Subgroups — C₃×#42987 #10661594

Order 768.

2574 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2818	C₂	1	2	yes	maximal, complemented
4	C₃×#2685	C₂	1	4	yes	maximal, complemented
5	C₃×#2670	C₂	1	4	yes	maximal, complemented
6	C₃×#2662	C₂	1	2	yes	maximal, complemented
7	C₃×#2632	C₂	1	2	yes	maximal, complemented
8	C₃×#2616	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2548	C₂	1	2	yes	maximal, complemented
10	C₃×#2540	C₂	1	2	yes	maximal, complemented
11	C₃×#2491	C₂	1	2	yes	maximal, complemented
12	C₃×#2435	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2426	C₂	1	2	yes	maximal, complemented
14	C₃×#2414	C₂	1	2	yes	maximal, complemented
15	C₃×#2408	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2388	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2347	C₂	1	1	yes	maximal, characteristic, complemented
18	#42987	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
21	C₃×#556	—	2	8	no	—
22	C₃×#535	—	2	8	no	—
23	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×#127	C₂²	1	2	yes	—
25	C₂×C₃×#126	C₂²	1	2	yes	—
26	C₂×C₃×#126	C₂²	1	2	yes	complemented
27	C₂×C₃×#124	C₂²	1	2	yes	—
28	C₂×C₃×#124	C₂²	1	2	yes	—
29	C₂×C₃×#124	C₂²	1	2	yes	—
30	C₂×C₃×#124	C₂²	1	4	yes	complemented
31	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₂×C₃×#121	C₂²	1	2	yes	—
35	C₂×C₃×#121	C₂²	1	2	yes	—
36	C₂×C₃×#121	C₂²	1	2	yes	—
37	C₂×C₃×#120	C₂²	1	4	yes	—
38	C₂×C₃×#120	C₂²	1	2	yes	—
39	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	complemented
40	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
43	C₂×C₃×#117	C₂²	1	1	yes	characteristic
44	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
45	C₃×#399	C₂²	1	4	yes	complemented
46	C₃×#396	C₂²	1	4	yes	complemented
47	C₃×#395	C₂²	1	2	yes	complemented
48	C₃×#395	C₂²	1	1	yes	characteristic, complemented
49	C₃×#394	C₂²	1	4	yes	—
50	C₃×#394	C₂²	1	2	yes	—
51	C₃×#394	C₂²	1	2	yes	—
52	C₃×#394	C₂²	1	2	yes	—
53	C₃×#394	C₂²	1	2	yes	—
54	C₃×#394	C₂²	1	2	yes	complemented
55	C₃×#394	C₂²	1	1	yes	characteristic, complemented
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×#393	C₂²	1	4	yes	complemented
60	C₃×#393	C₂²	1	1	yes	characteristic, complemented
61	C₃×#392	C₂²	1	2	yes	—
62	C₃×#392	C₂²	1	2	yes	—
63	C₃×#392	C₂²	1	1	yes	characteristic, complemented
64	C₃×#392	C₂²	1	4	yes	complemented
65	C₃×#392	C₂²	1	4	yes	complemented
66	C₃×#390	C₂²	1	2	yes	—
67	C₃×#390	C₂²	1	2	yes	—
68	C₃×#390	C₂²	1	4	yes	complemented
69	C₃×#390	C₂²	1	4	yes	complemented
70	C₃×#390	C₂²	1	4	yes	complemented
71	C₃×#390	C₂²	1	4	yes	complemented
72	C₃×#389	C₂²	1	2	yes	complemented
73	C₃×#388	C₂²	1	4	yes	—
74	C₃×#388	C₂²	1	4	yes	complemented
75	C₃×#388	C₂²	1	4	yes	complemented
76	C₃×#388	C₂²	1	4	yes	complemented
77	C₃×#383	C₂²	1	2	yes	complemented
78	C₃×#380	C₂²	1	1	yes	characteristic
79	C₃×#380	C₂²	1	2	yes	complemented
80	C₃×#379	C₂²	1	2	yes	—
81	C₃×#379	C₂²	1	4	yes	—
82	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
83	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
84	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
85	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
86	C₂×#556	C₂×C₃	1	1	yes	characteristic, complemented
87	C₂×#535	C₂×C₃	1	1	yes	characteristic, complemented
88	#2818	C₂×C₃	1	2	yes	complemented
