Subgroups — C₃×#36231 #10654838

Order 768.

2596 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2854	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2850	C₂	1	2	yes	maximal, complemented
5	C₃×#2610	C₂	1	2	yes	maximal, complemented
6	C₃×#2609	C₂	1	2	yes	maximal, complemented
7	C₃×#2464	C₂	1	2	yes	maximal, complemented
8	C₃×#2461	C₂	1	2	yes	maximal, complemented
9	C₃×#2459	C₂	1	2	yes	maximal, complemented
10	C₃×#2456	C₂	1	2	yes	maximal, complemented
11	C₃×#2452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2451	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2431	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2428	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2426	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2407	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2366	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2362	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2346	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×C₄×#123	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2290	C₂	1	2	yes	maximal, complemented
24	#36231	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
26	C₃×#555	—	2	8	no	—
27	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×#127	C₂²	1	1	yes	characteristic
29	C₂×C₃×#124	C₂²	1	1	yes	characteristic
30	C₂×C₃×#124	C₂²	1	2	yes	—
31	C₂×C₃×#124	C₂²	1	2	yes	—
32	C₂×C₃×#123	C₂²	1	1	yes	characteristic
33	C₂×C₃×#123	C₂²	1	2	yes	—
34	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
36	C₂×C₃×#121	C₂²	1	1	yes	characteristic
37	C₂×C₃×#121	C₂²	1	1	yes	characteristic
38	C₂×C₃×#121	C₂²	1	1	yes	characteristic
39	C₂×C₃×#121	C₂²	1	2	yes	—
40	C₂×C₃×#121	C₂²	1	2	yes	—
41	C₃×C₄×#41	—	2	8	no	—
42	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
45	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
46	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
47	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
48	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
49	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
50	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
51	C₂×C₃×#117	C₂²	1	1	yes	characteristic
52	C₂×C₃×#117	C₂²	1	2	yes	—
53	C₂×C₃×#117	C₂²	1	2	yes	—
54	C₂×C₃×#117	C₂²	1	1	yes	characteristic
55	C₂²×C₃×C₄²	C₂²	1	2	yes	—
56	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
57	C₃×#398	C₂²	1	2	yes	—
58	C₃×#396	C₂²	1	2	yes	—
59	C₃×#396	C₂²	1	2	yes	—
60	C₃×#395	C₂²	1	2	yes	—
61	C₃×#394	C₂²	1	2	yes	—
62	C₃×#394	C₂²	1	2	yes	—
63	C₃×#394	C₂²	1	2	yes	—
64	C₃×#393	C₂²	1	2	yes	—
65	C₃×#392	C₂²	1	2	yes	—
66	C₃×#392	C₂²	1	2	yes	—
67	C₃×#392	C₂²	1	2	yes	—
68	C₃×#392	C₂²	1	2	yes	—
69	C₃×#391	C₂²	1	1	yes	characteristic
70	C₃×#391	C₂²	1	1	yes	characteristic
71	C₃×#391	C₂²	1	2	yes	—
72	C₃×#390	C₂²	1	1	yes	characteristic
73	C₃×#390	C₂²	1	2	yes	—
74	C₃×#390	C₂²	1	1	yes	characteristic
75	C₃×#390	C₂²	1	1	yes	characteristic
76	C₃×#390	C₂²	1	2	yes	—
77	C₃×#390	C₂²	1	1	yes	characteristic
78	C₃×#390	C₂²	1	2	yes	—
79	C₃×#389	C₂²	1	1	yes	characteristic
80	C₃×#389	C₂²	1	1	yes	characteristic
81	C₃×#389	C₂²	1	1	yes	characteristic
82	C₃×#389	C₂²	1	1	yes	characteristic
83	C₃×#388	C₂²	1	2	yes	—
84	C₃×#388	C₂²	1	2	yes	—
85	C₃×#388	C₂²	1	2	yes	—
86	C₃×#388	C₂²	1	2	yes	—
87	C₃×#388	C₂²	1	2	yes	—
88	C₃×#388	C₂²	1	2	yes	—
89	C₃×#388	C₂²	1	2	yes	—
90	C₃×#388	C₂²	1	2	yes	—
91	C₃×#388	C₂²	1	2	yes	—
92	C₃×#388	C₂²	1	1	yes	characteristic
93	C₃×#388	C₂²	1	1	yes	characteristic
94	C₃×#388	C₂²	1	2	yes	—
95	C₃×#387	C₂²	1	2	yes	—
96	C₃×#387	C₂²	1	2	yes	—
97	C₃×#387	C₂²	1	1	yes	characteristic
98	C₃×#387	C₂²	1	1	yes	characteristic
99	C₃×#386	C₂²	1	2	yes	—
100	C₃×#386	C₂²	1	2	yes	—
101	C₃×#386	C₂²	1	2	yes	—
102	C₃×#386	C₂²	1	2	yes	—
103	C₃×#386	C₂²	1	2	yes	—
104	C₃×#386	C₂²	1	2	yes	—
105	C₃×#386	C₂²	1	2	yes	—
106	C₃×#386	C₂²	1	2	yes	—
107	C₃×#386	C₂²	1	1	yes	characteristic
108	C₃×#385	C₂²	1	2	yes	—
109	C₃×#385	C₂²	1	2	yes	—
110	C₃×#385	C₂²	1	2	yes	—
111	C₃×#385	C₂²	1	1	yes	characteristic
112	C₃×#382	C₂²	1	2	yes	—
113	C₃×#381	C₂²	1	1	yes	characteristic
114	C₃×#380	C₂²	1	1	yes	characteristic
115	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
116	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
117	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
