600	C₃×Q₈	C₂²×D₄	1	2	yes	—
601	C₃×D₄	—	2	4	no	—
602	C₃×D₄	—	2	8	no	—
603	C₃×D₄	—	2	4	no	—
604	C₃×D₄	—	2	4	no	—
605	C₃×D₄	—	2	2	no	—
606	C₃×D₄	—	2	4	no	—
607	C₃×D₄	—	2	1	no	—
608	C₃×D₄	—	2	2	no	—
609	C₃×D₄	—	2	4	no	—
610	C₃×D₄	—	4	2	no	—
611	C₃×D₄	—	4	8	no	—
612	C₃×D₄	—	4	8	no	—
613	C₃×D₄	—	4	8	no	—
614	C₃×D₄	—	4	4	no	—
615	C₃×D₄	—	4	4	no	—
616	C₃×D₄	—	4	4	no	—
617	C₃×D₄	—	4	2	no	—
618	C₃×D₄	—	4	4	no	—
619	C₃×D₄	—	8	1	no	—
620	C₃×D₄	—	8	2	no	—
621	C₃×D₄	—	8	2	no	—
622	C₃×D₄	—	8	4	no	—
623	C₃×D₄	—	8	4	no	—
624	C₃×D₄	—	8	4	no	—
625	C₃×D₄	C₂²×D₄	1	2	yes	—
626	C₂×C₃×C₄	—	2	4	no	—
627	C₂×C₃×C₄	—	2	1	no	—
628	C₂×C₃×C₄	—	2	2	no	—
629	C₂×C₃×C₄	—	2	4	no	—
630	C₂×C₃×C₄	—	2	2	no	—
631	C₂×C₃×C₄	—	2	4	no	—
632	C₂×C₃×C₄	—	2	4	no	—
633	C₂×C₃×C₄	—	2	1	no	—
634	C₂×C₃×C₄	—	2	1	no	—
635	C₂×C₃×C₄	—	2	2	no	—
636	C₂×C₃×C₄	—	2	2	no	—
637	C₂×C₃×C₄	—	4	1	no	—
638	C₂×C₃×C₄	—	4	8	no	—
639	C₂×C₃×C₄	—	4	8	no	—
640	C₂×C₃×C₄	—	4	8	no	—
641	C₂×C₃×C₄	—	4	2	no	—
642	C₂×C₃×C₄	—	4	4	no	—
643	C₂×C₃×C₄	—	4	2	no	—
644	C₂×C₃×C₄	—	8	1	no	—
645	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
646	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
647	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
648	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
649	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
650	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
651	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
652	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
653	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
654	C₃×C₈	—	2	2	no	—
655	C₃×C₈	—	2	2	no	—
656	C₃×C₈	—	2	2	no	—
657	C₃×C₈	C₂²×D₄	1	4	yes	—
658	C₂⁴	—	2	4	no	—
659	C₂⁴	—	2	2	no	—
660	#41	—	2	4	no	—
661	#41	—	2	2	no	—
662	#41	—	2	4	no	—
663	#41	—	2	8	no	—
664	#41	—	2	8	no	—
665	#41	—	2	4	no	—
666	#41	—	2	4	no	—
667	#41	—	4	4	no	—
668	#41	—	4	4	no	—
669	#41	—	4	16	no	—
670	#41	—	4	8	no	—
671	#41	—	4	8	no	—
672	#41	C₂×C₃×D₄	1	4	yes	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	—	2	4	no	—
675	C₂×Q₈	—	2	2	no	—
676	C₂×Q₈	—	2	8	no	—
677	C₂×Q₈	—	4	4	no	—
678	C₂×Q₈	—	4	8	no	—
679	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
680	C₂×Q₈	C₂×C₃×D₄	1	4	yes	complemented
681	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
682	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
683	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	8	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	4	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	4	no	—
702	C₂×D₄	—	4	4	no	—
703	C₂×D₄	—	4	8	no	—
704	C₂×D₄	—	4	16	no	—
705	C₂×D₄	—	8	2	no	—
706	C₂×D₄	—	8	4	no	—
707	C₂×D₄	—	8	2	no	—
708	C₂×D₄	—	8	4	no	—
709	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
710	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