89	#2685	C₂×C₃	1	4	yes	complemented
90	#2670	C₂×C₃	1	4	yes	complemented
91	#2662	C₂×C₃	1	2	yes	complemented
92	#2632	C₂×C₃	1	2	yes	complemented
93	#2616	C₂×C₃	1	1	yes	characteristic, complemented
94	#2548	C₂×C₃	1	2	yes	complemented
95	#2540	C₂×C₃	1	2	yes	complemented
96	#2491	C₂×C₃	1	2	yes	complemented
97	#2435	C₂×C₃	1	1	yes	characteristic, complemented
98	#2426	C₂×C₃	1	2	yes	complemented
99	#2414	C₂×C₃	1	2	yes	complemented
100	#2408	C₂×C₃	1	1	yes	characteristic, complemented
101	#2388	C₂×C₃	1	1	yes	characteristic, complemented
102	#2347	C₂×C₃	1	1	yes	characteristic, complemented
103	C₂⁵×C₃	C₂³	1	2	yes	—
104	C₂×C₃×#41	—	2	4	no	—
105	C₂×C₃×#41	—	4	4	no	—
106	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
107	C₂²×C₃×Q₈	C₂³	1	2	yes	—
108	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
109	C₂²×C₃×D₄	—	2	4	no	—
110	C₂²×C₃×D₄	—	4	4	no	—
111	C₂²×C₃×D₄	C₂³	1	2	yes	—
112	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
113	C₂²×C₃×D₄	C₂³	1	2	yes	—
114	C₂²×C₃×D₄	C₂³	1	2	yes	—
115	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
116	C₂²×C₃×D₄	C₂³	1	4	yes	—
117	C₂²×C₃×D₄	C₂³	1	4	yes	—
118	C₂²×C₃×D₄	C₂³	1	4	yes	—
119	C₂²×C₃×D₄	C₂³	1	2	yes	—
120	C₂³×C₃×C₄	C₂³	1	2	yes	—
121	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
122	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
123	C₃×C₄⋊Q₈	—	2	4	no	—
124	C₃×#127	—	2	8	no	—
125	C₃×#126	—	2	8	no	—
126	C₃×#126	—	2	8	no	—
127	C₃×#124	—	2	8	no	—
128	C₃×#124	—	2	8	no	—
129	C₃×#124	—	4	4	no	—
130	C₃×#124	—	4	8	no	—
131	C₃×C₂²⋊Q₈	—	2	4	no	—
132	C₃×C₂²⋊Q₈	—	2	4	no	—
133	C₃×C₂²⋊Q₈	—	4	4	no	—
134	C₃×#121	—	2	8	no	—
135	C₃×#121	—	2	8	no	—
136	C₃×#121	—	4	4	no	—
137	C₃×#120	—	2	16	no	—
138	C₃×#120	—	4	4	no	—
139	C₃×C₄×Q₈	—	2	4	no	—
140	C₃×C₄×Q₈	—	2	8	no	—
141	C₃×C₄×D₄	—	2	4	no	—
142	C₃×C₄×D₄	—	4	4	no	—
143	C₃×#117	—	2	4	no	—
144	C₃×#117	D₄	1	8	yes	complemented
145	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
153	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
155	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
161	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
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	1	yes	characteristic
165	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
170	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
171	C₂×C₃×C₂²⋊C₄	C₂³	1	4	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	4	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	2	yes	—
178	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
179	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₄²	C₂³	1	2	yes	—
181	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
182	C₂×C₃×C₄²	C₂³	1	2	yes	—
183	C₂×C₃×C₄²	C₂³	1	2	yes	—
184	C₂×C₃×C₄²	C₂³	1	4	yes	—
185	C₂×C₃×C₄²	C₂³	1	2	yes	—
186	C₃×#95	C₂³	1	1	yes	characteristic
187	C₃×#95	C₂³	1	1	yes	characteristic
188	C₃×#95	C₂³	1	2	yes	—
189	C₃×#95	C₂³	1	2	yes	—
190	C₃×#95	C₂³	1	2	yes	—
191	C₃×#95	C₂³	1	4	yes	—
192	C₃×#95	C₂³	1	4	yes	—
193	C₃×#95	C₂³	1	4	yes	—
194	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
195	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
196	#556	—	2	8	no	—
197	#535	—	2	8	no	—
198	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
199	C₂×#127	C₂²×C₃	1	2	yes	—
200	C₂×#126	C₂²×C₃	1	2	yes	—
