Subgroups — C₃×#62820 #10681427

Order 768.

7382 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3535	C₂	1	8	yes	maximal, complemented
2	C₃×#3534	C₂	1	8	yes	maximal, complemented
3	C₃×#3533	C₂	1	8	yes	maximal, complemented
4	C₃×#3513	C₂	1	16	yes	maximal, complemented
5	C₃×#3492	C₂	1	4	yes	maximal, complemented
6	C₃×#3491	C₂	1	4	yes	maximal, complemented
7	C₃×#3490	C₂	1	2	yes	maximal, complemented
8	C₃×#3490	C₂	1	4	yes	maximal, complemented
9	C₃×#3485	C₂	1	4	yes	maximal, complemented
10	C₃×#3484	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×#525	C₂	1	2	yes	maximal, complemented
12	C₂²×C₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
13	#62820	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂×C₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
15	C₂²×C₃×#41	C₂²	1	2	yes	complemented
16	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
17	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic, complemented
18	C₃×#563	C₂²	1	8	yes	complemented
19	C₃×#562	C₂²	1	16	yes	complemented
20	C₃×#560	C₂²	1	8	yes	complemented
21	C₃×#559	C₂²	1	8	yes	complemented
22	C₃×#554	C₂²	1	16	yes	complemented
23	C₃×#553	C₂²	1	16	yes	complemented
24	C₃×#553	C₂²	1	16	yes	complemented
25	C₃×#552	C₂²	1	16	yes	complemented
26	C₃×#552	C₂²	1	16	yes	complemented
27	C₃×#551	C₂²	1	16	yes	complemented
28	C₃×#551	C₂²	1	16	yes	complemented
29	C₃×#551	C₂²	1	16	yes	complemented
30	C₃×#551	C₂²	1	16	yes	complemented
31	C₃×#551	C₂²	1	8	yes	complemented
32	C₃×#547	C₂²	1	16	yes	complemented
33	C₃×#547	C₂²	1	16	yes	complemented
34	C₃×#546	C₂²	1	16	yes	complemented
35	C₃×#546	C₂²	1	16	yes	complemented
36	C₃×#546	C₂²	1	16	yes	complemented
37	C₃×#546	C₂²	1	16	yes	complemented
38	C₃×#546	C₂²	1	16	yes	complemented
39	C₃×D₄²	C₂²	1	16	yes	complemented
40	C₃×#544	C₂²	1	4	yes	complemented
41	C₃×#543	C₂²	1	2	yes	complemented
42	C₃×#543	C₂²	1	4	yes	complemented
43	C₃×#542	C₂²	1	16	yes	complemented
44	C₃×#540	C₂²	1	16	yes	complemented
45	C₃×#539	C₂²	1	8	yes	complemented
46	C₃×#539	C₂²	1	8	yes	complemented
47	C₃×#539	C₂²	1	16	yes	complemented
48	C₃×#539	C₂²	1	16	yes	complemented
49	C₃×#538	C₂²	1	8	yes	complemented
50	C₃×#538	C₂²	1	8	yes	complemented
51	C₃×#538	C₂²	1	8	yes	complemented
52	C₃×#538	C₂²	1	16	yes	complemented
53	C₃×#537	C₂²	1	4	yes	complemented
54	C₃×#536	C₂²	1	8	yes	complemented
55	C₃×#535	C₂²	1	4	yes	complemented
56	C₃×#534	C₂²	1	4	yes	—
57	C₃×#534	C₂²	1	4	yes	complemented
58	C₃×#534	C₂²	1	2	yes	complemented
59	C₃×#534	C₂²	1	4	yes	complemented
60	C₃×#534	C₂²	1	8	yes	complemented
61	C₃×#529	C₂²	1	16	yes	complemented
62	C₃×#525	C₂²	1	8	yes	complemented
63	C₃×#525	C₂²	1	4	yes	complemented
64	C₃×#525	C₂²	1	8	yes	complemented
65	C₃×#525	C₂²	1	8	yes	complemented
66	C₃×#525	C₂²	1	8	yes	complemented
67	C₃×#525	C₂²	1	8	yes	complemented
68	C₃×#525	C₂²	1	8	yes	complemented
69	C₂×C₃×#123	C₂²	1	4	yes	complemented
70	C₂×C₃×#123	C₂²	1	8	yes	complemented
71	C₂×C₃×#123	C₂²	1	4	yes	complemented
72	C₂×C₃×#123	C₂²	1	8	yes	complemented
73	C₂×C₃×#123	C₂²	1	4	yes	complemented
74	C₂×C₃×#123	C₂²	1	8	yes	complemented
75	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
76	C₂×C₃×#121	C₂²	1	4	yes	complemented
77	C₂×C₃×#120	C₂²	1	4	yes	complemented
78	C₂×C₃×#120	C₂²	1	4	yes	complemented
79	C₃×#520	C₂²	1	8	yes	complemented
80	C₃×#518	C₂²	1	2	yes	complemented
81	C₃×#518	C₂²	1	4	yes	complemented
82	C₃×#518	C₂²	1	8	yes	complemented
83	C₂×C₃×C₄×D₄	C₂²	1	8	yes	complemented
84	C₂×C₃×#117	C₂²	1	2	yes	complemented
85	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
86	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
87	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
88	#3535	C₂×C₃	1	8	yes	complemented
89	#3534	C₂×C₃	1	8	yes	complemented
90	#3533	C₂×C₃	1	8	yes	complemented
91	#3513	C₂×C₃	1	16	yes	complemented
92	#3492	C₂×C₃	1	4	yes	complemented
93	#3491	C₂×C₃	1	4	yes	complemented
94	#3490	C₂×C₃	1	2	yes	complemented
95	#3490	C₂×C₃	1	4	yes	complemented
96	#3485	C₂×C₃	1	4	yes	complemented
97	#3484	C₂×C₃	1	2	yes	complemented
98	C₂×#525	C₂×C₃	1	2	yes	complemented
99	C₂²×#123	C₂×C₃	1	1	yes	characteristic, complemented
100	C₂⁵×C₃	C₂³	1	1	yes	characteristic
101	C₂⁵×C₃	C₂³	1	1	yes	characteristic
102	C₃×H(5,𝔽₂)	—	4	8	no	—
103	C₂×C₃×#41	—	4	8	no	—
104	C₂×C₃×#41	C₂³	1	8	yes	—
105	C₂×C₃×#41	C₂³	1	4	yes	—
106	C₂×C₃×#41	C₂³	1	8	yes	—
107	C₂×C₃×#41	C₂³	1	8	yes	—
108	C₂×C₃×#41	C₂³	1	8	yes	complemented
109	C₂²×C₃×Q₈	C₂³	1	2	yes	complemented
110	C₂²×C₃×D₄	—	4	4	no	—
111	C₂²×C₃×D₄	C₂³	1	2	yes	—
112	C₂²×C₃×D₄	C₂³	1	4	yes	—
113	C₂²×C₃×D₄	C₂³	1	2	yes	—
114	C₂²×C₃×D₄	C₂³	1	8	yes	—
115	C₂²×C₃×D₄	C₂³	1	4	yes	—
116	C₂²×C₃×D₄	C₂³	1	8	yes	—
117	C₂²×C₃×D₄	C₂³	1	8	yes	—
118	C₂²×C₃×D₄	C₂³	1	8	yes	—
119	C₂²×C₃×D₄	C₂³	1	2	yes	complemented
120	C₂³×C₃×C₄	—	4	4	no	—
121	C₂³×C₃×C₄	C₂³	1	2	yes	—
122	C₂³×C₃×C₄	C₂³	1	2	yes	—
123	C₂³×C₃×C₄	C₂³	1	4	yes	—
124	C₂³×C₃×C₄	C₂³	1	4	yes	—
125	C₂³×C₃×C₄	C₂³	1	2	yes	—
