Subgroups — C₃×#35728 #10654335

Order 768.

3614 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#546	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2619	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2618	C₂	1	2	yes	maximal, complemented
6	C₃×#2548	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2543	C₂	1	2	yes	maximal, complemented
8	C₃×#2536	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2426	C₂	1	2	yes	maximal, complemented
10	C₃×#2424	C₂	1	4	yes	maximal, complemented
11	C₃×#2416	C₂	1	2	yes	maximal, complemented
12	C₃×#2411	C₂	1	4	yes	maximal, complemented
13	C₃×#2408	C₂	1	2	yes	maximal, complemented
14	C₃×#2392	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×#394	C₂	1	2	yes	maximal, complemented
16	C₃×#2349	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×D₄×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
18	#35728	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
20	C₂³×C₃×D₄	C₂²	1	2	yes	—
21	C₂³×C₃×D₄	C₂²	1	2	yes	—
22	C₃×#546	—	2	16	no	—
23	C₃×D₄²	—	2	8	no	—
24	C₂×C₃×#127	C₂²	1	1	yes	characteristic
25	C₂×C₃×#124	C₂²	1	2	yes	complemented
26	C₂×C₃×#123	C₂²	1	4	yes	complemented
27	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₂×C₃×#121	C₂²	1	2	yes	—
29	C₂×C₃×#121	C₂²	1	2	yes	—
30	C₂×C₃×#121	C₂²	1	2	yes	complemented
31	C₂×C₃×#121	C₂²	1	4	yes	complemented
32	C₂×C₃×#121	C₂²	1	4	yes	complemented
33	C₂×C₃×#120	C₂²	1	4	yes	—
34	C₂×C₃×#120	C₂²	1	4	yes	complemented
35	C₃×#520	—	2	8	no	—
36	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
41	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
43	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
44	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
45	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₃×#117	C₂²	1	2	yes	complemented
47	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
48	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₂²×C₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
50	C₂²×C₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
51	C₃×#398	C₂²	1	1	yes	characteristic, complemented
52	C₃×#398	C₂²	1	2	yes	complemented
53	C₃×#397	C₂²	1	1	yes	characteristic, complemented
54	C₃×#396	C₂²	1	4	yes	complemented
55	C₃×#396	C₂²	1	4	yes	complemented
56	C₃×#396	C₂²	1	2	yes	complemented
57	C₃×#394	C₂²	1	1	yes	characteristic
58	C₃×#394	C₂²	1	2	yes	—
59	C₃×#394	C₂²	1	2	yes	complemented
60	C₃×#394	C₂²	1	2	yes	complemented
61	C₃×#394	C₂²	1	2	yes	complemented
62	C₃×#394	C₂²	1	4	yes	complemented
63	C₃×#394	C₂²	1	4	yes	complemented
64	C₃×#394	C₂²	1	2	yes	complemented
65	C₃×#394	C₂²	1	2	yes	complemented
66	C₃×#392	C₂²	1	1	yes	characteristic
67	C₃×#392	C₂²	1	2	yes	complemented
68	C₃×#392	C₂²	1	2	yes	complemented
69	C₃×#390	C₂²	1	2	yes	complemented
70	C₃×#390	C₂²	1	4	yes	complemented
71	C₃×#390	C₂²	1	4	yes	complemented
72	C₃×#390	C₂²	1	2	yes	complemented
73	C₃×#389	C₂²	1	2	yes	complemented
74	C₃×#388	C₂²	1	4	yes	complemented
75	C₃×#388	C₂²	1	4	yes	complemented
76	C₃×#386	C₂²	1	4	yes	complemented
77	C₃×#386	C₂²	1	4	yes	complemented
78	C₃×#386	C₂²	1	4	yes	complemented
79	C₃×#385	C₂²	1	4	yes	complemented
80	C₃×#382	C₂²	1	1	yes	characteristic, complemented
81	C₃×#380	C₂²	1	2	yes	complemented
82	C₃×#380	C₂²	1	2	yes	complemented
83	C₃×#379	C₂²	1	4	yes	complemented
84	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
85	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
86	C₂×C₃×#95	C₂²	1	2	yes	complemented
87	C₂×#546	C₂×C₃	1	2	yes	complemented
88	C₂×D₄²	C₂×C₃	1	1	yes	characteristic, complemented
89	C₂×#520	C₂×C₃	1	1	yes	characteristic, complemented
90	#2619	C₂×C₃	1	1	yes	characteristic, complemented
91	#2618	C₂×C₃	1	2	yes	complemented
92	#2548	C₂×C₃	1	1	yes	characteristic, complemented
