Subgroups — C₃×#34475 #10653082

Order 768.

2280 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×#2381	C₂	1	2	yes	maximal, complemented
3	C₃×#2378	C₂	1	2	yes	maximal, complemented
4	C₃×#2368	C₂	1	2	yes	maximal, complemented
5	C₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2356	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2353	C₂	1	2	yes	maximal
10	C₃×#2352	C₂	1	1	yes	maximal, characteristic
11	C₃×Q₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×Q₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2332	C₂	1	2	yes	maximal, complemented
14	C₃×#2331	C₂	1	2	yes	maximal, complemented
15	C₃×#2329	C₂	1	2	yes	maximal, complemented
16	C₃×#2327	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2323	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2320	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2318	C₂	1	2	yes	maximal
20	C₃×#2310	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×C₄×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2290	C₂	1	1	yes	maximal, characteristic
24	#34475	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic
26	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic
27	C₃×D₄×Q₈	C₄	1	16	yes	complemented
28	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
32	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
34	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
41	C₂×C₃×#117	C₂²	1	1	yes	characteristic
42	C₂×C₃×#117	C₂²	1	1	yes	characteristic
43	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
45	C₃×#391	C₂²	1	1	yes	characteristic
46	C₃×#391	C₂²	1	1	yes	characteristic
47	C₃×#391	C₂²	1	2	yes	—
48	C₃×#391	C₂²	1	2	yes	—
49	C₃×#391	C₂²	1	2	yes	—
50	C₃×#391	C₂²	1	2	yes	—
51	C₃×#391	C₂²	1	2	yes	—
52	C₃×#391	C₂²	1	2	yes	—
53	C₃×#391	C₂²	1	1	yes	characteristic
54	C₃×#391	C₂²	1	1	yes	characteristic
55	C₃×#391	C₂²	1	2	yes	—
56	C₃×#391	C₂²	1	1	yes	characteristic
57	C₃×#391	C₂²	1	1	yes	characteristic
58	C₃×#391	C₂²	1	2	yes	—
59	C₃×#391	C₂²	1	1	yes	characteristic
60	C₃×#391	C₂²	1	1	yes	characteristic
61	C₃×#389	C₂²	1	1	yes	characteristic
62	C₃×#389	C₂²	1	2	yes	—
63	C₃×#389	C₂²	1	2	yes	—
64	C₃×#389	C₂²	1	1	yes	characteristic
65	C₃×#389	C₂²	1	2	yes	—
66	C₃×#388	C₂²	1	2	yes	—
67	C₃×#388	C₂²	1	2	yes	—
68	C₃×#388	C₂²	1	1	yes	characteristic
69	C₃×#388	C₂²	1	2	yes	—
70	C₃×#388	C₂²	1	2	yes	—
71	C₃×#388	C₂²	1	1	yes	characteristic
72	C₃×#388	C₂²	1	2	yes	—
73	C₃×#387	C₂²	1	2	yes	—
74	C₃×#387	C₂²	1	2	yes	—
75	C₃×#387	C₂²	1	2	yes	—
76	C₃×#387	C₂²	1	2	yes	—
77	C₃×#387	C₂²	1	2	yes	—
78	C₃×#387	C₂²	1	2	yes	—
79	C₃×#387	C₂²	1	2	yes	—
80	C₃×#387	C₂²	1	2	yes	—
81	C₃×#387	C₂²	1	2	yes	—
82	C₃×#387	C₂²	1	2	yes	—
83	C₃×#387	C₂²	1	1	yes	characteristic
84	C₃×#387	C₂²	1	2	yes	—
85	C₃×#387	C₂²	1	2	yes	—
86	C₃×#387	C₂²	1	1	yes	characteristic
87	C₃×#387	C₂²	1	2	yes	—
88	C₃×#387	C₂²	1	2	yes	—
89	C₃×#387	C₂²	1	2	yes	—
90	C₃×#386	C₂²	1	1	yes	characteristic
91	C₃×#386	C₂²	1	1	yes	characteristic
92	C₃×#386	C₂²	1	2	yes	—
93	C₃×#385	C₂²	1	2	yes	—
94	C₃×#385	C₂²	1	1	yes	characteristic
95	C₃×#385	C₂²	1	1	yes	characteristic
96	C₃×#385	C₂²	1	2	yes	—
97	C₃×#383	C₂²	1	2	yes	—
98	C₃×#383	C₂²	1	2	yes	—
99	C₃×#382	C₂²	1	2	yes	—
100	C₃×#382	C₂²	1	1	yes	characteristic
101	C₃×#381	C₂²	1	2	yes	—
102	C₃×#381	C₂²	1	2	yes	—
103	C₃×#380	C₂²	1	2	yes	—
104	C₃×#380	C₂²	1	1	yes	characteristic
105	C₃×#380	C₂²	1	1	yes	characteristic
106	C₃×#380	C₂²	1	2	yes	—
107	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
109	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
111	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
113	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
114	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
116	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
117	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₃×#376	C₂²	1	1	yes	characteristic
122	C₃×#376	C₂²	1	2	yes	—
123	C₂×C₃×#95	C₂²	1	2	yes	—
124	C₂×C₃×#95	C₂²	1	2	yes	—
125	C₂×D₄×Q₈	C₂×C₃	1	1	yes	characteristic
126	#2381	C₂×C₃	1	2	yes	complemented
