Subgroups — C₃×#37690 #10656297

Order 768.

2094 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2704	C₂	1	2	yes	maximal, complemented
5	C₃×#2692	C₂	1	2	yes	maximal
6	C₃×#2683	C₂	1	2	yes	maximal
7	C₃×#2677	C₂	1	2	yes	maximal, complemented
8	C₃×#2660	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2629	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2551	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2550	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2465	C₂	1	2	yes	maximal, complemented
13	C₃×#2462	C₂	1	2	yes	maximal, complemented
14	C₃×#2451	C₂	1	2	yes	maximal, complemented
15	C₃×#2441	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2440	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2439	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2439	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2429	C₂	1	2	yes	maximal, complemented
20	C₃×#2354	C₂	1	1	yes	maximal, characteristic
21	C₃×#2352	C₂	1	1	yes	maximal, characteristic
22	C₃×#2330	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2290	C₂	1	1	yes	maximal, characteristic
24	#37690	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃×#544	—	2	8	no	—
26	C₃×#533	—	2	8	no	—
27	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	—
31	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	—
33	C₂×C₃×#125	C₂²	1	1	yes	characteristic
34	C₂×C₃×#125	C₂²	1	1	yes	characteristic
35	C₂×C₃×#125	C₂²	1	2	yes	—
36	C₂×C₃×#125	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
38	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
39	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
40	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
41	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
42	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
44	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
45	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
46	C₂×C₃×#117	C₂²	1	1	yes	characteristic
47	C₂×C₃×#117	C₂²	1	1	yes	characteristic
48	C₂×C₃×#117	C₂²	1	1	yes	characteristic
49	C₂×C₃×#117	C₂²	1	1	yes	characteristic
50	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
52	C₃×#399	C₂²	1	2	yes	—
53	C₃×#398	C₂²	1	2	yes	—
54	C₃×#398	C₂²	1	2	yes	—
55	C₃×#398	C₂²	1	2	yes	—
56	C₃×#398	C₂²	1	2	yes	—
57	C₃×#398	C₂²	1	2	yes	—
58	C₃×#398	C₂²	1	2	yes	—
59	C₃×#396	C₂²	1	2	yes	—
60	C₃×#396	C₂²	1	2	yes	—
61	C₃×#396	C₂²	1	2	yes	—
62	C₃×#396	C₂²	1	2	yes	—
63	C₃×#396	C₂²	1	2	yes	—
64	C₃×#395	C₂²	1	2	yes	—
65	C₃×#395	C₂²	1	2	yes	—
66	C₃×#395	C₂²	1	2	yes	—
67	C₃×#395	C₂²	1	2	yes	—
68	C₃×#395	C₂²	1	2	yes	—
69	C₃×#395	C₂²	1	2	yes	—
70	C₃×#393	C₂²	1	2	yes	—
71	C₃×#393	C₂²	1	2	yes	—
72	C₃×#391	C₂²	1	2	yes	—
73	C₃×#391	C₂²	1	2	yes	—
74	C₃×#391	C₂²	1	2	yes	—
75	C₃×#391	C₂²	1	2	yes	—
76	C₃×#390	C₂²	1	2	yes	—
77	C₃×#389	C₂²	1	1	yes	characteristic
78	C₃×#389	C₂²	1	1	yes	characteristic
79	C₃×#389	C₂²	1	2	yes	—
80	C₃×#389	C₂²	1	2	yes	—
81	C₃×#389	C₂²	1	2	yes	—
82	C₃×#389	C₂²	1	2	yes	—
83	C₃×#389	C₂²	1	2	yes	—
84	C₃×#389	C₂²	1	1	yes	characteristic
85	C₃×#389	C₂²	1	1	yes	characteristic
86	C₃×#389	C₂²	1	1	yes	characteristic
87	C₃×#389	C₂²	1	1	yes	characteristic
88	C₃×#389	C₂²	1	2	yes	—
89	C₃×#388	C₂²	1	2	yes	—
90	C₃×#388	C₂²	1	2	yes	—
91	C₃×#388	C₂²	1	1	yes	characteristic
92	C₃×#388	C₂²	1	2	yes	—
93	C₃×#388	C₂²	1	1	yes	characteristic
94	C₃×#387	C₂²	1	2	yes	—
95	C₃×#387	C₂²	1	2	yes	—
96	C₃×#387	C₂²	1	2	yes	—
97	C₃×#387	C₂²	1	2	yes	—
98	C₃×#387	C₂²	1	2	yes	—
99	C₃×#387	C₂²	1	1	yes	characteristic
100	C₃×#387	C₂²	1	2	yes	—
101	C₃×#387	C₂²	1	1	yes	characteristic
102	C₃×#386	C₂²	1	1	yes	characteristic
103	C₃×#386	C₂²	1	2	yes	—
104	C₃×#386	C₂²	1	1	yes	characteristic
105	C₃×#385	C₂²	1	1	yes	characteristic