93	#2543	C₂×C₃	1	2	yes	complemented
94	#2536	C₂×C₃	1	1	yes	characteristic, complemented
95	#2426	C₂×C₃	1	2	yes	complemented
96	#2424	C₂×C₃	1	4	yes	complemented
97	#2416	C₂×C₃	1	2	yes	complemented
98	#2411	C₂×C₃	1	4	yes	complemented
99	#2408	C₂×C₃	1	2	yes	complemented
100	#2392	C₂×C₃	1	1	yes	characteristic, complemented
101	C₂×#394	C₂×C₃	1	2	yes	complemented
102	#2349	C₂×C₃	1	1	yes	characteristic, complemented
103	D₄×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
104	C₂⁵×C₃	C₂³	1	4	yes	—
105	C₂×C₃×#41	—	2	4	no	—
106	C₂×C₃×#41	—	2	4	no	—
107	C₂×C₃×#41	D₄	1	8	yes	complemented
108	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
109	C₂²×C₃×D₄	—	2	8	no	—
110	C₂²×C₃×D₄	—	2	8	no	—
111	C₂²×C₃×D₄	—	2	8	no	—
112	C₂²×C₃×D₄	—	2	8	no	—
113	C₂²×C₃×D₄	—	4	8	no	—
114	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
115	C₂²×C₃×D₄	C₂³	1	4	yes	—
116	C₂²×C₃×D₄	C₂³	1	2	yes	—
117	C₂²×C₃×D₄	C₂³	1	4	yes	—
118	C₂²×C₃×D₄	C₂³	1	2	yes	—
119	C₂²×C₃×D₄	C₂³	1	2	yes	—
120	C₂²×C₃×D₄	C₂³	1	2	yes	—
121	C₂²×C₃×D₄	C₂³	1	4	yes	—
122	C₂²×C₃×D₄	C₂³	1	2	yes	—
123	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
124	C₂³×C₃×C₄	C₂³	1	2	yes	—
125	C₂³×C₃×C₄	C₂³	1	2	yes	—
126	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
127	C₂³×C₃×C₄	C₂³	1	4	yes	—
128	C₂³×C₃×C₄	C₂³	1	2	yes	—
129	C₂³×C₃×C₄	C₂³	1	2	yes	—
130	C₂³×C₃×C₄	C₂³	1	2	yes	—
131	C₃×#127	—	2	4	no	—
132	C₃×#124	—	2	8	no	—
133	C₃×#123	—	2	16	no	—
134	C₃×C₂²⋊Q₈	—	2	8	no	—
135	C₃×#121	—	2	16	no	—
136	C₃×#121	—	2	8	no	—
137	C₃×#121	—	2	8	no	—
138	C₃×#121	—	2	8	no	—
139	C₃×#121	—	4	8	no	—
140	C₃×#120	—	2	16	no	—
141	C₃×#120	—	2	16	no	—
142	C₃×C₄×Q₈	—	2	4	no	—
143	C₃×C₄×Q₈	—	2	4	no	—
144	C₃×C₄×D₄	—	2	4	no	—
145	C₃×C₄×D₄	—	2	8	no	—
146	C₃×C₄×D₄	—	2	8	no	—
147	C₃×C₄×D₄	—	2	8	no	—
148	C₃×C₄×D₄	—	2	8	no	—
149	C₃×C₄×D₄	—	2	4	no	—
150	C₃×C₄×D₄	D₄	1	8	yes	complemented
151	C₃×#117	—	2	8	no	—
152	C₃×#117	—	2	4	no	—
153	C₂×C₃×C₄⋊C₄	—	2	8	no	—
154	C₂×C₃×C₄⋊C₄	—	2	4	no	—
155	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
158	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
167	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₃×C₂²⋊C₄	—	2	16	no	—
169	C₂×C₃×C₂²⋊C₄	—	4	8	no	—
170	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
173	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
174	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
176	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
178	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
179	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
180	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
184	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
186	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
187	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
188	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
189	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
191	C₂×C₃×C₄²	C₂³	1	2	yes	—
192	C₂×C₃×C₄²	C₂³	1	2	yes	—
193	C₂×C₃×C₄²	C₂³	1	2	yes	—
194	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
195	C₃×#95	C₂³	1	1	yes	characteristic
196	C₃×#95	C₂³	1	2	yes	—
197	C₃×#95	C₂³	1	4	yes	—
198	C₃×#95	C₂³	1	2	yes	—
199	C₃×#95	C₂³	1	2	yes	—
200	C₃×#95	C₂³	1	1	yes	characteristic
201	C₃×#95	C₂³	1	4	yes	—
202	C₃×#95	C₂³	1	2	yes	—
203	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
204	C₂³×D₄	C₂²×C₃	1	2	yes	—
205	C₂³×D₄	C₂²×C₃	1	2	yes	—
206	#546	—	2	16	no	—
207	D₄²	—	2	8	no	—
208	C₂×#127	C₂²×C₃	1	1	yes	characteristic
209	C₂×#124	C₂²×C₃	1	2	yes	complemented
210	C₂×#123	C₂²×C₃	1	4	yes	complemented
211	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
212	C₂×#121	C₂²×C₃	1	2	yes	—
213	C₂×#121	C₂²×C₃	1	2	yes	—
214	C₂×#121	C₂²×C₃	1	2	yes	complemented