118	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
119	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
120	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
121	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
122	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
123	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
124	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
125	C₃×#376	C₂²	1	2	yes	—
126	C₂×#555	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂×C₄×#41	C₂×C₃	1	1	yes	characteristic, complemented
128	#2854	C₂×C₃	1	1	yes	characteristic, complemented
129	#2850	C₂×C₃	1	2	yes	complemented
130	#2610	C₂×C₃	1	2	yes	complemented
131	#2609	C₂×C₃	1	2	yes	complemented
132	#2464	C₂×C₃	1	2	yes	complemented
133	#2461	C₂×C₃	1	2	yes	complemented
134	#2459	C₂×C₃	1	2	yes	complemented
135	#2456	C₂×C₃	1	2	yes	complemented
136	#2452	C₂×C₃	1	1	yes	characteristic, complemented
137	#2451	C₂×C₃	1	1	yes	characteristic, complemented
138	#2431	C₂×C₃	1	1	yes	characteristic, complemented
139	#2428	C₂×C₃	1	1	yes	characteristic, complemented
140	#2426	C₂×C₃	1	1	yes	characteristic, complemented
141	#2407	C₂×C₃	1	1	yes	characteristic, complemented
142	#2367	C₂×C₃	1	1	yes	characteristic, complemented
143	#2366	C₂×C₃	1	1	yes	characteristic, complemented
144	#2363	C₂×C₃	1	1	yes	characteristic, complemented
145	#2362	C₂×C₃	1	1	yes	characteristic, complemented
146	#2346	C₂×C₃	1	1	yes	characteristic, complemented
147	C₄×#123	C₂×C₃	1	1	yes	characteristic, complemented
148	#2290	C₂×C₃	1	2	yes	complemented
149	C₂×C₃×#41	—	2	4	no	—
150	C₂×C₃×#41	—	2	4	no	—
151	C₂×C₃×#41	—	2	4	no	—
152	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
153	C₂²×C₃×Q₈	C₂³	1	2	yes	—
154	C₂²×C₃×D₄	C₂³	1	2	yes	—
155	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
156	C₂²×C₃×D₄	C₂³	1	2	yes	—
157	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
158	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
159	C₂²×C₃×D₄	C₂³	1	2	yes	—
160	C₂²×C₃×D₄	C₂³	1	2	yes	—
161	C₂²×C₃×D₄	C₂³	1	2	yes	—
162	C₂²×C₃×D₄	C₂³	1	2	yes	—
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	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
168	C₂³×C₃×C₄	C₂³	1	2	yes	—
169	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
170	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
171	C₃×C₄⋊Q₈	—	2	4	no	—
172	C₃×#127	—	2	4	no	—
173	C₃×#124	—	2	4	no	—
174	C₃×#124	—	2	8	no	—
175	C₃×#124	—	2	8	no	—
176	C₃×#123	—	2	4	no	—
177	C₃×#123	—	4	4	no	—
178	C₃×C₂²⋊Q₈	—	2	4	no	—
179	C₃×C₂²⋊Q₈	—	4	4	no	—
180	C₃×#121	—	2	4	no	—
181	C₃×#121	—	2	4	no	—
182	C₃×#121	—	2	4	no	—
183	C₃×#121	—	2	8	no	—
184	C₃×#121	—	4	4	no	—
185	C₃×C₄×Q₈	—	2	4	no	—
186	C₃×C₄×Q₈	—	2	4	no	—
187	C₃×C₄×D₄	—	2	4	no	—
188	C₃×C₄×D₄	—	2	4	no	—
189	C₃×C₄×D₄	—	2	4	no	—
190	C₃×C₄×D₄	—	2	4	no	—
191	C₃×C₄×D₄	—	2	8	no	—
192	C₃×C₄×D₄	—	2	8	no	—
193	C₃×C₄×D₄	—	2	8	no	—
194	C₃×#117	—	2	4	no	—
195	C₃×#117	—	2	8	no	—
196	C₃×#117	—	2	8	no	—
197	C₃×#117	D₄	1	8	yes	complemented
198	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
208	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
209	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
214	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
215	C₂×C₃×C₄⋊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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
219	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
220	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
233	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
234	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
235	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
236	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
237	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
238	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
239	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
240	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
241	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
242	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
243	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
244	C₂×C₃×C₄²	—	2	4	no	—
245	C₂×C₃×C₄²	—	2	8	no	—
246	C₂×C₃×C₄²	C₂³	1	2	yes	—
