Subgroups — C₃×#42966 #10661573

Order 768.

2984 conjugacy classes of subgroups.

The subgroup lattice has 864 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	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2813	C₂	1	2	yes	maximal, complemented
4	C₃×#2679	C₂	1	4	yes	maximal, complemented
5	C₃×#2678	C₂	1	4	yes	maximal, complemented
6	C₃×#2661	C₂	1	2	yes	maximal, complemented
7	C₃×#2624	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2617	C₂	1	2	yes	maximal, complemented
9	C₃×#2548	C₂	1	2	yes	maximal, complemented
10	C₃×#2539	C₂	1	2	yes	maximal, complemented
11	C₃×#2445	C₂	1	2	yes	maximal, complemented
12	C₃×#2433	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2433	C₂	1	2	yes	maximal, complemented
14	C₃×#2426	C₂	1	2	yes	maximal, complemented
15	C₃×#2408	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2395	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2341	C₂	1	1	yes	maximal, characteristic, complemented
18	#42966	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	1	yes	characteristic, complemented
21	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic, complemented
22	C₃×#546	—	2	8	no	—
23	C₃×#535	—	2	8	no	—
24	C₂×C₃×#127	C₂²	1	2	yes	—
25	C₂×C₃×#127	C₂²	1	2	yes	—
26	C₂×C₃×#124	C₂²	1	2	yes	complemented
27	C₂×C₃×#124	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×#123	C₂²	1	2	yes	complemented
29	C₂×C₃×#123	C₂²	1	4	yes	complemented
30	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×#121	C₂²	1	1	yes	characteristic
32	C₂×C₃×#121	C₂²	1	2	yes	—
33	C₂×C₃×#121	C₂²	1	2	yes	—
34	C₂×C₃×#121	C₂²	1	2	yes	complemented
35	C₂×C₃×#121	C₂²	1	2	yes	complemented
36	C₂×C₃×#120	C₂²	1	2	yes	—
37	C₂×C₃×#120	C₂²	1	2	yes	—
38	C₂×C₃×#120	C₂²	1	4	yes	complemented
39	C₂×C₃×#120	C₂²	1	4	yes	complemented
40	C₂×C₃×#120	C₂²	1	4	yes	complemented
41	C₂×C₃×#120	C₂²	1	4	yes	complemented
42	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	complemented
43	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
44	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
47	C₃×#400	C₂²	1	1	yes	characteristic, complemented
48	C₃×#399	C₂²	1	2	yes	complemented
49	C₃×#399	C₂²	1	1	yes	characteristic, complemented
50	C₃×#398	C₂²	1	1	yes	characteristic, complemented
51	C₃×#397	C₂²	1	1	yes	characteristic, complemented
52	C₃×#397	C₂²	1	2	yes	complemented
53	C₃×#397	C₂²	1	2	yes	complemented
54	C₃×#396	C₂²	1	4	yes	complemented
55	C₃×#394	C₂²	1	2	yes	—
56	C₃×#394	C₂²	1	4	yes	complemented
57	C₃×#394	C₂²	1	4	yes	complemented
58	C₃×#394	C₂²	1	4	yes	complemented
59	C₃×#394	C₂²	1	2	yes	complemented
60	C₃×#394	C₂²	1	4	yes	complemented
61	C₃×#394	C₂²	1	4	yes	complemented
62	C₃×#394	C₂²	1	4	yes	complemented
63	C₃×#392	C₂²	1	2	yes	—
64	C₃×#392	C₂²	1	2	yes	complemented
65	C₃×#392	C₂²	1	4	yes	complemented
66	C₃×#392	C₂²	1	2	yes	complemented
67	C₃×#392	C₂²	1	4	yes	complemented
68	C₃×#390	C₂²	1	2	yes	complemented
69	C₃×#390	C₂²	1	4	yes	complemented
70	C₃×#390	C₂²	1	2	yes	complemented
71	C₃×#390	C₂²	1	4	yes	complemented
72	C₃×#390	C₂²	1	4	yes	complemented
73	C₃×#390	C₂²	1	4	yes	complemented
74	C₃×#390	C₂²	1	2	yes	complemented
75	C₃×#390	C₂²	1	2	yes	complemented
76	C₃×#389	C₂²	1	2	yes	complemented
77	C₃×#388	C₂²	1	4	yes	complemented
78	C₃×#386	C₂²	1	4	yes	complemented
79	C₃×#380	C₂²	1	2	yes	complemented
80	C₃×#380	C₂²	1	1	yes	characteristic, complemented
81	C₃×#379	C₂²	1	2	yes	complemented
82	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
83	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
84	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
85	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
