Subgroups — C₃×#34511 #10653118

Order 768.

2544 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#560	C₂	1	1	yes	maximal, characteristic
2	C₃×#2375	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2375	C₂	1	2	yes	maximal, complemented
4	C₃×#2374	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2373	C₂	1	2	yes	maximal, complemented
6	C₃×#2366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2364	C₂	1	2	yes	maximal, complemented
8	C₃×#2363	C₂	1	2	yes	maximal, complemented
9	C₃×#2361	C₂	1	2	yes	maximal, complemented
10	C₃×#2359	C₂	1	2	yes	maximal, complemented
11	C₃×#2335	C₂	1	2	yes	maximal, complemented
12	C₃×#2334	C₂	1	2	yes	maximal, complemented
13	C₃×#2333	C₂	1	2	yes	maximal, complemented
14	C₃×#2328	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2325	C₂	1	2	yes	maximal, complemented
16	C₃×#2324	C₂	1	2	yes	maximal, complemented
17	C₃×#2322	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×C₄×#120	C₂	1	2	yes	maximal, complemented
19	C₃×C₄×#120	C₂	1	1	yes	maximal, characteristic, complemented
20	#34511	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
22	C₃×#560	C₄	1	16	yes	complemented
23	C₂×C₃×#127	C₂²	1	1	yes	characteristic
24	C₂×C₃×#126	C₂²	1	2	yes	—
25	C₂×C₃×#123	C₂²	1	1	yes	characteristic
26	C₂×C₃×#123	C₂²	1	2	yes	—
27	C₂×C₃×#121	C₂²	1	2	yes	—
28	C₂×C₃×#121	C₂²	1	2	yes	—
29	C₂×C₃×#121	C₂²	1	2	yes	—
30	C₂×C₃×#120	C₂²	1	2	yes	—
31	C₂×C₃×#120	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
33	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
34	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
35	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
37	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
38	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×#117	C₂²	1	2	yes	complemented
40	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	C₃×#390	C₂²	1	2	yes	—
42	C₃×#390	C₂²	1	2	yes	—
43	C₃×#390	C₂²	1	2	yes	—
44	C₃×#390	C₂²	1	2	yes	—
45	C₃×#390	C₂²	1	1	yes	characteristic
46	C₃×#390	C₂²	1	2	yes	complemented
47	C₃×#390	C₂²	1	1	yes	characteristic, complemented
48	C₃×#389	C₂²	1	2	yes	complemented
49	C₃×#389	C₂²	1	2	yes	complemented
50	C₃×#389	C₂²	1	2	yes	complemented
51	C₃×#388	C₂²	1	2	yes	—
52	C₃×#388	C₂²	1	2	yes	—
53	C₃×#388	C₂²	1	2	yes	—
54	C₃×#388	C₂²	1	2	yes	—
55	C₃×#388	C₂²	1	2	yes	—
56	C₃×#388	C₂²	1	2	yes	—
57	C₃×#388	C₂²	1	2	yes	—
58	C₃×#388	C₂²	1	2	yes	—
59	C₃×#388	C₂²	1	2	yes	—
60	C₃×#388	C₂²	1	2	yes	complemented
61	C₃×#388	C₂²	1	2	yes	complemented
62	C₃×#388	C₂²	1	2	yes	complemented
63	C₃×#387	C₂²	1	2	yes	complemented
64	C₃×#387	C₂²	1	2	yes	complemented
65	C₃×#387	C₂²	1	2	yes	complemented
66	C₃×#387	C₂²	1	2	yes	complemented
67	C₃×#387	C₂²	1	2	yes	complemented
68	C₃×#387	C₂²	1	2	yes	complemented
69	C₃×#386	C₂²	1	2	yes	—
70	C₃×#386	C₂²	1	2	yes	—
71	C₃×#386	C₂²	1	2	yes	—
72	C₃×#386	C₂²	1	2	yes	—
73	C₃×#386	C₂²	1	1	yes	characteristic
74	C₃×#386	C₂²	1	1	yes	characteristic
75	C₃×#386	C₂²	1	2	yes	—
76	C₃×#386	C₂²	1	2	yes	—
77	C₃×#386	C₂²	1	2	yes	—
78	C₃×#386	C₂²	1	2	yes	—
79	C₃×#386	C₂²	1	2	yes	complemented
80	C₃×#386	C₂²	1	2	yes	complemented
81	C₃×#386	C₂²	1	2	yes	complemented
82	C₃×#385	C₂²	1	2	yes	—
83	C₃×#385	C₂²	1	2	yes	—
84	C₃×#385	C₂²	1	2	yes	—
85	C₃×#385	C₂²	1	2	yes	—
86	C₃×#385	C₂²	1	1	yes	characteristic
87	C₃×#385	C₂²	1	2	yes	complemented
88	C₃×#385	C₂²	1	1	yes	characteristic, complemented
89	C₃×#382	C₂²	1	1	yes	characteristic, complemented
90	C₃×#381	C₂²	1	1	yes	characteristic, complemented
91	C₃×#380	C₂²	1	2	yes	complemented
92	C₃×#379	C₂²	1	1	yes	characteristic
93	C₃×#379	C₂²	1	2	yes	—
94	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
95	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
96	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
97	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
98	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
99	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
103	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
104	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