247	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
248	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
249	C₂×C₃×C₄²	C₂³	1	2	yes	—
250	C₂×C₃×C₄²	C₂³	1	2	yes	—
251	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
252	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
253	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
254	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
255	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
256	C₂×C₃×C₄²	C₂³	1	2	yes	—
257	C₂×C₃×C₄²	C₂³	1	2	yes	—
258	C₂×C₃×C₄²	C₂³	1	2	yes	—
259	C₃×#95	C₂³	1	1	yes	characteristic
260	C₃×#95	C₂³	1	2	yes	—
261	C₃×#95	C₂³	1	2	yes	—
262	C₃×#95	C₂³	1	2	yes	—
263	C₃×#95	C₂³	1	1	yes	characteristic
264	C₃×#95	C₂³	1	1	yes	characteristic
265	C₃×#95	C₂³	1	1	yes	characteristic
266	C₃×#95	C₂³	1	1	yes	characteristic
267	C₃×#95	C₂³	1	1	yes	characteristic
268	C₃×#95	C₂³	1	2	yes	—
269	C₃×#95	C₂³	1	1	yes	characteristic
270	C₃×#95	C₂³	1	2	yes	—
271	C₃×#95	C₂³	1	1	yes	characteristic
272	C₃×#95	C₂³	1	1	yes	characteristic
273	C₃×#95	C₂³	1	2	yes	—
274	C₃×#95	C₂³	1	2	yes	—
275	C₃×#95	C₂³	1	1	yes	characteristic
276	C₃×#95	C₂³	1	2	yes	—
277	C₃×#95	C₂³	1	2	yes	—
278	C₃×#95	C₂³	1	2	yes	—
279	C₃×#95	C₂³	1	2	yes	—
280	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
281	#555	—	2	8	no	—
282	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
283	C₂×#127	C₂²×C₃	1	1	yes	characteristic
284	C₂×#124	C₂²×C₃	1	2	yes	—
285	C₂×#124	C₂²×C₃	1	1	yes	characteristic
286	C₂×#124	C₂²×C₃	1	2	yes	—
287	C₂×#123	C₂²×C₃	1	1	yes	characteristic
288	C₂×#123	C₂²×C₃	1	2	yes	—
289	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
290	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
291	C₂×#121	C₂²×C₃	1	1	yes	characteristic
292	C₂×#121	C₂²×C₃	1	1	yes	characteristic
293	C₂×#121	C₂²×C₃	1	1	yes	characteristic
294	C₂×#121	C₂²×C₃	1	2	yes	—
295	C₂×#121	C₂²×C₃	1	2	yes	—
296	C₄×#41	—	2	8	no	—
297	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
298	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
299	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
300	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
301	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
302	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
303	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
304	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
305	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
306	C₂×#117	C₂²×C₃	1	2	yes	—
307	C₂×#117	C₂²×C₃	1	2	yes	—
308	C₂×#117	C₂²×C₃	1	1	yes	characteristic
309	C₂×#117	C₂²×C₃	1	1	yes	characteristic
310	C₂²×C₄²	C₂²×C₃	1	2	yes	—
311	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
312	#398	C₂²×C₃	1	2	yes	—
313	#396	C₂²×C₃	1	2	yes	—
314	#396	C₂²×C₃	1	2	yes	—
315	#395	C₂²×C₃	1	2	yes	—
316	#394	C₂²×C₃	1	2	yes	—
317	#394	C₂²×C₃	1	2	yes	—
318	#394	C₂²×C₃	1	2	yes	—
319	#393	C₂²×C₃	1	2	yes	—
320	#392	C₂²×C₃	1	2	yes	—
321	#392	C₂²×C₃	1	2	yes	—
322	#392	C₂²×C₃	1	2	yes	—
323	#392	C₂²×C₃	1	2	yes	—
324	#391	C₂²×C₃	1	2	yes	—
325	#391	C₂²×C₃	1	1	yes	characteristic
326	#391	C₂²×C₃	1	1	yes	characteristic
327	#390	C₂²×C₃	1	2	yes	—
328	#390	C₂²×C₃	1	1	yes	characteristic
329	#390	C₂²×C₃	1	1	yes	characteristic
330	#390	C₂²×C₃	1	2	yes	—
331	#390	C₂²×C₃	1	2	yes	—
332	#390	C₂²×C₃	1	1	yes	characteristic
333	#390	C₂²×C₃	1	1	yes	characteristic
334	#389	C₂²×C₃	1	1	yes	characteristic
335	#389	C₂²×C₃	1	1	yes	characteristic
336	#389	C₂²×C₃	1	1	yes	characteristic
337	#389	C₂²×C₃	1	1	yes	characteristic
338	#388	C₂²×C₃	1	1	yes	characteristic
339	#388	C₂²×C₃	1	2	yes	—
340	#388	C₂²×C₃	1	2	yes	—
341	#388	C₂²×C₃	1	2	yes	—
342	#388	C₂²×C₃	1	2	yes	—
343	#388	C₂²×C₃	1	2	yes	—
344	#388	C₂²×C₃	1	2	yes	—
345	#388	C₂²×C₃	1	2	yes	—
346	#388	C₂²×C₃	1	1	yes	characteristic
347	#388	C₂²×C₃	1	2	yes	—
348	#388	C₂²×C₃	1	2	yes	—
349	#388	C₂²×C₃	1	2	yes	—
350	#387	C₂²×C₃	1	1	yes	characteristic
351	#387	C₂²×C₃	1	2	yes	—
352	#387	C₂²×C₃	1	2	yes	—
353	#387	C₂²×C₃	1	1	yes	characteristic
354	#386	C₂²×C₃	1	2	yes	—
355	#386	C₂²×C₃	1	2	yes	—
356	#386	C₂²×C₃	1	2	yes	—
357	#386	C₂²×C₃	1	2	yes	—
358	#386	C₂²×C₃	1	2	yes	—
359	#386	C₂²×C₃	1	2	yes	—
360	#386	C₂²×C₃	1	2	yes	—
361	#386	C₂²×C₃	1	2	yes	—
362	#386	C₂²×C₃	1	1	yes	characteristic
363	#385	C₂²×C₃	1	2	yes	—