127	#2378	C₂×C₃	1	2	yes	complemented
128	#2368	C₂×C₃	1	2	yes	complemented
129	#2365	C₂×C₃	1	1	yes	characteristic, complemented
130	#2362	C₂×C₃	1	1	yes	characteristic, complemented
131	#2360	C₂×C₃	1	1	yes	characteristic, complemented
132	#2356	C₂×C₃	1	1	yes	characteristic, complemented
133	#2353	C₂×C₃	1	2	yes	—
134	#2352	C₂×C₃	1	1	yes	characteristic
135	Q₈×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
136	Q₈×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
137	#2332	C₂×C₃	1	2	yes	complemented
138	#2331	C₂×C₃	1	2	yes	complemented
139	#2329	C₂×C₃	1	2	yes	complemented
140	#2327	C₂×C₃	1	1	yes	characteristic, complemented
141	#2323	C₂×C₃	1	1	yes	characteristic, complemented
142	#2320	C₂×C₃	1	1	yes	characteristic, complemented
143	#2318	C₂×C₃	1	2	yes	—
144	#2310	C₂×C₃	1	1	yes	characteristic, complemented
145	C₄×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
146	C₂×#391	C₂×C₃	1	1	yes	characteristic, complemented
147	#2290	C₂×C₃	1	1	yes	characteristic
148	C₂²×C₃×Q₈	—	4	2	no	—
149	C₂²×C₃×Q₈	—	4	2	no	—
150	C₂²×C₃×Q₈	—	4	2	no	—
151	C₂²×C₃×Q₈	—	4	2	no	—
152	C₂²×C₃×Q₈	C₂×C₄	1	8	yes	—
153	C₂²×C₃×Q₈	C₂×C₄	1	8	yes	complemented
154	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
155	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
156	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
157	C₂²×C₃×Q₈	C₂³	1	2	yes	—
158	C₂²×C₃×Q₈	C₂³	1	2	yes	—
159	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
160	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
161	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
162	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
163	C₂³×C₃×C₄	C₂³	1	2	yes	—
164	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
165	C₂³×C₃×C₄	C₂³	1	2	yes	—
166	C₂³×C₃×C₄	C₂³	1	2	yes	—
167	C₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
168	C₃×C₄⋊Q₈	C₂×C₄	1	16	yes	complemented
169	C₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
170	C₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
171	C₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
172	C₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
173	C₃×C₄×Q₈	—	4	2	no	—
174	C₃×C₄×Q₈	—	4	2	no	—
175	C₃×C₄×Q₈	—	4	2	no	—
176	C₃×C₄×Q₈	—	4	2	no	—
177	C₃×C₄×Q₈	C₂×C₄	1	8	yes	complemented
178	C₃×C₄×D₄	C₂×C₄	1	8	yes	—
179	C₃×C₄×D₄	C₂×C₄	1	16	yes	—
180	C₃×#117	—	4	2	no	—
181	C₃×#117	—	4	2	no	—
182	C₂×C₃×C₄⋊C₄	—	4	2	no	—
183	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
194	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
195	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
200	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
201	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
209	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
210	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
212	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
214	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
218	C₂×C₃×C₄²	—	4	2	no	—
219	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
220	C₂×C₃×C₄²	C₂³	1	2	yes	—
221	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
222	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₄²	C₂³	1	2	yes	—
225	C₂×C₃×C₄²	C₂³	1	2	yes	—
226	C₂×C₃×C₄²	C₂³	1	2	yes	—
227	C₂×C₃×C₄²	C₂³	1	2	yes	—
228	C₂×C₃×C₄²	C₂³	1	2	yes	—
229	C₂×C₃×C₄²	C₂³	1	2	yes	—
230	C₂×C₃×C₄²	C₂³	1	2	yes	—
231	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
232	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
233	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
234	C₂×C₃×C₄²	C₂³	1	2	yes	—
235	C₃×#95	C₂³	1	2	yes	—
236	C₃×#95	C₂³	1	2	yes	—
237	C₃×#95	C₂³	1	2	yes	—
238	C₃×#95	C₂³	1	2	yes	—
239	C₃×#95	C₂³	1	2	yes	—
240	C₃×#95	C₂³	1	2	yes	—
241	C₃×#95	C₂³	1	2	yes	—
242	C₃×#95	C₂³	1	2	yes	—
243	C₃×#95	C₂³	1	1	yes	characteristic
244	C₃×#95	C₂³	1	2	yes	—
245	C₃×#95	C₂³	1	1	yes	characteristic
246	C₃×#95	C₂³	1	2	yes	—
247	C₃×#95	C₂³	1	1	yes	characteristic
248	C₃×#95	C₂³	1	1	yes	characteristic
249	C₃×#95	C₂³	1	1	yes	characteristic