711	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
712	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
713	C₂×D₄	C₂⁴×C₃	1	2	yes	—
714	C₂×D₄	C₂⁴×C₃	1	4	yes	—
715	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	1	no	—
720	C₂²×C₄	—	2	1	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	2	4	no	—
723	C₂²×C₄	—	2	4	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
726	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
728	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
729	Q₁₆	—	2	4	no	—
730	Q₁₆	C₂×C₃×D₄	1	8	yes	complemented
731	SD₁₆	—	2	8	no	—
732	SD₁₆	—	2	8	no	—
733	SD₁₆	—	2	4	no	—
734	SD₁₆	—	2	4	no	—
735	SD₁₆	—	2	8	no	—
736	SD₁₆	—	4	4	no	—
737	SD₁₆	C₂×C₃×D₄	1	8	yes	complemented
738	D₈	—	2	4	no	—
739	D₈	—	2	8	no	—
740	D₈	—	4	4	no	—
741	M₁₆	—	2	2	no	—
742	M₁₆	—	2	8	no	—
743	M₁₆	C₂×C₃×D₄	1	4	yes	complemented
744	C₂×C₈	—	2	4	no	—
745	C₂×C₈	—	2	8	no	—
746	C₂×C₈	C₂⁴×C₃	1	2	yes	—
747	C₂×C₈	C₂⁴×C₃	1	2	yes	—
748	C₂×C₈	C₂⁴×C₃	1	2	yes	—
749	C₂×C₈	C₂⁴×C₃	1	2	yes	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	—	2	1	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	1	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	4	no	—
758	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
759	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
760	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
761	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
762	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
763	C₂²⋊C₄	—	2	1	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	1	no	—
766	C₂²⋊C₄	—	2	1	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
773	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
774	C₄²	—	2	1	no	—
775	C₄²	—	2	1	no	—
776	C₄²	—	2	1	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	2	no	—
779	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
780	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
781	C₄²	C₂⁴×C₃	1	1	yes	characteristic
782	C₄²	C₂⁴×C₃	1	1	yes	characteristic
783	C₂²×C₃	—	2	1	no	—
784	C₂²×C₃	—	2	1	no	—
785	C₂²×C₃	—	2	4	no	—
786	C₂²×C₃	—	2	4	no	—
787	C₂²×C₃	—	2	2	no	—
788	C₂²×C₃	—	2	4	no	—
789	C₂²×C₃	—	4	1	no	—
790	C₂²×C₃	—	4	1	no	—
791	C₂²×C₃	—	4	4	no	—
792	C₂²×C₃	—	4	2	no	—
793	C₂²×C₃	—	4	2	no	—
794	C₂²×C₃	—	4	4	no	—
795	C₂²×C₃	—	4	4	no	—
796	C₂²×C₃	—	4	2	no	—
797	C₂²×C₃	—	16	4	no	—
798	C₂²×C₃	—	16	8	no	—
799	C₂²×C₃	D₄²	1	2	yes	—
800	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
801	C₃×C₄	—	2	1	no	—
802	C₃×C₄	—	2	1	no	—
803	C₃×C₄	—	2	2	no	—
804	C₃×C₄	—	2	4	no	—
805	C₃×C₄	—	2	4	no	—
806	C₃×C₄	—	2	1	no	—
807	C₃×C₄	—	4	1	no	—
808	C₃×C₄	—	4	2	no	—
809	C₃×C₄	—	4	2	no	—
810	C₃×C₄	—	4	1	no	—
811	C₃×C₄	D₄²	1	2	yes	—
812	C₃×C₄	#577	1	2	yes	complemented