201	C₂×#126	C₂²×C₃	1	2	yes	complemented
202	C₂×#124	C₂²×C₃	1	2	yes	—
203	C₂×#124	C₂²×C₃	1	2	yes	—
204	C₂×#124	C₂²×C₃	1	2	yes	—
205	C₂×#124	C₂²×C₃	1	4	yes	complemented
206	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
207	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
208	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
209	C₂×#121	C₂²×C₃	1	2	yes	—
210	C₂×#121	C₂²×C₃	1	2	yes	—
211	C₂×#121	C₂²×C₃	1	2	yes	—
212	C₂×#120	C₂²×C₃	1	4	yes	—
213	C₂×#120	C₂²×C₃	1	2	yes	—
214	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
215	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
216	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
217	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
218	C₂×#117	C₂²×C₃	1	1	yes	characteristic
219	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
220	#399	C₂²×C₃	1	4	yes	complemented
221	#396	C₂²×C₃	1	4	yes	complemented
222	#395	C₂²×C₃	1	2	yes	complemented
223	#395	C₂²×C₃	1	1	yes	characteristic, complemented
224	#394	C₂²×C₃	1	2	yes	—
225	#394	C₂²×C₃	1	4	yes	—
226	#394	C₂²×C₃	1	2	yes	—
227	#394	C₂²×C₃	1	2	yes	—
228	#394	C₂²×C₃	1	2	yes	—
229	#394	C₂²×C₃	1	2	yes	complemented
230	#394	C₂²×C₃	1	4	yes	complemented
231	#394	C₂²×C₃	1	4	yes	complemented
232	#394	C₂²×C₃	1	1	yes	characteristic, complemented
233	#394	C₂²×C₃	1	4	yes	complemented
234	#393	C₂²×C₃	1	4	yes	complemented
235	#393	C₂²×C₃	1	1	yes	characteristic, complemented
236	#392	C₂²×C₃	1	2	yes	—
237	#392	C₂²×C₃	1	2	yes	—
238	#392	C₂²×C₃	1	1	yes	characteristic, complemented
239	#392	C₂²×C₃	1	4	yes	complemented
240	#392	C₂²×C₃	1	4	yes	complemented
241	#390	C₂²×C₃	1	2	yes	—
242	#390	C₂²×C₃	1	2	yes	—
243	#390	C₂²×C₃	1	4	yes	complemented
244	#390	C₂²×C₃	1	4	yes	complemented
245	#390	C₂²×C₃	1	4	yes	complemented
246	#390	C₂²×C₃	1	4	yes	complemented
247	#389	C₂²×C₃	1	2	yes	complemented
248	#388	C₂²×C₃	1	4	yes	—
249	#388	C₂²×C₃	1	4	yes	complemented
250	#388	C₂²×C₃	1	4	yes	complemented
251	#388	C₂²×C₃	1	4	yes	complemented
252	#383	C₂²×C₃	1	2	yes	complemented
253	#380	C₂²×C₃	1	1	yes	characteristic
254	#380	C₂²×C₃	1	2	yes	complemented
255	#379	C₂²×C₃	1	2	yes	—
256	#379	C₂²×C₃	1	4	yes	—
257	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
258	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
259	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
260	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
261	C₂⁴×C₃	—	2	4	no	—
262	C₂⁴×C₃	—	4	4	no	—
263	C₂⁴×C₃	—	4	4	no	—
264	C₂⁴×C₃	—	4	2	no	—
265	C₂⁴×C₃	—	4	2	no	—
266	C₂⁴×C₃	C₂⁴	1	4	yes	—
267	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
268	C₂⁴×C₃	C₂⁴	1	2	yes	—
269	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
270	C₃×#41	—	4	16	no	—
271	C₂×C₃×Q₈	—	2	2	no	—
272	C₂×C₃×Q₈	—	2	4	no	—
273	C₂×C₃×Q₈	—	2	2	no	—
274	C₂×C₃×Q₈	—	2	4	no	—
275	C₂×C₃×Q₈	—	2	4	no	—
276	C₂×C₃×Q₈	—	4	2	no	—
277	C₂×C₃×Q₈	—	4	2	no	—
278	C₂×C₃×D₄	—	2	2	no	—
279	C₂×C₃×D₄	—	2	4	no	—
280	C₂×C₃×D₄	—	2	4	no	—
281	C₂×C₃×D₄	—	2	4	no	—
282	C₂×C₃×D₄	—	2	2	no	—
283	C₂×C₃×D₄	—	2	8	no	—
284	C₂×C₃×D₄	—	2	8	no	—
285	C₂×C₃×D₄	—	2	2	no	—
286	C₂×C₃×D₄	—	2	4	no	—
287	C₂×C₃×D₄	—	2	4	no	—
288	C₂×C₃×D₄	—	4	2	no	—
289	C₂×C₃×D₄	—	4	4	no	—
290	C₂×C₃×D₄	—	4	1	no	—
291	C₂×C₃×D₄	—	4	2	no	—
292	C₂×C₃×D₄	—	4	2	no	—