126	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
127	C₂³×C₃×C₄	C₂³	1	2	yes	—
128	C₂³×C₃×C₄	C₂³	1	4	yes	complemented
129	C₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
130	C₃×#127	C₂³	1	8	yes	—
131	C₃×#126	C₂³	1	16	yes	complemented
132	C₃×#126	C₂³	1	16	yes	complemented
133	C₃×#126	C₂³	1	16	yes	complemented
134	C₃×#126	C₂³	1	16	yes	complemented
135	C₃×#126	C₂³	1	16	yes	complemented
136	C₃×#125	C₂³	1	16	yes	complemented
137	C₃×#125	C₂³	1	16	yes	complemented
138	C₃×#125	C₂³	1	16	yes	complemented
139	C₃×#124	C₂³	1	8	yes	—
140	C₃×#124	C₂³	1	16	yes	complemented
141	C₃×#124	C₂³	1	16	yes	complemented
142	C₃×#124	C₂³	1	16	yes	complemented
143	C₃×#123	C₂³	1	8	yes	—
144	C₃×#123	C₂³	1	8	yes	—
145	C₃×#123	C₂³	1	8	yes	—
146	C₃×#123	C₂³	1	8	yes	—
147	C₃×#123	C₂³	1	8	yes	—
148	C₃×#123	C₂³	1	16	yes	—
149	C₃×#123	C₂³	1	16	yes	—
150	C₃×#123	C₂³	1	16	yes	—
151	C₃×#123	C₂³	1	8	yes	—
152	C₃×#123	C₂³	1	8	yes	—
153	C₃×#123	C₂³	1	16	yes	—
154	C₃×#123	C₂³	1	16	yes	complemented
155	C₃×#123	C₂³	1	16	yes	complemented
156	C₃×#123	C₂³	1	16	yes	complemented
157	C₃×#123	C₂³	1	16	yes	complemented
158	C₃×#123	C₂³	1	16	yes	complemented
159	C₃×#123	C₂³	1	8	yes	complemented
160	C₃×#123	C₂³	1	8	yes	complemented
161	C₃×#123	C₂³	1	8	yes	complemented
162	C₃×#123	C₂³	1	16	yes	complemented
163	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
164	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
165	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
166	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
167	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
168	C₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
169	C₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
170	C₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
171	C₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
172	C₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
173	C₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
174	C₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
175	C₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
176	C₃×#121	C₂³	1	16	yes	—
177	C₃×#121	C₂³	1	16	yes	—
178	C₃×#121	C₂³	1	8	yes	—
179	C₃×#121	C₂³	1	8	yes	—
180	C₃×#121	C₂³	1	8	yes	—
181	C₃×#121	C₂³	1	8	yes	—
182	C₃×#121	C₂³	1	8	yes	—
183	C₃×#121	C₂³	1	16	yes	—
184	C₃×#121	C₂³	1	8	yes	complemented
185	C₃×#121	C₂³	1	16	yes	complemented
186	C₃×#121	C₂³	1	16	yes	complemented
187	C₃×#121	C₂³	1	16	yes	complemented
188	C₃×#121	C₂³	1	8	yes	complemented
189	C₃×#121	C₂³	1	16	yes	complemented
190	C₃×#120	C₂³	1	8	yes	—
191	C₃×#120	C₂³	1	8	yes	—
192	C₃×#120	C₂³	1	8	yes	—
193	C₃×#120	C₂³	1	16	yes	—
194	C₃×#120	C₂³	1	8	yes	—
195	C₃×#120	C₂³	1	16	yes	—
196	C₃×#120	C₂³	1	8	yes	—
197	C₃×#120	C₂³	1	16	yes	complemented
198	C₃×#120	C₂³	1	8	yes	complemented
199	C₃×C₄×Q₈	C₂³	1	16	yes	complemented
200	C₃×C₄×D₄	C₂³	1	16	yes	—
201	C₃×C₄×D₄	C₂³	1	16	yes	—
202	C₃×C₄×D₄	C₂³	1	16	yes	—
203	C₃×C₄×D₄	C₂³	1	16	yes	—
204	C₃×C₄×D₄	C₂³	1	16	yes	—
205	C₃×C₄×D₄	C₂³	1	16	yes	—
206	C₃×C₄×D₄	C₂³	1	16	yes	complemented
207	C₃×C₄×D₄	C₂³	1	16	yes	complemented
208	C₃×C₄×D₄	C₂³	1	16	yes	complemented
209	C₃×C₄×D₄	C₂³	1	16	yes	complemented
210	C₃×C₄×D₄	C₂³	1	16	yes	complemented
211	C₃×C₄×D₄	C₂³	1	16	yes	complemented
212	C₃×#117	C₂³	1	8	yes	—
213	C₃×#117	C₂³	1	4	yes	—
214	C₃×#117	C₂³	1	8	yes	—
215	C₃×#117	C₂³	1	8	yes	complemented
216	C₃×#117	C₂³	1	8	yes	complemented
217	C₃×#117	C₂³	1	16	yes	complemented
218	C₃×#117	C₂³	1	16	yes	complemented
219	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
220	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
221	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
222	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
223	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	complemented
224	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	complemented
225	C₂×C₃×C₄⋊C₄	C₂³	1	16	yes	complemented
226	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
228	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
229	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
230	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
231	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
232	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
233	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
234	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
235	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
236	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
237	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
238	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
239	C₂×C₃×C₂²⋊C₄	C₂³	1	16	yes	complemented
240	C₂×C₃×C₄²	C₂³	1	4	yes	complemented
241	C₂×H(5,𝔽₂)	C₂²×C₃	1	2	yes	complemented
242	C₂²×#41	C₂²×C₃	1	2	yes	complemented
243	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
244	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
245	#563	C₂²×C₃	1	8	yes	complemented