86	C₂×#546	C₂×C₃	1	1	yes	characteristic, complemented
87	C₂×#535	C₂×C₃	1	1	yes	characteristic, complemented
88	#2813	C₂×C₃	1	2	yes	complemented
89	#2679	C₂×C₃	1	4	yes	complemented
90	#2678	C₂×C₃	1	4	yes	complemented
91	#2661	C₂×C₃	1	2	yes	complemented
92	#2624	C₂×C₃	1	1	yes	characteristic, complemented
93	#2617	C₂×C₃	1	2	yes	complemented
94	#2548	C₂×C₃	1	2	yes	complemented
95	#2539	C₂×C₃	1	2	yes	complemented
96	#2445	C₂×C₃	1	2	yes	complemented
97	#2433	C₂×C₃	1	2	yes	complemented
98	#2433	C₂×C₃	1	1	yes	characteristic, complemented
99	#2426	C₂×C₃	1	2	yes	complemented
100	#2408	C₂×C₃	1	1	yes	characteristic, complemented
101	#2395	C₂×C₃	1	1	yes	characteristic, complemented
102	#2341	C₂×C₃	1	1	yes	characteristic, complemented
103	C₂⁵×C₃	C₂³	1	2	yes	—
104	C₂⁵×C₃	C₂³	1	2	yes	—
105	C₂×C₃×#41	—	4	4	no	—
106	C₂×C₃×#41	D₄	1	8	yes	complemented
107	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
108	C₂²×C₃×D₄	—	2	4	no	—
109	C₂²×C₃×D₄	—	2	4	no	—
110	C₂²×C₃×D₄	—	4	4	no	—
111	C₂²×C₃×D₄	—	4	4	no	—
112	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
113	C₂²×C₃×D₄	C₂³	1	2	yes	—
114	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
115	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
116	C₂²×C₃×D₄	C₂³	1	2	yes	—
117	C₂²×C₃×D₄	C₂³	1	2	yes	—
118	C₂²×C₃×D₄	C₂³	1	4	yes	—
119	C₂²×C₃×D₄	C₂³	1	4	yes	—
120	C₂²×C₃×D₄	C₂³	1	4	yes	—
121	C₂²×C₃×D₄	C₂³	1	4	yes	—
122	C₂²×C₃×D₄	C₂³	1	2	yes	—
123	C₂²×C₃×D₄	C₂³	1	4	yes	—
124	C₂²×C₃×D₄	C₂³	1	2	yes	—
125	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
126	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
127	C₂³×C₃×C₄	C₂³	1	2	yes	—
128	C₂³×C₃×C₄	C₂³	1	2	yes	—
129	C₃×#127	—	2	8	no	—
130	C₃×#127	—	4	4	no	—
131	C₃×#124	—	2	8	no	—
132	C₃×#124	—	2	4	no	—
133	C₃×#123	—	2	8	no	—
134	C₃×#123	—	4	8	no	—
135	C₃×C₂²⋊Q₈	—	2	4	no	—
136	C₃×#121	—	2	8	no	—
137	C₃×#121	—	2	4	no	—
138	C₃×#121	—	2	8	no	—
139	C₃×#121	—	2	8	no	—
140	C₃×#121	—	4	4	no	—
141	C₃×#120	—	2	8	no	—
142	C₃×#120	—	2	16	no	—
143	C₃×#120	—	4	8	no	—
144	C₃×#120	—	4	8	no	—
145	C₃×#120	—	4	8	no	—
146	C₃×#120	—	4	4	no	—
147	C₃×C₄×Q₈	—	4	4	no	—
148	C₃×C₄×D₄	—	2	4	no	—
149	C₃×C₄×D₄	—	2	4	no	—
150	C₃×#117	—	2	4	no	—
151	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
160	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
161	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
162	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
163	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
168	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
169	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
174	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₃×C₂²⋊C₄	C₂³	1	2	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	4	yes	—
181	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
182	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
183	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
184	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
185	C₂×C₃×C₄²	C₂³	1	2	yes	—
186	C₂×C₃×C₄²	C₂³	1	2	yes	—
187	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
188	C₂×C₃×C₄²	C₂³	1	4	yes	—
189	C₃×#95	C₂³	1	1	yes	characteristic
190	C₃×#95	C₂³	1	2	yes	—
191	C₃×#95	C₂³	1	1	yes	characteristic
192	C₃×#95	C₂³	1	2	yes	—
193	C₃×#95	C₂³	1	2	yes	—
194	C₃×#95	C₂³	1	2	yes	—
195	C₃×#95	C₂³	1	2	yes	—
196	C₃×#95	C₂³	1	4	yes	—
197	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
198	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
199	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
200	#546	—	2	8	no	—
201	#535	—	2	8	no	—
202	C₂×#127	C₂²×C₃	1	2	yes	—
203	C₂×#127	C₂²×C₃	1	2	yes	—