250	C₃×#95	C₂³	1	1	yes	characteristic
251	C₃×#95	C₂³	1	2	yes	—
252	C₃×#95	C₂³	1	2	yes	—
253	C₃×#95	C₂³	1	2	yes	—
254	C₃×#95	C₂³	1	2	yes	—
255	C₃×#95	C₂³	1	2	yes	—
256	C₃×#95	C₂³	1	2	yes	—
257	C₃×#95	C₂³	1	2	yes	—
258	C₃×#95	C₂³	1	2	yes	—
259	C₃×#95	C₂³	1	2	yes	—
260	C₃×#95	C₂³	1	1	yes	characteristic
261	C₃×#95	C₂³	1	1	yes	characteristic
262	C₃×#95	C₂³	1	1	yes	characteristic
263	C₃×#95	C₂³	1	2	yes	—
264	C₃×#95	C₂³	1	2	yes	—
265	C₃×#95	C₂³	1	2	yes	—
266	C₃×#95	C₂³	1	2	yes	—
267	C₃×#95	C₂³	1	1	yes	characteristic
268	C₃×#95	C₂³	1	2	yes	—
269	C₃×#95	C₂³	1	2	yes	—
270	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic
271	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic
272	D₄×Q₈	C₃×C₄	1	16	yes	complemented
273	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
274	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
275	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
276	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
277	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
278	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
279	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
280	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
281	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
282	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
283	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
284	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
285	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
286	C₂×#117	C₂²×C₃	1	1	yes	characteristic
287	C₂×#117	C₂²×C₃	1	1	yes	characteristic
288	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
289	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
290	#391	C₂²×C₃	1	1	yes	characteristic
291	#391	C₂²×C₃	1	1	yes	characteristic
292	#391	C₂²×C₃	1	2	yes	—
293	#391	C₂²×C₃	1	1	yes	characteristic
294	#391	C₂²×C₃	1	1	yes	characteristic
295	#391	C₂²×C₃	1	2	yes	—
296	#391	C₂²×C₃	1	1	yes	characteristic
297	#391	C₂²×C₃	1	1	yes	characteristic
298	#391	C₂²×C₃	1	2	yes	—
299	#391	C₂²×C₃	1	2	yes	—
300	#391	C₂²×C₃	1	2	yes	—
301	#391	C₂²×C₃	1	2	yes	—
302	#391	C₂²×C₃	1	2	yes	—
303	#391	C₂²×C₃	1	1	yes	characteristic
304	#391	C₂²×C₃	1	1	yes	characteristic
305	#391	C₂²×C₃	1	2	yes	—
306	#389	C₂²×C₃	1	1	yes	characteristic
307	#389	C₂²×C₃	1	1	yes	characteristic
308	#389	C₂²×C₃	1	2	yes	—
309	#389	C₂²×C₃	1	2	yes	—
310	#389	C₂²×C₃	1	2	yes	—
311	#388	C₂²×C₃	1	2	yes	—
312	#388	C₂²×C₃	1	2	yes	—
313	#388	C₂²×C₃	1	2	yes	—
314	#388	C₂²×C₃	1	1	yes	characteristic
315	#388	C₂²×C₃	1	2	yes	—
316	#388	C₂²×C₃	1	2	yes	—
317	#388	C₂²×C₃	1	1	yes	characteristic
318	#387	C₂²×C₃	1	2	yes	—
319	#387	C₂²×C₃	1	2	yes	—
320	#387	C₂²×C₃	1	2	yes	—
321	#387	C₂²×C₃	1	2	yes	—
322	#387	C₂²×C₃	1	2	yes	—
323	#387	C₂²×C₃	1	2	yes	—
324	#387	C₂²×C₃	1	2	yes	—
325	#387	C₂²×C₃	1	2	yes	—
326	#387	C₂²×C₃	1	2	yes	—
327	#387	C₂²×C₃	1	2	yes	—
328	#387	C₂²×C₃	1	1	yes	characteristic
329	#387	C₂²×C₃	1	2	yes	—
330	#387	C₂²×C₃	1	2	yes	—
331	#387	C₂²×C₃	1	2	yes	—
332	#387	C₂²×C₃	1	2	yes	—
333	#387	C₂²×C₃	1	2	yes	—
334	#387	C₂²×C₃	1	1	yes	characteristic
335	#386	C₂²×C₃	1	1	yes	characteristic
336	#386	C₂²×C₃	1	2	yes	—
337	#386	C₂²×C₃	1	1	yes	characteristic
338	#385	C₂²×C₃	1	2	yes	—
339	#385	C₂²×C₃	1	2	yes	—
340	#385	C₂²×C₃	1	1	yes	characteristic
341	#385	C₂²×C₃	1	1	yes	characteristic
342	#383	C₂²×C₃	1	2	yes	—
343	#383	C₂²×C₃	1	2	yes	—
344	#382	C₂²×C₃	1	2	yes	—
345	#382	C₂²×C₃	1	1	yes	characteristic
346	#381	C₂²×C₃	1	2	yes	—
347	#381	C₂²×C₃	1	2	yes	—
348	#380	C₂²×C₃	1	2	yes	—
349	#380	C₂²×C₃	1	1	yes	characteristic
350	#380	C₂²×C₃	1	2	yes	—
351	#380	C₂²×C₃	1	1	yes	characteristic
352	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
353	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
354	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
355	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
356	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
357	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