364	#385	C₂²×C₃	1	2	yes	—
365	#385	C₂²×C₃	1	2	yes	—
366	#385	C₂²×C₃	1	1	yes	characteristic
367	#382	C₂²×C₃	1	2	yes	—
368	#381	C₂²×C₃	1	1	yes	characteristic
369	#380	C₂²×C₃	1	1	yes	characteristic
370	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
371	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
372	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
373	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
374	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
375	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
376	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
377	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
378	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
379	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
380	#376	C₂²×C₃	1	2	yes	—
381	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
382	C₂⁴×C₃	C₂⁴	1	2	yes	—
383	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
384	C₂⁴×C₃	C₂⁴	1	2	yes	—
385	C₃×#41	—	2	32	no	—
386	C₂×C₃×Q₈	—	2	2	no	—
387	C₂×C₃×Q₈	—	2	4	no	—
388	C₂×C₃×Q₈	—	2	2	no	—
389	C₂×C₃×Q₈	—	4	2	no	—
390	C₂×C₃×Q₈	—	4	2	no	—
391	C₂×C₃×Q₈	#41	1	4	yes	—
392	C₂×C₃×D₄	—	2	4	no	—
393	C₂×C₃×D₄	—	2	4	no	—
394	C₂×C₃×D₄	—	2	2	no	—
395	C₂×C₃×D₄	—	2	4	no	—
396	C₂×C₃×D₄	—	2	4	no	—
397	C₂×C₃×D₄	—	2	4	no	—
398	C₂×C₃×D₄	—	2	4	no	—
399	C₂×C₃×D₄	—	2	2	no	—
400	C₂×C₃×D₄	—	2	2	no	—
401	C₂×C₃×D₄	—	2	4	no	—
402	C₂×C₃×D₄	—	2	4	no	—
403	C₂×C₃×D₄	—	2	2	no	—
404	C₂×C₃×D₄	—	2	4	no	—
405	C₂×C₃×D₄	—	2	2	no	—
406	C₂×C₃×D₄	—	2	2	no	—
407	C₂×C₃×D₄	—	2	2	no	—
408	C₂×C₃×D₄	—	4	2	no	—
409	C₂×C₃×D₄	—	4	1	no	—
410	C₂×C₃×D₄	—	4	2	no	—
411	C₂×C₃×D₄	—	4	2	no	—
412	C₂×C₃×D₄	—	4	2	no	—
413	C₂×C₃×D₄	—	4	2	no	—
414	C₂×C₃×D₄	—	4	2	no	—
415	C₂×C₃×D₄	—	4	2	no	—
416	C₂×C₃×D₄	—	4	2	no	—
417	C₂×C₃×D₄	—	4	2	no	—
418	C₂×C₃×D₄	#41	1	4	yes	—
419	C₂²×C₃×C₄	—	2	4	no	—
420	C₂²×C₃×C₄	—	2	4	no	—
421	C₂²×C₃×C₄	—	2	4	no	—
422	C₂²×C₃×C₄	—	2	2	no	—
423	C₂²×C₃×C₄	—	2	2	no	—
424	C₂²×C₃×C₄	—	2	2	no	—
425	C₂²×C₃×C₄	—	2	2	no	—
426	C₂²×C₃×C₄	—	2	4	no	—
427	C₂²×C₃×C₄	—	2	4	no	—
428	C₂²×C₃×C₄	—	2	4	no	—
429	C₂²×C₃×C₄	—	2	2	no	—
430	C₂²×C₃×C₄	—	2	4	no	—
431	C₂²×C₃×C₄	—	2	4	no	—
432	C₂²×C₃×C₄	—	2	2	no	—
433	C₂²×C₃×C₄	—	2	2	no	—
434	C₂²×C₃×C₄	—	2	2	no	—
435	C₂²×C₃×C₄	—	2	4	no	—
436	C₂²×C₃×C₄	—	2	2	no	—
437	C₂²×C₃×C₄	—	4	2	no	—
438	C₂²×C₃×C₄	—	4	2	no	—
439	C₂²×C₃×C₄	—	4	2	no	—
440	C₂²×C₃×C₄	—	4	1	no	—
441	C₂²×C₃×C₄	—	4	1	no	—
442	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
443	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
444	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
445	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
446	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
447	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
448	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
449	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
450	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
451	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
452	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
453	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
454	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
455	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
456	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
457	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
458	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
459	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
460	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
461	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
462	C₃×C₄⋊C₄	—	2	2	no	—
463	C₃×C₄⋊C₄	—	2	4	no	—
464	C₃×C₄⋊C₄	—	2	4	no	—
465	C₃×C₄⋊C₄	—	2	4	no	—
466	C₃×C₄⋊C₄	—	2	2	no	—
467	C₃×C₄⋊C₄	—	2	2	no	—
468	C₃×C₄⋊C₄	—	2	2	no	—
469	C₃×C₄⋊C₄	—	2	4	no	—
470	C₃×C₄⋊C₄	—	2	2	no	—
471	C₃×C₄⋊C₄	—	2	2	no	—
472	C₃×C₄⋊C₄	—	2	4	no	—
473	C₃×C₄⋊C₄	—	4	1	no	—
474	C₃×C₄⋊C₄	—	4	2	no	—
475	C₃×C₄⋊C₄	—	4	2	no	—
476	C₃×C₄⋊C₄	—	4	2	no	—
477	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
478	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
479	C₃×C₄⋊C₄	#41	1	4	yes	complemented
480	C₃×C₂²⋊C₄	—	2	2	no	—
481	C₃×C₂²⋊C₄	—	2	4	no	—
482	C₃×C₂²⋊C₄	—	2	4	no	—
483	C₃×C₂²⋊C₄	—	2	4	no	—
484	C₃×C₂²⋊C₄	—	2	4	no	—