215	C₂×#121	C₂²×C₃	1	4	yes	complemented
216	C₂×#121	C₂²×C₃	1	4	yes	complemented
217	C₂×#120	C₂²×C₃	1	4	yes	—
218	C₂×#120	C₂²×C₃	1	4	yes	complemented
219	#520	—	2	8	no	—
220	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
221	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
222	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
223	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
224	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
225	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
226	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
227	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
228	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
229	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
230	C₂×#117	C₂²×C₃	1	2	yes	complemented
231	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
232	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
233	C₂²×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
234	C₂²×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
235	#398	C₂²×C₃	1	1	yes	characteristic, complemented
236	#398	C₂²×C₃	1	2	yes	complemented
237	#397	C₂²×C₃	1	1	yes	characteristic, complemented
238	#396	C₂²×C₃	1	4	yes	complemented
239	#396	C₂²×C₃	1	4	yes	complemented
240	#396	C₂²×C₃	1	2	yes	complemented
241	#394	C₂²×C₃	1	1	yes	characteristic
242	#394	C₂²×C₃	1	2	yes	—
243	#394	C₂²×C₃	1	2	yes	complemented
244	#394	C₂²×C₃	1	2	yes	complemented
245	#394	C₂²×C₃	1	2	yes	complemented
246	#394	C₂²×C₃	1	4	yes	complemented
247	#394	C₂²×C₃	1	4	yes	complemented
248	#394	C₂²×C₃	1	2	yes	complemented
249	#394	C₂²×C₃	1	2	yes	complemented
250	#392	C₂²×C₃	1	1	yes	characteristic
251	#392	C₂²×C₃	1	2	yes	complemented
252	#392	C₂²×C₃	1	2	yes	complemented
253	#390	C₂²×C₃	1	2	yes	complemented
254	#390	C₂²×C₃	1	2	yes	complemented
255	#390	C₂²×C₃	1	4	yes	complemented
256	#390	C₂²×C₃	1	4	yes	complemented
257	#389	C₂²×C₃	1	2	yes	complemented
258	#388	C₂²×C₃	1	4	yes	complemented
259	#388	C₂²×C₃	1	4	yes	complemented
260	#386	C₂²×C₃	1	4	yes	complemented
261	#386	C₂²×C₃	1	4	yes	complemented
262	#386	C₂²×C₃	1	4	yes	complemented
263	#385	C₂²×C₃	1	4	yes	complemented
264	#382	C₂²×C₃	1	1	yes	characteristic, complemented
265	#380	C₂²×C₃	1	2	yes	complemented
266	#380	C₂²×C₃	1	2	yes	complemented
267	#379	C₂²×C₃	1	4	yes	complemented
268	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
269	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
270	C₂×#95	C₂²×C₃	1	2	yes	complemented
271	C₂⁴×C₃	—	2	8	no	—
272	C₂⁴×C₃	—	2	8	no	—
273	C₂⁴×C₃	—	2	8	no	—
274	C₂⁴×C₃	—	2	8	no	—
275	C₂⁴×C₃	—	4	4	no	—
276	C₂⁴×C₃	—	4	4	no	—
277	C₂⁴×C₃	—	4	4	no	—
278	C₂⁴×C₃	C₂⁴	1	4	yes	—
279	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
280	C₂⁴×C₃	C₂⁴	1	2	yes	—
281	C₂⁴×C₃	C₂⁴	1	2	yes	—
282	C₃×#41	—	2	32	no	—
283	C₂×C₃×Q₈	—	2	2	no	—
284	C₂×C₃×Q₈	—	2	2	no	—
285	C₂×C₃×Q₈	C₂×D₄	1	4	yes	complemented
286	C₂×C₃×D₄	—	2	4	no	—
287	C₂×C₃×D₄	—	2	4	no	—
288	C₂×C₃×D₄	—	2	4	no	—
289	C₂×C₃×D₄	—	2	4	no	—
290	C₂×C₃×D₄	—	2	8	no	—
291	C₂×C₃×D₄	—	2	8	no	—
292	C₂×C₃×D₄	—	2	8	no	—
293	C₂×C₃×D₄	—	2	4	no	—
294	C₂×C₃×D₄	—	2	8	no	—
295	C₂×C₃×D₄	—	2	8	no	—
296	C₂×C₃×D₄	—	2	2	no	—
297	C₂×C₃×D₄	—	2	8	no	—
298	C₂×C₃×D₄	—	2	4	no	—
299	C₂×C₃×D₄	—	2	4	no	—
300	C₂×C₃×D₄	—	2	4	no	—
301	C₂×C₃×D₄	—	2	4	no	—
302	C₂×C₃×D₄	—	2	4	no	—
303	C₂×C₃×D₄	—	4	4	no	—
304	C₂×C₃×D₄	—	4	4	no	—
305	C₂×C₃×D₄	—	4	2	no	—
306	C₂×C₃×D₄	—	4	4	no	—
307	C₂×C₃×D₄	—	4	4	no	—
308	C₂×C₃×D₄	—	4	4	no	—
309	C₂×C₃×D₄	—	4	32	no	—
310	C₂×C₃×D₄	—	4	32	no	—
311	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
312	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
313	C₂×C₃×D₄	C₂×D₄	1	8	yes	complemented
314	C₂×C₃×D₄	#41	1	4	yes	—
315	C₂²×C₃×C₄	—	2	4	no	—
316	C₂²×C₃×C₄	—	2	4	no	—