246	#562	C₂²×C₃	1	16	yes	complemented
247	#560	C₂²×C₃	1	8	yes	complemented
248	#559	C₂²×C₃	1	8	yes	complemented
249	#554	C₂²×C₃	1	16	yes	complemented
250	#553	C₂²×C₃	1	16	yes	complemented
251	#553	C₂²×C₃	1	16	yes	complemented
252	#552	C₂²×C₃	1	16	yes	complemented
253	#552	C₂²×C₃	1	16	yes	complemented
254	#551	C₂²×C₃	1	16	yes	complemented
255	#551	C₂²×C₃	1	16	yes	complemented
256	#551	C₂²×C₃	1	16	yes	complemented
257	#551	C₂²×C₃	1	16	yes	complemented
258	#551	C₂²×C₃	1	8	yes	complemented
259	#547	C₂²×C₃	1	16	yes	complemented
260	#547	C₂²×C₃	1	16	yes	complemented
261	#546	C₂²×C₃	1	16	yes	complemented
262	#546	C₂²×C₃	1	16	yes	complemented
263	#546	C₂²×C₃	1	16	yes	complemented
264	#546	C₂²×C₃	1	16	yes	complemented
265	#546	C₂²×C₃	1	16	yes	complemented
266	D₄²	C₂²×C₃	1	16	yes	complemented
267	#544	C₂²×C₃	1	4	yes	complemented
268	#543	C₂²×C₃	1	2	yes	complemented
269	#543	C₂²×C₃	1	4	yes	complemented
270	#542	C₂²×C₃	1	16	yes	complemented
271	#540	C₂²×C₃	1	16	yes	complemented
272	#539	C₂²×C₃	1	8	yes	complemented
273	#539	C₂²×C₃	1	8	yes	complemented
274	#539	C₂²×C₃	1	16	yes	complemented
275	#539	C₂²×C₃	1	16	yes	complemented
276	#538	C₂²×C₃	1	8	yes	complemented
277	#538	C₂²×C₃	1	8	yes	complemented
278	#538	C₂²×C₃	1	8	yes	complemented
279	#538	C₂²×C₃	1	16	yes	complemented
280	#537	C₂²×C₃	1	4	yes	complemented
281	#536	C₂²×C₃	1	8	yes	complemented
282	#535	C₂²×C₃	1	4	yes	complemented
283	#534	C₂²×C₃	1	4	yes	—
284	#534	C₂²×C₃	1	4	yes	complemented
285	#534	C₂²×C₃	1	2	yes	complemented
286	#534	C₂²×C₃	1	4	yes	complemented
287	#534	C₂²×C₃	1	8	yes	complemented
288	#529	C₂²×C₃	1	16	yes	complemented
289	#525	C₂²×C₃	1	8	yes	complemented
290	#525	C₂²×C₃	1	4	yes	complemented
291	#525	C₂²×C₃	1	8	yes	complemented
292	#525	C₂²×C₃	1	8	yes	complemented
293	#525	C₂²×C₃	1	8	yes	complemented
294	#525	C₂²×C₃	1	8	yes	complemented
295	#525	C₂²×C₃	1	8	yes	complemented
296	C₂×#123	C₂²×C₃	1	4	yes	complemented
297	C₂×#123	C₂²×C₃	1	8	yes	complemented
298	C₂×#123	C₂²×C₃	1	4	yes	complemented
299	C₂×#123	C₂²×C₃	1	8	yes	complemented
300	C₂×#123	C₂²×C₃	1	4	yes	complemented
301	C₂×#123	C₂²×C₃	1	8	yes	complemented
302	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
303	C₂×#121	C₂²×C₃	1	4	yes	complemented
304	C₂×#120	C₂²×C₃	1	4	yes	complemented
305	C₂×#120	C₂²×C₃	1	4	yes	complemented
306	#520	C₂²×C₃	1	8	yes	complemented
307	#518	C₂²×C₃	1	2	yes	complemented
308	#518	C₂²×C₃	1	4	yes	complemented
309	#518	C₂²×C₃	1	8	yes	complemented
310	C₂×C₄×D₄	C₂²×C₃	1	8	yes	complemented
311	C₂×#117	C₂²×C₃	1	2	yes	complemented
312	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
313	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
314	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
315	C₂⁴×C₃	—	2	4	no	—
316	C₂⁴×C₃	—	4	4	no	—
317	C₂⁴×C₃	—	4	4	no	—
318	C₂⁴×C₃	—	4	2	no	—
319	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
320	C₂⁴×C₃	C₂⁴	1	4	yes	—
321	C₂⁴×C₃	C₂⁴	1	2	yes	—
322	C₂⁴×C₃	C₂⁴	1	4	yes	—
323	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
324	C₂⁴×C₃	C₂⁴	1	4	yes	—
325	C₂⁴×C₃	C₂⁴	1	4	yes	—
326	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
327	C₃×#41	—	4	16	no	—
328	C₃×#41	—	4	16	no	—
329	C₃×#41	—	4	16	no	—
330	C₃×#41	—	4	8	no	—
331	C₃×#41	—	4	16	no	—
332	C₂×C₃×Q₈	—	4	4	no	—
333	C₂×C₃×Q₈	C₂⁴	1	8	yes	—
334	C₂×C₃×Q₈	C₂⁴	1	8	yes	—
335	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
336	C₂×C₃×D₄	—	2	8	no	—
337	C₂×C₃×D₄	—	2	16	no	—
338	C₂×C₃×D₄	—	4	4	no	—
339	C₂×C₃×D₄	—	4	4	no	—
340	C₂×C₃×D₄	—	4	16	no	—
341	C₂×C₃×D₄	—	4	16	no	—
342	C₂×C₃×D₄	—	4	16	no	—
343	C₂×C₃×D₄	—	4	16	no	—
344	C₂×C₃×D₄	—	4	8	no	—
345	C₂×C₃×D₄	C₂⁴	1	16	yes	—
346	C₂×C₃×D₄	C₂⁴	1	8	yes	—
347	C₂×C₃×D₄	C₂⁴	1	8	yes	—
348	C₂×C₃×D₄	C₂⁴	1	8	yes	—
349	C₂×C₃×D₄	C₂⁴	1	16	yes	—
350	C₂×C₃×D₄	C₂⁴	1	16	yes	—
351	C₂×C₃×D₄	C₂⁴	1	8	yes	—
352	C₂×C₃×D₄	C₂⁴	1	8	yes	—
353	C₂×C₃×D₄	C₂⁴	1	8	yes	—
354	C₂×C₃×D₄	C₂⁴	1	8	yes	—
355	C₂×C₃×D₄	C₂⁴	1	4	yes	—
356	C₂²×C₃×C₄	—	2	8	no	—
357	C₂²×C₃×C₄	—	4	8	no	—
358	C₂²×C₃×C₄	—	4	8	no	—
359	C₂²×C₃×C₄	—	4	4	no	—
360	C₂²×C₃×C₄	—	4	4	no	—
361	C₂²×C₃×C₄	—	4	4	no	—
362	C₂²×C₃×C₄	—	4	2	no	—
363	C₂²×C₃×C₄	—	4	8	no	—
364	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
365	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
366	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
367	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
368	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
369	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
370	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
371	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
372	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
373	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
374	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
375	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
376	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