204	C₂×#124	C₂²×C₃	1	2	yes	complemented
205	C₂×#124	C₂²×C₃	1	1	yes	characteristic, complemented
206	C₂×#123	C₂²×C₃	1	2	yes	complemented
207	C₂×#123	C₂²×C₃	1	4	yes	complemented
208	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
209	C₂×#121	C₂²×C₃	1	1	yes	characteristic
210	C₂×#121	C₂²×C₃	1	2	yes	—
211	C₂×#121	C₂²×C₃	1	2	yes	—
212	C₂×#121	C₂²×C₃	1	2	yes	complemented
213	C₂×#121	C₂²×C₃	1	2	yes	complemented
214	C₂×#120	C₂²×C₃	1	2	yes	—
215	C₂×#120	C₂²×C₃	1	2	yes	—
216	C₂×#120	C₂²×C₃	1	4	yes	complemented
217	C₂×#120	C₂²×C₃	1	4	yes	complemented
218	C₂×#120	C₂²×C₃	1	4	yes	complemented
219	C₂×#120	C₂²×C₃	1	4	yes	complemented
220	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
221	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
222	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
223	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
224	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
225	#400	C₂²×C₃	1	1	yes	characteristic, complemented
226	#399	C₂²×C₃	1	2	yes	complemented
227	#399	C₂²×C₃	1	1	yes	characteristic, complemented
228	#398	C₂²×C₃	1	1	yes	characteristic, complemented
229	#397	C₂²×C₃	1	1	yes	characteristic, complemented
230	#397	C₂²×C₃	1	2	yes	complemented
231	#397	C₂²×C₃	1	2	yes	complemented
232	#396	C₂²×C₃	1	4	yes	complemented
233	#394	C₂²×C₃	1	2	yes	—
234	#394	C₂²×C₃	1	4	yes	complemented
235	#394	C₂²×C₃	1	4	yes	complemented
236	#394	C₂²×C₃	1	4	yes	complemented
237	#394	C₂²×C₃	1	2	yes	complemented
238	#394	C₂²×C₃	1	4	yes	complemented
239	#394	C₂²×C₃	1	4	yes	complemented
240	#394	C₂²×C₃	1	4	yes	complemented
241	#392	C₂²×C₃	1	2	yes	—
242	#392	C₂²×C₃	1	2	yes	complemented
243	#392	C₂²×C₃	1	4	yes	complemented
244	#392	C₂²×C₃	1	2	yes	complemented
245	#392	C₂²×C₃	1	4	yes	complemented
246	#390	C₂²×C₃	1	4	yes	complemented
247	#390	C₂²×C₃	1	2	yes	complemented
248	#390	C₂²×C₃	1	2	yes	complemented
249	#390	C₂²×C₃	1	4	yes	complemented
250	#390	C₂²×C₃	1	2	yes	complemented
251	#390	C₂²×C₃	1	4	yes	complemented
252	#390	C₂²×C₃	1	4	yes	complemented
253	#390	C₂²×C₃	1	2	yes	complemented
254	#389	C₂²×C₃	1	2	yes	complemented
255	#388	C₂²×C₃	1	4	yes	complemented
256	#386	C₂²×C₃	1	4	yes	complemented
257	#380	C₂²×C₃	1	2	yes	complemented
258	#380	C₂²×C₃	1	1	yes	characteristic, complemented
259	#379	C₂²×C₃	1	2	yes	complemented
260	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
261	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
262	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
263	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
264	C₂⁴×C₃	—	2	4	no	—
265	C₂⁴×C₃	—	2	4	no	—
266	C₂⁴×C₃	—	2	4	no	—
267	C₂⁴×C₃	—	4	2	no	—
268	C₂⁴×C₃	—	4	4	no	—
269	C₂⁴×C₃	—	4	4	no	—
270	C₂⁴×C₃	—	4	2	no	—
271	C₂⁴×C₃	—	4	4	no	—
272	C₂⁴×C₃	—	4	4	no	—
273	C₂⁴×C₃	—	4	2	no	—
274	C₂⁴×C₃	C₂⁴	1	2	yes	—
275	C₂⁴×C₃	C₂⁴	1	4	yes	—
276	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
277	C₂⁴×C₃	C₂⁴	1	2	yes	—
278	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
279	C₃×#41	—	4	16	no	—
280	C₂×C₃×Q₈	—	2	4	no	—
281	C₂×C₃×Q₈	C₂×D₄	1	4	yes	—
282	C₂×C₃×D₄	—	2	2	no	—
283	C₂×C₃×D₄	—	2	4	no	—
284	C₂×C₃×D₄	—	2	2	no	—
285	C₂×C₃×D₄	—	2	4	no	—
286	C₂×C₃×D₄	—	2	8	no	—
287	C₂×C₃×D₄	—	2	8	no	—
288	C₂×C₃×D₄	—	2	8	no	—
289	C₂×C₃×D₄	—	2	4	no	—
290	C₂×C₃×D₄	—	2	2	no	—
291	C₂×C₃×D₄	—	2	4	no	—
292	C₂×C₃×D₄	—	2	4	no	—
293	C₂×C₃×D₄	—	2	4	no	—
294	C₂×C₃×D₄	—	2	4	no	—
295	C₂×C₃×D₄	—	2	4	no	—
296	C₂×C₃×D₄	—	2	8	no	—
297	C₂×C₃×D₄	—	4	4	no	—
298	C₂×C₃×D₄	—	4	4	no	—
299	C₂×C₃×D₄	—	4	1	no	—
300	C₂×C₃×D₄	—	4	4	no	—
301	C₂×C₃×D₄	—	4	16	no	—
302	C₂×C₃×D₄	—	4	4	no	—
303	C₂×C₃×D₄	—	4	4	no	—
304	C₂×C₃×D₄	—	4	4	no	—