358	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
359	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
360	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
361	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
362	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
363	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
364	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
365	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
366	#376	C₂²×C₃	1	1	yes	characteristic
367	#376	C₂²×C₃	1	2	yes	—
368	C₂×#95	C₂²×C₃	1	2	yes	—
369	C₂×#95	C₂²×C₃	1	2	yes	—
370	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
371	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
372	C₂×C₃×Q₈	—	2	2	no	—
373	C₂×C₃×Q₈	—	2	2	no	—
374	C₂×C₃×Q₈	—	2	2	no	—
375	C₂×C₃×Q₈	—	2	2	no	—
376	C₂×C₃×Q₈	—	2	2	no	—
377	C₂×C₃×Q₈	—	2	2	no	—
378	C₂×C₃×Q₈	—	4	2	no	—
379	C₂×C₃×Q₈	—	4	2	no	—
380	C₂×C₃×Q₈	—	4	2	no	—
381	C₂×C₃×Q₈	—	4	2	no	—
382	C₂×C₃×Q₈	—	4	16	no	—
383	C₂×C₃×Q₈	—	4	16	no	—
384	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
385	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
386	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
387	C₂×C₃×Q₈	C₂²×C₄	1	8	yes	—
388	C₂×C₃×Q₈	C₂²×C₄	1	8	yes	—
389	C₂×C₃×D₄	—	2	2	no	—
390	C₂×C₃×D₄	—	2	2	no	—
391	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
392	C₂²×C₃×C₄	—	2	2	no	—
393	C₂²×C₃×C₄	—	2	2	no	—
394	C₂²×C₃×C₄	—	2	2	no	—
395	C₂²×C₃×C₄	—	2	2	no	—
396	C₂²×C₃×C₄	—	2	2	no	—
397	C₂²×C₃×C₄	—	2	2	no	—
398	C₂²×C₃×C₄	—	2	4	no	—
399	C₂²×C₃×C₄	—	2	2	no	—
400	C₂²×C₃×C₄	—	4	1	no	—
401	C₂²×C₃×C₄	—	4	1	no	—
402	C₂²×C₃×C₄	—	4	1	no	—
403	C₂²×C₃×C₄	—	4	2	no	—
404	C₂²×C₃×C₄	—	4	2	no	—
405	C₂²×C₃×C₄	—	4	2	no	—
406	C₂²×C₃×C₄	—	4	2	no	—
407	C₂²×C₃×C₄	—	4	2	no	—
408	C₂²×C₃×C₄	—	4	2	no	—
409	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
410	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
411	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
412	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
413	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
414	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
415	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
416	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
417	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
418	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
419	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
420	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
421	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
422	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
423	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
424	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
425	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
426	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
427	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
428	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
429	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
430	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
431	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
432	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
433	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
434	C₃×C₄⋊C₄	—	2	2	no	—
435	C₃×C₄⋊C₄	—	2	2	no	—
436	C₃×C₄⋊C₄	—	2	2	no	—
437	C₃×C₄⋊C₄	—	2	2	no	—
438	C₃×C₄⋊C₄	—	2	2	no	—
439	C₃×C₄⋊C₄	—	4	2	no	—
440	C₃×C₄⋊C₄	—	4	1	no	—
441	C₃×C₄⋊C₄	—	4	2	no	—
442	C₃×C₄⋊C₄	—	4	2	no	—
443	C₃×C₄⋊C₄	—	4	1	no	—
444	C₃×C₄⋊C₄	—	4	1	no	—
445	C₃×C₄⋊C₄	—	4	2	no	—
446	C₃×C₄⋊C₄	—	4	2	no	—
447	C₃×C₄⋊C₄	—	4	2	no	—
448	C₃×C₄⋊C₄	—	4	2	no	—
449	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
450	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
451	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
452	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
453	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
454	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