106	C₃×#385	C₂²	1	2	yes	—
107	C₃×#385	C₂²	1	1	yes	characteristic
108	C₃×#384	C₂²	1	1	yes	characteristic
109	C₃×#384	C₂²	1	1	yes	characteristic
110	C₃×#384	C₂²	1	1	yes	characteristic
111	C₃×#382	C₂²	1	1	yes	characteristic
112	C₃×#382	C₂²	1	1	yes	characteristic
113	C₃×#380	C₂²	1	1	yes	characteristic
114	C₃×#380	C₂²	1	1	yes	characteristic
115	C₃×#380	C₂²	1	2	yes	—
116	C₃×#380	C₂²	1	1	yes	characteristic
117	C₃×#380	C₂²	1	1	yes	characteristic
118	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
119	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
120	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
121	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
122	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
123	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
124	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
125	C₃×#376	C₂²	1	1	yes	characteristic
126	C₂×#544	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂×#533	C₂×C₃	1	1	yes	characteristic, complemented
128	#2857	C₂×C₃	1	1	yes	characteristic, complemented
129	#2704	C₂×C₃	1	2	yes	complemented
130	#2692	C₂×C₃	1	2	yes	—
131	#2683	C₂×C₃	1	2	yes	—
132	#2677	C₂×C₃	1	2	yes	complemented
133	#2660	C₂×C₃	1	1	yes	characteristic, complemented
134	#2629	C₂×C₃	1	1	yes	characteristic, complemented
135	#2551	C₂×C₃	1	1	yes	characteristic, complemented
136	#2550	C₂×C₃	1	1	yes	characteristic, complemented
137	#2465	C₂×C₃	1	2	yes	complemented
138	#2462	C₂×C₃	1	2	yes	complemented
139	#2451	C₂×C₃	1	2	yes	complemented
140	#2441	C₂×C₃	1	1	yes	characteristic, complemented
141	#2440	C₂×C₃	1	1	yes	characteristic, complemented
142	#2439	C₂×C₃	1	1	yes	characteristic, complemented
143	#2439	C₂×C₃	1	1	yes	characteristic, complemented
144	#2429	C₂×C₃	1	2	yes	complemented
145	#2354	C₂×C₃	1	1	yes	characteristic
146	#2352	C₂×C₃	1	1	yes	characteristic
147	#2330	C₂×C₃	1	1	yes	characteristic, complemented
148	#2290	C₂×C₃	1	1	yes	characteristic
149	C₂²×C₃×Q₈	C₂³	1	2	yes	—
150	C₂²×C₃×Q₈	C₂³	1	2	yes	—
151	C₂²×C₃×Q₈	C₂³	1	2	yes	—
152	C₂²×C₃×Q₈	C₂³	1	2	yes	—
153	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
154	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
155	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
156	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
157	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
158	C₂³×C₃×C₄	C₂³	1	2	yes	—
159	C₃×C₄⋊Q₈	—	2	4	no	—
160	C₃×C₄⋊Q₈	—	2	4	no	—
161	C₃×C₄⋊Q₈	—	2	8	no	—
162	C₃×C₄⋊Q₈	—	2	4	no	—
163	C₃×C₄⋊Q₈	—	2	4	no	—
164	C₃×C₄⋊Q₈	—	4	4	no	—
165	C₃×#125	—	2	8	no	—
166	C₃×#125	—	2	4	no	—
167	C₃×#125	—	2	4	no	—
168	C₃×#125	D₄	1	8	yes	complemented
169	C₃×C₂²⋊Q₈	—	2	8	no	—
170	C₃×C₂²⋊Q₈	—	2	8	no	—
171	C₃×C₂²⋊Q₈	—	2	8	no	—
172	C₃×C₂²⋊Q₈	—	2	8	no	—
173	C₃×C₂²⋊Q₈	—	4	4	no	—
174	C₃×C₂²⋊Q₈	—	4	4	no	—
175	C₃×C₄×Q₈	—	2	8	no	—
176	C₃×C₄×Q₈	—	2	8	no	—
177	C₃×C₄×D₄	Q₈	1	8	yes	complemented
178	C₃×#117	—	2	4	no	—
179	C₃×#117	—	2	4	no	—
180	C₃×#117	—	2	4	no	—
181	C₃×#117	—	2	4	no	—
182	C₂×C₃×C₄⋊C₄	—	2	4	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	1	yes	characteristic
189	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
193	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
195	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
204	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
207	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
208	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
209	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
210	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
211	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
212	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