485	C₃×C₂²⋊C₄	—	2	4	no	—
486	C₃×C₂²⋊C₄	—	2	4	no	—
487	C₃×C₂²⋊C₄	—	2	2	no	—
488	C₃×C₂²⋊C₄	—	2	4	no	—
489	C₃×C₂²⋊C₄	—	2	4	no	—
490	C₃×C₂²⋊C₄	—	2	4	no	—
491	C₃×C₂²⋊C₄	—	2	4	no	—
492	C₃×C₂²⋊C₄	—	2	2	no	—
493	C₃×C₂²⋊C₄	—	2	2	no	—
494	C₃×C₂²⋊C₄	—	2	2	no	—
495	C₃×C₂²⋊C₄	—	2	4	no	—
496	C₃×C₂²⋊C₄	—	2	4	no	—
497	C₃×C₂²⋊C₄	—	2	2	no	—
498	C₃×C₂²⋊C₄	—	2	4	no	—
499	C₃×C₂²⋊C₄	—	4	1	no	—
500	C₃×C₂²⋊C₄	—	4	2	no	—
501	C₃×C₂²⋊C₄	—	4	1	no	—
502	C₃×C₂²⋊C₄	—	4	2	no	—
503	C₃×C₂²⋊C₄	—	4	2	no	—
504	C₃×C₂²⋊C₄	—	4	2	no	—
505	C₃×C₂²⋊C₄	—	4	2	no	—
506	C₃×C₂²⋊C₄	—	4	2	no	—
507	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
508	C₃×C₄²	—	2	2	no	—
509	C₃×C₄²	—	2	2	no	—
510	C₃×C₄²	—	2	4	no	—
511	C₃×C₄²	—	2	4	no	—
512	C₃×C₄²	—	2	2	no	—
513	C₃×C₄²	—	2	2	no	—
514	C₃×C₄²	—	2	4	no	—
515	C₃×C₄²	—	2	2	no	—
516	C₃×C₄²	—	2	4	no	—
517	C₃×C₄²	—	2	2	no	—
518	C₃×C₄²	—	2	2	no	—
519	C₃×C₄²	—	4	2	no	—
520	C₃×C₄²	C₂×D₄	1	8	yes	—
521	C₂×#41	—	2	4	no	—
522	C₂×#41	—	2	4	no	—
523	C₂×#41	—	2	4	no	—
524	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
525	C₂²×Q₈	C₂³×C₃	1	2	yes	—
526	C₂²×D₄	C₂³×C₃	1	2	yes	—
527	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
528	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
529	C₂²×D₄	C₂³×C₃	1	2	yes	—
530	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
531	C₂²×D₄	C₂³×C₃	1	2	yes	—
532	C₂²×D₄	C₂³×C₃	1	2	yes	—
533	C₂²×D₄	C₂³×C₃	1	2	yes	—
534	C₂²×D₄	C₂³×C₃	1	2	yes	—
535	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
536	C₂³×C₄	C₂³×C₃	1	2	yes	—
537	C₂³×C₄	C₂³×C₃	1	2	yes	—
538	C₂³×C₄	C₂³×C₃	1	2	yes	—
539	C₂³×C₄	C₂³×C₃	1	2	yes	—
540	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
543	C₄⋊Q₈	—	2	4	no	—
544	#127	—	2	4	no	—
545	#124	—	2	4	no	—
546	#124	—	2	8	no	—
547	#124	—	2	8	no	—
548	#123	—	2	4	no	—
549	#123	—	4	4	no	—
550	C₂²⋊Q₈	—	2	4	no	—
551	C₂²⋊Q₈	—	4	4	no	—
552	#121	—	2	4	no	—
553	#121	—	2	4	no	—
554	#121	—	2	4	no	—
555	#121	—	2	8	no	—
556	#121	—	4	4	no	—
557	C₄×Q₈	—	2	4	no	—
558	C₄×Q₈	—	2	4	no	—
559	C₄×D₄	—	2	4	no	—
560	C₄×D₄	—	2	4	no	—
561	C₄×D₄	—	2	4	no	—
562	C₄×D₄	—	2	4	no	—
563	C₄×D₄	—	2	8	no	—
564	C₄×D₄	—	2	8	no	—
565	C₄×D₄	—	2	8	no	—
566	#117	—	2	4	no	—
567	#117	—	2	8	no	—
568	#117	—	2	8	no	—
569	#117	C₃×D₄	1	8	yes	complemented
570	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
588	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
594	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
595	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
599	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
603	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
604	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
605	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
614	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
616	C₂×C₄²	—	2	4	no	—
617	C₂×C₄²	—	2	8	no	—
618	C₂×C₄²	C₂³×C₃	1	2	yes	—
619	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₃	1	2	yes	—
622	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₃	1	2	yes	—
625	C₂×C₄²	C₂³×C₃	1	2	yes	—
626	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
629	C₂×C₄²	C₂³×C₃	1	2	yes	—
630	C₂×C₄²	C₂³×C₃	1	2	yes	—
631	#95	C₂³×C₃	1	1	yes	characteristic
632	#95	C₂³×C₃	1	2	yes	—
633	#95	C₂³×C₃	1	2	yes	—
634	#95	C₂³×C₃	1	2	yes	—
635	#95	C₂³×C₃	1	1	yes	characteristic
636	#95	C₂³×C₃	1	1	yes	characteristic
637	#95	C₂³×C₃	1	1	yes	characteristic
638	#95	C₂³×C₃	1	1	yes	characteristic
639	#95	C₂³×C₃	1	1	yes	characteristic
640	#95	C₂³×C₃	1	2	yes	—
641	#95	C₂³×C₃	1	1	yes	characteristic
642	#95	C₂³×C₃	1	2	yes	—
643	#95	C₂³×C₃	1	1	yes	characteristic
644	#95	C₂³×C₃	1	1	yes	characteristic
645	#95	C₂³×C₃	1	2	yes	—
646	#95	C₂³×C₃	1	2	yes	—
647	#95	C₂³×C₃	1	1	yes	characteristic
648	#95	C₂³×C₃	1	2	yes	—
649	#95	C₂³×C₃	1	2	yes	—
650	#95	C₂³×C₃	1	2	yes	—
651	#95	C₂³×C₃	1	2	yes	—
652	C₂³×C₃	—	2	2	no	—
653	C₂³×C₃	—	2	1	no	—
654	C₂³×C₃	—	2	2	no	—
655	C₂³×C₃	—	2	1	no	—
656	C₂³×C₃	—	2	1	no	—
657	C₂³×C₃	—	2	2	no	—
658	C₂³×C₃	—	2	1	no	—
659	C₂³×C₃	—	2	2	no	—
660	C₂³×C₃	—	2	1	no	—
661	C₂³×C₃	—	2	2	no	—
662	C₂³×C₃	—	2	1	no	—
663	C₂³×C₃	—	2	2	no	—
664	C₂³×C₃	—	2	1	no	—
665	C₂³×C₃	—	2	2	no	—
666	C₂³×C₃	—	2	1	no	—
667	C₂³×C₃	—	2	2	no	—
668	C₂³×C₃	—	2	1	no	—
669	C₂³×C₃	—	2	2	no	—
670	C₂³×C₃	—	2	1	no	—
671	C₂³×C₃	—	2	2	no	—