455	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
456	C₃×C₂²⋊C₄	—	2	2	no	—
457	C₃×C₂²⋊C₄	—	2	4	no	—
458	C₃×C₂²⋊C₄	—	2	2	no	—
459	C₃×C₂²⋊C₄	—	2	2	no	—
460	C₃×C₂²⋊C₄	—	4	2	no	—
461	C₃×C₂²⋊C₄	—	4	1	no	—
462	C₃×C₂²⋊C₄	—	4	1	no	—
463	C₃×C₂²⋊C₄	—	4	1	no	—
464	C₃×C₂²⋊C₄	—	4	2	no	—
465	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
466	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
467	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
468	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
469	C₃×C₄²	—	2	2	no	—
470	C₃×C₄²	—	2	2	no	—
471	C₃×C₄²	—	2	2	no	—
472	C₃×C₄²	—	2	2	no	—
473	C₃×C₄²	—	2	4	no	—
474	C₃×C₄²	—	4	1	no	—
475	C₃×C₄²	—	4	1	no	—
476	C₃×C₄²	—	4	2	no	—
477	C₃×C₄²	—	4	2	no	—
478	C₃×C₄²	—	4	2	no	—
479	C₃×C₄²	—	4	2	no	—
480	C₃×C₄²	—	4	2	no	—
481	C₃×C₄²	—	4	2	no	—
482	C₃×C₄²	—	4	2	no	—
483	C₃×C₄²	C₂²×C₄	1	8	yes	—
484	C₃×C₄²	C₂²×C₄	1	4	yes	—
485	C₂²×Q₈	—	4	2	no	—
486	C₂²×Q₈	—	4	2	no	—
487	C₂²×Q₈	—	4	2	no	—
488	C₂²×Q₈	—	4	2	no	—
489	C₂²×Q₈	C₂×C₃×C₄	1	8	yes	—
490	C₂²×Q₈	C₂×C₃×C₄	1	8	yes	complemented
491	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
492	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
493	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
494	C₂²×Q₈	C₂³×C₃	1	2	yes	—
495	C₂²×Q₈	C₂³×C₃	1	2	yes	—
496	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
497	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
498	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
500	C₂³×C₄	C₂³×C₃	1	2	yes	—
501	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₃	1	2	yes	—
503	C₂³×C₄	C₂³×C₃	1	2	yes	—
504	C₄⋊Q₈	C₂×C₃×C₄	1	8	yes	complemented
505	C₄⋊Q₈	C₂×C₃×C₄	1	16	yes	complemented
506	C₂²⋊Q₈	C₂×C₃×C₄	1	8	yes	—
507	C₂²⋊Q₈	C₂×C₃×C₄	1	16	yes	—
508	C₂²⋊Q₈	C₂×C₃×C₄	1	8	yes	complemented
509	C₂²⋊Q₈	C₂×C₃×C₄	1	16	yes	complemented
510	C₄×Q₈	—	4	2	no	—
511	C₄×Q₈	—	4	2	no	—
512	C₄×Q₈	—	4	2	no	—
513	C₄×Q₈	—	4	2	no	—
514	C₄×Q₈	C₂×C₃×C₄	1	8	yes	complemented
515	C₄×D₄	C₂×C₃×C₄	1	8	yes	—
516	C₄×D₄	C₂×C₃×C₄	1	16	yes	—
517	#117	—	4	2	no	—
518	#117	—	4	2	no	—
519	C₂×C₄⋊C₄	—	4	2	no	—
520	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
535	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
544	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
545	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
547	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
548	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
551	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
553	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
555	C₂×C₄²	—	4	2	no	—
556	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
557	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
558	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
559	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₃	1	2	yes	—
561	C₂×C₄²	C₂³×C₃	1	2	yes	—
562	C₂×C₄²	C₂³×C₃	1	2	yes	—
563	C₂×C₄²	C₂³×C₃	1	2	yes	—
564	C₂×C₄²	C₂³×C₃	1	2	yes	—
565	C₂×C₄²	C₂³×C₃	1	2	yes	—
566	C₂×C₄²	C₂³×C₃	1	2	yes	—
567	C₂×C₄²	C₂³×C₃	1	2	yes	—
568	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
569	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
570	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₃	1	2	yes	—
572	#95	C₂³×C₃	1	2	yes	—
573	#95	C₂³×C₃	1	2	yes	—
574	#95	C₂³×C₃	1	2	yes	—
575	#95	C₂³×C₃	1	2	yes	—
576	#95	C₂³×C₃	1	2	yes	—
577	#95	C₂³×C₃	1	2	yes	—
578	#95	C₂³×C₃	1	2	yes	—
579	#95	C₂³×C₃	1	2	yes	—
580	#95	C₂³×C₃	1	1	yes	characteristic
581	#95	C₂³×C₃	1	2	yes	—
582	#95	C₂³×C₃	1	1	yes	characteristic
583	#95	C₂³×C₃	1	2	yes	—
584	#95	C₂³×C₃	1	1	yes	characteristic
585	#95	C₂³×C₃	1	1	yes	characteristic
586	#95	C₂³×C₃	1	1	yes	characteristic
587	#95	C₂³×C₃	1	1	yes	characteristic
588	#95	C₂³×C₃	1	2	yes	—
589	#95	C₂³×C₃	1	2	yes	—
590	#95	C₂³×C₃	1	2	yes	—
591	#95	C₂³×C₃	1	2	yes	—
592	#95	C₂³×C₃	1	2	yes	—
593	#95	C₂³×C₃	1	2	yes	—
594	#95	C₂³×C₃	1	2	yes	—
595	#95	C₂³×C₃	1	2	yes	—
596	#95	C₂³×C₃	1	2	yes	—
597	#95	C₂³×C₃	1	1	yes	characteristic
598	#95	C₂³×C₃	1	1	yes	characteristic