813	C₃×C₄	C₂³×D₄	1	1	yes	characteristic
814	C₃×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
815	C₂³	—	2	1	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	4	no	—
818	C₂³	—	4	8	no	—
819	C₂³	—	4	4	no	—
820	C₂³	—	8	2	no	—
821	C₂³	—	8	2	no	—
822	C₂³	—	8	4	no	—
823	C₂³	—	8	4	no	—
824	C₂³	C₂²×C₃×D₄	1	4	yes	—
825	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
826	Q₈	—	2	2	no	—
827	Q₈	—	2	1	no	—
828	Q₈	—	2	4	no	—
829	Q₈	—	2	4	no	—
830	Q₈	—	2	2	no	—
831	Q₈	—	2	2	no	—
832	Q₈	—	4	8	no	—
833	Q₈	C₂²×C₃×D₄	1	4	yes	—
834	Q₈	C₂²×C₃×D₄	1	2	yes	—
835	D₄	—	2	4	no	—
836	D₄	—	2	8	no	—
837	D₄	—	2	4	no	—
838	D₄	—	2	2	no	—
839	D₄	—	2	4	no	—
840	D₄	—	2	1	no	—
841	D₄	—	2	2	no	—
842	D₄	—	2	4	no	—
843	D₄	—	2	4	no	—
844	D₄	—	4	2	no	—
845	D₄	—	4	8	no	—
846	D₄	—	4	8	no	—
847	D₄	—	4	8	no	—
848	D₄	—	4	4	no	—
849	D₄	—	4	4	no	—
850	D₄	—	4	4	no	—
851	D₄	—	4	2	no	—
852	D₄	—	4	4	no	—
853	D₄	—	8	2	no	—
854	D₄	—	8	2	no	—
855	D₄	—	8	1	no	—
856	D₄	—	8	4	no	—
857	D₄	—	8	4	no	—
858	D₄	—	8	4	no	—
859	D₄	C₂²×C₃×D₄	1	2	yes	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	4	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	4	no	—
865	C₂×C₄	—	2	4	no	—
866	C₂×C₄	—	2	4	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	4	1	no	—
872	C₂×C₄	—	4	8	no	—
873	C₂×C₄	—	4	8	no	—
874	C₂×C₄	—	4	8	no	—
875	C₂×C₄	—	4	2	no	—
876	C₂×C₄	—	4	2	no	—
877	C₂×C₄	—	4	4	no	—
878	C₂×C₄	—	8	1	no	—
879	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
880	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
881	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
882	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
883	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
884	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
885	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
886	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
887	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
888	C₈	—	2	2	no	—
889	C₈	—	2	2	no	—
890	C₈	—	2	2	no	—
891	C₈	C₂²×C₃×D₄	1	4	yes	—
892	C₂×C₃	—	2	2	no	—
893	C₂×C₃	—	4	4	no	—
894	C₂×C₃	—	4	2	no	—
895	C₂×C₃	—	8	2	no	—
896	C₂×C₃	—	8	4	no	—
897	C₂×C₃	C₂×D₄²	1	1	yes	characteristic
898	C₂×C₃	C₂×#577	1	1	yes	characteristic
899	C₂×C₃	#3585	1	1	yes	characteristic
900	C₂²	—	2	1	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	4	no	—
903	C₂²	—	2	2	no	—
904	C₂²	—	2	4	no	—
905	C₂²	—	2	4	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	4	1	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	4	no	—
910	C₂²	—	4	4	no	—
911	C₂²	—	4	2	no	—
912	C₂²	—	4	4	no	—
913	C₂²	—	4	2	no	—
914	C₂²	—	16	4	no	—
915	C₂²	—	16	8	no	—
916	C₂²	C₃×D₄²	1	2	yes	—
917	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
918	C₄	—	2	2	no	—
919	C₄	—	2	4	no	—