213	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
214	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
215	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
217	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
218	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
219	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
220	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
221	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
228	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
229	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
230	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
231	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
233	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
234	C₂×C₃×C₄²	—	2	4	no	—
235	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
236	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
237	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
238	C₂×C₃×C₄²	C₂³	1	2	yes	—
239	C₂×C₃×C₄²	C₂³	1	2	yes	—
240	C₂×C₃×C₄²	C₂³	1	2	yes	—
241	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
242	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
243	C₂×C₃×C₄²	C₂³	1	2	yes	—
244	C₂×C₃×C₄²	C₂³	1	2	yes	—
245	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
246	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
254	C₃×#95	C₂³	1	1	yes	characteristic
255	C₃×#95	C₂³	1	1	yes	characteristic
256	C₃×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
268	C₃×#95	C₂³	1	2	yes	—
269	C₃×#95	C₂³	1	2	yes	—
270	C₃×#95	C₂³	1	2	yes	—
271	C₃×#95	C₂³	1	2	yes	—
272	C₃×#95	C₂³	1	2	yes	—
273	#544	—	2	8	no	—
274	#533	—	2	8	no	—
275	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
276	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
277	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
278	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
279	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
280	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
281	C₂×#125	C₂²×C₃	1	1	yes	characteristic
282	C₂×#125	C₂²×C₃	1	1	yes	characteristic
283	C₂×#125	C₂²×C₃	1	2	yes	—
284	C₂×#125	C₂²×C₃	1	1	yes	characteristic
285	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
286	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
287	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
288	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
289	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
290	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
291	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
292	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
293	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
294	C₂×#117	C₂²×C₃	1	1	yes	characteristic
295	C₂×#117	C₂²×C₃	1	1	yes	characteristic
296	C₂×#117	C₂²×C₃	1	1	yes	characteristic
297	C₂×#117	C₂²×C₃	1	1	yes	characteristic
298	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
299	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
300	#399	C₂²×C₃	1	2	yes	—
301	#398	C₂²×C₃	1	2	yes	—
302	#398	C₂²×C₃	1	2	yes	—
303	#398	C₂²×C₃	1	2	yes	—
304	#398	C₂²×C₃	1	2	yes	—
305	#398	C₂²×C₃	1	2	yes	—
306	#398	C₂²×C₃	1	2	yes	—
307	#396	C₂²×C₃	1	2	yes	—
308	#396	C₂²×C₃	1	2	yes	—
309	#396	C₂²×C₃	1	2	yes	—
310	#396	C₂²×C₃	1	2	yes	—
311	#396	C₂²×C₃	1	2	yes	—
312	#395	C₂²×C₃	1	2	yes	—
313	#395	C₂²×C₃	1	2	yes	—
314	#395	C₂²×C₃	1	2	yes	—
315	#395	C₂²×C₃	1	2	yes	—
316	#395	C₂²×C₃	1	2	yes	—
317	#395	C₂²×C₃	1	2	yes	—
318	#393	C₂²×C₃	1	2	yes	—
319	#393	C₂²×C₃	1	2	yes	—
320	#391	C₂²×C₃	1	2	yes	—
321	#391	C₂²×C₃	1	2	yes	—
322	#391	C₂²×C₃	1	2	yes	—
323	#391	C₂²×C₃	1	2	yes	—
324	#390	C₂²×C₃	1	2	yes	—
325	#389	C₂²×C₃	1	2	yes	—