599	#95	C₂³×C₃	1	1	yes	characteristic
600	#95	C₂³×C₃	1	2	yes	—
601	#95	C₂³×C₃	1	2	yes	—
602	#95	C₂³×C₃	1	2	yes	—
603	#95	C₂³×C₃	1	2	yes	—
604	#95	C₂³×C₃	1	1	yes	characteristic
605	#95	C₂³×C₃	1	2	yes	—
606	#95	C₂³×C₃	1	2	yes	—
607	C₂³×C₃	—	2	1	no	—
608	C₂³×C₃	—	2	1	no	—
609	C₂³×C₃	—	2	1	no	—
610	C₂³×C₃	—	2	1	no	—
611	C₂³×C₃	—	2	1	no	—
612	C₂³×C₃	—	2	1	no	—
613	C₂³×C₃	—	2	1	no	—
614	C₂³×C₃	—	2	1	no	—
615	C₂³×C₃	—	2	1	no	—
616	C₂³×C₃	—	2	1	no	—
617	C₂³×C₃	C₂³×C₄	1	2	yes	—
618	C₂³×C₃	C₂³×C₄	1	2	yes	—
619	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
620	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
621	C₂³×C₃	C₂⁵	1	1	yes	characteristic
622	C₃×Q₈	—	2	8	no	—
623	C₃×Q₈	—	2	8	no	—
624	C₃×Q₈	—	2	8	no	—
625	C₃×Q₈	—	4	8	no	—
626	C₃×Q₈	—	4	8	no	—
627	C₃×D₄	—	2	8	no	—
628	C₂×C₃×C₄	—	2	1	no	—
629	C₂×C₃×C₄	—	2	1	no	—
630	C₂×C₃×C₄	—	2	1	no	—
631	C₂×C₃×C₄	—	2	2	no	—
632	C₂×C₃×C₄	—	2	2	no	—
633	C₂×C₃×C₄	—	2	2	no	—
634	C₂×C₃×C₄	—	2	2	no	—
635	C₂×C₃×C₄	—	2	1	no	—
636	C₂×C₃×C₄	—	2	1	no	—
637	C₂×C₃×C₄	—	2	2	no	—
638	C₂×C₃×C₄	—	2	2	no	—
639	C₂×C₃×C₄	—	2	2	no	—
640	C₂×C₃×C₄	—	2	1	no	—
641	C₂×C₃×C₄	—	2	1	no	—
642	C₂×C₃×C₄	—	2	1	no	—
643	C₂×C₃×C₄	—	2	1	no	—
644	C₂×C₃×C₄	—	2	1	no	—
645	C₂×C₃×C₄	—	2	2	no	—
646	C₂×C₃×C₄	—	2	8	no	—
647	C₂×C₃×C₄	—	2	8	no	—
648	C₂×C₃×C₄	—	2	1	no	—
649	C₂×C₃×C₄	—	2	1	no	—
650	C₂×C₃×C₄	—	2	1	no	—
651	C₂×C₃×C₄	—	2	1	no	—
652	C₂×C₃×C₄	—	2	1	no	—
653	C₂×C₃×C₄	—	2	1	no	—
654	C₂×C₃×C₄	—	2	1	no	—
655	C₂×C₃×C₄	—	2	2	no	—
656	C₂×C₃×C₄	—	2	2	no	—
657	C₂×C₃×C₄	—	2	2	no	—
658	C₂×C₃×C₄	—	2	2	no	—
659	C₂×C₃×C₄	—	2	2	no	—
660	C₂×C₃×C₄	—	2	1	no	—
661	C₂×C₃×C₄	—	2	1	no	—
662	C₂×C₃×C₄	—	2	2	no	—
663	C₂×C₃×C₄	—	2	1	no	—
664	C₂×C₃×C₄	—	2	2	no	—
665	C₂×C₃×C₄	—	2	1	no	—
666	C₂×C₃×C₄	—	2	1	no	—
667	C₂×C₃×C₄	—	2	1	no	—
668	C₂×C₃×C₄	—	2	1	no	—
669	C₂×C₃×C₄	—	2	1	no	—
670	C₂×C₃×C₄	—	2	1	no	—
671	C₂×C₃×C₄	—	2	1	no	—
672	C₂×C₃×C₄	—	2	2	no	—
673	C₂×C₃×C₄	—	2	2	no	—
674	C₂×C₃×C₄	—	2	1	no	—
675	C₂×C₃×C₄	—	2	2	no	—
676	C₂×C₃×C₄	—	2	2	no	—
677	C₂×C₃×C₄	—	2	2	no	—
678	C₂×C₃×C₄	—	2	1	no	—
679	C₂×C₃×C₄	—	2	1	no	—
680	C₂×C₃×C₄	—	2	1	no	—
681	C₂×C₃×C₄	—	4	8	no	—
682	C₂×C₃×C₄	—	4	8	no	—
683	C₂×C₃×C₄	—	4	4	no	—
684	C₂×C₃×C₄	—	4	4	no	—
685	C₂×C₃×C₄	—	8	4	no	—
686	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
687	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
688	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
689	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
690	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
691	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
692	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
693	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
694	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
695	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
696	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
697	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
698	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
699	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
700	C₂×Q₈	—	2	2	no	—
701	C₂×Q₈	—	2	2	no	—
702	C₂×Q₈	—	2	2	no	—
703	C₂×Q₈	—	2	2	no	—
704	C₂×Q₈	—	2	2	no	—
705	C₂×Q₈	—	2	2	no	—
706	C₂×Q₈	—	4	2	no	—
707	C₂×Q₈	—	4	2	no	—
708	C₂×Q₈	—	4	2	no	—
709	C₂×Q₈	—	4	2	no	—
710	C₂×Q₈	—	4	16	no	—
711	C₂×Q₈	—	4	16	no	—
712	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
713	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
714	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
715	C₂×Q₈	C₂²×C₃×C₄	1	8	yes	—
716	C₂×Q₈	C₂²×C₃×C₄	1	8	yes	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	4	1	no	—
729	C₂²×C₄	—	4	1	no	—
730	C₂²×C₄	—	4	2	no	—
731	C₂²×C₄	—	4	2	no	—
732	C₂²×C₄	—	4	2	no	—
733	C₂²×C₄	—	4	2	no	—
734	C₂²×C₄	—	4	1	no	—
735	C₂²×C₄	—	4	2	no	—
736	C₂²×C₄	—	4	2	no	—
737	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
738	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
739	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
740	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