105	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
106	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
107	C₃×#376	C₂²	1	1	yes	characteristic, complemented
108	C₂×C₃×#95	C₂²	1	2	yes	complemented
109	C₂×#560	C₂×C₃	1	1	yes	characteristic
110	#2375	C₂×C₃	1	1	yes	characteristic, complemented
111	#2375	C₂×C₃	1	2	yes	complemented
112	#2374	C₂×C₃	1	1	yes	characteristic, complemented
113	#2373	C₂×C₃	1	2	yes	complemented
114	#2366	C₂×C₃	1	1	yes	characteristic, complemented
115	#2364	C₂×C₃	1	2	yes	complemented
116	#2363	C₂×C₃	1	2	yes	complemented
117	#2361	C₂×C₃	1	2	yes	complemented
118	#2359	C₂×C₃	1	2	yes	complemented
119	#2335	C₂×C₃	1	2	yes	complemented
120	#2334	C₂×C₃	1	2	yes	complemented
121	#2333	C₂×C₃	1	2	yes	complemented
122	#2328	C₂×C₃	1	1	yes	characteristic, complemented
123	#2325	C₂×C₃	1	2	yes	complemented
124	#2324	C₂×C₃	1	2	yes	complemented
125	#2322	C₂×C₃	1	1	yes	characteristic, complemented
126	C₄×#120	C₂×C₃	1	1	yes	characteristic, complemented
127	C₄×#120	C₂×C₃	1	2	yes	complemented
128	C₂⁵×C₃	C₂³	1	1	yes	characteristic
129	C₂²×C₃×D₄	C₂³	1	2	yes	—
130	C₂²×C₃×D₄	C₂³	1	2	yes	—
131	C₂²×C₃×D₄	C₂³	1	2	yes	—
132	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
133	C₂²×C₃×D₄	C₂³	1	2	yes	—
134	C₂²×C₃×D₄	C₂³	1	2	yes	—
135	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
136	C₂³×C₃×C₄	—	4	4	no	—
137	C₂³×C₃×C₄	—	4	2	no	—
138	C₂³×C₃×C₄	C₂³	1	2	yes	—
139	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
140	C₂³×C₃×C₄	C₂³	1	2	yes	—
141	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
142	C₂³×C₃×C₄	C₂³	1	2	yes	—
143	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
144	C₂³×C₃×C₄	C₂³	1	2	yes	—
145	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
146	C₂³×C₃×C₄	C₂³	1	2	yes	—
147	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
148	C₃×#127	C₂×C₄	1	8	yes	complemented
149	C₃×#126	C₂×C₄	1	16	yes	complemented
150	C₃×#123	C₂×C₄	1	8	yes	complemented
151	C₃×#123	C₂×C₄	1	16	yes	complemented
152	C₃×#121	C₂×C₄	1	16	yes	complemented
153	C₃×#121	C₂×C₄	1	16	yes	complemented
154	C₃×#121	C₂×C₄	1	16	yes	complemented
155	C₃×#120	C₂×C₄	1	16	yes	complemented
156	C₃×#120	C₂×C₄	1	8	yes	complemented
157	C₃×C₄×D₄	—	4	2	no	—
158	C₃×C₄×D₄	—	4	4	no	—
159	C₃×C₄×D₄	—	4	2	no	—
160	C₃×C₄×D₄	—	4	4	no	—
161	C₃×C₄×D₄	—	4	4	no	—
162	C₃×C₄×D₄	—	4	4	no	—
163	C₃×C₄×D₄	—	4	4	no	—
164	C₃×#117	—	4	4	no	—
165	C₂×C₃×C₄⋊C₄	—	4	2	no	—
166	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
207	C₂×C₃×C₄²	C₂³	1	2	yes	—
208	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
209	C₂×C₃×C₄²	C₂³	1	2	yes	—
210	C₂×C₃×C₄²	C₂³	1	2	yes	—
211	C₂×C₃×C₄²	C₂³	1	2	yes	—
212	C₂×C₃×C₄²	C₂³	1	2	yes	—
213	C₂×C₃×C₄²	C₂³	1	2	yes	—
214	C₂×C₃×C₄²	C₂³	1	2	yes	—
215	C₂×C₃×C₄²	C₂³	1	2	yes	—
216	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
217	C₃×#95	C₂³	1	2	yes	—
218	C₃×#95	C₂³	1	2	yes	—
219	C₃×#95	C₂³	1	2	yes	—
220	C₃×#95	C₂³	1	2	yes	—
221	C₃×#95	C₂³	1	2	yes	—
222	C₃×#95	C₂³	1	2	yes	—
223	C₃×#95	C₂³	1	2	yes	—
224	C₃×#95	C₂³	1	2	yes	—
225	C₃×#95	C₂³	1	2	yes	—
226	C₃×#95	C₂³	1	2	yes	—
227	C₃×#95	C₂³	1	2	yes	—
228	C₃×#95	C₂³	1	2	yes	—
229	C₃×#95	C₂³	1	2	yes	—
230	C₃×#95	C₂³	1	2	yes	—
231	C₃×#95	C₂³	1	2	yes	—
232	C₃×#95	C₂³	1	2	yes	—
233	C₃×#95	C₂³	1	2	yes	—
234	C₃×#95	C₂³	1	2	yes	—
235	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
236	#560	C₃×C₄	1	16	yes	complemented
237	C₂×#127	C₂²×C₃	1	1	yes	characteristic
238	C₂×#126	C₂²×C₃	1	2	yes	—
239	C₂×#123	C₂²×C₃	1	1	yes	characteristic
240	C₂×#123	C₂²×C₃	1	2	yes	—
241	C₂×#121	C₂²×C₃	1	2	yes	—
242	C₂×#121	C₂²×C₃	1	2	yes	—
243	C₂×#121	C₂²×C₃	1	2	yes	—
244	C₂×#120	C₂²×C₃	1	1	yes	characteristic
245	C₂×#120	C₂²×C₃	1	2	yes	—
246	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
247	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
248	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
249	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
250	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
251	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