326	#389	C₂²×C₃	1	2	yes	—
327	#389	C₂²×C₃	1	1	yes	characteristic
328	#389	C₂²×C₃	1	1	yes	characteristic
329	#389	C₂²×C₃	1	2	yes	—
330	#389	C₂²×C₃	1	1	yes	characteristic
331	#389	C₂²×C₃	1	1	yes	characteristic
332	#389	C₂²×C₃	1	1	yes	characteristic
333	#389	C₂²×C₃	1	1	yes	characteristic
334	#389	C₂²×C₃	1	2	yes	—
335	#389	C₂²×C₃	1	2	yes	—
336	#389	C₂²×C₃	1	2	yes	—
337	#388	C₂²×C₃	1	2	yes	—
338	#388	C₂²×C₃	1	2	yes	—
339	#388	C₂²×C₃	1	2	yes	—
340	#388	C₂²×C₃	1	1	yes	characteristic
341	#388	C₂²×C₃	1	1	yes	characteristic
342	#387	C₂²×C₃	1	2	yes	—
343	#387	C₂²×C₃	1	2	yes	—
344	#387	C₂²×C₃	1	2	yes	—
345	#387	C₂²×C₃	1	2	yes	—
346	#387	C₂²×C₃	1	2	yes	—
347	#387	C₂²×C₃	1	2	yes	—
348	#387	C₂²×C₃	1	1	yes	characteristic
349	#387	C₂²×C₃	1	1	yes	characteristic
350	#386	C₂²×C₃	1	2	yes	—
351	#386	C₂²×C₃	1	1	yes	characteristic
352	#386	C₂²×C₃	1	1	yes	characteristic
353	#385	C₂²×C₃	1	1	yes	characteristic
354	#385	C₂²×C₃	1	2	yes	—
355	#385	C₂²×C₃	1	1	yes	characteristic
356	#384	C₂²×C₃	1	1	yes	characteristic
357	#384	C₂²×C₃	1	1	yes	characteristic
358	#384	C₂²×C₃	1	1	yes	characteristic
359	#382	C₂²×C₃	1	1	yes	characteristic
360	#382	C₂²×C₃	1	1	yes	characteristic
361	#380	C₂²×C₃	1	1	yes	characteristic
362	#380	C₂²×C₃	1	1	yes	characteristic
363	#380	C₂²×C₃	1	2	yes	—
364	#380	C₂²×C₃	1	1	yes	characteristic
365	#380	C₂²×C₃	1	1	yes	characteristic
366	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
367	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
368	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
369	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
370	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
371	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
372	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
373	#376	C₂²×C₃	1	1	yes	characteristic
374	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
375	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
376	C₂×C₃×Q₈	—	2	4	no	—
377	C₂×C₃×Q₈	—	2	4	no	—
378	C₂×C₃×Q₈	—	2	4	no	—
379	C₂×C₃×Q₈	—	2	4	no	—
380	C₂×C₃×Q₈	—	2	4	no	—
381	C₂×C₃×Q₈	—	2	4	no	—
382	C₂×C₃×Q₈	—	4	2	no	—
383	C₂×C₃×Q₈	—	4	2	no	—
384	C₂×C₃×Q₈	—	4	2	no	—
385	C₂×C₃×Q₈	—	4	2	no	—
386	C₂×C₃×Q₈	—	4	2	no	—
387	C₂×C₃×Q₈	—	4	2	no	—
388	C₂×C₃×D₄	—	4	1	no	—
389	C₂×C₃×D₄	—	4	1	no	—
390	C₂×C₃×D₄	C₂×Q₈	1	4	yes	—
391	C₂²×C₃×C₄	—	2	2	no	—
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	2	no	—
399	C₂²×C₃×C₄	—	2	4	no	—
400	C₂²×C₃×C₄	—	4	1	no	—
401	C₂²×C₃×C₄	—	4	1	no	—
402	C₂²×C₃×C₄	—	4	2	no	—
403	C₂²×C₃×C₄	—	4	2	no	—
404	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
405	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
406	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
407	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
408	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
409	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
410	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
411	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
412	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
413	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
414	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
415	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
416	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
417	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
418	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
419	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
420	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
421	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
422	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
423	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