305	C₂×C₃×D₄	—	4	4	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	4	no	—
310	C₂×C₃×D₄	—	4	4	no	—
311	C₂×C₃×D₄	—	4	4	no	—
312	C₂×C₃×D₄	—	4	4	no	—
313	C₂×C₃×D₄	—	4	4	no	—
314	C₂×C₃×D₄	—	4	16	no	—
315	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
316	C₂×C₃×D₄	C₂×D₄	1	8	yes	—
317	C₂²×C₃×C₄	—	2	4	no	—
318	C₂²×C₃×C₄	—	2	4	no	—
319	C₂²×C₃×C₄	—	2	2	no	—
320	C₂²×C₃×C₄	—	2	4	no	—
321	C₂²×C₃×C₄	—	4	4	no	—
322	C₂²×C₃×C₄	—	4	4	no	—
323	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
324	C₂²×C₃×C₄	C₂×D₄	1	8	yes	—
325	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
326	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
327	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
328	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
329	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
330	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
331	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
332	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
333	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
334	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
335	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
336	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
337	C₃×C₄⋊C₄	—	2	2	no	—
338	C₃×C₄⋊C₄	—	2	2	no	—
339	C₃×C₄⋊C₄	—	2	2	no	—
340	C₃×C₄⋊C₄	—	2	2	no	—
341	C₃×C₄⋊C₄	—	2	4	no	—
342	C₃×C₄⋊C₄	—	2	4	no	—
343	C₃×C₄⋊C₄	—	2	4	no	—
344	C₃×C₄⋊C₄	—	4	2	no	—
345	C₃×C₄⋊C₄	—	4	4	no	—
346	C₃×C₄⋊C₄	—	4	4	no	—
347	C₃×C₂²⋊C₄	—	2	4	no	—
348	C₃×C₂²⋊C₄	—	2	4	no	—
349	C₃×C₂²⋊C₄	—	2	2	no	—
350	C₃×C₂²⋊C₄	—	2	4	no	—
351	C₃×C₂²⋊C₄	—	2	2	no	—
352	C₃×C₂²⋊C₄	—	2	4	no	—
353	C₃×C₂²⋊C₄	—	2	4	no	—
354	C₃×C₂²⋊C₄	—	2	4	no	—
355	C₃×C₂²⋊C₄	—	2	8	no	—
356	C₃×C₂²⋊C₄	—	2	8	no	—
357	C₃×C₂²⋊C₄	—	2	4	no	—
358	C₃×C₂²⋊C₄	—	2	4	no	—
359	C₃×C₂²⋊C₄	—	2	4	no	—
360	C₃×C₂²⋊C₄	—	2	8	no	—
361	C₃×C₂²⋊C₄	—	2	8	no	—
362	C₃×C₂²⋊C₄	—	4	4	no	—
363	C₃×C₂²⋊C₄	—	4	4	no	—
364	C₃×C₂²⋊C₄	—	4	4	no	—
365	C₃×C₂²⋊C₄	—	4	4	no	—
366	C₃×C₂²⋊C₄	—	4	2	no	—
367	C₃×C₂²⋊C₄	—	4	4	no	—
368	C₃×C₂²⋊C₄	—	4	4	no	—
369	C₃×C₂²⋊C₄	—	4	4	no	—
370	C₃×C₄²	—	2	4	no	—
371	C₃×C₄²	—	2	2	no	—
372	C₃×C₄²	—	2	4	no	—
373	C₃×C₄²	—	4	4	no	—
374	C₂⁵	C₂³×C₃	1	2	yes	—
375	C₂⁵	C₂³×C₃	1	2	yes	—
376	C₂×#41	—	4	4	no	—
377	C₂×#41	C₃×D₄	1	8	yes	complemented
378	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
379	C₂²×D₄	—	2	4	no	—
380	C₂²×D₄	—	2	4	no	—
381	C₂²×D₄	—	4	4	no	—
382	C₂²×D₄	—	4	4	no	—
383	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
384	C₂²×D₄	C₂³×C₃	1	2	yes	—
385	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
386	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
387	C₂²×D₄	C₂³×C₃	1	2	yes	—
388	C₂²×D₄	C₂³×C₃	1	4	yes	—
389	C₂²×D₄	C₂³×C₃	1	4	yes	—
390	C₂²×D₄	C₂³×C₃	1	4	yes	—
391	C₂²×D₄	C₂³×C₃	1	4	yes	—
392	C₂²×D₄	C₂³×C₃	1	2	yes	—
393	C₂²×D₄	C₂³×C₃	1	2	yes	—
394	C₂²×D₄	C₂³×C₃	1	4	yes	—
395	C₂²×D₄	C₂³×C₃	1	2	yes	—
396	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
397	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
398	C₂³×C₄	C₂³×C₃	1	2	yes	—
399	C₂³×C₄	C₂³×C₃	1	2	yes	—
400	#127	—	2	8	no	—
401	#127	—	4	4	no	—
402	#124	—	2	8	no	—
403	#124	—	2	4	no	—
404	#123	—	2	8	no	—
405	#123	—	4	8	no	—
406	C₂²⋊Q₈	—	2	4	no	—
407	#121	—	2	8	no	—
408	#121	—	2	4	no	—
409	#121	—	2	8	no	—
410	#121	—	2	8	no	—
411	#121	—	4	4	no	—
412	#120	—	2	8	no	—
413	#120	—	2	16	no	—
414	#120	—	4	8	no	—
415	#120	—	4	8	no	—
416	#120	—	4	8	no	—
417	#120	—	4	4	no	—
418	C₄×Q₈	—	4	4	no	—
419	C₄×D₄	—	2	4	no	—
420	C₄×D₄	—	2	4	no	—
421	#117	—	2	4	no	—
422	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
427	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