252	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
253	C₂×#117	C₂²×C₃	1	2	yes	complemented
254	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
255	#390	C₂²×C₃	1	2	yes	—
256	#390	C₂²×C₃	1	2	yes	—
257	#390	C₂²×C₃	1	1	yes	characteristic
258	#390	C₂²×C₃	1	2	yes	—
259	#390	C₂²×C₃	1	2	yes	—
260	#390	C₂²×C₃	1	1	yes	characteristic, complemented
261	#390	C₂²×C₃	1	2	yes	complemented
262	#389	C₂²×C₃	1	2	yes	complemented
263	#389	C₂²×C₃	1	2	yes	complemented
264	#389	C₂²×C₃	1	2	yes	complemented
265	#388	C₂²×C₃	1	2	yes	—
266	#388	C₂²×C₃	1	2	yes	—
267	#388	C₂²×C₃	1	2	yes	—
268	#388	C₂²×C₃	1	2	yes	—
269	#388	C₂²×C₃	1	2	yes	—
270	#388	C₂²×C₃	1	2	yes	—
271	#388	C₂²×C₃	1	2	yes	—
272	#388	C₂²×C₃	1	2	yes	—
273	#388	C₂²×C₃	1	2	yes	—
274	#388	C₂²×C₃	1	2	yes	complemented
275	#388	C₂²×C₃	1	2	yes	complemented
276	#388	C₂²×C₃	1	2	yes	complemented
277	#387	C₂²×C₃	1	2	yes	complemented
278	#387	C₂²×C₃	1	2	yes	complemented
279	#387	C₂²×C₃	1	2	yes	complemented
280	#387	C₂²×C₃	1	2	yes	complemented
281	#387	C₂²×C₃	1	2	yes	complemented
282	#387	C₂²×C₃	1	2	yes	complemented
283	#386	C₂²×C₃	1	1	yes	characteristic
284	#386	C₂²×C₃	1	2	yes	—
285	#386	C₂²×C₃	1	2	yes	—
286	#386	C₂²×C₃	1	2	yes	—
287	#386	C₂²×C₃	1	2	yes	—
288	#386	C₂²×C₃	1	2	yes	—
289	#386	C₂²×C₃	1	2	yes	—
290	#386	C₂²×C₃	1	2	yes	—
291	#386	C₂²×C₃	1	2	yes	—
292	#386	C₂²×C₃	1	1	yes	characteristic
293	#386	C₂²×C₃	1	2	yes	complemented
294	#386	C₂²×C₃	1	2	yes	complemented
295	#386	C₂²×C₃	1	2	yes	complemented
296	#385	C₂²×C₃	1	2	yes	—
297	#385	C₂²×C₃	1	2	yes	—
298	#385	C₂²×C₃	1	2	yes	—
299	#385	C₂²×C₃	1	1	yes	characteristic
300	#385	C₂²×C₃	1	2	yes	—
301	#385	C₂²×C₃	1	1	yes	characteristic, complemented
302	#385	C₂²×C₃	1	2	yes	complemented
303	#382	C₂²×C₃	1	1	yes	characteristic, complemented
304	#381	C₂²×C₃	1	1	yes	characteristic, complemented
305	#380	C₂²×C₃	1	2	yes	complemented
306	#379	C₂²×C₃	1	2	yes	—
307	#379	C₂²×C₃	1	1	yes	characteristic
308	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
309	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
310	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
311	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
312	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
313	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
314	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
315	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
316	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
317	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
318	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
319	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
320	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
321	#376	C₂²×C₃	1	1	yes	characteristic, complemented
322	C₂×#95	C₂²×C₃	1	2	yes	complemented
323	C₂⁴×C₃	—	4	1	no	—
324	C₂⁴×C₃	—	4	2	no	—
325	C₂⁴×C₃	—	4	2	no	—
326	C₂⁴×C₃	—	4	1	no	—
327	C₂⁴×C₃	C₂²×C₄	1	4	yes	—
328	C₂⁴×C₃	C₂⁴	1	2	yes	—
329	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
330	C₂⁴×C₃	C₂⁴	1	2	yes	—
331	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
332	C₂×C₃×D₄	—	4	2	no	—
333	C₂×C₃×D₄	—	4	1	no	—
334	C₂×C₃×D₄	—	4	1	no	—
335	C₂×C₃×D₄	—	4	2	no	—
336	C₂×C₃×D₄	—	4	2	no	—
337	C₂×C₃×D₄	—	4	2	no	—
338	C₂×C₃×D₄	—	4	2	no	—
339	C₂×C₃×D₄	—	4	2	no	—
340	C₂×C₃×D₄	—	4	2	no	—
341	C₂×C₃×D₄	—	4	1	no	—
342	C₂×C₃×D₄	—	4	1	no	—
343	C₂×C₃×D₄	—	4	2	no	—
344	C₂×C₃×D₄	—	4	2	no	—
345	C₂×C₃×D₄	—	4	2	no	—
346	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
347	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
348	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
349	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
350	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
351	C₂×C₃×D₄	C₂²×C₄	1	8	yes	complemented
352	C₂×C₃×D₄	C₂²×C₄	1	4	yes	complemented
353	C₂²×C₃×C₄	—	2	4	no	—
354	C₂²×C₃×C₄	—	2	4	no	—
355	C₂²×C₃×C₄	—	2	4	no	—
356	C₂²×C₃×C₄	—	2	4	no	—
357	C₂²×C₃×C₄	—	2	2	no	—
358	C₂²×C₃×C₄	—	2	2	no	—
359	C₂²×C₃×C₄	—	2	4	no	—
360	C₂²×C₃×C₄	—	4	1	no	—
361	C₂²×C₃×C₄	—	4	2	no	—
362	C₂²×C₃×C₄	—	4	2	no	—
363	C₂²×C₃×C₄	—	4	1	no	—
