Subgroups — C₃×#63000 #10681607

Order 768.

7170 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3522	C₂	1	2	yes	maximal, complemented
2	C₃×#3520	C₂	1	12	yes	maximal, complemented
3	C₃×#3516	C₂	1	4	yes	maximal, complemented
4	C₃×#3515	C₂	1	6	yes	maximal, complemented
5	C₃×#3511	C₂	1	3	yes	maximal, complemented
6	C₃×#3507	C₂	1	3	yes	maximal, complemented
7	C₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#3495	C₂	1	6	yes	maximal, complemented
9	C₃×#3492	C₂	1	6	yes	maximal, complemented
10	C₃×#3489	C₂	1	2	yes	maximal, complemented
11	C₃×#3481	C₂	1	6	yes	maximal, complemented
12	C₃×Q₈×#41	C₂	1	2	yes	maximal, complemented
13	C₃×#3475	C₂	1	3	yes	maximal, complemented
14	C₂×C₃×#554	C₂	1	3	yes	maximal, complemented
15	C₃×D₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×C₄×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₃×#520	C₂	1	2	yes	maximal, complemented
18	#63000	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
20	C₂²×C₃×#41	C₂²	1	2	yes	—
21	C₃×#559	C₂²	1	6	yes	complemented
22	C₃×Q₈²	C₂²	1	2	yes	complemented
23	C₃×#557	C₂²	1	6	yes	complemented
24	C₃×#557	C₂²	1	2	yes	complemented
25	C₃×#556	C₂²	1	3	yes	complemented
26	C₃×#556	C₂²	1	6	yes	complemented
27	C₃×#556	C₂²	1	12	yes	complemented
28	C₃×#555	C₂²	1	3	yes	complemented
29	C₃×#554	C₂²	1	3	yes	—
30	C₃×#554	C₂²	1	6	yes	—
31	C₃×#554	C₂²	1	12	yes	complemented
32	C₃×#554	C₂²	1	6	yes	complemented
33	C₃×#554	C₂²	1	6	yes	complemented
34	C₃×#554	C₂²	1	12	yes	complemented
35	C₃×#554	C₂²	1	12	yes	complemented
36	C₃×#554	C₂²	1	6	yes	complemented
37	C₃×#553	C₂²	1	6	yes	complemented
38	C₃×#553	C₂²	1	12	yes	complemented
39	C₃×#553	C₂²	1	12	yes	complemented
40	C₃×#552	C₂²	1	6	yes	complemented
41	C₃×#552	C₂²	1	6	yes	complemented
42	C₃×#552	C₂²	1	12	yes	complemented
43	C₃×#552	C₂²	1	12	yes	complemented
44	C₃×#552	C₂²	1	24	yes	complemented
45	C₃×#551	C₂²	1	12	yes	complemented
46	C₃×#551	C₂²	1	24	yes	complemented
47	C₃×#550	C₂²	1	1	yes	characteristic
48	C₃×D₄×Q₈	C₂²	1	1	yes	characteristic
49	C₃×D₄×Q₈	C₂²	1	4	yes	complemented
50	C₃×D₄×Q₈	C₂²	1	6	yes	complemented
51	C₃×#548	C₂²	1	2	yes	—
52	C₃×#548	C₂²	1	4	yes	complemented
53	C₃×#548	C₂²	1	12	yes	complemented
54	C₃×#547	C₂²	1	3	yes	—
55	C₃×#547	C₂²	1	1	yes	characteristic
56	C₃×#547	C₂²	1	12	yes	complemented
57	C₃×#547	C₂²	1	6	yes	complemented
58	C₃×#547	C₂²	1	12	yes	complemented
59	C₃×#546	C₂²	1	6	yes	—
60	C₃×#546	C₂²	1	6	yes	—
61	C₃×#546	C₂²	1	12	yes	complemented
62	C₃×D₄²	C₂²	1	3	yes	—
63	C₃×#544	C₂²	1	6	yes	complemented
64	C₃×#542	C₂²	1	12	yes	complemented
65	C₃×#542	C₂²	1	12	yes	complemented
66	C₃×#541	C₂²	1	12	yes	complemented
67	C₃×#539	C₂²	1	24	yes	complemented
68	C₃×#539	C₂²	1	12	yes	complemented
69	C₃×#537	C₂²	1	6	yes	complemented
70	C₃×#536	C₂²	1	6	yes	complemented
71	C₃×#533	C₂²	1	3	yes	complemented