317	C₂²×C₃×C₄	—	2	2	no	—
318	C₂²×C₃×C₄	—	2	2	no	—
319	C₂²×C₃×C₄	—	2	8	no	—
320	C₂²×C₃×C₄	—	2	4	no	—
321	C₂²×C₃×C₄	—	2	4	no	—
322	C₂²×C₃×C₄	—	2	4	no	—
323	C₂²×C₃×C₄	—	2	4	no	—
324	C₂²×C₃×C₄	—	2	4	no	—
325	C₂²×C₃×C₄	—	4	4	no	—
326	C₂²×C₃×C₄	—	4	4	no	—
327	C₂²×C₃×C₄	—	4	4	no	—
328	C₂²×C₃×C₄	—	4	4	no	—
329	C₂²×C₃×C₄	—	4	4	no	—
330	C₂²×C₃×C₄	C₂×D₄	1	8	yes	—
331	C₂²×C₃×C₄	C₂×D₄	1	8	yes	complemented
332	C₂²×C₃×C₄	C₂×D₄	1	4	yes	complemented
333	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
334	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
335	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
336	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
337	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
338	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
339	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
340	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
341	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
342	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
343	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
344	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
345	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
346	C₃×C₄⋊C₄	—	2	4	no	—
347	C₃×C₄⋊C₄	—	2	2	no	—
348	C₃×C₄⋊C₄	—	2	4	no	—
349	C₃×C₄⋊C₄	—	2	4	no	—
350	C₃×C₄⋊C₄	—	2	2	no	—
351	C₃×C₄⋊C₄	—	2	2	no	—
352	C₃×C₄⋊C₄	—	2	2	no	—
353	C₃×C₄⋊C₄	—	2	4	no	—
354	C₃×C₄⋊C₄	—	2	4	no	—
355	C₃×C₄⋊C₄	—	2	8	no	—
356	C₃×C₄⋊C₄	—	4	2	no	—
357	C₃×C₄⋊C₄	—	4	4	no	—
358	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
359	C₃×C₂²⋊C₄	—	2	4	no	—
360	C₃×C₂²⋊C₄	—	2	8	no	—
361	C₃×C₂²⋊C₄	—	2	4	no	—
362	C₃×C₂²⋊C₄	—	2	4	no	—
363	C₃×C₂²⋊C₄	—	2	8	no	—
364	C₃×C₂²⋊C₄	—	2	4	no	—
365	C₃×C₂²⋊C₄	—	2	8	no	—
366	C₃×C₂²⋊C₄	—	2	8	no	—
367	C₃×C₂²⋊C₄	—	2	8	no	—
368	C₃×C₂²⋊C₄	—	2	2	no	—
369	C₃×C₂²⋊C₄	—	2	2	no	—
370	C₃×C₂²⋊C₄	—	2	4	no	—
371	C₃×C₂²⋊C₄	—	2	8	no	—
372	C₃×C₂²⋊C₄	—	2	8	no	—
373	C₃×C₂²⋊C₄	—	4	4	no	—
374	C₃×C₂²⋊C₄	—	4	4	no	—
375	C₃×C₂²⋊C₄	—	4	2	no	—
376	C₃×C₂²⋊C₄	—	4	4	no	—
377	C₃×C₂²⋊C₄	—	4	4	no	—
378	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
379	C₃×C₄²	—	2	4	no	—
380	C₃×C₄²	—	2	4	no	—
381	C₃×C₄²	—	2	2	no	—
382	C₃×C₄²	—	2	4	no	—
383	C₃×C₄²	C₂×D₄	1	4	yes	—
384	C₂⁵	C₂³×C₃	1	4	yes	—
385	C₂×#41	—	2	4	no	—
386	C₂×#41	—	2	4	no	—
387	C₂×#41	C₃×D₄	1	8	yes	complemented
388	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
389	C₂²×D₄	—	2	8	no	—
390	C₂²×D₄	—	2	8	no	—
391	C₂²×D₄	—	2	8	no	—
392	C₂²×D₄	—	2	8	no	—
393	C₂²×D₄	—	4	8	no	—
394	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
395	C₂²×D₄	C₂³×C₃	1	4	yes	—
396	C₂²×D₄	C₂³×C₃	1	2	yes	—
397	C₂²×D₄	C₂³×C₃	1	2	yes	—
398	C₂²×D₄	C₂³×C₃	1	4	yes	—
399	C₂²×D₄	C₂³×C₃	1	2	yes	—
400	C₂²×D₄	C₂³×C₃	1	2	yes	—
401	C₂²×D₄	C₂³×C₃	1	4	yes	—
402	C₂²×D₄	C₂³×C₃	1	2	yes	—
403	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
404	C₂³×C₄	C₂³×C₃	1	2	yes	—
405	C₂³×C₄	C₂³×C₃	1	2	yes	—
406	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
407	C₂³×C₄	C₂³×C₃	1	2	yes	—
408	C₂³×C₄	C₂³×C₃	1	4	yes	—
409	C₂³×C₄	C₂³×C₃	1	2	yes	—
410	C₂³×C₄	C₂³×C₃	1	2	yes	—
411	#127	—	2	4	no	—
412	#124	—	2	8	no	—
413	#123	—	2	16	no	—
414	C₂²⋊Q₈	—	2	8	no	—
415	#121	—	2	16	no	—
416	#121	—	2	8	no	—
417	#121	—	2	8	no	—
418	#121	—	2	8	no	—
419	#121	—	4	8	no	—
420	#120	—	2	16	no	—
421	#120	—	2	16	no	—
422	C₄×Q₈	—	2	4	no	—
423	C₄×Q₈	—	2	4	no	—
424	C₄×D₄	—	2	4	no	—
425	C₄×D₄	—	2	8	no	—
426	C₄×D₄	—	2	8	no	—
427	C₄×D₄	—	2	8	no	—
428	C₄×D₄	—	2	8	no	—
429	C₄×D₄	—	2	4	no	—
430	C₄×D₄	C₃×D₄	1	8	yes	complemented
431	#117	—	2	8	no	—
432	#117	—	2	4	no	—
433	C₂×C₄⋊C₄	—	2	8	no	—
434	C₂×C₄⋊C₄	—	2	4	no	—
435	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
437	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