293	C₂×C₃×D₄	—	4	2	no	—
294	C₂×C₃×D₄	—	4	2	no	—
295	C₂×C₃×D₄	—	4	2	no	—
296	C₂×C₃×D₄	—	4	16	no	—
297	C₂×C₃×D₄	—	4	4	no	—
298	C₂×C₃×D₄	—	4	4	no	—
299	C₂×C₃×D₄	—	4	4	no	—
300	C₂×C₃×D₄	—	4	4	no	—
301	C₂×C₃×D₄	—	4	4	no	—
302	C₂×C₃×D₄	—	4	4	no	—
303	C₂×C₃×D₄	—	4	4	no	—
304	C₂²×C₃×C₄	—	2	4	no	—
305	C₂²×C₃×C₄	—	2	2	no	—
306	C₂²×C₃×C₄	—	2	4	no	—
307	C₂²×C₃×C₄	—	2	4	no	—
308	C₂²×C₃×C₄	—	2	4	no	—
309	C₂²×C₃×C₄	—	2	4	no	—
310	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
311	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
312	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
313	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
314	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
315	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
316	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
317	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
318	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
319	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
320	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
321	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
322	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
323	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
324	C₃×C₄⋊C₄	—	2	2	no	—
325	C₃×C₄⋊C₄	—	2	2	no	—
326	C₃×C₄⋊C₄	—	2	4	no	—
327	C₃×C₄⋊C₄	—	2	4	no	—
328	C₃×C₄⋊C₄	—	2	4	no	—
329	C₃×C₄⋊C₄	—	2	4	no	—
330	C₃×C₄⋊C₄	—	2	4	no	—
331	C₃×C₄⋊C₄	—	4	4	no	—
332	C₃×C₄⋊C₄	—	4	2	no	—
333	C₃×C₄⋊C₄	—	4	4	no	—
334	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
335	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
336	C₃×C₂²⋊C₄	—	2	2	no	—
337	C₃×C₂²⋊C₄	—	2	4	no	—
338	C₃×C₂²⋊C₄	—	2	4	no	—
339	C₃×C₂²⋊C₄	—	2	2	no	—
340	C₃×C₂²⋊C₄	—	2	8	no	—
341	C₃×C₂²⋊C₄	—	2	8	no	—
342	C₃×C₂²⋊C₄	—	2	4	no	—
343	C₃×C₂²⋊C₄	—	2	8	no	—
344	C₃×C₂²⋊C₄	—	2	4	no	—
345	C₃×C₂²⋊C₄	—	4	2	no	—
346	C₃×C₂²⋊C₄	—	4	4	no	—
347	C₃×C₂²⋊C₄	—	4	4	no	—
348	C₃×C₂²⋊C₄	—	4	2	no	—
349	C₃×C₂²⋊C₄	—	4	2	no	—
350	C₃×C₂²⋊C₄	—	4	2	no	—
351	C₃×C₂²⋊C₄	—	4	2	no	—
352	C₃×C₂²⋊C₄	—	4	4	no	—
353	C₃×C₂²⋊C₄	—	4	4	no	—
354	C₃×C₂²⋊C₄	—	4	4	no	—
355	C₃×C₂²⋊C₄	—	4	4	no	—
356	C₃×C₂²⋊C₄	—	4	4	no	—
357	C₃×C₂²⋊C₄	—	4	4	no	—
358	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
359	C₃×C₄²	—	2	4	no	—
360	C₃×C₄²	—	2	2	no	—
361	C₃×C₄²	—	2	4	no	—
362	C₃×C₄²	—	2	4	no	—
363	C₃×C₄²	—	4	4	no	—
364	C₃×C₄²	C₂×D₄	1	8	yes	—
365	C₂⁵	C₂³×C₃	1	2	yes	—
366	C₂×#41	—	2	4	no	—
367	C₂×#41	—	4	4	no	—
368	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
369	C₂²×Q₈	C₂³×C₃	1	2	yes	—
370	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
371	C₂²×D₄	—	2	4	no	—
372	C₂²×D₄	—	4	4	no	—
373	C₂²×D₄	C₂³×C₃	1	2	yes	—
374	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
375	C₂²×D₄	C₂³×C₃	1	2	yes	—
376	C₂²×D₄	C₂³×C₃	1	4	yes	—
377	C₂²×D₄	C₂³×C₃	1	4	yes	—
378	C₂²×D₄	C₂³×C₃	1	2	yes	—
379	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
380	C₂²×D₄	C₂³×C₃	1	2	yes	—
381	C₂²×D₄	C₂³×C₃	1	4	yes	—
382	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
383	C₂³×C₄	C₂³×C₃	1	2	yes	—
384	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
385	C₄⋊Q₈	—	2	4	no	—
386	#127	—	2	8	no	—
387	#126	—	2	8	no	—
388	#126	—	2	8	no	—
389	#124	—	2	8	no	—
390	#124	—	2	8	no	—
391	#124	—	4	4	no	—
392	#124	—	4	8	no	—