428	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
429	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
430	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
431	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
432	C₂×C₂²⋊C₄	—	2	8	no	—
433	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
434	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
439	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
444	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₃	1	4	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×C₄²	C₂³×C₃	1	2	yes	—
457	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
458	C₂×C₄²	C₂³×C₃	1	2	yes	—
459	C₂×C₄²	C₂³×C₃	1	4	yes	—
460	#95	C₂³×C₃	1	1	yes	characteristic
461	#95	C₂³×C₃	1	2	yes	—
462	#95	C₂³×C₃	1	1	yes	characteristic
463	#95	C₂³×C₃	1	2	yes	—
464	#95	C₂³×C₃	1	2	yes	—
465	#95	C₂³×C₃	1	2	yes	—
466	#95	C₂³×C₃	1	2	yes	—
467	#95	C₂³×C₃	1	4	yes	—
468	C₂³×C₃	—	2	1	no	—
469	C₂³×C₃	—	2	4	no	—
470	C₂³×C₃	—	2	2	no	—
471	C₂³×C₃	—	2	2	no	—
472	C₂³×C₃	—	2	1	no	—
473	C₂³×C₃	—	2	2	no	—
474	C₂³×C₃	—	2	2	no	—
475	C₂³×C₃	—	2	2	no	—
476	C₂³×C₃	—	2	4	no	—
477	C₂³×C₃	—	2	2	no	—
478	C₂³×C₃	—	2	1	no	—
479	C₂³×C₃	—	2	1	no	—
480	C₂³×C₃	—	2	2	no	—
481	C₂³×C₃	—	2	4	no	—
482	C₂³×C₃	—	2	4	no	—
483	C₂³×C₃	—	2	2	no	—
484	C₂³×C₃	—	2	4	no	—
485	C₂³×C₃	—	2	4	no	—
486	C₂³×C₃	—	2	4	no	—
487	C₂³×C₃	—	2	4	no	—
488	C₂³×C₃	—	2	4	no	—
489	C₂³×C₃	—	2	4	no	—
490	C₂³×C₃	—	2	4	no	—
491	C₂³×C₃	—	2	2	no	—
492	C₂³×C₃	—	4	8	no	—
493	C₂³×C₃	—	4	8	no	—
494	C₂³×C₃	—	4	8	no	—
495	C₂³×C₃	—	8	4	no	—
496	C₂³×C₃	—	8	4	no	—
497	C₂³×C₃	—	8	4	no	—
498	C₂³×C₃	—	8	8	no	—
499	C₂³×C₃	—	8	8	no	—
500	C₂³×C₃	—	8	8	no	—
501	C₂³×C₃	—	8	8	no	—
502	C₂³×C₃	C₂²×D₄	1	2	yes	—
503	C₂³×C₃	C₂²×D₄	1	4	yes	—
504	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
505	C₂³×C₃	C₂⁵	1	1	yes	characteristic
506	C₃×Q₈	—	2	8	no	—
507	C₃×D₄	—	2	8	no	—
508	C₃×D₄	—	4	8	no	—
509	C₃×D₄	—	4	8	no	—
510	C₃×D₄	—	4	4	no	—
511	C₃×D₄	—	4	8	no	—
512	C₃×D₄	—	4	4	no	—
513	C₃×D₄	—	4	8	no	—
514	C₃×D₄	—	8	8	no	—
515	C₃×D₄	—	8	8	no	—
516	C₃×D₄	—	8	4	no	—
517	C₃×D₄	—	8	8	no	—
518	C₃×D₄	—	8	8	no	—
519	C₃×D₄	—	8	8	no	—
520	C₂×C₃×C₄	—	2	2	no	—
521	C₂×C₃×C₄	—	2	4	no	—
522	C₂×C₃×C₄	—	2	2	no	—
523	C₂×C₃×C₄	—	2	2	no	—
524	C₂×C₃×C₄	—	2	8	no	—
525	C₂×C₃×C₄	—	2	1	no	—
526	C₂×C₃×C₄	—	2	1	no	—
527	C₂×C₃×C₄	—	2	2	no	—
528	C₂×C₃×C₄	—	2	2	no	—
529	C₂×C₃×C₄	—	2	2	no	—
530	C₂×C₃×C₄	—	2	1	no	—
531	C₂×C₃×C₄	—	2	2	no	—
532	C₂×C₃×C₄	—	2	4	no	—
533	C₂×C₃×C₄	—	2	4	no	—
534	C₂×C₃×C₄	—	2	2	no	—
535	C₂×C₃×C₄	—	2	2	no	—
536	C₂×C₃×C₄	—	2	2	no	—
537	C₂×C₃×C₄	—	2	2	no	—
538	C₂×C₃×C₄	—	2	4	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	1	no	—
545	C₂×C₃×C₄	—	2	2	no	—
546	C₂×C₃×C₄	—	4	8	no	—
547	C₂×C₃×C₄	—	4	4	no	—
548	C₂×C₃×C₄	—	8	4	no	—
549	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
550	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
551	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
552	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
553	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
554	C₂⁴	—	2	4	no	—
555	C₂⁴	—	2	4	no	—
556	C₂⁴	—	2	4	no	—
557	C₂⁴	—	4	4	no	—
558	C₂⁴	—	4	4	no	—
559	C₂⁴	—	4	2	no	—
560	C₂⁴	—	4	4	no	—
561	C₂⁴	—	4	4	no	—
562	C₂⁴	—	4	2	no	—
563	C₂⁴	—	4	2	no	—
564	C₂⁴	C₂⁴×C₃	1	2	yes	—
565	C₂⁴	C₂⁴×C₃	1	4	yes	—
566	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
567	C₂⁴	C₂⁴×C₃	1	2	yes	—
568	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
569	#41	—	4	16	no	—
570	C₂×Q₈	—	2	4	no	—
571	C₂×Q₈	C₂×C₃×D₄	1	4	yes	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	4	no	—
576	C₂×D₄	—	2	8	no	—