440	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
444	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
445	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
446	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
448	C₂×C₂²⋊C₄	—	2	16	no	—
449	C₂×C₂²⋊C₄	—	4	8	no	—
450	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
458	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
459	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
470	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
471	C₂×C₄²	C₂³×C₃	1	2	yes	—
472	C₂×C₄²	C₂³×C₃	1	2	yes	—
473	C₂×C₄²	C₂³×C₃	1	2	yes	—
474	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
475	#95	C₂³×C₃	1	1	yes	characteristic
476	#95	C₂³×C₃	1	2	yes	—
477	#95	C₂³×C₃	1	4	yes	—
478	#95	C₂³×C₃	1	2	yes	—
479	#95	C₂³×C₃	1	2	yes	—
480	#95	C₂³×C₃	1	1	yes	characteristic
481	#95	C₂³×C₃	1	4	yes	—
482	#95	C₂³×C₃	1	2	yes	—
483	C₂³×C₃	—	2	4	no	—
484	C₂³×C₃	—	2	4	no	—
485	C₂³×C₃	—	2	2	no	—
486	C₂³×C₃	—	2	1	no	—
487	C₂³×C₃	—	2	2	no	—
488	C₂³×C₃	—	2	1	no	—
489	C₂³×C₃	—	2	2	no	—
490	C₂³×C₃	—	2	2	no	—
491	C₂³×C₃	—	2	2	no	—
492	C₂³×C₃	—	2	2	no	—
493	C₂³×C₃	—	2	2	no	—
494	C₂³×C₃	—	2	2	no	—
495	C₂³×C₃	—	2	4	no	—
496	C₂³×C₃	—	2	4	no	—
497	C₂³×C₃	—	2	4	no	—
498	C₂³×C₃	—	2	4	no	—
499	C₂³×C₃	—	2	4	no	—
500	C₂³×C₃	—	2	4	no	—
501	C₂³×C₃	—	2	4	no	—
502	C₂³×C₃	—	4	16	no	—
503	C₂³×C₃	—	4	16	no	—
504	C₂³×C₃	—	4	16	no	—
505	C₂³×C₃	—	4	16	no	—
506	C₂³×C₃	—	8	8	no	—
507	C₂³×C₃	—	8	8	no	—
508	C₂³×C₃	—	8	8	no	—
509	C₂³×C₃	C₂²×D₄	1	2	yes	—
510	C₂³×C₃	C₂²×D₄	1	4	yes	—
511	C₂³×C₃	C₂²×D₄	1	4	yes	—
512	C₂³×C₃	C₂×#41	1	4	yes	—
513	C₂³×C₃	H(5,𝔽₂)	1	4	yes	—
514	C₂³×C₃	C₂⁵	1	1	yes	characteristic
515	C₃×Q₈	—	2	8	no	—
516	C₃×D₄	—	2	8	no	—
517	C₃×D₄	—	2	16	no	—
518	C₃×D₄	—	4	16	no	—
519	C₃×D₄	—	4	8	no	—
520	C₃×D₄	—	4	8	no	—
521	C₃×D₄	—	4	16	no	—
522	C₃×D₄	—	4	8	no	—
523	C₃×D₄	—	8	4	no	—
524	C₃×D₄	—	8	8	no	—
525	C₃×D₄	#121	1	16	yes	complemented
526	C₂×C₃×C₄	—	2	16	no	—
527	C₂×C₃×C₄	—	2	2	no	—
528	C₂×C₃×C₄	—	2	1	no	—
529	C₂×C₃×C₄	—	2	1	no	—
530	C₂×C₃×C₄	—	2	2	no	—
531	C₂×C₃×C₄	—	2	4	no	—
532	C₂×C₃×C₄	—	2	2	no	—
533	C₂×C₃×C₄	—	2	2	no	—
534	C₂×C₃×C₄	—	2	8	no	—
535	C₂×C₃×C₄	—	2	1	no	—
536	C₂×C₃×C₄	—	2	2	no	—
537	C₂×C₃×C₄	—	2	2	no	—
538	C₂×C₃×C₄	—	2	2	no	—
539	C₂×C₃×C₄	—	2	1	no	—
540	C₂×C₃×C₄	—	2	4	no	—
541	C₂×C₃×C₄	—	2	2	no	—
542	C₂×C₃×C₄	—	2	2	no	—
543	C₂×C₃×C₄	—	2	2	no	—
544	C₂×C₃×C₄	—	2	2	no	—
545	C₂×C₃×C₄	—	2	4	no	—
546	C₂×C₃×C₄	—	2	2	no	—
547	C₂×C₃×C₄	—	2	4	no	—
548	C₂×C₃×C₄	—	2	2	no	—
549	C₂×C₃×C₄	—	2	2	no	—
550	C₂×C₃×C₄	—	2	2	no	—
551	C₂×C₃×C₄	—	2	4	no	—
552	C₂×C₃×C₄	—	2	2	no	—
553	C₂×C₃×C₄	—	4	8	no	—
554	C₂×C₃×C₄	—	4	8	no	—
555	C₂×C₃×C₄	—	8	4	no	—
556	C₂×C₃×C₄	—	8	4	no	—
557	C₂×C₃×C₄	—	8	8	no	—
558	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
559	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
560	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
561	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
562	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
563	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
564	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
565	C₂×C₃×C₄	C₂×#41	1	2	yes	—
566	C₂⁴	—	2	8	no	—
567	C₂⁴	—	2	8	no	—
568	C₂⁴	—	2	8	no	—
569	C₂⁴	—	2	8	no	—
570	C₂⁴	—	4	4	no	—
571	C₂⁴	—	4	4	no	—
572	C₂⁴	—	4	4	no	—
573	C₂⁴	C₂⁴×C₃	1	4	yes	—
574	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
575	C₂⁴	C₂⁴×C₃	1	2	yes	—
576	C₂⁴	C₂⁴×C₃	1	2	yes	—
577	#41	—	2	32	no	—
578	C₂×Q₈	—	2	2	no	—
579	C₂×Q₈	—	2	2	no	—
580	C₂×Q₈	C₂×C₃×D₄	1	4	yes	complemented
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	8	no	—
586	C₂×D₄	—	2	8	no	—
587	C₂×D₄	—	2	8	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	8	no	—