393	C₂²⋊Q₈	—	2	4	no	—
394	C₂²⋊Q₈	—	2	4	no	—
395	C₂²⋊Q₈	—	4	4	no	—
396	#121	—	2	8	no	—
397	#121	—	2	8	no	—
398	#121	—	4	4	no	—
399	#120	—	2	16	no	—
400	#120	—	4	4	no	—
401	C₄×Q₈	—	2	4	no	—
402	C₄×Q₈	—	2	8	no	—
403	C₄×D₄	—	2	4	no	—
404	C₄×D₄	—	4	4	no	—
405	#117	—	2	4	no	—
406	#117	C₃×D₄	1	8	yes	complemented
407	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
410	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
411	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
414	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
415	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
416	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
417	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
419	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
421	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
442	C₂×C₄²	C₂³×C₃	1	2	yes	—
443	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
444	C₂×C₄²	C₂³×C₃	1	2	yes	—
445	C₂×C₄²	C₂³×C₃	1	2	yes	—
446	C₂×C₄²	C₂³×C₃	1	4	yes	—
447	C₂×C₄²	C₂³×C₃	1	2	yes	—
448	#95	C₂³×C₃	1	1	yes	characteristic
449	#95	C₂³×C₃	1	1	yes	characteristic
450	#95	C₂³×C₃	1	2	yes	—
451	#95	C₂³×C₃	1	2	yes	—
452	#95	C₂³×C₃	1	2	yes	—
453	#95	C₂³×C₃	1	4	yes	—
454	#95	C₂³×C₃	1	4	yes	—
455	#95	C₂³×C₃	1	4	yes	—
456	C₂³×C₃	—	2	1	no	—
457	C₂³×C₃	—	2	2	no	—
458	C₂³×C₃	—	2	2	no	—
459	C₂³×C₃	—	2	1	no	—
460	C₂³×C₃	—	2	1	no	—
461	C₂³×C₃	—	2	4	no	—
462	C₂³×C₃	—	2	2	no	—
463	C₂³×C₃	—	2	2	no	—
464	C₂³×C₃	—	2	4	no	—
465	C₂³×C₃	—	2	2	no	—
466	C₂³×C₃	—	2	4	no	—
467	C₂³×C₃	—	2	2	no	—
468	C₂³×C₃	—	2	2	no	—
469	C₂³×C₃	—	2	4	no	—
470	C₂³×C₃	—	2	1	no	—
471	C₂³×C₃	—	2	2	no	—
472	C₂³×C₃	—	2	4	no	—
473	C₂³×C₃	—	2	4	no	—
474	C₂³×C₃	—	2	1	no	—
475	C₂³×C₃	—	2	2	no	—
476	C₂³×C₃	—	2	2	no	—
477	C₂³×C₃	—	2	2	no	—
478	C₂³×C₃	—	2	4	no	—
479	C₂³×C₃	—	4	8	no	—
480	C₂³×C₃	—	8	4	no	—
481	C₂³×C₃	—	8	4	no	—
482	C₂³×C₃	—	8	8	no	—
483	C₂³×C₃	—	8	8	no	—
484	C₂³×C₃	C₂²×D₄	1	2	yes	—
485	C₂³×C₃	C₂⁵	1	1	yes	characteristic
486	C₃×Q₈	—	4	8	no	—
487	C₃×Q₈	—	4	4	no	—
488	C₃×Q₈	—	4	4	no	—
489	C₃×D₄	—	4	4	no	—
490	C₃×D₄	—	4	8	no	—
491	C₃×D₄	—	4	4	no	—
492	C₃×D₄	—	4	8	no	—
493	C₃×D₄	—	4	8	no	—
494	C₃×D₄	—	4	8	no	—
495	C₃×D₄	—	8	8	no	—
496	C₃×D₄	—	8	8	no	—
497	C₃×D₄	—	8	8	no	—
498	C₂×C₃×C₄	—	2	1	no	—
499	C₂×C₃×C₄	—	2	2	no	—
500	C₂×C₃×C₄	—	2	2	no	—
501	C₂×C₃×C₄	—	2	4	no	—
502	C₂×C₃×C₄	—	2	2	no	—
503	C₂×C₃×C₄	—	2	1	no	—
504	C₂×C₃×C₄	—	2	8	no	—
505	C₂×C₃×C₄	—	2	1	no	—
506	C₂×C₃×C₄	—	2	1	no	—
507	C₂×C₃×C₄	—	2	2	no	—
508	C₂×C₃×C₄	—	2	2	no	—
509	C₂×C₃×C₄	—	2	2	no	—
510	C₂×C₃×C₄	—	2	2	no	—
511	C₂×C₃×C₄	—	2	2	no	—
512	C₂×C₃×C₄	—	2	2	no	—
513	C₂×C₃×C₄	—	2	4	no	—
514	C₂×C₃×C₄	—	2	2	no	—
515	C₂×C₃×C₄	—	2	2	no	—
516	C₂×C₃×C₄	—	2	4	no	—
517	C₂×C₃×C₄	—	2	4	no	—
518	C₂×C₃×C₄	—	2	2	no	—
519	C₂×C₃×C₄	—	2	2	no	—
520	C₂×C₃×C₄	—	2	2	no	—
521	C₂×C₃×C₄	—	2	2	no	—
522	C₂×C₃×C₄	—	2	2	no	—
523	C₂×C₃×C₄	—	2	2	no	—
524	C₂×C₃×C₄	—	2	2	no	—
525	C₂×C₃×C₄	—	2	4	no	—
526	C₂×C₃×C₄	—	4	4	no	—
527	C₂×C₃×C₄	—	4	8	no	—
528	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
529	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
530	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
531	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
532	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