577	C₂×D₄	—	2	8	no	—
578	C₂×D₄	—	2	8	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	2	no	—
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	4	no	—
586	C₂×D₄	—	2	8	no	—
587	C₂×D₄	—	4	4	no	—
588	C₂×D₄	—	4	4	no	—
589	C₂×D₄	—	4	4	no	—
590	C₂×D₄	—	4	1	no	—
591	C₂×D₄	—	4	16	no	—
592	C₂×D₄	—	4	4	no	—
593	C₂×D₄	—	4	4	no	—
594	C₂×D₄	—	4	4	no	—
595	C₂×D₄	—	4	4	no	—
596	C₂×D₄	—	4	4	no	—
597	C₂×D₄	—	4	4	no	—
598	C₂×D₄	—	4	4	no	—
599	C₂×D₄	—	4	4	no	—
600	C₂×D₄	—	4	4	no	—
601	C₂×D₄	—	4	4	no	—
602	C₂×D₄	—	4	4	no	—
603	C₂×D₄	—	4	4	no	—
604	C₂×D₄	—	4	16	no	—
605	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
606	C₂×D₄	C₂×C₃×D₄	1	8	yes	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	4	4	no	—
612	C₂²×C₄	—	4	4	no	—
613	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
614	C₂²×C₄	C₂×C₃×D₄	1	8	yes	—
615	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
620	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
621	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
624	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
627	C₄⋊C₄	—	2	2	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	4	4	no	—
635	C₄⋊C₄	—	4	4	no	—
636	C₄⋊C₄	—	4	2	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	8	no	—
646	C₂²⋊C₄	—	2	8	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	8	no	—
651	C₂²⋊C₄	—	2	8	no	—
652	C₂²⋊C₄	—	4	4	no	—
653	C₂²⋊C₄	—	4	4	no	—
654	C₂²⋊C₄	—	4	4	no	—
655	C₂²⋊C₄	—	4	4	no	—
656	C₂²⋊C₄	—	4	2	no	—
657	C₂²⋊C₄	—	4	4	no	—
658	C₂²⋊C₄	—	4	4	no	—
659	C₂²⋊C₄	—	4	4	no	—
660	C₄²	—	2	4	no	—
661	C₄²	—	2	2	no	—
662	C₄²	—	2	4	no	—
663	C₄²	—	4	4	no	—
664	C₂²×C₃	—	2	2	no	—
665	C₂²×C₃	—	2	4	no	—
666	C₂²×C₃	—	2	2	no	—
667	C₂²×C₃	—	2	2	no	—
668	C₂²×C₃	—	2	4	no	—
669	C₂²×C₃	—	2	4	no	—
670	C₂²×C₃	—	2	2	no	—
671	C₂²×C₃	—	2	4	no	—
672	C₂²×C₃	—	4	1	no	—
673	C₂²×C₃	—	4	1	no	—
674	C₂²×C₃	—	4	4	no	—
675	C₂²×C₃	—	4	2	no	—
676	C₂²×C₃	—	4	4	no	—
677	C₂²×C₃	—	4	2	no	—
678	C₂²×C₃	—	4	2	no	—
679	C₂²×C₃	—	4	4	no	—
680	C₂²×C₃	—	4	2	no	—
681	C₂²×C₃	—	4	4	no	—
682	C₂²×C₃	—	4	2	no	—
683	C₂²×C₃	—	4	2	no	—
684	C₂²×C₃	—	4	4	no	—
685	C₂²×C₃	—	4	4	no	—
686	C₂²×C₃	—	4	4	no	—
687	C₂²×C₃	—	4	4	no	—
688	C₂²×C₃	—	4	4	no	—
689	C₂²×C₃	—	4	4	no	—
690	C₂²×C₃	—	4	4	no	—
691	C₂²×C₃	—	8	16	no	—
692	C₂²×C₃	—	8	16	no	—
693	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
694	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
695	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
696	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
697	C₂²×C₃	#585	1	1	yes	characteristic
698	C₃×C₄	—	2	2	no	—
699	C₃×C₄	—	2	4	no	—
700	C₃×C₄	—	2	4	no	—
701	C₃×C₄	—	4	1	no	—
702	C₃×C₄	—	4	1	no	—
703	C₃×C₄	—	4	2	no	—
704	C₃×C₄	—	4	1	no	—
705	C₃×C₄	—	4	2	no	—
706	C₃×C₄	—	4	2	no	—
707	C₃×C₄	—	4	4	no	—
708	C₃×C₄	—	4	2	no	—
709	C₃×C₄	#534	1	4	yes	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	4	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	4	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	4	no	—
724	C₂³	—	2	4	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	4	no	—
727	C₂³	—	2	4	no	—
728	C₂³	—	2	4	no	—
729	C₂³	—	2	4	no	—
730	C₂³	—	2	4	no	—
731	C₂³	—	2	4	no	—
732	C₂³	—	2	4	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	4	8	no	—
735	C₂³	—	4	8	no	—
736	C₂³	—	4	8	no	—
737	C₂³	—	8	4	no	—
738	C₂³	—	8	4	no	—
739	C₂³	—	8	4	no	—
740	C₂³	—	8	8	no	—
741	C₂³	—	8	8	no	—
742	C₂³	—	8	8	no	—
743	C₂³	—	8	8	no	—
744	C₂³	C₂²×C₃×D₄	1	2	yes	—
745	C₂³	C₂²×C₃×D₄	1	4	yes	—
746	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
747	C₂³	C₂⁵×C₃	1	1	yes	characteristic
748	Q₈	—	2	8	no	—
749	D₄	—	2	8	no	—
750	D₄	—	4	8	no	—
751	D₄	—	4	8	no	—