590	C₂×D₄	—	2	8	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	8	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	4	4	no	—
599	C₂×D₄	—	4	4	no	—
600	C₂×D₄	—	4	2	no	—
601	C₂×D₄	—	4	4	no	—
602	C₂×D₄	—	4	4	no	—
603	C₂×D₄	—	4	4	no	—
604	C₂×D₄	—	4	32	no	—
605	C₂×D₄	—	4	32	no	—
606	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
607	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
608	C₂×D₄	C₂×C₃×D₄	1	8	yes	complemented
609	C₂×D₄	C₃×#41	1	4	yes	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	8	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	4	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	4	4	no	—
621	C₂²×C₄	—	4	4	no	—
622	C₂²×C₄	—	4	4	no	—
623	C₂²×C₄	—	4	4	no	—
624	C₂²×C₄	—	4	4	no	—
625	C₂²×C₄	C₂×C₃×D₄	1	8	yes	—
626	C₂²×C₄	C₂×C₃×D₄	1	8	yes	complemented
627	C₂²×C₄	C₂×C₃×D₄	1	4	yes	complemented
628	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
630	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
634	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
636	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
637	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	8	no	—
651	C₄⋊C₄	—	4	4	no	—
652	C₄⋊C₄	—	4	2	no	—
653	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	8	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	8	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	8	no	—
661	C₂²⋊C₄	—	2	8	no	—
662	C₂²⋊C₄	—	2	8	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	8	no	—
667	C₂²⋊C₄	—	2	8	no	—
668	C₂²⋊C₄	—	4	4	no	—
669	C₂²⋊C₄	—	4	4	no	—
670	C₂²⋊C₄	—	4	4	no	—
671	C₂²⋊C₄	—	4	2	no	—
672	C₂²⋊C₄	—	4	4	no	—
673	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
674	C₄²	—	2	4	no	—
675	C₄²	—	2	4	no	—
676	C₄²	—	2	2	no	—
677	C₄²	—	2	4	no	—
678	C₄²	C₂×C₃×D₄	1	4	yes	—
679	C₂²×C₃	—	2	4	no	—
680	C₂²×C₃	—	2	8	no	—
681	C₂²×C₃	—	2	4	no	—
682	C₂²×C₃	—	2	8	no	—
683	C₂²×C₃	—	2	2	no	—
684	C₂²×C₃	—	2	4	no	—
685	C₂²×C₃	—	2	4	no	—
686	C₂²×C₃	—	2	4	no	—
687	C₂²×C₃	—	2	4	no	—
688	C₂²×C₃	—	4	2	no	—
689	C₂²×C₃	—	4	1	no	—
690	C₂²×C₃	—	4	2	no	—
691	C₂²×C₃	—	4	1	no	—
692	C₂²×C₃	—	4	2	no	—
693	C₂²×C₃	—	4	2	no	—
694	C₂²×C₃	—	4	2	no	—
695	C₂²×C₃	—	4	4	no	—
696	C₂²×C₃	—	4	4	no	—
697	C₂²×C₃	—	4	4	no	—
698	C₂²×C₃	—	4	4	no	—
699	C₂²×C₃	—	4	4	no	—
700	C₂²×C₃	—	4	4	no	—
701	C₂²×C₃	—	4	4	no	—
702	C₂²×C₃	—	8	32	no	—
703	C₂²×C₃	C₂×#121	1	8	yes	—
704	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
705	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
706	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
707	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
708	C₂²×C₃	#585	1	2	yes	—
709	C₃×C₄	—	2	2	no	—
710	C₃×C₄	—	2	4	no	—
711	C₃×C₄	—	2	2	no	—
712	C₃×C₄	—	2	4	no	—
713	C₃×C₄	—	2	2	no	—
714	C₃×C₄	—	4	2	no	—
715	C₃×C₄	—	4	2	no	—
716	C₃×C₄	—	4	1	no	—
717	C₃×C₄	—	4	2	no	—
718	C₃×C₄	—	4	4	no	—
719	C₃×C₄	—	4	2	no	—
720	C₃×C₄	—	4	1	no	—
721	C₃×C₄	C₂×#121	1	4	yes	—
722	C₂³	—	2	4	no	—
723	C₂³	—	2	4	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	1	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	4	no	—
735	C₂³	—	2	4	no	—
736	C₂³	—	2	4	no	—
737	C₂³	—	2	4	no	—
738	C₂³	—	2	4	no	—
739	C₂³	—	2	4	no	—
740	C₂³	—	2	4	no	—
741	C₂³	—	4	16	no	—
742	C₂³	—	4	16	no	—
743	C₂³	—	4	16	no	—
744	C₂³	—	4	16	no	—
745	C₂³	—	8	8	no	—
746	C₂³	—	8	8	no	—
747	C₂³	—	8	8	no	—
748	C₂³	C₂²×C₃×D₄	1	2	yes	—
749	C₂³	C₂²×C₃×D₄	1	4	yes	—
750	C₂³	C₂²×C₃×D₄	1	4	yes	—
751	C₂³	C₂×C₃×#41	1	4	yes	—
752	C₂³	C₃×H(5,𝔽₂)	1	4	yes	—
753	C₂³	C₂⁵×C₃	1	1	yes	characteristic
754	Q₈	—	2	8	no	—
755	D₄	—	2	8	no	—
756	D₄	—	2	16	no	—
757	D₄	—	4	16	no	—
758	D₄	—	4	8	no	—
759	D₄	—	4	8	no	—
760	D₄	—	4	16	no	—
761	D₄	—	4	8	no	—
762	D₄	—	8	4	no	—
763	D₄	—	8	8	no	—
764	D₄	C₃×#121	1	16	yes	complemented
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	4	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	16	no	—