533	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
534	C₂⁴	—	2	4	no	—
535	C₂⁴	—	4	4	no	—
536	C₂⁴	—	4	2	no	—
537	C₂⁴	—	4	4	no	—
538	C₂⁴	—	4	2	no	—
539	C₂⁴	C₂⁴×C₃	1	4	yes	—
540	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
541	C₂⁴	C₂⁴×C₃	1	2	yes	—
542	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
543	#41	—	4	16	no	—
544	C₂×Q₈	—	2	2	no	—
545	C₂×Q₈	—	2	4	no	—
546	C₂×Q₈	—	2	2	no	—
547	C₂×Q₈	—	2	4	no	—
548	C₂×Q₈	—	2	4	no	—
549	C₂×Q₈	—	4	2	no	—
550	C₂×Q₈	—	4	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	4	no	—
553	C₂×D₄	—	2	4	no	—
554	C₂×D₄	—	2	4	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	2	8	no	—
557	C₂×D₄	—	2	8	no	—
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	—	2	4	no	—
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	4	2	no	—
562	C₂×D₄	—	4	4	no	—
563	C₂×D₄	—	4	2	no	—
564	C₂×D₄	—	4	2	no	—
565	C₂×D₄	—	4	2	no	—
566	C₂×D₄	—	4	1	no	—
567	C₂×D₄	—	4	2	no	—
568	C₂×D₄	—	4	2	no	—
569	C₂×D₄	—	4	16	no	—
570	C₂×D₄	—	4	4	no	—
571	C₂×D₄	—	4	4	no	—
572	C₂×D₄	—	4	4	no	—
573	C₂×D₄	—	4	4	no	—
574	C₂×D₄	—	4	4	no	—
575	C₂×D₄	—	4	4	no	—
576	C₂×D₄	—	4	4	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
584	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
586	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
591	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
593	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	4	2	no	—
605	C₄⋊C₄	—	4	4	no	—
606	C₄⋊C₄	—	4	4	no	—
607	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
608	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	2	2	no	—
613	C₂²⋊C₄	—	2	8	no	—
614	C₂²⋊C₄	—	2	8	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	8	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	4	2	no	—
619	C₂²⋊C₄	—	4	2	no	—
620	C₂²⋊C₄	—	4	2	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	—	4	4	no	—
626	C₂²⋊C₄	—	4	4	no	—
627	C₂²⋊C₄	—	4	2	no	—
628	C₂²⋊C₄	—	4	4	no	—
629	C₂²⋊C₄	—	4	4	no	—
630	C₂²⋊C₄	—	4	2	no	—
631	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	2	no	—
634	C₄²	—	2	4	no	—
635	C₄²	—	2	4	no	—
636	C₄²	—	4	4	no	—
637	C₄²	C₂×C₃×D₄	1	8	yes	—
638	C₂²×C₃	—	2	2	no	—
639	C₂²×C₃	—	2	2	no	—
640	C₂²×C₃	—	2	2	no	—
641	C₂²×C₃	—	4	2	no	—
642	C₂²×C₃	—	4	2	no	—
643	C₂²×C₃	—	4	2	no	—
644	C₂²×C₃	—	4	1	no	—
645	C₂²×C₃	—	4	4	no	—
646	C₂²×C₃	—	4	1	no	—
647	C₂²×C₃	—	4	2	no	—
648	C₂²×C₃	—	4	4	no	—
649	C₂²×C₃	—	4	2	no	—
650	C₂²×C₃	—	4	4	no	—
651	C₂²×C₃	—	4	1	no	—
652	C₂²×C₃	—	4	2	no	—
653	C₂²×C₃	—	4	2	no	—
654	C₂²×C₃	—	4	2	no	—
655	C₂²×C₃	—	4	4	no	—
656	C₂²×C₃	—	4	4	no	—
657	C₂²×C₃	—	4	2	no	—
658	C₂²×C₃	—	4	4	no	—
659	C₂²×C₃	—	4	2	no	—
660	C₂²×C₃	—	4	2	no	—
661	C₂²×C₃	—	4	4	no	—
662	C₂²×C₃	—	8	16	no	—
663	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
664	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
665	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
666	C₂²×C₃	#585	1	1	yes	characteristic
667	C₂²×C₃	#585	1	2	yes	—
668	C₃×C₄	—	2	2	no	—
669	C₃×C₄	—	2	4	no	—
670	C₃×C₄	—	2	2	no	—
671	C₃×C₄	—	2	4	no	—
672	C₃×C₄	—	4	1	no	—
673	C₃×C₄	—	4	2	no	—
674	C₃×C₄	—	4	2	no	—
675	C₃×C₄	—	4	2	no	—
676	C₃×C₄	—	4	1	no	—
677	C₃×C₄	—	4	2	no	—
678	C₃×C₄	—	4	2	no	—
679	C₃×C₄	—	4	4	no	—
680	C₃×C₄	#535	1	4	yes	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	1	no	—