672	C₂³×C₃	—	2	2	no	—
673	C₂³×C₃	—	2	1	no	—
674	C₂³×C₃	—	2	2	no	—
675	C₂³×C₃	—	2	1	no	—
676	C₂³×C₃	—	2	1	no	—
677	C₂³×C₃	—	2	2	no	—
678	C₂³×C₃	C₂²×D₄	1	2	yes	—
679	C₂³×C₃	C₂×#41	1	4	yes	—
680	C₂³×C₃	C₂⁵	1	1	yes	characteristic
681	C₃×Q₈	—	2	8	no	—
682	C₃×Q₈	—	8	4	no	—
683	C₃×D₄	—	2	16	no	—
684	C₃×D₄	—	2	8	no	—
685	C₃×D₄	—	4	4	no	—
686	C₃×D₄	—	4	8	no	—
687	C₃×D₄	—	4	4	no	—
688	C₃×D₄	—	8	4	no	—
689	C₃×D₄	—	8	4	no	—
690	C₃×D₄	—	8	4	no	—
691	C₃×D₄	—	8	4	no	—
692	C₂×C₃×C₄	—	2	16	no	—
693	C₂×C₃×C₄	—	2	1	no	—
694	C₂×C₃×C₄	—	2	1	no	—
695	C₂×C₃×C₄	—	2	2	no	—
696	C₂×C₃×C₄	—	2	1	no	—
697	C₂×C₃×C₄	—	2	2	no	—
698	C₂×C₃×C₄	—	2	1	no	—
699	C₂×C₃×C₄	—	2	1	no	—
700	C₂×C₃×C₄	—	2	1	no	—
701	C₂×C₃×C₄	—	2	2	no	—
702	C₂×C₃×C₄	—	2	2	no	—
703	C₂×C₃×C₄	—	2	2	no	—
704	C₂×C₃×C₄	—	2	1	no	—
705	C₂×C₃×C₄	—	2	1	no	—
706	C₂×C₃×C₄	—	2	1	no	—
707	C₂×C₃×C₄	—	2	1	no	—
708	C₂×C₃×C₄	—	2	2	no	—
709	C₂×C₃×C₄	—	2	8	no	—
710	C₂×C₃×C₄	—	2	1	no	—
711	C₂×C₃×C₄	—	2	1	no	—
712	C₂×C₃×C₄	—	2	1	no	—
713	C₂×C₃×C₄	—	2	1	no	—
714	C₂×C₃×C₄	—	2	2	no	—
715	C₂×C₃×C₄	—	2	1	no	—
716	C₂×C₃×C₄	—	2	2	no	—
717	C₂×C₃×C₄	—	2	1	no	—
718	C₂×C₃×C₄	—	2	1	no	—
719	C₂×C₃×C₄	—	2	1	no	—
720	C₂×C₃×C₄	—	2	1	no	—
721	C₂×C₃×C₄	—	2	2	no	—
722	C₂×C₃×C₄	—	2	1	no	—
723	C₂×C₃×C₄	—	2	2	no	—
724	C₂×C₃×C₄	—	2	1	no	—
725	C₂×C₃×C₄	—	2	2	no	—
726	C₂×C₃×C₄	—	2	1	no	—
727	C₂×C₃×C₄	—	2	2	no	—
728	C₂×C₃×C₄	—	2	1	no	—
729	C₂×C₃×C₄	—	2	1	no	—
730	C₂×C₃×C₄	—	2	1	no	—
731	C₂×C₃×C₄	—	2	2	no	—
732	C₂×C₃×C₄	—	2	1	no	—
733	C₂×C₃×C₄	—	2	2	no	—
734	C₂×C₃×C₄	—	2	1	no	—
735	C₂×C₃×C₄	—	2	1	no	—
736	C₂×C₃×C₄	—	2	1	no	—
737	C₂×C₃×C₄	—	2	1	no	—
738	C₂×C₃×C₄	—	2	2	no	—
739	C₂×C₃×C₄	—	2	1	no	—
740	C₂×C₃×C₄	—	4	8	no	—
741	C₂×C₃×C₄	—	4	8	no	—
742	C₂×C₃×C₄	—	4	8	no	—
743	C₂×C₃×C₄	—	4	4	no	—
744	C₂×C₃×C₄	—	4	4	no	—
745	C₂×C₃×C₄	—	4	4	no	—
746	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
747	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
748	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
749	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
750	C₂×C₃×C₄	C₂×#41	1	2	yes	—
751	C₂×C₃×C₄	C₂×#41	1	4	yes	—
752	C₂×C₃×C₄	C₂×#41	1	2	yes	—
753	C₂×C₃×C₄	C₂×#41	1	2	yes	—
754	C₂×C₃×C₄	C₂×#41	1	2	yes	—
755	C₂×C₃×C₄	C₂×#41	1	2	yes	—
756	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
757	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
758	C₂⁴	C₂⁴×C₃	1	2	yes	—
759	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
760	C₂⁴	C₂⁴×C₃	1	2	yes	—
761	#41	—	2	32	no	—
762	C₂×Q₈	—	2	2	no	—
763	C₂×Q₈	—	2	4	no	—
764	C₂×Q₈	—	2	2	no	—
765	C₂×Q₈	—	4	2	no	—
766	C₂×Q₈	—	4	2	no	—
767	C₂×Q₈	C₃×#41	1	4	yes	—
768	C₂×D₄	—	2	4	no	—
769	C₂×D₄	—	2	4	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	4	no	—
772	C₂×D₄	—	2	4	no	—
773	C₂×D₄	—	2	4	no	—
774	C₂×D₄	—	2	4	no	—
775	C₂×D₄	—	2	2	no	—
776	C₂×D₄	—	2	2	no	—
777	C₂×D₄	—	2	4	no	—
778	C₂×D₄	—	2	4	no	—
779	C₂×D₄	—	2	2	no	—
780	C₂×D₄	—	2	4	no	—
781	C₂×D₄	—	2	2	no	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	4	2	no	—
785	C₂×D₄	—	4	1	no	—
786	C₂×D₄	—	4	2	no	—
787	C₂×D₄	—	4	2	no	—
788	C₂×D₄	—	4	2	no	—
789	C₂×D₄	—	4	2	no	—
790	C₂×D₄	—	4	2	no	—
791	C₂×D₄	—	4	2	no	—
792	C₂×D₄	—	4	2	no	—
793	C₂×D₄	—	4	2	no	—
794	C₂×D₄	C₃×#41	1	4	yes	—
795	C₂²×C₄	—	2	4	no	—
796	C₂²×C₄	—	2	4	no	—
797	C₂²×C₄	—	2	4	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	4	no	—
803	C₂²×C₄	—	2	4	no	—
804	C₂²×C₄	—	2	4	no	—
805	C₂²×C₄	—	2	2	no	—
806	C₂²×C₄	—	2	4	no	—
807	C₂²×C₄	—	2	4	no	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	2	2	no	—
810	C₂²×C₄	—	2	2	no	—
811	C₂²×C₄	—	2	4	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	4	2	no	—
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	1	no	—
817	C₂²×C₄	—	4	1	no	—
818	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
819	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
822	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
823	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
828	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
831	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
832	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
835	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	4	no	—
840	C₄⋊C₄	—	2	4	no	—