377	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
378	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
379	C₂²×C₃×C₄	C₂⁴	1	16	yes	—
380	C₂²×C₃×C₄	C₂⁴	1	16	yes	—
381	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
382	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
383	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
384	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
385	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
386	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
387	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
388	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
389	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
390	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
391	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
392	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
393	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
394	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
395	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
396	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
397	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
398	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
399	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
400	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
401	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
402	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
403	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
404	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
405	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
406	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
407	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
408	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
409	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
410	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
411	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
412	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
413	C₃×C₄²	C₂⁴	1	16	yes	—
414	C₃×C₄²	C₂⁴	1	8	yes	—
415	C₃×C₄²	C₂⁴	1	16	yes	—
416	C₂⁵	C₂³×C₃	1	1	yes	characteristic
417	C₂⁵	C₂³×C₃	1	1	yes	characteristic
418	H(5,𝔽₂)	—	4	8	no	—
419	C₂×#41	—	4	8	no	—
420	C₂×#41	C₂³×C₃	1	8	yes	—
421	C₂×#41	C₂³×C₃	1	8	yes	—
422	C₂×#41	C₂³×C₃	1	4	yes	—
423	C₂×#41	C₂³×C₃	1	8	yes	—
424	C₂×#41	C₂³×C₃	1	8	yes	complemented
425	C₂²×Q₈	C₂³×C₃	1	2	yes	complemented
426	C₂²×D₄	—	4	4	no	—
427	C₂²×D₄	C₂³×C₃	1	4	yes	—
428	C₂²×D₄	C₂³×C₃	1	2	yes	—
429	C₂²×D₄	C₂³×C₃	1	8	yes	—
430	C₂²×D₄	C₂³×C₃	1	8	yes	—
431	C₂²×D₄	C₂³×C₃	1	4	yes	—
432	C₂²×D₄	C₂³×C₃	1	2	yes	—
433	C₂²×D₄	C₂³×C₃	1	8	yes	—
434	C₂²×D₄	C₂³×C₃	1	8	yes	—
435	C₂²×D₄	C₂³×C₃	1	2	yes	complemented
436	C₂³×C₄	—	4	4	no	—
437	C₂³×C₄	C₂³×C₃	1	2	yes	—
438	C₂³×C₄	C₂³×C₃	1	2	yes	—
439	C₂³×C₄	C₂³×C₃	1	2	yes	—
440	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
441	C₂³×C₄	C₂³×C₃	1	4	yes	—
442	C₂³×C₄	C₂³×C₃	1	4	yes	—
443	C₂³×C₄	C₂³×C₃	1	2	yes	—
444	C₂³×C₄	C₂³×C₃	1	4	yes	complemented
445	C₄⋊Q₈	C₂³×C₃	1	16	yes	complemented
446	#127	C₂³×C₃	1	8	yes	—
447	#126	C₂³×C₃	1	16	yes	complemented
448	#126	C₂³×C₃	1	16	yes	complemented
449	#126	C₂³×C₃	1	16	yes	complemented
450	#126	C₂³×C₃	1	16	yes	complemented
451	#126	C₂³×C₃	1	16	yes	complemented
452	#125	C₂³×C₃	1	16	yes	complemented
453	#125	C₂³×C₃	1	16	yes	complemented
454	#125	C₂³×C₃	1	16	yes	complemented
455	#124	C₂³×C₃	1	8	yes	—
456	#124	C₂³×C₃	1	16	yes	complemented
457	#124	C₂³×C₃	1	16	yes	complemented
458	#124	C₂³×C₃	1	16	yes	complemented
459	#123	C₂³×C₃	1	8	yes	—
460	#123	C₂³×C₃	1	8	yes	—
461	#123	C₂³×C₃	1	16	yes	—
462	#123	C₂³×C₃	1	16	yes	—
463	#123	C₂³×C₃	1	8	yes	—
464	#123	C₂³×C₃	1	8	yes	—
465	#123	C₂³×C₃	1	16	yes	—
466	#123	C₂³×C₃	1	8	yes	—
467	#123	C₂³×C₃	1	8	yes	—
468	#123	C₂³×C₃	1	16	yes	—
469	#123	C₂³×C₃	1	8	yes	—
470	#123	C₂³×C₃	1	8	yes	complemented
471	#123	C₂³×C₃	1	8	yes	complemented
472	#123	C₂³×C₃	1	8	yes	complemented
473	#123	C₂³×C₃	1	16	yes	complemented
474	#123	C₂³×C₃	1	16	yes	complemented
475	#123	C₂³×C₃	1	16	yes	complemented
476	#123	C₂³×C₃	1	16	yes	complemented
477	#123	C₂³×C₃	1	16	yes	complemented
478	#123	C₂³×C₃	1	16	yes	complemented
479	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
480	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
481	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
482	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
483	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
484	C₂²⋊Q₈	C₂³×C₃	1	8	yes	complemented
485	C₂²⋊Q₈	C₂³×C₃	1	8	yes	complemented
486	C₂²⋊Q₈	C₂³×C₃	1	16	yes	complemented
487	C₂²⋊Q₈	C₂³×C₃	1	16	yes	complemented
488	C₂²⋊Q₈	C₂³×C₃	1	16	yes	complemented
489	C₂²⋊Q₈	C₂³×C₃	1	16	yes	complemented
490	C₂²⋊Q₈	C₂³×C₃	1	16	yes	complemented
491	C₂²⋊Q₈	C₂³×C₃	1	16	yes	complemented
492	#121	C₂³×C₃	1	8	yes	—
493	#121	C₂³×C₃	1	8	yes	—
494	#121	C₂³×C₃	1	8	yes	—
495	#121	C₂³×C₃	1	8	yes	—