685	C₂³	—	2	1	no	—
686	C₂³	—	2	4	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	4	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	4	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	2	4	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	4	no	—
698	C₂³	—	2	4	no	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	4	no	—
704	C₂³	—	4	8	no	—
705	C₂³	—	8	4	no	—
706	C₂³	—	8	4	no	—
707	C₂³	—	8	8	no	—
708	C₂³	—	8	8	no	—
709	C₂³	C₂²×C₃×D₄	1	2	yes	—
710	C₂³	C₂⁵×C₃	1	1	yes	characteristic
711	Q₈	—	4	8	no	—
712	Q₈	—	4	4	no	—
713	Q₈	—	4	4	no	—
714	D₄	—	4	4	no	—
715	D₄	—	4	8	no	—
716	D₄	—	4	4	no	—
717	D₄	—	4	8	no	—
718	D₄	—	4	8	no	—
719	D₄	—	4	8	no	—
720	D₄	—	8	8	no	—
721	D₄	—	8	8	no	—
722	D₄	—	8	8	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	8	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	4	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	4	no	—
742	C₂×C₄	—	2	4	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	4	8	no	—
752	C₂×C₄	—	4	4	no	—
753	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
754	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
755	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
756	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
757	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
758	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
759	C₂×C₃	—	4	2	no	—
760	C₂×C₃	—	8	2	no	—
761	C₂×C₃	—	8	1	no	—
762	C₂×C₃	—	8	4	no	—
763	C₂×C₃	C₂×#535	1	1	yes	characteristic
764	C₂×C₃	#3488	1	1	yes	characteristic
765	C₂×C₃	#3500	1	1	yes	characteristic
766	C₂×C₃	#3540	1	2	yes	—
767	C₂×C₃	#3546	1	2	yes	—
768	C₂²	—	2	2	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	4	4	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	4	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	4	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	4	no	—
785	C₂²	—	4	4	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	4	no	—
789	C₂²	—	4	4	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	8	16	no	—
793	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
794	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
795	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
796	C₂²	C₃×#585	1	1	yes	characteristic
797	C₂²	C₃×#585	1	2	yes	—
798	C₄	—	2	2	no	—
799	C₄	—	2	4	no	—
800	C₄	—	2	2	no	—
801	C₄	—	2	4	no	—
802	C₄	—	4	2	no	—
803	C₄	—	4	1	no	—
804	C₄	—	4	2	no	—
805	C₄	—	4	2	no	—
806	C₄	—	4	1	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	4	no	—
809	C₄	—	4	2	no	—
810	C₄	C₃×#535	1	4	yes	—
811	C₃	#42987	1	1	yes	characteristic, direct product factor, Sylow
812	C₂	—	4	2	no	—
813	C₂	—	8	4	no	—
814	C₂	—	8	2	no	—
815	C₂	—	8	1	no	—
816	C₂	C₂×C₃×#535	1	1	yes	characteristic
817	C₂	C₃×#3488	1	1	yes	characteristic
818	C₂	C₃×#3500	1	1	yes	characteristic
819	C₂	C₃×#3540	1	2	yes	—
820	C₂	C₃×#3546	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×#556	C₂	semidirect
2. C₂×C₃×#535	C₂	semidirect
3. C₃×#2818	C₂	semidirect
4. C₃×#2685	C₂	semidirect
5. C₃×#2670	C₂	semidirect
6. C₃×#2662	C₂	semidirect
7. C₃×#2632	C₂	semidirect
8. C₃×#2616	C₂	semidirect
9. C₃×#2548	C₂	semidirect
10. C₃×#2540	C₂	semidirect
11. C₃×#2491	C₂	semidirect
12. C₃×#2435	C₂	semidirect
13. C₃×#2426	C₂	semidirect
14. C₃×#2414	C₂	semidirect