364	C₂²×C₃×C₄	—	4	2	no	—
365	C₂²×C₃×C₄	—	4	2	no	—
366	C₂²×C₃×C₄	—	4	2	no	—
367	C₂²×C₃×C₄	—	4	1	no	—
368	C₂²×C₃×C₄	—	4	2	no	—
369	C₂²×C₃×C₄	—	4	1	no	—
370	C₂²×C₃×C₄	—	4	2	no	—
371	C₂²×C₃×C₄	—	4	2	no	—
372	C₂²×C₃×C₄	—	4	2	no	—
373	C₂²×C₃×C₄	—	4	2	no	—
374	C₂²×C₃×C₄	—	4	2	no	—
375	C₂²×C₃×C₄	—	4	2	no	—
376	C₂²×C₃×C₄	—	4	2	no	—
377	C₂²×C₃×C₄	—	4	16	no	—
378	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	complemented
379	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	complemented
380	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
381	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
382	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
383	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
384	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
385	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
386	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
387	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
388	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
389	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
390	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
391	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
392	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
393	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
394	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
395	C₃×C₄⋊C₄	—	2	4	no	—
396	C₃×C₄⋊C₄	—	2	4	no	—
397	C₃×C₄⋊C₄	—	2	4	no	—
398	C₃×C₄⋊C₄	—	4	2	no	—
399	C₃×C₄⋊C₄	—	4	2	no	—
400	C₃×C₄⋊C₄	—	4	2	no	—
401	C₃×C₄⋊C₄	—	4	2	no	—
402	C₃×C₄⋊C₄	—	4	2	no	—
403	C₃×C₄⋊C₄	—	4	1	no	—
404	C₃×C₄⋊C₄	—	4	1	no	—
405	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	complemented
406	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	complemented
407	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	complemented
408	C₃×C₂²⋊C₄	—	2	4	no	—
409	C₃×C₂²⋊C₄	—	2	4	no	—
410	C₃×C₂²⋊C₄	—	2	4	no	—
411	C₃×C₂²⋊C₄	—	4	2	no	—
412	C₃×C₂²⋊C₄	—	4	1	no	—
413	C₃×C₂²⋊C₄	—	4	2	no	—
414	C₃×C₂²⋊C₄	—	4	2	no	—
415	C₃×C₂²⋊C₄	—	4	2	no	—
416	C₃×C₂²⋊C₄	—	4	1	no	—
417	C₃×C₂²⋊C₄	—	4	2	no	—
418	C₃×C₂²⋊C₄	—	4	2	no	—
419	C₃×C₂²⋊C₄	—	4	2	no	—
420	C₃×C₂²⋊C₄	—	4	2	no	—
421	C₃×C₂²⋊C₄	—	4	2	no	—
422	C₃×C₂²⋊C₄	—	4	1	no	—
423	C₃×C₂²⋊C₄	—	4	1	no	—
424	C₃×C₂²⋊C₄	—	4	2	no	—
425	C₃×C₂²⋊C₄	—	4	2	no	—
426	C₃×C₂²⋊C₄	—	4	2	no	—
427	C₃×C₂²⋊C₄	—	4	2	no	—
428	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
429	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
430	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
431	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
432	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
433	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	complemented
434	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	complemented
435	C₃×C₄²	—	2	4	no	—
436	C₃×C₄²	—	2	2	no	—
437	C₃×C₄²	—	4	2	no	—
438	C₃×C₄²	—	4	2	no	—
439	C₃×C₄²	—	4	1	no	—
440	C₃×C₄²	—	4	2	no	—
441	C₃×C₄²	—	4	2	no	—
442	C₃×C₄²	—	4	2	no	—
443	C₃×C₄²	—	4	2	no	—
444	C₃×C₄²	—	4	2	no	—
445	C₃×C₄²	C₂²×C₄	1	4	yes	complemented
446	C₂⁵	C₂³×C₃	1	1	yes	characteristic
447	C₂²×D₄	C₂³×C₃	1	2	yes	—
448	C₂²×D₄	C₂³×C₃	1	2	yes	—
449	C₂²×D₄	C₂³×C₃	1	2	yes	—
450	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
451	C₂²×D₄	C₂³×C₃	1	2	yes	—
452	C₂²×D₄	C₂³×C₃	1	2	yes	—
453	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
454	C₂³×C₄	—	4	4	no	—
455	C₂³×C₄	—	4	2	no	—
456	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₃	1	2	yes	—
458	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₃	1	2	yes	—
460	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
461	C₂³×C₄	C₂³×C₃	1	2	yes	—
462	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
463	C₂³×C₄	C₂³×C₃	1	2	yes	—
464	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₃	1	2	yes	—
466	#127	C₂×C₃×C₄	1	8	yes	complemented
467	#126	C₂×C₃×C₄	1	16	yes	complemented
468	#123	C₂×C₃×C₄	1	8	yes	complemented
469	#123	C₂×C₃×C₄	1	16	yes	complemented
470	#121	C₂×C₃×C₄	1	16	yes	complemented
471	#121	C₂×C₃×C₄	1	16	yes	complemented