72	C₃×#533	C₂²	1	12	yes	complemented
73	C₃×#533	C₂²	1	6	yes	complemented
74	C₃×#532	C₂²	1	3	yes	—
75	C₃×#532	C₂²	1	6	yes	complemented
76	C₂×C₃×C₄⋊Q₈	C₂²	1	3	yes	complemented
77	C₃×#529	C₂²	1	6	yes	complemented
78	C₃×#529	C₂²	1	12	yes	complemented
79	C₃×#529	C₂²	1	12	yes	complemented
80	C₃×#529	C₂²	1	12	yes	complemented
81	C₂×C₃×#125	C₂²	1	6	yes	complemented
82	C₃×#525	C₂²	1	6	yes	—
83	C₃×#525	C₂²	1	6	yes	complemented
84	C₃×#525	C₂²	1	24	yes	complemented
85	C₂×C₃×C₂²⋊Q₈	C₂²	1	6	yes	complemented
86	C₂×C₃×C₂²⋊Q₈	C₂²	1	12	yes	complemented
87	C₃×#520	C₂²	1	1	yes	characteristic
88	C₃×#520	C₂²	1	2	yes	—
89	C₃×#520	C₂²	1	6	yes	complemented
90	C₃×#520	C₂²	1	6	yes	complemented
91	C₃×#520	C₂²	1	12	yes	complemented
92	C₃×#520	C₂²	1	4	yes	complemented
93	C₃×#520	C₂²	1	3	yes	complemented
94	C₃×#520	C₂²	1	6	yes	complemented
95	C₃×#519	C₂²	1	3	yes	complemented
96	C₃×#519	C₂²	1	2	yes	complemented
97	C₃×C₄×#41	C₂²	1	1	yes	characteristic
98	C₃×C₄×#41	C₂²	1	6	yes	—
99	C₃×C₄×#41	C₂²	1	3	yes	complemented
100	C₃×C₄×#41	C₂²	1	6	yes	complemented
101	C₂×C₃×C₄×Q₈	C₂²	1	4	yes	complemented
102	C₂×C₃×C₄×Q₈	C₂²	1	3	yes	complemented
103	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	complemented
104	C₂×C₃×C₄×D₄	C₂²	1	3	yes	—
105	C₂×C₃×C₄×D₄	C₂²	1	6	yes	—
106	C₂×C₃×C₄×D₄	C₂²	1	12	yes	complemented
107	C₂×C₃×#117	C₂²	1	6	yes	complemented
108	C₂²×C₃×C₄⋊C₄	C₂²	1	6	yes	complemented
109	#3522	C₂×C₃	1	2	yes	complemented
110	#3520	C₂×C₃	1	12	yes	complemented
111	#3516	C₂×C₃	1	4	yes	complemented
112	#3515	C₂×C₃	1	6	yes	complemented
113	#3511	C₂×C₃	1	3	yes	complemented
114	#3507	C₂×C₃	1	3	yes	complemented
115	#3503	C₂×C₃	1	1	yes	characteristic, complemented
116	#3495	C₂×C₃	1	6	yes	complemented
117	#3492	C₂×C₃	1	6	yes	complemented
118	#3489	C₂×C₃	1	2	yes	complemented
119	#3481	C₂×C₃	1	6	yes	complemented
120	Q₈×#41	C₂×C₃	1	2	yes	complemented
121	#3475	C₂×C₃	1	3	yes	complemented
122	C₂×#554	C₂×C₃	1	3	yes	complemented
123	D₄×#41	C₂×C₃	1	1	yes	characteristic, complemented
124	C₄×2₋¹⁺⁴	C₂×C₃	1	1	yes	characteristic, complemented
125	C₂×#520	C₂×C₃	1	2	yes	complemented
126	C₃×2₋¹⁺⁴	—	2	8	no	—
127	C₂×C₃×#41	—	2	16	no	—
128	C₂×C₃×#41	C₂³	1	6	yes	—
129	C₂×C₃×#41	C₂³	1	6	yes	—
130	C₂×C₃×#41	C₂³	1	2	yes	—
131	C₂×C₃×#41	C₂³	1	3	yes	—
132	C₂×C₃×#41	C₂³	1	6	yes	—
133	C₂×C₃×#41	C₂³	1	2	yes	—
134	C₂×C₃×#41	C₂³	1	12	yes	—
135	C₂×C₃×#41	C₂³	1	1	yes	characteristic
136	C₂²×C₃×Q₈	C₂³	1	2	yes	—
137	C₂²×C₃×Q₈	C₂³	1	3	yes	—
138	C₂²×C₃×Q₈	C₂³	1	2	yes	—
139	C₂²×C₃×Q₈	C₂³	1	6	yes	—
140	C₂²×C₃×D₄	C₂³	1	6	yes	—
141	C₂²×C₃×D₄	C₂³	1	3	yes	—
142	C₂³×C₃×C₄	C₂³	1	6	yes	—
143	C₂³×C₃×C₄	C₂³	1	12	yes	—
144	C₃×C₄⋊Q₈	C₂³	1	6	yes	—
145	C₃×C₄⋊Q₈	C₂³	1	12	yes	—
146	C₃×C₄⋊Q₈	C₂³	1	3	yes	—
147	C₃×C₄⋊Q₈	C₂³	1	6	yes	—
148	C₃×C₄⋊Q₈	C₂³	1	6	yes	—
149	C₃×C₄⋊Q₈	C₂³	1	3	yes	—