424	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
425	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
426	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
427	C₃×C₄⋊C₄	—	2	4	no	—
428	C₃×C₄⋊C₄	—	2	2	no	—
429	C₃×C₄⋊C₄	—	2	2	no	—
430	C₃×C₄⋊C₄	—	2	2	no	—
431	C₃×C₄⋊C₄	—	2	2	no	—
432	C₃×C₄⋊C₄	—	2	2	no	—
433	C₃×C₄⋊C₄	—	2	2	no	—
434	C₃×C₄⋊C₄	—	2	4	no	—
435	C₃×C₄⋊C₄	—	2	4	no	—
436	C₃×C₄⋊C₄	—	2	4	no	—
437	C₃×C₄⋊C₄	—	2	4	no	—
438	C₃×C₄⋊C₄	—	2	4	no	—
439	C₃×C₄⋊C₄	—	2	4	no	—
440	C₃×C₄⋊C₄	—	2	4	no	—
441	C₃×C₄⋊C₄	—	2	4	no	—
442	C₃×C₄⋊C₄	—	2	4	no	—
443	C₃×C₄⋊C₄	—	2	4	no	—
444	C₃×C₄⋊C₄	—	2	2	no	—
445	C₃×C₄⋊C₄	—	2	2	no	—
446	C₃×C₄⋊C₄	—	2	2	no	—
447	C₃×C₄⋊C₄	—	2	2	no	—
448	C₃×C₄⋊C₄	—	4	2	no	—
449	C₃×C₄⋊C₄	—	4	2	no	—
450	C₃×C₄⋊C₄	—	4	2	no	—
451	C₃×C₄⋊C₄	—	4	2	no	—
452	C₃×C₄⋊C₄	—	4	2	no	—
453	C₃×C₄⋊C₄	—	4	2	no	—
454	C₃×C₄⋊C₄	—	4	2	no	—
455	C₃×C₄⋊C₄	—	4	2	no	—
456	C₃×C₄⋊C₄	—	4	2	no	—
457	C₃×C₄⋊C₄	—	4	2	no	—
458	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
459	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
460	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
461	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
462	C₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
463	C₃×C₂²⋊C₄	—	2	2	no	—
464	C₃×C₂²⋊C₄	—	2	4	no	—
465	C₃×C₂²⋊C₄	—	2	4	no	—
466	C₃×C₂²⋊C₄	—	2	4	no	—
467	C₃×C₂²⋊C₄	—	2	2	no	—
468	C₃×C₂²⋊C₄	—	2	2	no	—
469	C₃×C₂²⋊C₄	—	2	2	no	—
470	C₃×C₂²⋊C₄	—	4	1	no	—
471	C₃×C₂²⋊C₄	—	4	2	no	—
472	C₃×C₂²⋊C₄	—	4	1	no	—
473	C₃×C₂²⋊C₄	—	4	2	no	—
474	C₃×C₂²⋊C₄	—	4	2	no	—
475	C₃×C₂²⋊C₄	—	4	2	no	—
476	C₃×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
477	C₃×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
478	C₃×C₄²	—	2	2	no	—
479	C₃×C₄²	—	2	2	no	—
480	C₃×C₄²	—	2	2	no	—
481	C₃×C₄²	—	2	4	no	—
482	C₃×C₄²	—	2	4	no	—
483	C₃×C₄²	—	2	4	no	—
484	C₃×C₄²	—	2	2	no	—
485	C₃×C₄²	—	2	2	no	—
486	C₃×C₄²	—	4	2	no	—
487	C₃×C₄²	—	4	2	no	—
488	C₃×C₄²	C₂×D₄	1	4	yes	—
489	C₃×C₄²	C₂×Q₈	1	4	yes	—
490	C₂²×Q₈	C₂³×C₃	1	2	yes	—
491	C₂²×Q₈	C₂³×C₃	1	2	yes	—
492	C₂²×Q₈	C₂³×C₃	1	2	yes	—
493	C₂²×Q₈	C₂³×C₃	1	2	yes	—
494	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
495	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
496	C₂³×C₄	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	2	yes	—
500	C₄⋊Q₈	—	2	4	no	—
501	C₄⋊Q₈	—	2	4	no	—
502	C₄⋊Q₈	—	2	8	no	—
503	C₄⋊Q₈	—	2	4	no	—
504	C₄⋊Q₈	—	2	4	no	—
505	C₄⋊Q₈	—	4	4	no	—
506	#125	—	2	8	no	—
507	#125	—	2	4	no	—
508	#125	—	2	4	no	—
509	#125	C₃×D₄	1	8	yes	complemented
510	C₂²⋊Q₈	—	2	8	no	—
511	C₂²⋊Q₈	—	2	8	no	—
512	C₂²⋊Q₈	—	2	8	no	—
513	C₂²⋊Q₈	—	2	8	no	—
514	C₂²⋊Q₈	—	4	4	no	—
515	C₂²⋊Q₈	—	4	4	no	—
516	C₄×Q₈	—	2	8	no	—
517	C₄×Q₈	—	2	8	no	—
518	C₄×D₄	C₃×Q₈	1	8	yes	complemented
519	#117	—	2	4	no	—
520	#117	—	2	4	no	—
521	#117	—	2	4	no	—
522	#117	—	2	4	no	—
523	C₂×C₄⋊C₄	—	2	4	no	—
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	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
560	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
562	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
563	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
566	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
567	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
572	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
573	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
574	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
575	C₂×C₄²	—	2	4	no	—
576	C₂×C₄²	C₂³×C₃	1	2	yes	—
577	C₂×C₄²	C₂³×C₃	1	2	yes	—
578	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
579	C₂×C₄²	C₂³×C₃	1	2	yes	—
580	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
581	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