472	#121	C₂×C₃×C₄	1	16	yes	complemented
473	#120	C₂×C₃×C₄	1	8	yes	complemented
474	#120	C₂×C₃×C₄	1	16	yes	complemented
475	C₄×D₄	—	4	2	no	—
476	C₄×D₄	—	4	4	no	—
477	C₄×D₄	—	4	2	no	—
478	C₄×D₄	—	4	4	no	—
479	C₄×D₄	—	4	4	no	—
480	C₄×D₄	—	4	4	no	—
481	C₄×D₄	—	4	4	no	—
482	#117	—	4	4	no	—
483	C₂×C₄⋊C₄	—	4	2	no	—
484	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
502	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
508	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
513	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
515	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
522	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
524	C₂×C₄²	C₂³×C₃	1	2	yes	—
525	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₃	1	2	yes	—
527	C₂×C₄²	C₂³×C₃	1	2	yes	—
528	C₂×C₄²	C₂³×C₃	1	2	yes	—
529	C₂×C₄²	C₂³×C₃	1	2	yes	—
530	C₂×C₄²	C₂³×C₃	1	2	yes	—
531	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₃	1	2	yes	—
533	C₂×C₄²	C₂³×C₃	1	2	yes	—
534	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
535	#95	C₂³×C₃	1	2	yes	—
536	#95	C₂³×C₃	1	2	yes	—
537	#95	C₂³×C₃	1	2	yes	—
538	#95	C₂³×C₃	1	2	yes	—
539	#95	C₂³×C₃	1	2	yes	—
540	#95	C₂³×C₃	1	2	yes	—
541	#95	C₂³×C₃	1	2	yes	—
542	#95	C₂³×C₃	1	2	yes	—
543	#95	C₂³×C₃	1	2	yes	—
544	#95	C₂³×C₃	1	2	yes	—
545	#95	C₂³×C₃	1	2	yes	—
546	#95	C₂³×C₃	1	2	yes	—
547	#95	C₂³×C₃	1	2	yes	—
548	#95	C₂³×C₃	1	2	yes	—
549	#95	C₂³×C₃	1	2	yes	—
550	#95	C₂³×C₃	1	2	yes	—
551	#95	C₂³×C₃	1	2	yes	—
552	#95	C₂³×C₃	1	2	yes	—
553	C₂³×C₃	—	2	2	no	—
554	C₂³×C₃	—	2	2	no	—
555	C₂³×C₃	—	2	2	no	—
556	C₂³×C₃	—	2	2	no	—
557	C₂³×C₃	—	2	1	no	—
558	C₂³×C₃	—	2	2	no	—
559	C₂³×C₃	—	2	2	no	—
560	C₂³×C₃	—	2	2	no	—
561	C₂³×C₃	—	2	1	no	—
562	C₂³×C₃	—	2	2	no	—
563	C₂³×C₃	—	2	1	no	—
564	C₂³×C₃	—	2	2	no	—
565	C₂³×C₃	—	2	2	no	—
566	C₂³×C₃	—	2	2	no	—
567	C₂³×C₃	—	2	1	no	—
568	C₂³×C₃	—	2	2	no	—
569	C₂³×C₃	—	2	2	no	—
570	C₂³×C₃	—	2	2	no	—
571	C₂³×C₃	—	2	2	no	—
572	C₂³×C₃	—	2	2	no	—
573	C₂³×C₃	—	4	8	no	—
574	C₂³×C₃	—	4	4	no	—
575	C₂³×C₃	—	4	4	no	—
576	C₂³×C₃	—	4	8	no	—
577	C₂³×C₃	—	4	4	no	—
578	C₂³×C₃	C₂³×C₄	1	4	yes	—
579	C₂³×C₃	C₂³×C₄	1	2	yes	—
580	C₂³×C₃	C₂³×C₄	1	4	yes	—
581	C₂³×C₃	C₂³×C₄	1	2	yes	—
582	C₂³×C₃	C₂⁵	1	1	yes	characteristic
583	C₃×D₄	—	4	8	no	—
584	C₃×D₄	—	4	8	no	—
585	C₃×D₄	—	4	8	no	—
586	C₃×D₄	—	4	4	no	—
587	C₃×D₄	—	4	8	no	—
588	C₃×D₄	—	4	4	no	—
589	C₃×D₄	—	4	8	no	—
590	C₂×C₃×C₄	—	2	2	no	—
591	C₂×C₃×C₄	—	2	1	no	—
592	C₂×C₃×C₄	—	2	2	no	—
593	C₂×C₃×C₄	—	2	2	no	—
594	C₂×C₃×C₄	—	2	2	no	—
595	C₂×C₃×C₄	—	2	2	no	—
596	C₂×C₃×C₄	—	2	2	no	—
597	C₂×C₃×C₄	—	2	2	no	—
598	C₂×C₃×C₄	—	2	2	no	—
599	C₂×C₃×C₄	—	2	2	no	—
600	C₂×C₃×C₄	—	2	1	no	—
601	C₂×C₃×C₄	—	2	2	no	—
602	C₂×C₃×C₄	—	2	2	no	—
603	C₂×C₃×C₄	—	2	2	no	—
604	C₂×C₃×C₄	—	2	1	no	—
605	C₂×C₃×C₄	—	2	2	no	—
606	C₂×C₃×C₄	—	2	2	no	—
607	C₂×C₃×C₄	—	2	2	no	—
608	C₂×C₃×C₄	—	2	2	no	—
609	C₂×C₃×C₄	—	2	2	no	—
610	C₂×C₃×C₄	—	2	2	no	—
611	C₂×C₃×C₄	—	2	2	no	—
612	C₂×C₃×C₄	—	2	1	no	—
613	C₂×C₃×C₄	—	2	2	no	—
614	C₂×C₃×C₄	—	2	1	no	—
615	C₂×C₃×C₄	—	2	2	no	—
616	C₂×C₃×C₄	—	2	2	no	—
617	C₂×C₃×C₄	—	2	2	no	—
618	C₂×C₃×C₄	—	2	2	no	—
619	C₂×C₃×C₄	—	2	2	no	—
620	C₂×C₃×C₄	—	2	2	no	—
621	C₂×C₃×C₄	—	2	2	no	—
622	C₂×C₃×C₄	—	2	2	no	—
623	C₂×C₃×C₄	—	2	2	no	—
624	C₂×C₃×C₄	—	4	4	no	—
625	C₂×C₃×C₄	—	4	8	no	—
626	C₂×C₃×C₄	—	4	8	no	—
627	C₂×C₃×C₄	—	4	4	no	—
628	C₂×C₃×C₄	—	4	4	no	—
629	C₂×C₃×C₄	—	4	8	no	—
630	C₂×C₃×C₄	—	8	2	no	—
631	C₂×C₃×C₄	—	8	4	no	—
632	C₂×C₃×C₄	—	8	2	no	—
633	C₂×C₃×C₄	—	8	4	no	—
634	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
635	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
636	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
637	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
638	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
639	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
640	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
641	C₂⁴	—	4	2	no	—
642	C₂⁴	—	4	1	no	—
643	C₂⁴	—	4	1	no	—
644	C₂⁴	—	4	2	no	—
645	C₂⁴	C₂²×C₃×C₄	1	4	yes	—
646	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
647	C₂⁴	C₂⁴×C₃	1	2	yes	—
648	C₂⁴	C₂⁴×C₃	1	2	yes	—