741	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
749	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	4	2	no	—
768	C₄⋊C₄	—	4	1	no	—
769	C₄⋊C₄	—	4	1	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	—	4	2	no	—
774	C₄⋊C₄	—	4	1	no	—
775	C₄⋊C₄	—	4	2	no	—
776	C₄⋊C₄	—	4	2	no	—
777	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
778	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
779	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
780	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
781	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
782	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
783	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
784	C₂²⋊C₄	—	2	4	no	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	4	1	no	—
789	C₂²⋊C₄	—	4	1	no	—
790	C₂²⋊C₄	—	4	2	no	—
791	C₂²⋊C₄	—	4	2	no	—
792	C₂²⋊C₄	—	4	1	no	—
793	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
794	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
795	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
796	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
797	C₄²	—	2	2	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	2	2	no	—
800	C₄²	—	2	2	no	—
801	C₄²	—	2	4	no	—
802	C₄²	—	4	1	no	—
803	C₄²	—	4	1	no	—
804	C₄²	—	4	2	no	—
805	C₄²	—	4	2	no	—
806	C₄²	—	4	2	no	—
807	C₄²	—	4	2	no	—
808	C₄²	—	4	2	no	—
809	C₄²	—	4	2	no	—
810	C₄²	—	4	2	no	—
811	C₄²	C₂²×C₃×C₄	1	8	yes	—
812	C₄²	C₂²×C₃×C₄	1	4	yes	—
813	C₂²×C₃	—	2	2	no	—
814	C₂²×C₃	—	2	2	no	—
815	C₂²×C₃	—	2	2	no	—
816	C₂²×C₃	—	2	2	no	—
817	C₂²×C₃	—	2	2	no	—
818	C₂²×C₃	—	2	2	no	—
819	C₂²×C₃	—	2	2	no	—
820	C₂²×C₃	—	2	2	no	—
821	C₂²×C₃	—	2	2	no	—
822	C₂²×C₃	—	4	1	no	—
823	C₂²×C₃	—	4	1	no	—
824	C₂²×C₃	—	4	1	no	—
825	C₂²×C₃	—	4	1	no	—
826	C₂²×C₃	#519	1	4	yes	—
827	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
828	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
829	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
830	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
831	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
832	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
833	C₂²×C₃	#585	1	1	yes	characteristic
834	C₃×C₄	—	2	2	no	—
835	C₃×C₄	—	2	2	no	—
836	C₃×C₄	—	2	4	no	—
837	C₃×C₄	—	2	4	no	—
838	C₃×C₄	—	2	4	no	—
839	C₃×C₄	—	2	2	no	—
840	C₃×C₄	—	2	4	no	—
841	C₃×C₄	—	2	2	no	—
842	C₃×C₄	—	2	2	no	—
843	C₃×C₄	—	4	1	no	—
844	C₃×C₄	—	4	1	no	—
845	C₃×C₄	—	4	1	no	—
846	C₃×C₄	—	4	2	no	—
847	C₃×C₄	—	4	1	no	—
848	C₃×C₄	—	4	1	no	—
849	C₃×C₄	—	4	1	no	—
850	C₃×C₄	—	4	2	no	—
851	C₃×C₄	—	4	1	no	—
852	C₃×C₄	—	4	2	no	—
853	C₃×C₄	—	4	2	no	—
854	C₃×C₄	#518	1	4	yes	—
855	C₂³	—	2	1	no	—
856	C₂³	—	2	1	no	—
857	C₂³	—	2	1	no	—
858	C₂³	—	2	1	no	—
859	C₂³	—	2	1	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	1	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	1	no	—
865	C₂³	C₂³×C₃×C₄	1	2	yes	—
866	C₂³	C₂³×C₃×C₄	1	2	yes	—
867	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
868	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
869	C₂³	C₂⁵×C₃	1	1	yes	characteristic
870	Q₈	—	2	8	no	—
871	Q₈	—	2	8	no	—
872	Q₈	—	2	8	no	—
873	Q₈	—	4	8	no	—
874	Q₈	—	4	8	no	—
875	D₄	—	2	8	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	8	no	—
895	C₂×C₄	—	2	8	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	4	8	no	—
930	C₂×C₄	—	4	8	no	—
931	C₂×C₄	—	4	4	no	—
932	C₂×C₄	—	4	4	no	—
933	C₂×C₄	—	8	4	no	—
934	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
935	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
936	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
937	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
938	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
939	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
940	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
941	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
942	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
943	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