841	C₄⋊C₄	—	2	4	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	4	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	4	no	—
849	C₄⋊C₄	—	4	2	no	—
850	C₄⋊C₄	—	4	2	no	—
851	C₄⋊C₄	—	4	2	no	—
852	C₄⋊C₄	—	4	1	no	—
853	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
854	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
855	C₄⋊C₄	C₃×#41	1	4	yes	complemented
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	4	no	—
858	C₂²⋊C₄	—	2	4	no	—
859	C₂²⋊C₄	—	2	4	no	—
860	C₂²⋊C₄	—	2	4	no	—
861	C₂²⋊C₄	—	2	4	no	—
862	C₂²⋊C₄	—	2	4	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	4	no	—
865	C₂²⋊C₄	—	2	4	no	—
866	C₂²⋊C₄	—	2	4	no	—
867	C₂²⋊C₄	—	2	4	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	4	no	—
872	C₂²⋊C₄	—	2	4	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	4	no	—
875	C₂²⋊C₄	—	4	2	no	—
876	C₂²⋊C₄	—	4	2	no	—
877	C₂²⋊C₄	—	4	2	no	—
878	C₂²⋊C₄	—	4	2	no	—
879	C₂²⋊C₄	—	4	1	no	—
880	C₂²⋊C₄	—	4	2	no	—
881	C₂²⋊C₄	—	4	1	no	—
882	C₂²⋊C₄	—	4	2	no	—
883	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
884	C₄²	—	2	2	no	—
885	C₄²	—	2	2	no	—
886	C₄²	—	2	4	no	—
887	C₄²	—	2	4	no	—
888	C₄²	—	2	2	no	—
889	C₄²	—	2	2	no	—
890	C₄²	—	2	4	no	—
891	C₄²	—	2	2	no	—
892	C₄²	—	2	4	no	—
893	C₄²	—	2	2	no	—
894	C₄²	—	2	2	no	—
895	C₄²	—	4	2	no	—
896	C₄²	C₂×C₃×D₄	1	8	yes	—
897	C₂²×C₃	—	2	2	no	—
898	C₂²×C₃	—	2	4	no	—
899	C₂²×C₃	—	2	2	no	—
900	C₂²×C₃	—	2	4	no	—
901	C₂²×C₃	—	2	2	no	—
902	C₂²×C₃	—	2	4	no	—
903	C₂²×C₃	—	4	2	no	—
904	C₂²×C₃	—	4	1	no	—
905	C₂²×C₃	—	4	1	no	—
906	C₂²×C₃	—	4	2	no	—
907	C₂²×C₃	—	4	2	no	—
908	C₂²×C₃	—	4	1	no	—
909	C₂²×C₃	—	4	1	no	—
910	C₂²×C₃	—	4	2	no	—
911	C₂²×C₃	—	4	1	no	—
912	C₂²×C₃	—	4	2	no	—
913	C₂²×C₃	—	4	2	no	—
914	C₂²×C₃	—	4	1	no	—
915	C₂²×C₃	—	4	2	no	—
916	C₂²×C₃	—	4	1	no	—
917	C₂²×C₃	—	4	1	no	—
918	C₂²×C₃	—	4	2	no	—
919	C₂²×C₃	—	4	1	no	—
920	C₂²×C₃	—	4	2	no	—
921	C₂²×C₃	—	4	1	no	—
922	C₂²×C₃	—	4	2	no	—
923	C₂²×C₃	—	4	1	no	—
924	C₂²×C₃	—	4	2	no	—
925	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
926	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
927	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
928	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
929	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
930	C₂²×C₃	#585	1	1	yes	characteristic
931	C₂²×C₃	#585	1	1	yes	characteristic
932	C₃×C₄	—	2	2	no	—
933	C₃×C₄	—	2	4	no	—
934	C₃×C₄	—	2	2	no	—
935	C₃×C₄	—	2	4	no	—
936	C₃×C₄	—	2	2	no	—
937	C₃×C₄	—	2	2	no	—
938	C₃×C₄	—	2	2	no	—
939	C₃×C₄	—	2	4	no	—
940	C₃×C₄	—	4	1	no	—
941	C₃×C₄	—	4	1	no	—
942	C₃×C₄	—	4	1	no	—
943	C₃×C₄	—	4	2	no	—
944	C₃×C₄	—	4	1	no	—
945	C₃×C₄	—	4	2	no	—
946	C₃×C₄	—	4	1	no	—
947	C₃×C₄	—	4	2	no	—
948	C₃×C₄	—	4	1	no	—
949	C₃×C₄	—	4	1	no	—
950	C₃×C₄	#525	1	4	yes	—
951	C₂³	—	2	2	no	—
952	C₂³	—	2	1	no	—
953	C₂³	—	2	2	no	—
954	C₂³	—	2	1	no	—
955	C₂³	—	2	1	no	—
956	C₂³	—	2	2	no	—
957	C₂³	—	2	1	no	—
958	C₂³	—	2	2	no	—
959	C₂³	—	2	1	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	2	1	no	—
962	C₂³	—	2	2	no	—
963	C₂³	—	2	1	no	—
964	C₂³	—	2	2	no	—
965	C₂³	—	2	1	no	—
966	C₂³	—	2	2	no	—
967	C₂³	—	2	1	no	—
968	C₂³	—	2	2	no	—
969	C₂³	—	2	1	no	—
970	C₂³	—	2	2	no	—
971	C₂³	—	2	2	no	—
972	C₂³	—	2	1	no	—
973	C₂³	—	2	2	no	—
974	C₂³	—	2	1	no	—
975	C₂³	—	2	1	no	—
976	C₂³	—	2	2	no	—
977	C₂³	C₂²×C₃×D₄	1	2	yes	—
978	C₂³	C₂×C₃×#41	1	4	yes	—
979	C₂³	C₂⁵×C₃	1	1	yes	characteristic
980	Q₈	—	2	8	no	—
981	Q₈	—	8	4	no	—
982	D₄	—	2	16	no	—
983	D₄	—	2	8	no	—
984	D₄	—	4	4	no	—
985	D₄	—	4	8	no	—
986	D₄	—	4	4	no	—
987	D₄	—	8	4	no	—
988	D₄	—	8	4	no	—
989	D₄	—	8	4	no	—
990	D₄	—	8	4	no	—
991	C₂×C₄	—	2	16	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	8	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	4	8	no	—
1040	C₂×C₄	—	4	8	no	—
1041	C₂×C₄	—	4	8	no	—
1042	C₂×C₄	—	4	4	no	—
1043	C₂×C₄	—	4	4	no	—
1044	C₂×C₄	—	4	4	no	—
1045	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1046	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
1047	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
1048	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1049	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1050	C₂×C₄	C₂×C₃×#41	1	4	yes	—
1051	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1052	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1053	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1054	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1055	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1056	C₂×C₃	—	4	2	no	—