582	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
583	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₃	1	2	yes	—
585	C₂×C₄²	C₂³×C₃	1	2	yes	—
586	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
587	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
588	#95	C₂³×C₃	1	1	yes	characteristic
589	#95	C₂³×C₃	1	1	yes	characteristic
590	#95	C₂³×C₃	1	1	yes	characteristic
591	#95	C₂³×C₃	1	1	yes	characteristic
592	#95	C₂³×C₃	1	2	yes	—
593	#95	C₂³×C₃	1	2	yes	—
594	#95	C₂³×C₃	1	1	yes	characteristic
595	#95	C₂³×C₃	1	1	yes	characteristic
596	#95	C₂³×C₃	1	1	yes	characteristic
597	#95	C₂³×C₃	1	1	yes	characteristic
598	#95	C₂³×C₃	1	2	yes	—
599	#95	C₂³×C₃	1	2	yes	—
600	#95	C₂³×C₃	1	2	yes	—
601	#95	C₂³×C₃	1	1	yes	characteristic
602	#95	C₂³×C₃	1	1	yes	characteristic
603	#95	C₂³×C₃	1	2	yes	—
604	#95	C₂³×C₃	1	2	yes	—
605	#95	C₂³×C₃	1	2	yes	—
606	#95	C₂³×C₃	1	2	yes	—
607	#95	C₂³×C₃	1	2	yes	—
608	#95	C₂³×C₃	1	2	yes	—
609	#95	C₂³×C₃	1	2	yes	—
610	#95	C₂³×C₃	1	2	yes	—
611	#95	C₂³×C₃	1	2	yes	—
612	#95	C₂³×C₃	1	2	yes	—
613	#95	C₂³×C₃	1	2	yes	—
614	C₂³×C₃	—	2	1	no	—
615	C₂³×C₃	—	2	1	no	—
616	C₂³×C₃	—	2	1	no	—
617	C₂³×C₃	—	2	1	no	—
618	C₂³×C₃	—	2	1	no	—
619	C₂³×C₃	—	2	1	no	—
620	C₂³×C₃	—	2	1	no	—
621	C₂³×C₃	—	2	1	no	—
622	C₂³×C₃	—	2	1	no	—
623	C₂³×C₃	—	2	1	no	—
624	C₂³×C₃	—	2	1	no	—
625	C₂³×C₃	—	2	1	no	—
626	C₂³×C₃	C₂²×Q₈	1	2	yes	—
627	C₂³×C₃	C₂²×Q₈	1	2	yes	—
628	C₂³×C₃	C₂⁵	1	1	yes	characteristic
629	C₃×Q₈	—	4	8	no	—
630	C₃×Q₈	—	4	8	no	—
631	C₃×Q₈	—	8	4	no	—
632	C₃×Q₈	—	8	4	no	—
633	C₃×D₄	—	4	4	no	—
634	C₂×C₃×C₄	—	2	1	no	—
635	C₂×C₃×C₄	—	2	1	no	—
636	C₂×C₃×C₄	—	2	1	no	—
637	C₂×C₃×C₄	—	2	1	no	—
638	C₂×C₃×C₄	—	2	1	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	1	no	—
647	C₂×C₃×C₄	—	2	2	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	2	no	—
653	C₂×C₃×C₄	—	2	1	no	—
654	C₂×C₃×C₄	—	2	8	no	—
655	C₂×C₃×C₄	—	2	8	no	—
656	C₂×C₃×C₄	—	2	1	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	2	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	2	no	—
666	C₂×C₃×C₄	—	2	2	no	—
667	C₂×C₃×C₄	—	2	2	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	1	no	—
673	C₂×C₃×C₄	—	2	2	no	—
674	C₂×C₃×C₄	—	2	2	no	—
675	C₂×C₃×C₄	—	2	2	no	—
676	C₂×C₃×C₄	—	2	2	no	—
677	C₂×C₃×C₄	—	2	1	no	—
678	C₂×C₃×C₄	—	2	2	no	—
679	C₂×C₃×C₄	—	2	1	no	—
680	C₂×C₃×C₄	—	2	1	no	—
681	C₂×C₃×C₄	—	2	2	no	—
682	C₂×C₃×C₄	—	2	1	no	—
683	C₂×C₃×C₄	—	2	2	no	—
684	C₂×C₃×C₄	—	2	2	no	—
685	C₂×C₃×C₄	—	2	2	no	—
686	C₂×C₃×C₄	—	4	4	no	—
687	C₂×C₃×C₄	—	4	4	no	—
688	C₂×C₃×C₄	—	8	4	no	—
689	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
690	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
691	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
692	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
693	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
694	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
695	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
696	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
697	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
698	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
699	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
700	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
701	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
702	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
703	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
704	C₂×Q₈	—	2	4	no	—
705	C₂×Q₈	—	2	4	no	—
706	C₂×Q₈	—	2	4	no	—
707	C₂×Q₈	—	2	4	no	—
708	C₂×Q₈	—	2	4	no	—
709	C₂×Q₈	—	2	4	no	—
710	C₂×Q₈	—	4	2	no	—
711	C₂×Q₈	—	4	2	no	—
712	C₂×Q₈	—	4	2	no	—
713	C₂×Q₈	—	4	2	no	—
714	C₂×Q₈	—	4	2	no	—
715	C₂×Q₈	—	4	2	no	—