773	C₂×C₄	—	2	8	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	4	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	4	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	4	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	4	8	no	—
793	C₂×C₄	—	4	8	no	—
794	C₂×C₄	—	8	4	no	—
795	C₂×C₄	—	8	4	no	—
796	C₂×C₄	—	8	8	no	—
797	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
798	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
799	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
800	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
801	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
802	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
803	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
804	C₂×C₄	C₂×C₃×#41	1	2	yes	—
805	C₂×C₃	—	2	8	no	—
806	C₂×C₃	—	4	2	no	—
807	C₂×C₃	—	4	4	no	—
808	C₂×C₃	—	8	4	no	—
809	C₂×C₃	C₂²×#121	1	1	yes	characteristic
810	C₂×C₃	#3484	1	1	yes	characteristic
811	C₂×C₃	#3488	1	2	yes	—
812	C₂×C₃	#3500	1	1	yes	characteristic
813	C₂×C₃	#3513	1	2	yes	—
814	C₂²	—	2	4	no	—
815	C₂²	—	2	8	no	—
816	C₂²	—	2	4	no	—
817	C₂²	—	2	8	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	4	no	—
820	C₂²	—	2	4	no	—
821	C₂²	—	2	4	no	—
822	C₂²	—	2	4	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	4	no	—
831	C₂²	—	4	4	no	—
832	C₂²	—	4	4	no	—
833	C₂²	—	4	4	no	—
834	C₂²	—	4	4	no	—
835	C₂²	—	4	4	no	—
836	C₂²	—	4	4	no	—
837	C₂²	—	8	32	no	—
838	C₂²	C₂×C₃×#121	1	8	yes	—
839	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
840	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
841	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
842	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
843	C₂²	C₃×#585	1	2	yes	—
844	C₄	—	2	2	no	—
845	C₄	—	2	4	no	—
846	C₄	—	2	2	no	—
847	C₄	—	2	4	no	—
848	C₄	—	2	2	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	4	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	1	no	—
856	C₄	C₂×C₃×#121	1	4	yes	—
857	C₃	#35728	1	1	yes	characteristic, direct product factor, Sylow
858	C₂	—	2	8	no	—
859	C₂	—	4	4	no	—
860	C₂	—	4	2	no	—
861	C₂	—	8	4	no	—
862	C₂	C₂²×C₃×#121	1	1	yes	characteristic
863	C₂	C₃×#3484	1	1	yes	characteristic
864	C₂	C₃×#3488	1	2	yes	—
865	C₂	C₃×#3500	1	1	yes	characteristic
866	C₂	C₃×#3513	1	2	yes	—

	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×#546	C₂	semidirect
2. C₂×C₃×D₄²	C₂	semidirect
3. C₂×C₃×#520	C₂	semidirect
4. C₃×#2619	C₂	semidirect
5. C₃×#2618	C₂	semidirect
6. C₃×#2548	C₂	semidirect
7. C₃×#2543	C₂	semidirect
8. C₃×#2536	C₂	semidirect
9. C₃×#2426	C₂	semidirect
10. C₃×#2424	C₂	semidirect
11. C₃×#2416	C₂	semidirect
12. C₃×#2411	C₂	semidirect
13. C₃×#2408	C₂	semidirect
14. C₃×#2392	C₂	semidirect
15. C₂×C₃×#394	C₂	semidirect
16. C₃×#2349	C₂	semidirect
17. C₃×D₄×C₂²⋊C₄	C₂	semidirect
18. #35728	C₃	direct (N × H)
25. C₂×C₃×#124	C₂²	semidirect
26. C₂×C₃×#123	C₂²	semidirect
27. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
30. C₂×C₃×#121	C₂²	semidirect
31. C₂×C₃×#121	C₂²	semidirect
32. C₂×C₃×#121	C₂²	semidirect
34. C₂×C₃×#120	C₂²	semidirect
36. C₂×C₃×C₄×Q₈	C₂²	semidirect
37. C₂×C₃×C₄×Q₈	C₂²	semidirect
42. C₂×C₃×C₄×D₄	C₂²	semidirect
43. C₂×C₃×C₄×D₄	C₂²	semidirect
44. C₂×C₃×C₄×D₄	C₂²	semidirect
45. C₂×C₃×#117	C₂²	semidirect
46. C₂×C₃×#117	C₂²	semidirect
47. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
48. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
49. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
50. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
51. C₃×#398	C₂²	semidirect
52. C₃×#398	C₂²	semidirect
53. C₃×#397	C₂²	semidirect
54. C₃×#396	C₂²	semidirect
55. C₃×#396	C₂²	semidirect
56. C₃×#396	C₂²	semidirect
59. C₃×#394	C₂²	semidirect