920	C₄	—	2	4	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	1	no	—
923	C₄	—	2	1	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	1	no	—
926	C₄	—	4	1	no	—
927	C₄	—	4	2	no	—
928	C₄	C₃×D₄²	1	2	yes	—
929	C₄	C₃×#577	1	2	yes	complemented
930	C₄	C₂³×C₃×D₄	1	1	yes	characteristic
931	C₄	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
932	C₃	#61095	1	1	yes	characteristic, direct product factor, Sylow
933	C₂	—	2	2	no	—
934	C₂	—	4	4	no	—
935	C₂	—	4	2	no	—
936	C₂	—	8	4	no	—
937	C₂	—	8	2	no	—
938	C₂	C₂×C₃×D₄²	1	1	yes	characteristic
939	C₂	C₂×C₃×#577	1	1	yes	characteristic
940	C₂	C₃×#3585	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#577	C₂	semidirect
2. C₃×#3498	C₂	semidirect
3. C₃×#3497	C₂	semidirect
4. C₃×#3287	C₂	semidirect
5. C₃×D₄×SD₁₆	C₂	semidirect
6. C₃×#3278	C₂	semidirect
7. C₃×#3274	C₂	semidirect
8. C₃×#3271	C₂	semidirect
9. C₃×#3265	C₂	semidirect
10. C₃×#3151	C₂	semidirect
11. C₃×#3062	C₂	semidirect
12. C₃×#3035	C₂	semidirect
13. C₂×C₃×#460	C₂	semidirect
14. C₃×#3012	C₂	semidirect
15. C₃×#3010	C₂	semidirect
16. C₃×C₄×#137	C₂	semidirect
17. C₃×#2935	C₂	semidirect
18. #61095	C₃	direct (N × H)
19. C₂×C₃×2₋¹⁺⁴	C₂²	semidirect
23. C₂×C₃×#137	C₂²	semidirect
24. C₂×C₃×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂×C₃×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂×C₃×AGL(1,ℤ/8)	C₂²	semidirect
28. C₂×C₃×#135	C₂²	semidirect
29. C₂²×C₃×SD₁₆	C₂²	semidirect
30. C₂²×C₃×SD₁₆	C₂²	semidirect
31. C₂×C₃×#131	C₂²	semidirect
35. C₃×#550	C₂²	semidirect
37. C₃×D₄×Q₈	C₂²	semidirect
39. C₃×#548	C₂²	semidirect
45. C₃×#537	C₂²	semidirect
51. C₃×#532	C₂²	semidirect
55. C₂×C₃×C₄×Q₈	C₂²	semidirect
56. C₃×#496	C₂²	semidirect
57. C₃×#493	C₂²	semidirect
58. C₃×#492	C₂²	semidirect
59. C₃×#469	C₂²	semidirect
60. C₃×#468	C₂²	semidirect
61. C₃×#466	C₂²	semidirect
62. C₃×#465	C₂²	semidirect
63. C₃×#464	C₂²	semidirect
64. C₃×#463	C₂²	semidirect
65. C₃×#462	C₂²	semidirect
66. C₃×#461	C₂²	semidirect
67. C₃×#460	C₂²	semidirect
68. C₃×#460	C₂²	semidirect
69. C₃×#460	C₂²	semidirect
70. C₃×#460	C₂²	semidirect
71. C₃×#459	C₂²	semidirect
72. C₃×#452	C₂²	semidirect
73. C₃×#450	C₂²	semidirect
74. C₃×#449	C₂²	semidirect
75. C₃×#449	C₂²	semidirect
76. C₃×#449	C₂²	semidirect
77. C₃×#448	C₂²	semidirect
78. C₃×#448	C₂²	semidirect
79. C₃×#447	C₂²	semidirect
80. C₃×#441	C₂²	semidirect
81. C₃×#440	C₂²	semidirect
82. C₃×C₄×Q₁₆	C₂²	semidirect
83. C₃×C₄×SD₁₆	C₂²	semidirect
84. C₃×#436	C₂²	semidirect
85. C₃×#435	C₂²	semidirect
86. C₃×C₈×D₄	C₂²	semidirect
87. C₃×#428	C₂²	semidirect
88. C₂×C₃×C₄⋊C₈	C₂²	semidirect
89. C₃×#419	C₂²	semidirect
91. C₃×#416	C₂²	semidirect
92. C₂×C₃×#102	C₂²	semidirect
93. C₃×#408	C₂²	semidirect
94. C₃×C₄×M₁₆	C₂²	semidirect
95. C₂×#577	C₂×C₃	semidirect