716	C₂×D₄	—	4	1	no	—
717	C₂×D₄	—	4	1	no	—
718	C₂×D₄	C₂×C₃×Q₈	1	4	yes	—
719	C₂²×C₄	—	2	2	no	—
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	2	no	—
727	C₂²×C₄	—	2	4	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	C₂×C₃×Q₈	1	4	yes	—
733	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
734	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	4	no	—
763	C₄⋊C₄	—	2	4	no	—
764	C₄⋊C₄	—	2	4	no	—
765	C₄⋊C₄	—	2	4	no	—
766	C₄⋊C₄	—	2	4	no	—
767	C₄⋊C₄	—	2	4	no	—
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	2	4	no	—
770	C₄⋊C₄	—	2	4	no	—
771	C₄⋊C₄	—	2	4	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	4	2	no	—
777	C₄⋊C₄	—	4	2	no	—
778	C₄⋊C₄	—	4	2	no	—
779	C₄⋊C₄	—	4	2	no	—
780	C₄⋊C₄	—	4	2	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	—	4	2	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
787	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
788	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
789	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
790	C₄⋊C₄	C₂×C₃×Q₈	1	4	yes	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	4	2	no	—
799	C₂²⋊C₄	—	4	2	no	—
800	C₂²⋊C₄	—	4	2	no	—
801	C₂²⋊C₄	—	4	1	no	—
802	C₂²⋊C₄	—	4	2	no	—
803	C₂²⋊C₄	—	4	1	no	—
804	C₂²⋊C₄	C₂×C₃×Q₈	1	4	yes	—
805	C₂²⋊C₄	C₂×C₃×Q₈	1	4	yes	—
806	C₄²	—	2	2	no	—
807	C₄²	—	2	2	no	—
808	C₄²	—	2	2	no	—
809	C₄²	—	2	4	no	—
810	C₄²	—	2	4	no	—
811	C₄²	—	2	4	no	—
812	C₄²	—	2	2	no	—
813	C₄²	—	2	2	no	—
814	C₄²	—	4	2	no	—
815	C₄²	—	4	2	no	—
816	C₄²	C₂×C₃×D₄	1	4	yes	—
817	C₄²	C₂×C₃×Q₈	1	4	yes	—
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	—	2	2	no	—
823	C₂²×C₃	—	2	2	no	—
824	C₂²×C₃	—	4	1	no	—
825	C₂²×C₃	—	4	1	no	—
826	C₂²×C₃	—	4	1	no	—
827	C₂²×C₃	—	4	1	no	—
828	C₂²×C₃	—	4	1	no	—
829	C₂²×C₃	—	4	1	no	—
830	C₂²×C₃	—	4	1	no	—
831	C₂²×C₃	—	4	1	no	—
832	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
833	C₂²×C₃	C₂³×Q₈	1	1	yes	characteristic
834	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
835	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
836	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
837	C₂²×C₃	#585	1	1	yes	characteristic
838	C₂²×C₃	#585	1	1	yes	characteristic
839	C₃×C₄	—	2	2	no	—
840	C₃×C₄	—	2	2	no	—
841	C₃×C₄	—	2	2	no	—
842	C₃×C₄	—	2	2	no	—
843	C₃×C₄	—	2	2	no	—
844	C₃×C₄	—	2	4	no	—
845	C₃×C₄	—	2	2	no	—
846	C₃×C₄	—	2	2	no	—
847	C₃×C₄	—	2	4	no	—
848	C₃×C₄	—	2	2	no	—
849	C₃×C₄	—	4	2	no	—
850	C₃×C₄	—	4	2	no	—
851	C₃×C₄	—	4	2	no	—
852	C₃×C₄	—	4	1	no	—
853	C₃×C₄	—	4	1	no	—
854	C₃×C₄	—	4	2	no	—
855	C₃×C₄	—	4	2	no	—
856	C₃×C₄	—	4	1	no	—
857	C₃×C₄	—	4	2	no	—
858	C₃×C₄	—	4	1	no	—
859	C₃×C₄	D₄×Q₈	1	4	yes	—
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	—	2	1	no	—
866	C₂³	—	2	1	no	—
867	C₂³	—	2	1	no	—
868	C₂³	—	2	1	no	—
869	C₂³	—	2	1	no	—
870	C₂³	—	2	1	no	—
871	C₂³	—	2	1	no	—
872	C₂³	C₂²×C₃×Q₈	1	2	yes	—
873	C₂³	C₂²×C₃×Q₈	1	2	yes	—
874	C₂³	C₂⁵×C₃	1	1	yes	characteristic
875	Q₈	—	4	8	no	—
876	Q₈	—	4	8	no	—
877	Q₈	—	8	4	no	—
878	Q₈	—	8	4	no	—
879	D₄	—	4	4	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	8	no	—
901	C₂×C₄	—	2	8	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	1	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	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	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	4	4	no	—
933	C₂×C₄	—	4	4	no	—
934	C₂×C₄	—	8	4	no	—
935	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
936	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
937	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
938	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
939	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
940	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