649	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
650	C₂×D₄	—	4	2	no	—
651	C₂×D₄	—	4	1	no	—
652	C₂×D₄	—	4	1	no	—
653	C₂×D₄	—	4	2	no	—
654	C₂×D₄	—	4	2	no	—
655	C₂×D₄	—	4	2	no	—
656	C₂×D₄	—	4	2	no	—
657	C₂×D₄	—	4	2	no	—
658	C₂×D₄	—	4	2	no	—
659	C₂×D₄	—	4	1	no	—
660	C₂×D₄	—	4	1	no	—
661	C₂×D₄	—	4	2	no	—
662	C₂×D₄	—	4	2	no	—
663	C₂×D₄	—	4	2	no	—
664	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
665	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
666	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
667	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
668	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
669	C₂×D₄	C₂²×C₃×C₄	1	4	yes	complemented
670	C₂×D₄	C₂²×C₃×C₄	1	8	yes	complemented
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	2	4	no	—
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	2	4	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	4	no	—
678	C₂²×C₄	—	4	1	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	—	4	2	no	—
681	C₂²×C₄	—	4	1	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	—	4	2	no	—
684	C₂²×C₄	—	4	2	no	—
685	C₂²×C₄	—	4	1	no	—
686	C₂²×C₄	—	4	2	no	—
687	C₂²×C₄	—	4	1	no	—
688	C₂²×C₄	—	4	2	no	—
689	C₂²×C₄	—	4	2	no	—
690	C₂²×C₄	—	4	2	no	—
691	C₂²×C₄	—	4	2	no	—
692	C₂²×C₄	—	4	2	no	—
693	C₂²×C₄	—	4	2	no	—
694	C₂²×C₄	—	4	2	no	—
695	C₂²×C₄	—	4	16	no	—
696	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	complemented
697	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	complemented
698	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	4	2	no	—
717	C₄⋊C₄	—	4	2	no	—
718	C₄⋊C₄	—	4	2	no	—
719	C₄⋊C₄	—	4	1	no	—
720	C₄⋊C₄	—	4	1	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₄⋊C₄	—	4	2	no	—
723	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	complemented
724	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	complemented
725	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	complemented
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	4	2	no	—
730	C₂²⋊C₄	—	4	2	no	—
731	C₂²⋊C₄	—	4	2	no	—
732	C₂²⋊C₄	—	4	1	no	—
733	C₂²⋊C₄	—	4	1	no	—
734	C₂²⋊C₄	—	4	2	no	—
735	C₂²⋊C₄	—	4	2	no	—
736	C₂²⋊C₄	—	4	2	no	—
737	C₂²⋊C₄	—	4	2	no	—
738	C₂²⋊C₄	—	4	2	no	—
739	C₂²⋊C₄	—	4	1	no	—
740	C₂²⋊C₄	—	4	2	no	—
741	C₂²⋊C₄	—	4	2	no	—
742	C₂²⋊C₄	—	4	2	no	—
743	C₂²⋊C₄	—	4	1	no	—
744	C₂²⋊C₄	—	4	2	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
747	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
748	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
749	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
750	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
751	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	complemented
752	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	complemented
753	C₄²	—	2	4	no	—
754	C₄²	—	2	2	no	—
755	C₄²	—	4	2	no	—
756	C₄²	—	4	2	no	—
757	C₄²	—	4	2	no	—
758	C₄²	—	4	2	no	—
759	C₄²	—	4	2	no	—
760	C₄²	—	4	2	no	—
761	C₄²	—	4	2	no	—
762	C₄²	—	4	1	no	—
763	C₄²	C₂²×C₃×C₄	1	4	yes	complemented
764	C₂²×C₃	—	2	4	no	—
765	C₂²×C₃	—	2	2	no	—
766	C₂²×C₃	—	2	4	no	—
767	C₂²×C₃	—	2	4	no	—
768	C₂²×C₃	—	2	4	no	—
769	C₂²×C₃	—	2	4	no	—
770	C₂²×C₃	—	2	4	no	—
771	C₂²×C₃	—	2	4	no	—
772	C₂²×C₃	—	2	4	no	—
773	C₂²×C₃	—	2	2	no	—
774	C₂²×C₃	—	4	16	no	—
775	C₂²×C₃	—	4	2	no	—
776	C₂²×C₃	—	4	1	no	—
777	C₂²×C₃	—	4	1	no	—
778	C₂²×C₃	—	4	2	no	—
779	C₂²×C₃	—	4	2	no	—
780	C₂²×C₃	—	4	2	no	—
781	C₂²×C₃	—	4	2	no	—
782	C₂²×C₃	—	4	2	no	—
783	C₂²×C₃	—	4	2	no	—
784	C₂²×C₃	—	4	2	no	—
785	C₂²×C₃	—	4	2	no	—
786	C₂²×C₃	—	4	1	no	—
787	C₂²×C₃	—	4	1	no	—
788	C₂²×C₃	—	4	2	no	—
789	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
790	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
791	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
792	C₂²×C₃	#585	1	1	yes	characteristic
793	C₂²×C₃	#585	1	2	yes	—
794	C₃×C₄	—	2	4	no	—
795	C₃×C₄	—	2	4	no	—
796	C₃×C₄	—	2	4	no	—
797	C₃×C₄	—	2	2	no	—
798	C₃×C₄	—	2	4	no	—
799	C₃×C₄	—	2	2	no	—
800	C₃×C₄	—	2	4	no	—
801	C₃×C₄	—	4	1	no	—
802	C₃×C₄	—	4	1	no	—
803	C₃×C₄	—	4	2	no	—
804	C₃×C₄	—	4	2	no	—