944	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
945	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
946	C₂×C₃	—	2	4	no	—
947	C₂×C₃	—	4	2	no	—
948	C₂×C₃	C₂×#518	1	1	yes	characteristic
949	C₂×C₃	C₂×#519	1	1	yes	characteristic
950	C₂×C₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
951	C₂×C₃	#3538	1	1	yes	characteristic
952	C₂×C₃	#3541	1	1	yes	characteristic
953	C₂×C₃	#3552	1	1	yes	characteristic
954	C₂×C₃	#3561	1	1	yes	characteristic
955	C₂²	—	2	2	no	—
956	C₂²	—	2	2	no	—
957	C₂²	—	2	2	no	—
958	C₂²	—	2	2	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	2	2	no	—
961	C₂²	—	2	2	no	—
962	C₂²	—	2	2	no	—
963	C₂²	—	2	2	no	—
964	C₂²	—	4	1	no	—
965	C₂²	—	4	1	no	—
966	C₂²	—	4	1	no	—
967	C₂²	—	4	1	no	—
968	C₂²	C₃×#519	1	4	yes	—
969	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
970	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
971	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
972	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
973	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
974	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
975	C₂²	C₃×#585	1	1	yes	characteristic
976	C₄	—	2	2	no	—
977	C₄	—	2	2	no	—
978	C₄	—	2	4	no	—
979	C₄	—	2	4	no	—
980	C₄	—	2	4	no	—
981	C₄	—	2	2	no	—
982	C₄	—	2	4	no	—
983	C₄	—	2	2	no	—
984	C₄	—	2	2	no	—
985	C₄	—	4	1	no	—
986	C₄	—	4	1	no	—
987	C₄	—	4	1	no	—
988	C₄	—	4	1	no	—
989	C₄	—	4	1	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	1	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	2	no	—
994	C₄	—	4	2	no	—
995	C₄	—	4	1	no	—
996	C₄	C₃×#518	1	4	yes	—
997	C₃	#34475	1	1	yes	characteristic, direct product factor, Sylow
998	C₂	—	2	4	no	—
999	C₂	—	4	2	no	—
1000	C₂	C₂×C₃×#518	1	1	yes	characteristic
1001	C₂	C₂×C₃×#519	1	1	yes	characteristic
1002	C₂	C₃×C₄×2₋¹⁺⁴	1	1	yes	characteristic
1003	C₂	C₃×#3538	1	1	yes	characteristic
1004	C₂	C₃×#3541	1	1	yes	characteristic
1005	C₂	C₃×#3552	1	1	yes	characteristic
1006	C₂	C₃×#3561	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂²×C₃×D₄	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#2381	C₂	semidirect
3. C₃×#2378	C₂	semidirect
4. C₃×#2368	C₂	semidirect
5. C₃×#2365	C₂	semidirect
6. C₃×#2362	C₂	semidirect
7. C₃×#2360	C₂	semidirect
8. C₃×#2356	C₂	semidirect
11. C₃×Q₈×C₂²⋊C₄	C₂	semidirect
12. C₃×Q₈×C₂²⋊C₄	C₂	semidirect
13. C₃×#2332	C₂	semidirect
14. C₃×#2331	C₂	semidirect
15. C₃×#2329	C₂	semidirect
16. C₃×#2327	C₂	semidirect
17. C₃×#2323	C₂	semidirect
18. C₃×#2320	C₂	semidirect
20. C₃×#2310	C₂	semidirect
21. C₃×C₄×C₂²⋊Q₈	C₂	semidirect
22. C₂×C₃×#391	C₂	semidirect
24. #34475	C₃	direct (N × H)
27. C₃×D₄×Q₈	C₄	semidirect
126. #2381	C₂×C₃	semidirect
127. #2378	C₂×C₃	semidirect
128. #2368	C₂×C₃	semidirect
129. #2365	C₂×C₃	semidirect
130. #2362	C₂×C₃	semidirect
131. #2360	C₂×C₃	semidirect
132. #2356	C₂×C₃	semidirect
135. Q₈×C₂²⋊C₄	C₂×C₃	semidirect
136. Q₈×C₂²⋊C₄	C₂×C₃	semidirect
137. #2332	C₂×C₃	semidirect
138. #2331	C₂×C₃	semidirect
139. #2329	C₂×C₃	semidirect
140. #2327	C₂×C₃	semidirect
141. #2323	C₂×C₃	semidirect
142. #2320	C₂×C₃	semidirect
144. #2310	C₂×C₃	semidirect
145. C₄×C₂²⋊Q₈	C₂×C₃	semidirect
146. C₂×#391	C₂×C₃	semidirect
153. C₂²×C₃×Q₈	C₂×C₄	semidirect
167. C₃×C₄⋊Q₈	C₂×C₄	semidirect
168. C₃×C₄⋊Q₈	C₂×C₄	semidirect
171. C₃×C₂²⋊Q₈	C₂×C₄	semidirect
172. C₃×C₂²⋊Q₈	C₂×C₄	semidirect
177. C₃×C₄×Q₈	C₂×C₄	semidirect
272. D₄×Q₈	C₃×C₄	semidirect
490. C₂²×Q₈	C₂×C₃×C₄	semidirect
504. C₄⋊Q₈	C₂×C₃×C₄	semidirect
505. C₄⋊Q₈	C₂×C₃×C₄	semidirect
508. C₂²⋊Q₈	C₂×C₃×C₄	semidirect
509. C₂²⋊Q₈	C₂×C₃×C₄	semidirect
514. C₄×Q₈	C₂×C₃×C₄	semidirect
997. C₃	#34475	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×D₄×Q₈	2
C₃×#2381	2
C₃×#2378	2
C₃×#2368	2
C₃×#2365	2
C₃×#2362	2
C₃×#2360	2
C₃×#2356	2
C₃×#2353	2
C₃×#2352	2
C₃×Q₈×C₂²⋊C₄	2
C₃×#2332	2
C₃×#2331	2
C₃×#2329	2
C₃×#2327	2
C₃×#2323	2
C₃×#2320	2
C₃×#2318	2
C₃×#2310	2
C₃×C₄×C₂²⋊Q₈	2
C₂×C₃×#391	2
C₃×#2290	2
#34475	3

Subgroups — C3×#34475 #10653082

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#34475 #10653082