496	#121	C₂³×C₃	1	8	yes	—
497	#121	C₂³×C₃	1	16	yes	—
498	#121	C₂³×C₃	1	16	yes	—
499	#121	C₂³×C₃	1	16	yes	—
500	#121	C₂³×C₃	1	8	yes	complemented
501	#121	C₂³×C₃	1	8	yes	complemented
502	#121	C₂³×C₃	1	16	yes	complemented
503	#121	C₂³×C₃	1	16	yes	complemented
504	#121	C₂³×C₃	1	16	yes	complemented
505	#121	C₂³×C₃	1	16	yes	complemented
506	#120	C₂³×C₃	1	8	yes	—
507	#120	C₂³×C₃	1	8	yes	—
508	#120	C₂³×C₃	1	16	yes	—
509	#120	C₂³×C₃	1	8	yes	—
510	#120	C₂³×C₃	1	16	yes	—
511	#120	C₂³×C₃	1	8	yes	—
512	#120	C₂³×C₃	1	8	yes	—
513	#120	C₂³×C₃	1	8	yes	complemented
514	#120	C₂³×C₃	1	16	yes	complemented
515	C₄×Q₈	C₂³×C₃	1	16	yes	complemented
516	C₄×D₄	C₂³×C₃	1	16	yes	—
517	C₄×D₄	C₂³×C₃	1	16	yes	—
518	C₄×D₄	C₂³×C₃	1	16	yes	—
519	C₄×D₄	C₂³×C₃	1	16	yes	—
520	C₄×D₄	C₂³×C₃	1	16	yes	—
521	C₄×D₄	C₂³×C₃	1	16	yes	—
522	C₄×D₄	C₂³×C₃	1	16	yes	complemented
523	C₄×D₄	C₂³×C₃	1	16	yes	complemented
524	C₄×D₄	C₂³×C₃	1	16	yes	complemented
525	C₄×D₄	C₂³×C₃	1	16	yes	complemented
526	C₄×D₄	C₂³×C₃	1	16	yes	complemented
527	C₄×D₄	C₂³×C₃	1	16	yes	complemented
528	#117	C₂³×C₃	1	8	yes	—
529	#117	C₂³×C₃	1	4	yes	—
530	#117	C₂³×C₃	1	8	yes	—
531	#117	C₂³×C₃	1	8	yes	complemented
532	#117	C₂³×C₃	1	8	yes	complemented
533	#117	C₂³×C₃	1	16	yes	complemented
534	#117	C₂³×C₃	1	16	yes	complemented
535	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
536	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
537	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
538	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
539	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
540	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	complemented
541	C₂×C₄⋊C₄	C₂³×C₃	1	16	yes	complemented
542	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
554	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
555	C₂×C₂²⋊C₄	C₂³×C₃	1	16	yes	complemented
556	C₂×C₄²	C₂³×C₃	1	4	yes	complemented
557	C₂³×C₃	—	2	2	no	—
558	C₂³×C₃	—	2	4	no	—
559	C₂³×C₃	—	2	8	no	—
560	C₂³×C₃	—	2	2	no	—
561	C₂³×C₃	—	2	8	no	—
562	C₂³×C₃	—	2	8	no	—
563	C₂³×C₃	—	2	4	no	—
564	C₂³×C₃	—	2	8	no	—
565	C₂³×C₃	—	4	2	no	—
566	C₂³×C₃	—	4	4	no	—
567	C₂³×C₃	—	4	2	no	—
568	C₂³×C₃	—	4	4	no	—
569	C₂³×C₃	—	4	8	no	—
570	C₂³×C₃	—	4	4	no	—
571	C₂³×C₃	—	4	4	no	—
572	C₂³×C₃	—	4	4	no	—
573	C₂³×C₃	—	4	8	no	—
574	C₂³×C₃	—	4	16	no	—
575	C₂³×C₃	—	8	8	no	—
576	C₂³×C₃	H(5,𝔽₂)	1	4	yes	—
577	C₂³×C₃	C₂⁵	1	4	yes	—
578	C₂³×C₃	C₂⁵	1	2	yes	—
579	C₂³×C₃	C₂⁵	1	8	yes	—
580	C₂³×C₃	C₂⁵	1	2	yes	—
581	C₂³×C₃	C₂⁵	1	1	yes	characteristic
582	C₂³×C₃	C₂⁵	1	2	yes	—
583	C₃×Q₈	—	4	8	no	—
584	C₃×Q₈	—	4	8	no	—
585	C₃×Q₈	—	4	4	no	—
586	C₃×D₄	—	2	16	no	—
587	C₃×D₄	—	2	16	no	—
588	C₃×D₄	—	2	16	no	—
589	C₃×D₄	—	2	32	no	—
590	C₃×D₄	—	4	8	no	—
591	C₃×D₄	—	4	4	no	—
592	C₃×D₄	—	4	8	no	—
593	C₃×D₄	—	4	16	no	—
594	C₃×D₄	—	4	16	no	—
595	C₃×D₄	—	4	8	no	—
596	C₃×D₄	—	4	8	no	—
597	C₂×C₃×C₄	—	2	4	no	—
598	C₂×C₃×C₄	—	2	4	no	—
599	C₂×C₃×C₄	—	2	8	no	—
600	C₂×C₃×C₄	—	2	8	no	—
601	C₂×C₃×C₄	—	2	4	no	—
602	C₂×C₃×C₄	—	2	8	no	—
603	C₂×C₃×C₄	—	2	8	no	—
604	C₂×C₃×C₄	—	4	2	no	—
605	C₂×C₃×C₄	—	4	2	no	—
606	C₂×C₃×C₄	—	4	4	no	—
607	C₂×C₃×C₄	—	4	4	no	—
608	C₂×C₃×C₄	—	4	2	no	—
609	C₂×C₃×C₄	—	4	2	no	—
610	C₂×C₃×C₄	—	4	4	no	—
611	C₂×C₃×C₄	—	4	4	no	—
612	C₂×C₃×C₄	—	4	4	no	—
613	C₂×C₃×C₄	—	4	16	no	—
614	C₂×C₃×C₄	—	4	8	no	—
615	C₂×C₃×C₄	—	4	8	no	—
616	C₂×C₃×C₄	—	4	8	no	—
617	C₂×C₃×C₄	—	4	4	no	—
618	C₂×C₃×C₄	—	4	16	no	—
619	C₂×C₃×C₄	C₂⁵	1	16	yes	—
620	C₂×C₃×C₄	C₂⁵	1	4	yes	—
621	C₂×C₃×C₄	C₂⁵	1	8	yes	—
622	C₂×C₃×C₄	C₂⁵	1	8	yes	—
623	C₂×C₃×C₄	C₂⁵	1	4	yes	—
624	C₂×C₃×C₄	C₂⁵	1	4	yes	—
625	C₂⁴	—	2	4	no	—
626	C₂⁴	—	4	4	no	—
627	C₂⁴	—	4	2	no	—
628	C₂⁴	—	4	4	no	—
629	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
630	C₂⁴	C₂⁴×C₃	1	4	yes	—
631	C₂⁴	C₂⁴×C₃	1	2	yes	—
632	C₂⁴	C₂⁴×C₃	1	4	yes	—
633	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
634	C₂⁴	C₂⁴×C₃	1	4	yes	—
635	C₂⁴	C₂⁴×C₃	1	4	yes	—
636	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
637	#41	—	4	16	no	—
638	#41	—	4	16	no	—
639	#41	—	4	8	no	—
640	#41	—	4	16	no	—
641	#41	—	4	16	no	—
642	C₂×Q₈	—	4	4	no	—
643	C₂×Q₈	C₂⁴×C₃	1	8	yes	—
644	C₂×Q₈	C₂⁴×C₃	1	8	yes	—
645	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
646	C₂×D₄	—	2	8	no	—
647	C₂×D₄	—	2	16	no	—
648	C₂×D₄	—	4	4	no	—
649	C₂×D₄	—	4	4	no	—
650	C₂×D₄	—	4	16	no	—
651	C₂×D₄	—	4	16	no	—
652	C₂×D₄	—	4	8	no	—
653	C₂×D₄	—	4	16	no	—
654	C₂×D₄	—	4	16	no	—
655	C₂×D₄	C₂⁴×C₃	1	16	yes	—
656	C₂×D₄	C₂⁴×C₃	1	8	yes	—
657	C₂×D₄	C₂⁴×C₃	1	8	yes	—
658	C₂×D₄	C₂⁴×C₃	1	8	yes	—
659	C₂×D₄	C₂⁴×C₃	1	16	yes	—
660	C₂×D₄	C₂⁴×C₃	1	16	yes	—
661	C₂×D₄	C₂⁴×C₃	1	8	yes	—
662	C₂×D₄	C₂⁴×C₃	1	8	yes	—
663	C₂×D₄	C₂⁴×C₃	1	8	yes	—
664	C₂×D₄	C₂⁴×C₃	1	8	yes	—
665	C₂×D₄	C₂⁴×C₃	1	4	yes	—
666	C₂²×C₄	—	2	8	no	—
667	C₂²×C₄	—	4	8	no	—
668	C₂²×C₄	—	4	8	no	—
669	C₂²×C₄	—	4	4	no	—
670	C₂²×C₄	—	4	4	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	4	no	—
673	C₂²×C₄	—	4	8	no	—
674	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