805	C₃×C₄	—	4	2	no	—
806	C₃×C₄	—	4	2	no	—
807	C₃×C₄	—	4	2	no	—
808	C₃×C₄	—	4	1	no	—
809	C₂³	—	2	2	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	1	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	1	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	1	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	2	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	4	8	no	—
830	C₂³	—	4	4	no	—
831	C₂³	—	4	4	no	—
832	C₂³	—	4	8	no	—
833	C₂³	—	4	4	no	—
834	C₂³	C₂³×C₃×C₄	1	4	yes	—
835	C₂³	C₂³×C₃×C₄	1	2	yes	—
836	C₂³	C₂³×C₃×C₄	1	4	yes	—
837	C₂³	C₂³×C₃×C₄	1	2	yes	—
838	C₂³	C₂⁵×C₃	1	1	yes	characteristic
839	D₄	—	4	8	no	—
840	D₄	—	4	8	no	—
841	D₄	—	4	8	no	—
842	D₄	—	4	4	no	—
843	D₄	—	4	8	no	—
844	D₄	—	4	4	no	—
845	D₄	—	4	8	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	4	4	no	—
881	C₂×C₄	—	4	8	no	—
882	C₂×C₄	—	4	8	no	—
883	C₂×C₄	—	4	4	no	—
884	C₂×C₄	—	4	4	no	—
885	C₂×C₄	—	4	8	no	—
886	C₂×C₄	—	8	4	no	—
887	C₂×C₄	—	8	2	no	—
888	C₂×C₄	—	8	2	no	—
889	C₂×C₄	—	8	4	no	—
890	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
891	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
892	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
893	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
894	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
895	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
896	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
897	C₂×C₃	—	4	2	no	—
898	C₂×C₃	—	4	4	no	—
899	C₂×C₃	—	4	4	no	—
900	C₂×C₃	—	4	2	no	—
901	C₂×C₃	C₄×H(5,𝔽₂)	1	2	yes	—
902	C₂×C₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
903	C₂×C₃	#3532	1	1	yes	characteristic
904	C₂×C₃	#3539	1	2	yes	—
905	C₂×C₃	#3540	1	1	yes	characteristic
906	C₂²	—	2	4	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	2	4	no	—
909	C₂²	—	2	4	no	—
910	C₂²	—	2	4	no	—
911	C₂²	—	2	4	no	—
912	C₂²	—	2	4	no	—
913	C₂²	—	2	4	no	—
914	C₂²	—	2	4	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	4	16	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	4	1	no	—
919	C₂²	—	4	1	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	4	1	no	—
929	C₂²	—	4	2	no	—
930	C₂²	—	4	1	no	—
931	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
932	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
933	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
934	C₂²	C₃×#585	1	1	yes	characteristic
935	C₂²	C₃×#585	1	2	yes	—
936	C₄	—	2	4	no	—
937	C₄	—	2	4	no	—
938	C₄	—	2	4	no	—
939	C₄	—	2	2	no	—
940	C₄	—	2	4	no	—
941	C₄	—	2	2	no	—
942	C₄	—	2	4	no	—
943	C₄	—	4	1	no	—
944	C₄	—	4	2	no	—
945	C₄	—	4	1	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	1	no	—
950	C₄	—	4	2	no	—
951	C₃	#34511	1	1	yes	characteristic, direct product factor, Sylow
952	C₂	—	4	4	no	—
953	C₂	—	4	2	no	—
954	C₂	—	4	2	no	—
955	C₂	—	4	4	no	—
956	C₂	C₃×C₄×H(5,𝔽₂)	1	2	yes	—
957	C₂	C₃×C₄×H(5,𝔽₂)	1	1	yes	characteristic
958	C₂	C₃×#3532	1	1	yes	characteristic
959	C₂	C₃×#3539	1	2	yes	—
960	C₂	C₃×#3540	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#560	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#2375	C₂	semidirect
3. C₃×#2375	C₂	semidirect
4. C₃×#2374	C₂	semidirect
5. C₃×#2373	C₂	semidirect
6. C₃×#2366	C₂	semidirect
7. C₃×#2364	C₂	semidirect
8. C₃×#2363	C₂	semidirect
9. C₃×#2361	C₂	semidirect
10. C₃×#2359	C₂	semidirect
11. C₃×#2335	C₂	semidirect
12. C₃×#2334	C₂	semidirect
13. C₃×#2333	C₂	semidirect
14. C₃×#2328	C₂	semidirect
15. C₃×#2325	C₂	semidirect
16. C₃×#2324	C₂	semidirect
17. C₃×#2322	C₂	semidirect
18. C₃×C₄×#120	C₂	semidirect
19. C₃×C₄×#120	C₂	semidirect
20. #34511	C₃	direct (N × H)
22. C₃×#560	C₄	semidirect
37. C₂×C₃×C₄×D₄	C₂²	semidirect
38. C₂×C₃×C₄×D₄	C₂²	semidirect
39. C₂×C₃×#117	C₂²	semidirect
40. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
46. C₃×#390	C₂²	semidirect
47. C₃×#390	C₂²	semidirect
48. C₃×#389	C₂²	semidirect
49. C₃×#389	C₂²	semidirect
50. C₃×#389	C₂²	semidirect
60. C₃×#388	C₂²	semidirect
61. C₃×#388	C₂²	semidirect
62. C₃×#388	C₂²	semidirect
63. C₃×#387	C₂²	semidirect
64. C₃×#387	C₂²	semidirect
65. C₃×#387	C₂²	semidirect