96. #3498	C₂×C₃	semidirect
97. #3497	C₂×C₃	semidirect
98. #3287	C₂×C₃	semidirect
99. D₄×SD₁₆	C₂×C₃	semidirect
100. #3278	C₂×C₃	semidirect
101. #3274	C₂×C₃	semidirect
102. #3271	C₂×C₃	semidirect
103. #3265	C₂×C₃	semidirect
104. #3151	C₂×C₃	semidirect
105. #3062	C₂×C₃	semidirect
106. #3035	C₂×C₃	semidirect
107. C₂×#460	C₂×C₃	semidirect
108. #3012	C₂×C₃	semidirect
109. #3010	C₂×C₃	semidirect
110. C₄×#137	C₂×C₃	semidirect
111. #2935	C₂×C₃	semidirect
136. C₃×#137	D₄	semidirect
246. C₂×2₋¹⁺⁴	C₂²×C₃	semidirect
250. C₂×#137	C₂²×C₃	semidirect
251. C₂×AGL(1,ℤ/8)	C₂²×C₃	semidirect
252. C₂×AGL(1,ℤ/8)	C₂²×C₃	semidirect
253. C₂×AGL(1,ℤ/8)	C₂²×C₃	semidirect
255. C₂×#135	C₂²×C₃	semidirect
256. C₂²×SD₁₆	C₂²×C₃	semidirect
257. C₂²×SD₁₆	C₂²×C₃	semidirect
258. C₂×#131	C₂²×C₃	semidirect
262. #550	C₂²×C₃	semidirect
264. D₄×Q₈	C₂²×C₃	semidirect
266. #548	C₂²×C₃	semidirect
272. #537	C₂²×C₃	semidirect
278. #532	C₂²×C₃	semidirect
282. C₂×C₄×Q₈	C₂²×C₃	semidirect
283. #496	C₂²×C₃	semidirect
284. #493	C₂²×C₃	semidirect
285. #492	C₂²×C₃	semidirect
286. #469	C₂²×C₃	semidirect
287. #468	C₂²×C₃	semidirect
288. #466	C₂²×C₃	semidirect
289. #465	C₂²×C₃	semidirect
290. #464	C₂²×C₃	semidirect
291. #463	C₂²×C₃	semidirect
292. #462	C₂²×C₃	semidirect
293. #461	C₂²×C₃	semidirect
294. #460	C₂²×C₃	semidirect
295. #460	C₂²×C₃	semidirect
296. #460	C₂²×C₃	semidirect
297. #460	C₂²×C₃	semidirect
298. #459	C₂²×C₃	semidirect
299. #452	C₂²×C₃	semidirect
300. #450	C₂²×C₃	semidirect
301. #449	C₂²×C₃	semidirect
302. #449	C₂²×C₃	semidirect
303. #449	C₂²×C₃	semidirect
304. #448	C₂²×C₃	semidirect
305. #448	C₂²×C₃	semidirect
306. #447	C₂²×C₃	semidirect
307. #441	C₂²×C₃	semidirect
308. #440	C₂²×C₃	semidirect
309. C₄×Q₁₆	C₂²×C₃	semidirect
310. C₄×SD₁₆	C₂²×C₃	semidirect
311. #436	C₂²×C₃	semidirect
312. #435	C₂²×C₃	semidirect
313. C₈×D₄	C₂²×C₃	semidirect
314. #428	C₂²×C₃	semidirect
315. C₂×C₄⋊C₈	C₂²×C₃	semidirect
316. #419	C₂²×C₃	semidirect
318. #416	C₂²×C₃	semidirect
319. C₂×#102	C₂²×C₃	semidirect
320. #408	C₂²×C₃	semidirect
321. C₄×M₁₆	C₂²×C₃	semidirect
344. C₂×C₃×Q₈	C₂×D₄	semidirect
394. C₃×Q₁₆	C₂×D₄	semidirect
401. C₃×SD₁₆	C₂×D₄	semidirect
407. C₃×M₁₆	C₂×D₄	semidirect
471. #137	C₃×D₄	semidirect
680. C₂×Q₈	C₂×C₃×D₄	semidirect
730. Q₁₆	C₂×C₃×D₄	semidirect
737. SD₁₆	C₂×C₃×D₄	semidirect
743. M₁₆	C₂×C₃×D₄	semidirect
812. C₃×C₄	#577	semidirect
929. C₄	C₃×#577	semidirect
932. C₃	#61095	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
C₃×#3498	2
C₃×#3497	2
C₃×#3287	2
C₃×D₄×SD₁₆	2
C₃×#3278	2
C₃×#3274	2
C₃×#3271	2
C₃×#3265	2
C₃×#3151	2
C₃×#3062	2
C₃×#3035	2
C₂×C₃×#460	2
C₃×#3012	2
C₃×#3010	2
C₃×C₄×#137	2
C₃×#2935	2
#61095	3

Subgroups — C3×#61095 #10679702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61095 #10679702