676	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
677	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
678	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
679	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
682	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
683	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
684	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
686	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
688	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
689	C₂²×C₄	C₂⁴×C₃	1	16	yes	—
690	C₂²×C₄	C₂⁴×C₃	1	16	yes	—
691	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
692	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
693	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
695	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
696	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
697	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
698	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
699	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
700	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
701	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
702	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
703	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
704	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
705	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
706	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
707	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
708	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
709	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
710	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
711	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
712	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
713	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
714	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
715	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
716	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
717	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
718	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
719	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
720	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
721	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
722	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
723	C₄²	C₂⁴×C₃	1	16	yes	—
724	C₄²	C₂⁴×C₃	1	8	yes	—
725	C₄²	C₂⁴×C₃	1	16	yes	—
726	C₂²×C₃	—	2	8	no	—
727	C₂²×C₃	—	2	2	no	—
728	C₂²×C₃	—	2	2	no	—
729	C₂²×C₃	—	2	2	no	—
730	C₂²×C₃	—	2	4	no	—
731	C₂²×C₃	—	2	2	no	—
732	C₂²×C₃	—	2	8	no	—
733	C₂²×C₃	—	2	4	no	—
734	C₂²×C₃	—	2	16	no	—
735	C₂²×C₃	—	2	8	no	—
736	C₂²×C₃	—	2	4	no	—
737	C₂²×C₃	—	4	4	no	—
738	C₂²×C₃	—	4	16	no	—
739	C₂²×C₃	—	4	4	no	—
740	C₂²×C₃	—	8	8	no	—
741	C₂²×C₃	—	8	4	no	—
742	C₂²×C₃	—	8	8	no	—
743	C₂²×C₃	—	16	4	no	—
744	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
745	C₂²×C₃	C₂×H(5,𝔽₂)	1	4	yes	—
746	C₂²×C₃	#585	1	4	yes	—
747	C₂²×C₃	C₂⁶	1	1	yes	characteristic
748	C₃×C₄	—	2	4	no	—
749	C₃×C₄	—	2	4	no	—
750	C₃×C₄	—	2	4	no	—
751	C₃×C₄	—	2	8	no	—
752	C₃×C₄	—	2	8	no	—
753	C₃×C₄	—	2	16	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	4	no	—
756	C₂³	—	2	8	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	8	no	—
759	C₂³	—	2	8	no	—
760	C₂³	—	2	4	no	—
761	C₂³	—	2	8	no	—
762	C₂³	—	4	2	no	—
763	C₂³	—	4	4	no	—
764	C₂³	—	4	2	no	—
765	C₂³	—	4	4	no	—
766	C₂³	—	4	8	no	—
767	C₂³	—	4	4	no	—
768	C₂³	—	4	4	no	—
769	C₂³	—	4	4	no	—
770	C₂³	—	4	8	no	—
771	C₂³	—	4	16	no	—
772	C₂³	—	8	8	no	—
773	C₂³	C₃×H(5,𝔽₂)	1	4	yes	—
774	C₂³	C₂⁵×C₃	1	4	yes	—
775	C₂³	C₂⁵×C₃	1	2	yes	—
776	C₂³	C₂⁵×C₃	1	8	yes	—
777	C₂³	C₂⁵×C₃	1	2	yes	—
778	C₂³	C₂⁵×C₃	1	1	yes	characteristic
779	C₂³	C₂⁵×C₃	1	2	yes	—
780	Q₈	—	4	8	no	—
781	Q₈	—	4	4	no	—
782	Q₈	—	4	8	no	—
783	D₄	—	2	16	no	—
784	D₄	—	2	16	no	—
785	D₄	—	2	16	no	—
786	D₄	—	2	32	no	—
787	D₄	—	4	8	no	—
788	D₄	—	4	4	no	—
789	D₄	—	4	8	no	—
790	D₄	—	4	8	no	—
791	D₄	—	4	16	no	—
792	D₄	—	4	16	no	—
793	D₄	—	4	8	no	—
794	C₂×C₄	—	2	4	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	2	8	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	8	no	—
800	C₂×C₄	—	2	8	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	4	no	—
804	C₂×C₄	—	4	4	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	4	2	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	—	4	16	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	8	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	4	8	no	—
814	C₂×C₄	—	4	8	no	—
815	C₂×C₄	—	4	16	no	—
816	C₂×C₄	C₂⁵×C₃	1	16	yes	—
817	C₂×C₄	C₂⁵×C₃	1	4	yes	—
818	C₂×C₄	C₂⁵×C₃	1	8	yes	—
819	C₂×C₄	C₂⁵×C₃	1	8	yes	—
820	C₂×C₄	C₂⁵×C₃	1	4	yes	—
821	C₂×C₄	C₂⁵×C₃	1	4	yes	—
822	C₂×C₃	—	2	2	no	—
823	C₂×C₃	—	2	4	no	—
824	C₂×C₃	—	2	4	no	—
825	C₂×C₃	—	4	2	no	—
826	C₂×C₃	—	4	4	no	—
827	C₂×C₃	—	4	8	no	—
828	C₂×C₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