752	D₄	—	4	4	no	—
753	D₄	—	4	8	no	—
754	D₄	—	4	4	no	—
755	D₄	—	4	8	no	—
756	D₄	—	8	8	no	—
757	D₄	—	8	8	no	—
758	D₄	—	8	4	no	—
759	D₄	—	8	8	no	—
760	D₄	—	8	8	no	—
761	D₄	—	8	8	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	8	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	4	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	4	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	4	8	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	8	4	no	—
791	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
792	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
793	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
794	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
795	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
796	C₂×C₃	—	4	4	no	—
797	C₂×C₃	—	4	2	no	—
798	C₂×C₃	—	4	2	no	—
799	C₂×C₃	—	8	4	no	—
800	C₂×C₃	—	8	2	no	—
801	C₂×C₃	C₂×#534	1	1	yes	characteristic
802	C₂×C₃	#3488	1	1	yes	characteristic
803	C₂×C₃	#3498	1	1	yes	characteristic
804	C₂×C₃	#3543	1	2	yes	—
805	C₂×C₃	#3558	1	2	yes	—
806	C₂²	—	2	2	no	—
807	C₂²	—	2	4	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	2	no	—
810	C₂²	—	2	4	no	—
811	C₂²	—	2	4	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	4	no	—
814	C₂²	—	4	1	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	4	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	4	no	—
821	C₂²	—	4	4	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	4	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	4	no	—
827	C₂²	—	4	4	no	—
828	C₂²	—	4	4	no	—
829	C₂²	—	4	4	no	—
830	C₂²	—	4	4	no	—
831	C₂²	—	4	4	no	—
832	C₂²	—	4	4	no	—
833	C₂²	—	8	16	no	—
834	C₂²	—	8	16	no	—
835	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
836	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
837	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
838	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
839	C₂²	C₃×#585	1	1	yes	characteristic
840	C₄	—	2	2	no	—
841	C₄	—	2	4	no	—
842	C₄	—	2	4	no	—
843	C₄	—	4	1	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	4	no	—
851	C₄	C₃×#534	1	4	yes	—
852	C₃	#42966	1	1	yes	characteristic, direct product factor, Sylow
853	C₂	—	4	2	no	—
854	C₂	—	4	2	no	—
855	C₂	—	4	4	no	—
856	C₂	—	8	4	no	—
857	C₂	—	8	2	no	—
858	C₂	C₂×C₃×#534	1	1	yes	characteristic
859	C₂	C₃×#3488	1	1	yes	characteristic
860	C₂	C₃×#3498	1	1	yes	characteristic
861	C₂	C₃×#3543	1	2	yes	—
862	C₂	C₃×#3558	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×#535	C₂	semidirect
3. C₃×#2813	C₂	semidirect
4. C₃×#2679	C₂	semidirect
5. C₃×#2678	C₂	semidirect
6. C₃×#2661	C₂	semidirect
7. C₃×#2624	C₂	semidirect
8. C₃×#2617	C₂	semidirect
9. C₃×#2548	C₂	semidirect
10. C₃×#2539	C₂	semidirect
11. C₃×#2445	C₂	semidirect
12. C₃×#2433	C₂	semidirect
13. C₃×#2433	C₂	semidirect
14. C₃×#2426	C₂	semidirect
15. C₃×#2408	C₂	semidirect
16. C₃×#2395	C₂	semidirect
17. C₃×#2341	C₂	semidirect
18. #42966	C₃	direct (N × H)
20. C₂³×C₃×D₄	C₂²	semidirect
21. C₂³×C₃×D₄	C₂²	semidirect
26. C₂×C₃×#124	C₂²	semidirect
27. C₂×C₃×#124	C₂²	semidirect
28. C₂×C₃×#123	C₂²	semidirect
29. C₂×C₃×#123	C₂²	semidirect
30. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
34. C₂×C₃×#121	C₂²	semidirect
35. C₂×C₃×#121	C₂²	semidirect
38. C₂×C₃×#120	C₂²	semidirect
39. C₂×C₃×#120	C₂²	semidirect
40. C₂×C₃×#120	C₂²	semidirect
41. C₂×C₃×#120	C₂²	semidirect
42. C₂×C₃×C₄×Q₈	C₂²	semidirect
44. C₂×C₃×C₄×D₄	C₂²	semidirect
45. C₂×C₃×#117	C₂²	semidirect
46. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
47. C₃×#400	C₂²	semidirect
48. C₃×#399	C₂²	semidirect
49. C₃×#399	C₂²	semidirect
50. C₃×#398	C₂²	semidirect