941	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
942	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
943	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
944	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
945	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
946	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
947	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
948	C₂×C₃	—	4	2	no	—
949	C₂×C₃	—	4	2	no	—
950	C₂×C₃	#3458	1	1	yes	characteristic
951	C₂×C₃	C₂×D₄×Q₈	1	1	yes	characteristic
952	C₂×C₃	#3488	1	1	yes	characteristic
953	C₂×C₃	#3489	1	1	yes	characteristic
954	C₂×C₃	#3503	1	1	yes	characteristic
955	C₂×C₃	#3547	1	1	yes	characteristic
956	C₂×C₃	#3555	1	1	yes	characteristic
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	—	4	1	no	—
964	C₂²	—	4	1	no	—
965	C₂²	—	4	1	no	—
966	C₂²	—	4	1	no	—
967	C₂²	—	4	1	no	—
968	C₂²	—	4	1	no	—
969	C₂²	—	4	1	no	—
970	C₂²	—	4	1	no	—
971	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
972	C₂²	C₂³×C₃×Q₈	1	1	yes	characteristic
973	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
974	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
975	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
976	C₂²	C₃×#585	1	1	yes	characteristic
977	C₂²	C₃×#585	1	1	yes	characteristic
978	C₄	—	2	2	no	—
979	C₄	—	2	2	no	—
980	C₄	—	2	2	no	—
981	C₄	—	2	2	no	—
982	C₄	—	2	2	no	—
983	C₄	—	2	4	no	—
984	C₄	—	2	2	no	—
985	C₄	—	2	2	no	—
986	C₄	—	2	4	no	—
987	C₄	—	2	2	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	1	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	1	no	—
994	C₄	—	4	2	no	—
995	C₄	—	4	1	no	—
996	C₄	—	4	2	no	—
997	C₄	—	4	1	no	—
998	C₄	C₃×D₄×Q₈	1	4	yes	—
999	C₃	#37690	1	1	yes	characteristic, direct product factor, Sylow
1000	C₂	—	4	2	no	—
1001	C₂	—	4	2	no	—
1002	C₂	C₃×#3458	1	1	yes	characteristic
1003	C₂	C₂×C₃×D₄×Q₈	1	1	yes	characteristic
1004	C₂	C₃×#3488	1	1	yes	characteristic
1005	C₂	C₃×#3489	1	1	yes	characteristic
1006	C₂	C₃×#3503	1	1	yes	characteristic
1007	C₂	C₃×#3547	1	1	yes	characteristic
1008	C₂	C₃×#3555	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#544	C₂	semidirect
2. C₂×C₃×#533	C₂	semidirect
3. C₃×#2857	C₂	semidirect
4. C₃×#2704	C₂	semidirect
7. C₃×#2677	C₂	semidirect
8. C₃×#2660	C₂	semidirect
9. C₃×#2629	C₂	semidirect
10. C₃×#2551	C₂	semidirect
11. C₃×#2550	C₂	semidirect
12. C₃×#2465	C₂	semidirect
13. C₃×#2462	C₂	semidirect
14. C₃×#2451	C₂	semidirect
15. C₃×#2441	C₂	semidirect
16. C₃×#2440	C₂	semidirect
17. C₃×#2439	C₂	semidirect
18. C₃×#2439	C₂	semidirect
19. C₃×#2429	C₂	semidirect
22. C₃×#2330	C₂	semidirect
24. #37690	C₃	direct (N × H)
126. C₂×#544	C₂×C₃	semidirect
127. C₂×#533	C₂×C₃	semidirect
128. #2857	C₂×C₃	semidirect
129. #2704	C₂×C₃	semidirect
132. #2677	C₂×C₃	semidirect
133. #2660	C₂×C₃	semidirect
134. #2629	C₂×C₃	semidirect
135. #2551	C₂×C₃	semidirect
136. #2550	C₂×C₃	semidirect
137. #2465	C₂×C₃	semidirect
138. #2462	C₂×C₃	semidirect
139. #2451	C₂×C₃	semidirect
140. #2441	C₂×C₃	semidirect
141. #2440	C₂×C₃	semidirect
142. #2439	C₂×C₃	semidirect
143. #2439	C₂×C₃	semidirect
144. #2429	C₂×C₃	semidirect
147. #2330	C₂×C₃	semidirect
168. C₃×#125	D₄	semidirect
177. C₃×C₄×D₄	Q₈	semidirect
509. #125	C₃×D₄	semidirect
518. C₄×D₄	C₃×Q₈	semidirect
999. C₃	#37690	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×#544	2
C₂×C₃×#533	2
C₃×#2857	2
C₃×#2704	2
C₃×#2692	2
C₃×#2683	2
C₃×#2677	2
C₃×#2660	2
C₃×#2629	2
C₃×#2551	2
C₃×#2550	2
C₃×#2465	2
C₃×#2462	2
C₃×#2451	2
C₃×#2441	2
C₃×#2440	2
C₃×#2439	2
C₃×#2429	2
C₃×#2354	2
C₃×#2352	2
C₃×#2330	2
C₃×#2290	2
#37690	3

Subgroups — C3×#37690 #10656297

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37690 #10656297