829	C₂×C₃	C₂×#585	1	2	yes	—
830	C₂²	—	2	8	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	2	2	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	4	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	8	no	—
837	C₂²	—	2	4	no	—
838	C₂²	—	2	16	no	—
839	C₂²	—	2	8	no	—
840	C₂²	—	2	4	no	—
841	C₂²	—	4	4	no	—
842	C₂²	—	4	16	no	—
843	C₂²	—	4	4	no	—
844	C₂²	—	8	4	no	—
845	C₂²	—	8	8	no	—
846	C₂²	—	8	8	no	—
847	C₂²	—	16	4	no	—
848	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
849	C₂²	C₂×C₃×H(5,𝔽₂)	1	4	yes	—
850	C₂²	C₃×#585	1	4	yes	—
851	C₂²	C₂⁶×C₃	1	1	yes	characteristic
852	C₄	—	2	4	no	—
853	C₄	—	2	4	no	—
854	C₄	—	2	4	no	—
855	C₄	—	2	8	no	—
856	C₄	—	2	8	no	—
857	C₄	—	2	16	no	—
858	C₃	#62820	1	1	yes	characteristic, direct product factor, Sylow
859	C₂	—	2	2	no	—
860	C₂	—	2	4	no	—
861	C₂	—	2	4	no	—
862	C₂	—	4	2	no	—
863	C₂	—	4	4	no	—
864	C₂	—	4	8	no	—
865	C₂	C₂²×C₃×H(5,𝔽₂)	1	1	yes	characteristic
866	C₂	C₂×C₃×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3535	C₂	semidirect
2. C₃×#3534	C₂	semidirect
3. C₃×#3533	C₂	semidirect
4. C₃×#3513	C₂	semidirect
5. C₃×#3492	C₂	semidirect
6. C₃×#3491	C₂	semidirect
7. C₃×#3490	C₂	semidirect
8. C₃×#3490	C₂	semidirect
9. C₃×#3485	C₂	semidirect
10. C₃×#3484	C₂	semidirect
11. C₂×C₃×#525	C₂	semidirect
12. C₂²×C₃×#123	C₂	semidirect
13. #62820	C₃	direct (N × H)
14. C₂×C₃×H(5,𝔽₂)	C₂²	semidirect
15. C₂²×C₃×#41	C₂²	semidirect
17. C₂⁴×C₃×C₄	C₂²	semidirect
18. C₃×#563	C₂²	semidirect
19. C₃×#562	C₂²	semidirect
20. C₃×#560	C₂²	semidirect
21. C₃×#559	C₂²	semidirect
22. C₃×#554	C₂²	semidirect
23. C₃×#553	C₂²	semidirect
24. C₃×#553	C₂²	semidirect
25. C₃×#552	C₂²	semidirect
26. C₃×#552	C₂²	semidirect
27. C₃×#551	C₂²	semidirect
28. C₃×#551	C₂²	semidirect
29. C₃×#551	C₂²	semidirect
30. C₃×#551	C₂²	semidirect
31. C₃×#551	C₂²	semidirect
32. C₃×#547	C₂²	semidirect
33. C₃×#547	C₂²	semidirect
34. C₃×#546	C₂²	semidirect
35. C₃×#546	C₂²	semidirect
36. C₃×#546	C₂²	semidirect
37. C₃×#546	C₂²	semidirect
38. C₃×#546	C₂²	semidirect
39. C₃×D₄²	C₂²	semidirect
40. C₃×#544	C₂²	semidirect
41. C₃×#543	C₂²	semidirect
42. C₃×#543	C₂²	semidirect
43. C₃×#542	C₂²	semidirect
44. C₃×#540	C₂²	semidirect
45. C₃×#539	C₂²	semidirect
46. C₃×#539	C₂²	semidirect
47. C₃×#539	C₂²	semidirect
48. C₃×#539	C₂²	semidirect
49. C₃×#538	C₂²	semidirect
50. C₃×#538	C₂²	semidirect
51. C₃×#538	C₂²	semidirect
52. C₃×#538	C₂²	semidirect
53. C₃×#537	C₂²	semidirect
54. C₃×#536	C₂²	semidirect
55. C₃×#535	C₂²	semidirect
57. C₃×#534	C₂²	semidirect
58. C₃×#534	C₂²	semidirect
59. C₃×#534	C₂²	semidirect
60. C₃×#534	C₂²	semidirect
61. C₃×#529	C₂²	semidirect
62. C₃×#525	C₂²	semidirect
63. C₃×#525	C₂²	semidirect
64. C₃×#525	C₂²	semidirect
65. C₃×#525	C₂²	semidirect
66. C₃×#525	C₂²	semidirect
67. C₃×#525	C₂²	semidirect
68. C₃×#525	C₂²	semidirect
69. C₂×C₃×#123	C₂²	semidirect
70. C₂×C₃×#123	C₂²	semidirect
71. C₂×C₃×#123	C₂²	semidirect
72. C₂×C₃×#123	C₂²	semidirect
73. C₂×C₃×#123	C₂²	semidirect
74. C₂×C₃×#123	C₂²	semidirect
75. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
76. C₂×C₃×#121	C₂²	semidirect
77. C₂×C₃×#120	C₂²	semidirect
78. C₂×C₃×#120	C₂²	semidirect
79. C₃×#520	C₂²	semidirect
80. C₃×#518	C₂²	semidirect
81. C₃×#518	C₂²	semidirect
82. C₃×#518	C₂²	semidirect
83. C₂×C₃×C₄×D₄	C₂²	semidirect
84. C₂×C₃×#117	C₂²	semidirect
85. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
86. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
87. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
88. #3535	C₂×C₃	semidirect
89. #3534	C₂×C₃	semidirect
90. #3533	C₂×C₃	semidirect
91. #3513	C₂×C₃	semidirect
92. #3492	C₂×C₃	semidirect
93. #3491	C₂×C₃	semidirect
94. #3490	C₂×C₃	semidirect
95. #3490	C₂×C₃	semidirect
96. #3485	C₂×C₃	semidirect
97. #3484	C₂×C₃	semidirect
98. C₂×#525	C₂×C₃	semidirect
99. C₂²×#123	C₂×C₃	semidirect
108. C₂×C₃×#41	C₂³	semidirect
109. C₂²×C₃×Q₈	C₂³	semidirect
119. C₂²×C₃×D₄	C₂³	semidirect
128. C₂³×C₃×C₄	C₂³	semidirect
129. C₃×C₄⋊Q₈	C₂³	semidirect
131. C₃×#126	C₂³	semidirect
132. C₃×#126	C₂³	semidirect
133. C₃×#126	C₂³	semidirect
134. C₃×#126	C₂³	semidirect
135. C₃×#126	C₂³	semidirect
136. C₃×#125	C₂³	semidirect
137. C₃×#125	C₂³	semidirect
138. C₃×#125	C₂³	semidirect
140. C₃×#124	C₂³	semidirect
141. C₃×#124	C₂³	semidirect
142. C₃×#124	C₂³	semidirect
154. C₃×#123	C₂³	semidirect
155. C₃×#123	C₂³	semidirect
156. C₃×#123	C₂³	semidirect
157. C₃×#123	C₂³	semidirect
158. C₃×#123	C₂³	semidirect
159. C₃×#123	C₂³	semidirect
160. C₃×#123	C₂³	semidirect
161. C₃×#123	C₂³	semidirect
162. C₃×#123	C₂³	semidirect
168. C₃×C₂²⋊Q₈	C₂³	semidirect
169. C₃×C₂²⋊Q₈	C₂³	semidirect
170. C₃×C₂²⋊Q₈	C₂³	semidirect
171. C₃×C₂²⋊Q₈	C₂³	semidirect
172. C₃×C₂²⋊Q₈	C₂³	semidirect
173. C₃×C₂²⋊Q₈	C₂³	semidirect
174. C₃×C₂²⋊Q₈	C₂³	semidirect
175. C₃×C₂²⋊Q₈	C₂³	semidirect
184. C₃×#121	C₂³	semidirect
185. C₃×#121	C₂³	semidirect
186. C₃×#121	C₂³	semidirect
187. C₃×#121	C₂³	semidirect
188. C₃×#121	C₂³	semidirect