1057	C₂×C₃	—	4	4	no	—
1058	C₂×C₃	—	8	1	no	—
1059	C₂×C₃	—	8	2	no	—
1060	C₂×C₃	C₂×#525	1	1	yes	characteristic
1061	C₂×C₃	D₄×#41	1	1	yes	characteristic
1062	C₂×C₃	#3475	1	1	yes	characteristic
1063	C₂×C₃	#3483	1	1	yes	characteristic
1064	C₂×C₃	#3488	1	1	yes	characteristic
1065	C₂×C₃	#3514	1	1	yes	characteristic
1066	C₂×C₃	#3524	1	1	yes	characteristic
1067	C₂²	—	2	2	no	—
1068	C₂²	—	2	4	no	—
1069	C₂²	—	2	2	no	—
1070	C₂²	—	2	4	no	—
1071	C₂²	—	2	2	no	—
1072	C₂²	—	2	4	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	1	no	—
1075	C₂²	—	4	1	no	—
1076	C₂²	—	4	2	no	—
1077	C₂²	—	4	2	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	2	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	4	2	no	—
1083	C₂²	—	4	2	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	2	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	2	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	2	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	2	no	—
1095	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1096	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1097	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1098	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1099	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1100	C₂²	C₃×#585	1	1	yes	characteristic
1101	C₂²	C₃×#585	1	1	yes	characteristic
1102	C₄	—	2	2	no	—
1103	C₄	—	2	4	no	—
1104	C₄	—	2	2	no	—
1105	C₄	—	2	4	no	—
1106	C₄	—	2	2	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	4	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	2	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	2	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	1	no	—
1120	C₄	C₃×#525	1	4	yes	—
1121	C₃	#36231	1	1	yes	characteristic, direct product factor, Sylow
1122	C₂	—	4	2	no	—
1123	C₂	—	4	4	no	—
1124	C₂	—	8	1	no	—
1125	C₂	—	8	2	no	—
1126	C₂	C₂×C₃×#525	1	1	yes	characteristic
1127	C₂	C₃×D₄×#41	1	1	yes	characteristic
1128	C₂	C₃×#3475	1	1	yes	characteristic
1129	C₂	C₃×#3483	1	1	yes	characteristic
1130	C₂	C₃×#3488	1	1	yes	characteristic
1131	C₂	C₃×#3514	1	1	yes	characteristic
1132	C₂	C₃×#3524	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
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×#555	C₂	semidirect
2. C₂×C₃×C₄×#41	C₂	semidirect
3. C₃×#2854	C₂	semidirect
4. C₃×#2850	C₂	semidirect
5. C₃×#2610	C₂	semidirect
6. C₃×#2609	C₂	semidirect
7. C₃×#2464	C₂	semidirect
8. C₃×#2461	C₂	semidirect
9. C₃×#2459	C₂	semidirect
10. C₃×#2456	C₂	semidirect
11. C₃×#2452	C₂	semidirect
12. C₃×#2451	C₂	semidirect
13. C₃×#2431	C₂	semidirect
14. C₃×#2428	C₂	semidirect
15. C₃×#2426	C₂	semidirect
16. C₃×#2407	C₂	semidirect
17. C₃×#2367	C₂	semidirect
18. C₃×#2366	C₂	semidirect
19. C₃×#2363	C₂	semidirect
20. C₃×#2362	C₂	semidirect
21. C₃×#2346	C₂	semidirect
22. C₃×C₄×#123	C₂	semidirect
23. C₃×#2290	C₂	semidirect
24. #36231	C₃	direct (N × H)
126. C₂×#555	C₂×C₃	semidirect
127. C₂×C₄×#41	C₂×C₃	semidirect
128. #2854	C₂×C₃	semidirect
129. #2850	C₂×C₃	semidirect
130. #2610	C₂×C₃	semidirect
131. #2609	C₂×C₃	semidirect
132. #2464	C₂×C₃	semidirect
133. #2461	C₂×C₃	semidirect
134. #2459	C₂×C₃	semidirect
135. #2456	C₂×C₃	semidirect
136. #2452	C₂×C₃	semidirect
137. #2451	C₂×C₃	semidirect
138. #2431	C₂×C₃	semidirect
139. #2428	C₂×C₃	semidirect
140. #2426	C₂×C₃	semidirect
141. #2407	C₂×C₃	semidirect
142. #2367	C₂×C₃	semidirect
143. #2366	C₂×C₃	semidirect
144. #2363	C₂×C₃	semidirect
145. #2362	C₂×C₃	semidirect
146. #2346	C₂×C₃	semidirect
147. C₄×#123	C₂×C₃	semidirect
148. #2290	C₂×C₃	semidirect
197. C₃×#117	D₄	semidirect
479. C₃×C₄⋊C₄	#41	semidirect
569. #117	C₃×D₄	semidirect
855. C₄⋊C₄	C₃×#41	semidirect
1121. C₃	#36231	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×#555	2
C₂×C₃×C₄×#41	2
C₃×#2854	2
C₃×#2850	2
C₃×#2610	2
C₃×#2609	2
C₃×#2464	2
C₃×#2461	2
C₃×#2459	2
C₃×#2456	2
C₃×#2452	2
C₃×#2451	2
C₃×#2431	2
C₃×#2428	2
C₃×#2426	2
C₃×#2407	2
C₃×#2367	2
C₃×#2366	2
C₃×#2363	2
C₃×#2362	2
C₃×#2346	2
C₃×C₄×#123	2
C₃×#2290	2
#36231	3

Subgroups — C3×#36231 #10654838

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#36231 #10654838