66. C₃×#387	C₂²	semidirect
67. C₃×#387	C₂²	semidirect
68. C₃×#387	C₂²	semidirect
79. C₃×#386	C₂²	semidirect
80. C₃×#386	C₂²	semidirect
81. C₃×#386	C₂²	semidirect
87. C₃×#385	C₂²	semidirect
88. C₃×#385	C₂²	semidirect
89. C₃×#382	C₂²	semidirect
90. C₃×#381	C₂²	semidirect
91. C₃×#380	C₂²	semidirect
94. C₃×C₄×C₄⋊C₄	C₂²	semidirect
95. C₃×C₄×C₄⋊C₄	C₂²	semidirect
96. C₃×C₄×C₄⋊C₄	C₂²	semidirect
97. C₃×C₄×C₄⋊C₄	C₂²	semidirect
103. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
104. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
105. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
106. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
107. C₃×#376	C₂²	semidirect
108. C₂×C₃×#95	C₂²	semidirect
110. #2375	C₂×C₃	semidirect
111. #2375	C₂×C₃	semidirect
112. #2374	C₂×C₃	semidirect
113. #2373	C₂×C₃	semidirect
114. #2366	C₂×C₃	semidirect
115. #2364	C₂×C₃	semidirect
116. #2363	C₂×C₃	semidirect
117. #2361	C₂×C₃	semidirect
118. #2359	C₂×C₃	semidirect
119. #2335	C₂×C₃	semidirect
120. #2334	C₂×C₃	semidirect
121. #2333	C₂×C₃	semidirect
122. #2328	C₂×C₃	semidirect
123. #2325	C₂×C₃	semidirect
124. #2324	C₂×C₃	semidirect
125. #2322	C₂×C₃	semidirect
126. C₄×#120	C₂×C₃	semidirect
127. C₄×#120	C₂×C₃	semidirect
148. C₃×#127	C₂×C₄	semidirect
149. C₃×#126	C₂×C₄	semidirect
150. C₃×#123	C₂×C₄	semidirect
151. C₃×#123	C₂×C₄	semidirect
152. C₃×#121	C₂×C₄	semidirect
153. C₃×#121	C₂×C₄	semidirect
154. C₃×#121	C₂×C₄	semidirect
155. C₃×#120	C₂×C₄	semidirect
156. C₃×#120	C₂×C₄	semidirect
236. #560	C₃×C₄	semidirect
251. C₂×C₄×D₄	C₂²×C₃	semidirect
252. C₂×C₄×D₄	C₂²×C₃	semidirect
253. C₂×#117	C₂²×C₃	semidirect
254. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
260. #390	C₂²×C₃	semidirect
261. #390	C₂²×C₃	semidirect
262. #389	C₂²×C₃	semidirect
263. #389	C₂²×C₃	semidirect
264. #389	C₂²×C₃	semidirect
274. #388	C₂²×C₃	semidirect
275. #388	C₂²×C₃	semidirect
276. #388	C₂²×C₃	semidirect
277. #387	C₂²×C₃	semidirect
278. #387	C₂²×C₃	semidirect
279. #387	C₂²×C₃	semidirect
280. #387	C₂²×C₃	semidirect
281. #387	C₂²×C₃	semidirect
282. #387	C₂²×C₃	semidirect
293. #386	C₂²×C₃	semidirect
294. #386	C₂²×C₃	semidirect
295. #386	C₂²×C₃	semidirect
301. #385	C₂²×C₃	semidirect
302. #385	C₂²×C₃	semidirect
303. #382	C₂²×C₃	semidirect
304. #381	C₂²×C₃	semidirect
305. #380	C₂²×C₃	semidirect
308. C₄×C₄⋊C₄	C₂²×C₃	semidirect
309. C₄×C₄⋊C₄	C₂²×C₃	semidirect
310. C₄×C₄⋊C₄	C₂²×C₃	semidirect
311. C₄×C₄⋊C₄	C₂²×C₃	semidirect
317. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
318. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
319. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
320. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
321. #376	C₂²×C₃	semidirect
322. C₂×#95	C₂²×C₃	semidirect
351. C₂×C₃×D₄	C₂²×C₄	semidirect
352. C₂×C₃×D₄	C₂²×C₄	semidirect
378. C₂²×C₃×C₄	C₂²×C₄	semidirect
379. C₂²×C₃×C₄	C₂²×C₄	semidirect
405. C₃×C₄⋊C₄	C₂²×C₄	semidirect
406. C₃×C₄⋊C₄	C₂²×C₄	semidirect
407. C₃×C₄⋊C₄	C₂²×C₄	semidirect
433. C₃×C₂²⋊C₄	C₂²×C₄	semidirect
434. C₃×C₂²⋊C₄	C₂²×C₄	semidirect
445. C₃×C₄²	C₂²×C₄	semidirect
466. #127	C₂×C₃×C₄	semidirect
467. #126	C₂×C₃×C₄	semidirect
468. #123	C₂×C₃×C₄	semidirect
469. #123	C₂×C₃×C₄	semidirect
470. #121	C₂×C₃×C₄	semidirect
471. #121	C₂×C₃×C₄	semidirect
472. #121	C₂×C₃×C₄	semidirect
473. #120	C₂×C₃×C₄	semidirect
474. #120	C₂×C₃×C₄	semidirect
669. C₂×D₄	C₂²×C₃×C₄	semidirect
670. C₂×D₄	C₂²×C₃×C₄	semidirect
696. C₂²×C₄	C₂²×C₃×C₄	semidirect
697. C₂²×C₄	C₂²×C₃×C₄	semidirect
723. C₄⋊C₄	C₂²×C₃×C₄	semidirect
724. C₄⋊C₄	C₂²×C₃×C₄	semidirect
725. C₄⋊C₄	C₂²×C₃×C₄	semidirect
751. C₂²⋊C₄	C₂²×C₃×C₄	semidirect
752. C₂²⋊C₄	C₂²×C₃×C₄	semidirect
763. C₄²	C₂²×C₃×C₄	semidirect
951. C₃	#34511	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×#560	2
C₃×#2375	2
C₃×#2374	2
C₃×#2373	2
C₃×#2366	2
C₃×#2364	2
C₃×#2363	2
C₃×#2361	2
C₃×#2359	2
C₃×#2335	2
C₃×#2334	2
C₃×#2333	2
C₃×#2328	2
C₃×#2325	2
C₃×#2324	2
C₃×#2322	2
C₃×C₄×#120	2
#34511	3

Subgroups — C3×#34511 #10653118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#34511 #10653118