189. C₃×#121	C₂³	semidirect
197. C₃×#120	C₂³	semidirect
198. C₃×#120	C₂³	semidirect
199. C₃×C₄×Q₈	C₂³	semidirect
206. C₃×C₄×D₄	C₂³	semidirect
207. C₃×C₄×D₄	C₂³	semidirect
208. C₃×C₄×D₄	C₂³	semidirect
209. C₃×C₄×D₄	C₂³	semidirect
210. C₃×C₄×D₄	C₂³	semidirect
211. C₃×C₄×D₄	C₂³	semidirect
215. C₃×#117	C₂³	semidirect
216. C₃×#117	C₂³	semidirect
217. C₃×#117	C₂³	semidirect
218. C₃×#117	C₂³	semidirect
223. C₂×C₃×C₄⋊C₄	C₂³	semidirect
224. C₂×C₃×C₄⋊C₄	C₂³	semidirect
225. C₂×C₃×C₄⋊C₄	C₂³	semidirect
237. C₂×C₃×C₂²⋊C₄	C₂³	semidirect
238. C₂×C₃×C₂²⋊C₄	C₂³	semidirect
239. C₂×C₃×C₂²⋊C₄	C₂³	semidirect
240. C₂×C₃×C₄²	C₂³	semidirect
241. C₂×H(5,𝔽₂)	C₂²×C₃	semidirect
242. C₂²×#41	C₂²×C₃	semidirect
244. C₂⁴×C₄	C₂²×C₃	semidirect
245. #563	C₂²×C₃	semidirect
246. #562	C₂²×C₃	semidirect
247. #560	C₂²×C₃	semidirect
248. #559	C₂²×C₃	semidirect
249. #554	C₂²×C₃	semidirect
250. #553	C₂²×C₃	semidirect
251. #553	C₂²×C₃	semidirect
252. #552	C₂²×C₃	semidirect
253. #552	C₂²×C₃	semidirect
254. #551	C₂²×C₃	semidirect
255. #551	C₂²×C₃	semidirect
256. #551	C₂²×C₃	semidirect
257. #551	C₂²×C₃	semidirect
258. #551	C₂²×C₃	semidirect
259. #547	C₂²×C₃	semidirect
260. #547	C₂²×C₃	semidirect
261. #546	C₂²×C₃	semidirect
262. #546	C₂²×C₃	semidirect
263. #546	C₂²×C₃	semidirect
264. #546	C₂²×C₃	semidirect
265. #546	C₂²×C₃	semidirect
266. D₄²	C₂²×C₃	semidirect
267. #544	C₂²×C₃	semidirect
268. #543	C₂²×C₃	semidirect
269. #543	C₂²×C₃	semidirect
270. #542	C₂²×C₃	semidirect
271. #540	C₂²×C₃	semidirect
272. #539	C₂²×C₃	semidirect
273. #539	C₂²×C₃	semidirect
274. #539	C₂²×C₃	semidirect
275. #539	C₂²×C₃	semidirect
276. #538	C₂²×C₃	semidirect
277. #538	C₂²×C₃	semidirect
278. #538	C₂²×C₃	semidirect
279. #538	C₂²×C₃	semidirect
280. #537	C₂²×C₃	semidirect
281. #536	C₂²×C₃	semidirect
282. #535	C₂²×C₃	semidirect
284. #534	C₂²×C₃	semidirect
285. #534	C₂²×C₃	semidirect
286. #534	C₂²×C₃	semidirect
287. #534	C₂²×C₃	semidirect
288. #529	C₂²×C₃	semidirect
289. #525	C₂²×C₃	semidirect
290. #525	C₂²×C₃	semidirect
291. #525	C₂²×C₃	semidirect
292. #525	C₂²×C₃	semidirect
293. #525	C₂²×C₃	semidirect
294. #525	C₂²×C₃	semidirect
295. #525	C₂²×C₃	semidirect
296. C₂×#123	C₂²×C₃	semidirect
297. C₂×#123	C₂²×C₃	semidirect
298. C₂×#123	C₂²×C₃	semidirect
299. C₂×#123	C₂²×C₃	semidirect
300. C₂×#123	C₂²×C₃	semidirect
301. C₂×#123	C₂²×C₃	semidirect
302. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
303. C₂×#121	C₂²×C₃	semidirect
304. C₂×#120	C₂²×C₃	semidirect
305. C₂×#120	C₂²×C₃	semidirect
306. #520	C₂²×C₃	semidirect
307. #518	C₂²×C₃	semidirect
308. #518	C₂²×C₃	semidirect
309. #518	C₂²×C₃	semidirect
310. C₂×C₄×D₄	C₂²×C₃	semidirect
311. C₂×#117	C₂²×C₃	semidirect
312. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
313. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
314. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
424. C₂×#41	C₂³×C₃	semidirect
425. C₂²×Q₈	C₂³×C₃	semidirect
435. C₂²×D₄	C₂³×C₃	semidirect
444. C₂³×C₄	C₂³×C₃	semidirect
445. C₄⋊Q₈	C₂³×C₃	semidirect
447. #126	C₂³×C₃	semidirect
448. #126	C₂³×C₃	semidirect
449. #126	C₂³×C₃	semidirect
450. #126	C₂³×C₃	semidirect
451. #126	C₂³×C₃	semidirect
452. #125	C₂³×C₃	semidirect
453. #125	C₂³×C₃	semidirect
454. #125	C₂³×C₃	semidirect
456. #124	C₂³×C₃	semidirect
457. #124	C₂³×C₃	semidirect
458. #124	C₂³×C₃	semidirect
470. #123	C₂³×C₃	semidirect
471. #123	C₂³×C₃	semidirect
472. #123	C₂³×C₃	semidirect
473. #123	C₂³×C₃	semidirect
474. #123	C₂³×C₃	semidirect
475. #123	C₂³×C₃	semidirect
476. #123	C₂³×C₃	semidirect
477. #123	C₂³×C₃	semidirect
478. #123	C₂³×C₃	semidirect
484. C₂²⋊Q₈	C₂³×C₃	semidirect
485. C₂²⋊Q₈	C₂³×C₃	semidirect
486. C₂²⋊Q₈	C₂³×C₃	semidirect
487. C₂²⋊Q₈	C₂³×C₃	semidirect
488. C₂²⋊Q₈	C₂³×C₃	semidirect
489. C₂²⋊Q₈	C₂³×C₃	semidirect
490. C₂²⋊Q₈	C₂³×C₃	semidirect
491. C₂²⋊Q₈	C₂³×C₃	semidirect
500. #121	C₂³×C₃	semidirect
501. #121	C₂³×C₃	semidirect
502. #121	C₂³×C₃	semidirect
503. #121	C₂³×C₃	semidirect
504. #121	C₂³×C₃	semidirect
505. #121	C₂³×C₃	semidirect
513. #120	C₂³×C₃	semidirect
514. #120	C₂³×C₃	semidirect
515. C₄×Q₈	C₂³×C₃	semidirect
522. C₄×D₄	C₂³×C₃	semidirect
523. C₄×D₄	C₂³×C₃	semidirect
524. C₄×D₄	C₂³×C₃	semidirect
525. C₄×D₄	C₂³×C₃	semidirect
526. C₄×D₄	C₂³×C₃	semidirect
527. C₄×D₄	C₂³×C₃	semidirect
531. #117	C₂³×C₃	semidirect
532. #117	C₂³×C₃	semidirect
533. #117	C₂³×C₃	semidirect
534. #117	C₂³×C₃	semidirect
539. C₂×C₄⋊C₄	C₂³×C₃	semidirect
540. C₂×C₄⋊C₄	C₂³×C₃	semidirect
541. C₂×C₄⋊C₄	C₂³×C₃	semidirect
553. C₂×C₂²⋊C₄	C₂³×C₃	semidirect
554. C₂×C₂²⋊C₄	C₂³×C₃	semidirect
555. C₂×C₂²⋊C₄	C₂³×C₃	semidirect
556. C₂×C₄²	C₂³×C₃	semidirect
858. C₃	#62820	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×#3535	2
C₃×#3534	2
C₃×#3533	2
C₃×#3513	2
C₃×#3492	2
C₃×#3491	2
C₃×#3490	2
C₃×#3485	2
C₃×#3484	2
C₂×C₃×#525	2
C₂²×C₃×#123	2
#62820	3

Subgroups — C3×#62820 #10681427

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#62820 #10681427