60. C₃×#394	C₂²	semidirect
61. C₃×#394	C₂²	semidirect
62. C₃×#394	C₂²	semidirect
63. C₃×#394	C₂²	semidirect
64. C₃×#394	C₂²	semidirect
65. C₃×#394	C₂²	semidirect
67. C₃×#392	C₂²	semidirect
68. C₃×#392	C₂²	semidirect
69. C₃×#390	C₂²	semidirect
70. C₃×#390	C₂²	semidirect
71. C₃×#390	C₂²	semidirect
72. C₃×#390	C₂²	semidirect
73. C₃×#389	C₂²	semidirect
74. C₃×#388	C₂²	semidirect
75. C₃×#388	C₂²	semidirect
76. C₃×#386	C₂²	semidirect
77. C₃×#386	C₂²	semidirect
78. C₃×#386	C₂²	semidirect
79. C₃×#385	C₂²	semidirect
80. C₃×#382	C₂²	semidirect
81. C₃×#380	C₂²	semidirect
82. C₃×#380	C₂²	semidirect
83. C₃×#379	C₂²	semidirect
84. C₃×C₄×C₄⋊C₄	C₂²	semidirect
85. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
86. C₂×C₃×#95	C₂²	semidirect
87. C₂×#546	C₂×C₃	semidirect
88. C₂×D₄²	C₂×C₃	semidirect
89. C₂×#520	C₂×C₃	semidirect
90. #2619	C₂×C₃	semidirect
91. #2618	C₂×C₃	semidirect
92. #2548	C₂×C₃	semidirect
93. #2543	C₂×C₃	semidirect
94. #2536	C₂×C₃	semidirect
95. #2426	C₂×C₃	semidirect
96. #2424	C₂×C₃	semidirect
97. #2416	C₂×C₃	semidirect
98. #2411	C₂×C₃	semidirect
99. #2408	C₂×C₃	semidirect
100. #2392	C₂×C₃	semidirect
101. C₂×#394	C₂×C₃	semidirect
102. #2349	C₂×C₃	semidirect
103. D₄×C₂²⋊C₄	C₂×C₃	semidirect
107. C₂×C₃×#41	D₄	semidirect
150. C₃×C₄×D₄	D₄	semidirect
209. C₂×#124	C₂²×C₃	semidirect
210. C₂×#123	C₂²×C₃	semidirect
211. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
214. C₂×#121	C₂²×C₃	semidirect
215. C₂×#121	C₂²×C₃	semidirect
216. C₂×#121	C₂²×C₃	semidirect
218. C₂×#120	C₂²×C₃	semidirect
220. C₂×C₄×Q₈	C₂²×C₃	semidirect
221. C₂×C₄×Q₈	C₂²×C₃	semidirect
226. C₂×C₄×D₄	C₂²×C₃	semidirect
227. C₂×C₄×D₄	C₂²×C₃	semidirect
228. C₂×C₄×D₄	C₂²×C₃	semidirect
229. C₂×#117	C₂²×C₃	semidirect
230. C₂×#117	C₂²×C₃	semidirect
231. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
232. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
233. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
234. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
235. #398	C₂²×C₃	semidirect
236. #398	C₂²×C₃	semidirect
237. #397	C₂²×C₃	semidirect
238. #396	C₂²×C₃	semidirect
239. #396	C₂²×C₃	semidirect
240. #396	C₂²×C₃	semidirect
243. #394	C₂²×C₃	semidirect
244. #394	C₂²×C₃	semidirect
245. #394	C₂²×C₃	semidirect
246. #394	C₂²×C₃	semidirect
247. #394	C₂²×C₃	semidirect
248. #394	C₂²×C₃	semidirect
249. #394	C₂²×C₃	semidirect
251. #392	C₂²×C₃	semidirect
252. #392	C₂²×C₃	semidirect
253. #390	C₂²×C₃	semidirect
254. #390	C₂²×C₃	semidirect
255. #390	C₂²×C₃	semidirect
256. #390	C₂²×C₃	semidirect
257. #389	C₂²×C₃	semidirect
258. #388	C₂²×C₃	semidirect
259. #388	C₂²×C₃	semidirect
260. #386	C₂²×C₃	semidirect
261. #386	C₂²×C₃	semidirect
262. #386	C₂²×C₃	semidirect
263. #385	C₂²×C₃	semidirect
264. #382	C₂²×C₃	semidirect
265. #380	C₂²×C₃	semidirect
266. #380	C₂²×C₃	semidirect
267. #379	C₂²×C₃	semidirect
268. C₄×C₄⋊C₄	C₂²×C₃	semidirect
269. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
270. C₂×#95	C₂²×C₃	semidirect
285. C₂×C₃×Q₈	C₂×D₄	semidirect
313. C₂×C₃×D₄	C₂×D₄	semidirect
331. C₂²×C₃×C₄	C₂×D₄	semidirect
332. C₂²×C₃×C₄	C₂×D₄	semidirect
387. C₂×#41	C₃×D₄	semidirect
430. C₄×D₄	C₃×D₄	semidirect
525. C₃×D₄	#121	semidirect
580. C₂×Q₈	C₂×C₃×D₄	semidirect
608. C₂×D₄	C₂×C₃×D₄	semidirect
626. C₂²×C₄	C₂×C₃×D₄	semidirect
627. C₂²×C₄	C₂×C₃×D₄	semidirect
764. D₄	C₃×#121	semidirect
857. C₃	#35728	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×#546	2
C₂×C₃×D₄²	2
C₂×C₃×#520	2
C₃×#2619	2
C₃×#2618	2
C₃×#2548	2
C₃×#2543	2
C₃×#2536	2
C₃×#2426	2
C₃×#2424	2
C₃×#2416	2
C₃×#2411	2
C₃×#2408	2
C₃×#2392	2
C₂×C₃×#394	2
C₃×#2349	2
C₃×D₄×C₂²⋊C₄	2
#35728	3

Subgroups — C3×#35728 #10654335

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35728 #10654335