15. C₃×#2408	C₂	semidirect
16. C₃×#2388	C₂	semidirect
17. C₃×#2347	C₂	semidirect
18. #42987	C₃	direct (N × H)
23. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
26. C₂×C₃×#126	C₂²	semidirect
30. C₂×C₃×#124	C₂²	semidirect
32. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
33. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
39. C₂×C₃×C₄×Q₈	C₂²	semidirect
40. C₂×C₃×C₄×Q₈	C₂²	semidirect
42. C₂×C₃×C₄×D₄	C₂²	semidirect
44. C₂×C₃×#117	C₂²	semidirect
45. C₃×#399	C₂²	semidirect
46. C₃×#396	C₂²	semidirect
47. C₃×#395	C₂²	semidirect
48. C₃×#395	C₂²	semidirect
54. C₃×#394	C₂²	semidirect
55. C₃×#394	C₂²	semidirect
56. C₃×#394	C₂²	semidirect
57. C₃×#394	C₂²	semidirect
58. C₃×#394	C₂²	semidirect
59. C₃×#393	C₂²	semidirect
60. C₃×#393	C₂²	semidirect
63. C₃×#392	C₂²	semidirect
64. C₃×#392	C₂²	semidirect
65. 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×#389	C₂²	semidirect
74. C₃×#388	C₂²	semidirect
75. C₃×#388	C₂²	semidirect
76. C₃×#388	C₂²	semidirect
77. C₃×#383	C₂²	semidirect
79. C₃×#380	C₂²	semidirect
82. C₃×C₄×C₄⋊C₄	C₂²	semidirect
83. C₃×C₄×C₄⋊C₄	C₂²	semidirect
85. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
86. C₂×#556	C₂×C₃	semidirect
87. C₂×#535	C₂×C₃	semidirect
88. #2818	C₂×C₃	semidirect
89. #2685	C₂×C₃	semidirect
90. #2670	C₂×C₃	semidirect
91. #2662	C₂×C₃	semidirect
92. #2632	C₂×C₃	semidirect
93. #2616	C₂×C₃	semidirect
94. #2548	C₂×C₃	semidirect
95. #2540	C₂×C₃	semidirect
96. #2491	C₂×C₃	semidirect
97. #2435	C₂×C₃	semidirect
98. #2426	C₂×C₃	semidirect
99. #2414	C₂×C₃	semidirect
100. #2408	C₂×C₃	semidirect
101. #2388	C₂×C₃	semidirect
102. #2347	C₂×C₃	semidirect
144. C₃×#117	D₄	semidirect
198. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
201. C₂×#126	C₂²×C₃	semidirect
205. C₂×#124	C₂²×C₃	semidirect
207. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
208. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
214. C₂×C₄×Q₈	C₂²×C₃	semidirect
215. C₂×C₄×Q₈	C₂²×C₃	semidirect
217. C₂×C₄×D₄	C₂²×C₃	semidirect
219. C₂×#117	C₂²×C₃	semidirect
220. #399	C₂²×C₃	semidirect
221. #396	C₂²×C₃	semidirect
222. #395	C₂²×C₃	semidirect
223. #395	C₂²×C₃	semidirect
229. #394	C₂²×C₃	semidirect
230. #394	C₂²×C₃	semidirect
231. #394	C₂²×C₃	semidirect
232. #394	C₂²×C₃	semidirect
233. #394	C₂²×C₃	semidirect
234. #393	C₂²×C₃	semidirect
235. #393	C₂²×C₃	semidirect
238. #392	C₂²×C₃	semidirect
239. #392	C₂²×C₃	semidirect
240. #392	C₂²×C₃	semidirect
243. #390	C₂²×C₃	semidirect
244. #390	C₂²×C₃	semidirect
245. #390	C₂²×C₃	semidirect
246. #390	C₂²×C₃	semidirect
247. #389	C₂²×C₃	semidirect
249. #388	C₂²×C₃	semidirect
250. #388	C₂²×C₃	semidirect
251. #388	C₂²×C₃	semidirect
252. #383	C₂²×C₃	semidirect
254. #380	C₂²×C₃	semidirect
257. C₄×C₄⋊C₄	C₂²×C₃	semidirect
258. C₄×C₄⋊C₄	C₂²×C₃	semidirect
260. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
406. #117	C₃×D₄	semidirect
811. C₃	#42987	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×#556	2
C₂×C₃×#535	2
C₃×#2818	2
C₃×#2685	2
C₃×#2670	2
C₃×#2662	2
C₃×#2632	2
C₃×#2616	2
C₃×#2548	2
C₃×#2540	2
C₃×#2491	2
C₃×#2435	2
C₃×#2426	2
C₃×#2414	2
C₃×#2408	2
C₃×#2388	2
C₃×#2347	2
#42987	3

Subgroups — C3×#42987 #10661594

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#42987 #10661594