51. C₃×#397	C₂²	semidirect
52. C₃×#397	C₂²	semidirect
53. C₃×#397	C₂²	semidirect
54. C₃×#396	C₂²	semidirect
56. C₃×#394	C₂²	semidirect
57. C₃×#394	C₂²	semidirect
58. C₃×#394	C₂²	semidirect
59. C₃×#394	C₂²	semidirect
60. C₃×#394	C₂²	semidirect
61. C₃×#394	C₂²	semidirect
62. C₃×#394	C₂²	semidirect
64. C₃×#392	C₂²	semidirect
65. C₃×#392	C₂²	semidirect
66. C₃×#392	C₂²	semidirect
67. C₃×#392	C₂²	semidirect
68. C₃×#390	C₂²	semidirect
69. C₃×#390	C₂²	semidirect
70. C₃×#390	C₂²	semidirect
71. C₃×#390	C₂²	semidirect
72. C₃×#390	C₂²	semidirect
73. C₃×#390	C₂²	semidirect
74. C₃×#390	C₂²	semidirect
75. C₃×#390	C₂²	semidirect
76. C₃×#389	C₂²	semidirect
77. C₃×#388	C₂²	semidirect
78. C₃×#386	C₂²	semidirect
79. C₃×#380	C₂²	semidirect
80. C₃×#380	C₂²	semidirect
81. C₃×#379	C₂²	semidirect
82. C₃×C₄×C₄⋊C₄	C₂²	semidirect
83. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
84. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
85. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
86. C₂×#546	C₂×C₃	semidirect
87. C₂×#535	C₂×C₃	semidirect
88. #2813	C₂×C₃	semidirect
89. #2679	C₂×C₃	semidirect
90. #2678	C₂×C₃	semidirect
91. #2661	C₂×C₃	semidirect
92. #2624	C₂×C₃	semidirect
93. #2617	C₂×C₃	semidirect
94. #2548	C₂×C₃	semidirect
95. #2539	C₂×C₃	semidirect
96. #2445	C₂×C₃	semidirect
97. #2433	C₂×C₃	semidirect
98. #2433	C₂×C₃	semidirect
99. #2426	C₂×C₃	semidirect
100. #2408	C₂×C₃	semidirect
101. #2395	C₂×C₃	semidirect
102. #2341	C₂×C₃	semidirect
106. C₂×C₃×#41	D₄	semidirect
198. C₂³×D₄	C₂²×C₃	semidirect
199. C₂³×D₄	C₂²×C₃	semidirect
204. C₂×#124	C₂²×C₃	semidirect
205. C₂×#124	C₂²×C₃	semidirect
206. C₂×#123	C₂²×C₃	semidirect
207. C₂×#123	C₂²×C₃	semidirect
208. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
212. C₂×#121	C₂²×C₃	semidirect
213. C₂×#121	C₂²×C₃	semidirect
216. C₂×#120	C₂²×C₃	semidirect
217. C₂×#120	C₂²×C₃	semidirect
218. C₂×#120	C₂²×C₃	semidirect
219. C₂×#120	C₂²×C₃	semidirect
220. C₂×C₄×Q₈	C₂²×C₃	semidirect
222. C₂×C₄×D₄	C₂²×C₃	semidirect
223. C₂×#117	C₂²×C₃	semidirect
224. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
225. #400	C₂²×C₃	semidirect
226. #399	C₂²×C₃	semidirect
227. #399	C₂²×C₃	semidirect
228. #398	C₂²×C₃	semidirect
229. #397	C₂²×C₃	semidirect
230. #397	C₂²×C₃	semidirect
231. #397	C₂²×C₃	semidirect
232. #396	C₂²×C₃	semidirect
234. #394	C₂²×C₃	semidirect
235. #394	C₂²×C₃	semidirect
236. #394	C₂²×C₃	semidirect
237. #394	C₂²×C₃	semidirect
238. #394	C₂²×C₃	semidirect
239. #394	C₂²×C₃	semidirect
240. #394	C₂²×C₃	semidirect
242. #392	C₂²×C₃	semidirect
243. #392	C₂²×C₃	semidirect
244. #392	C₂²×C₃	semidirect
245. #392	C₂²×C₃	semidirect
246. #390	C₂²×C₃	semidirect
247. #390	C₂²×C₃	semidirect
248. #390	C₂²×C₃	semidirect
249. #390	C₂²×C₃	semidirect
250. #390	C₂²×C₃	semidirect
251. #390	C₂²×C₃	semidirect
252. #390	C₂²×C₃	semidirect
253. #390	C₂²×C₃	semidirect
254. #389	C₂²×C₃	semidirect
255. #388	C₂²×C₃	semidirect
256. #386	C₂²×C₃	semidirect
257. #380	C₂²×C₃	semidirect
258. #380	C₂²×C₃	semidirect
259. #379	C₂²×C₃	semidirect
260. C₄×C₄⋊C₄	C₂²×C₃	semidirect
261. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
262. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
263. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
377. C₂×#41	C₃×D₄	semidirect
852. C₃	#42966	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×#535	2
C₃×#2813	2
C₃×#2679	2
C₃×#2678	2
C₃×#2661	2
C₃×#2624	2
C₃×#2617	2
C₃×#2548	2
C₃×#2539	2
C₃×#2445	2
C₃×#2433	2
C₃×#2426	2
C₃×#2408	2
C₃×#2395	2
C₃×#2341	2
#42966	3

Subgroups — C3×#42966 #10661573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#42966 #10661573