150	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
151	C₃×C₄⋊Q₈	C₂³	1	12	yes	—
152	C₃×#127	C₂³	1	3	yes	—
153	C₃×#126	C₂³	1	12	yes	—
154	C₃×#126	C₂³	1	12	yes	—
155	C₃×#126	C₂³	1	24	yes	—
156	C₃×#126	C₂³	1	24	yes	—
157	C₃×#126	C₂³	1	12	yes	—
158	C₃×#125	C₂³	1	6	yes	—
159	C₃×#125	C₂³	1	12	yes	—
160	C₃×#125	C₂³	1	24	yes	—
161	C₃×#125	C₂³	1	12	yes	—
162	C₃×#125	C₂³	1	12	yes	—
163	C₃×#125	C₂³	1	24	yes	—
164	C₃×#125	C₂³	1	6	yes	—
165	C₃×#124	C₂³	1	6	yes	—
166	C₃×#124	C₂³	1	12	yes	—
167	C₃×#124	C₂³	1	12	yes	—
168	C₃×#124	C₂³	1	6	yes	—
169	C₃×#124	C₂³	1	12	yes	—
170	C₃×#123	C₂³	1	24	yes	—
171	C₃×#123	C₂³	1	12	yes	—
172	C₃×#123	C₂³	1	12	yes	—
173	C₃×#123	C₂³	1	24	yes	—
174	C₃×#123	C₂³	1	12	yes	—
175	C₃×#123	C₂³	1	4	yes	—
176	C₃×#123	C₂³	1	24	yes	—
177	C₃×#123	C₂³	1	12	yes	—
178	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
179	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
180	C₃×C₂²⋊Q₈	C₂³	1	24	yes	—
181	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
182	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
183	C₃×C₂²⋊Q₈	C₂³	1	24	yes	—
184	C₃×C₂²⋊Q₈	C₂³	1	24	yes	—
185	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
186	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
187	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
188	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
189	C₃×C₂²⋊Q₈	C₂³	1	24	yes	—
190	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
192	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
193	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
194	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
195	C₃×#121	C₂³	1	6	yes	—
196	C₃×#121	C₂³	1	6	yes	—
197	C₃×#121	C₂³	1	2	yes	—
198	C₃×#121	C₂³	1	12	yes	—
199	C₃×#121	C₂³	1	6	yes	—
200	C₃×#121	C₂³	1	24	yes	—
201	C₃×#121	C₂³	1	6	yes	—
202	C₃×#121	C₂³	1	6	yes	—
203	C₃×#121	C₂³	1	6	yes	—
204	C₃×#121	C₂³	1	12	yes	—
205	C₃×#120	C₂³	1	12	yes	—
206	C₃×#120	C₂³	1	12	yes	—
207	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
208	C₃×C₄×Q₈	C₂³	1	6	yes	—
209	C₃×C₄×Q₈	C₂³	1	4	yes	—
210	C₃×C₄×Q₈	C₂³	1	6	yes	—
211	C₃×C₄×Q₈	C₂³	1	2	yes	—
212	C₃×C₄×Q₈	C₂³	1	3	yes	—
213	C₃×C₄×Q₈	C₂³	1	6	yes	—
214	C₃×C₄×Q₈	C₂³	1	6	yes	—
215	C₃×C₄×Q₈	C₂³	1	6	yes	—
216	C₃×C₄×Q₈	C₂³	1	12	yes	—
217	C₃×C₄×Q₈	C₂³	1	12	yes	—
218	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
219	C₃×C₄×Q₈	C₂³	1	6	yes	—
220	C₃×C₄×Q₈	C₂³	1	6	yes	—
221	C₃×C₄×Q₈	C₂³	1	3	yes	—
222	C₃×C₄×Q₈	C₂³	1	6	yes	—
223	C₃×C₄×Q₈	C₂³	1	12	yes	—
224	C₃×C₄×D₄	C₂³	1	12	yes	—
225	C₃×C₄×D₄	C₂³	1	12	yes	—
226	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
227	C₃×C₄×D₄	C₂³	1	6	yes	—
228	C₃×C₄×D₄	C₂³	1	3	yes	—
229	C₃×C₄×D₄	C₂³	1	6	yes	—
230	C₃×C₄×D₄	C₂³	1	24	yes	—
231	C₃×C₄×D₄	C₂³	1	6	yes	—
232	C₃×C₄×D₄	C₂³	1	3	yes	—
233	C₃×C₄×D₄	C₂³	1	3	yes	—
234	C₃×C₄×D₄	C₂³	1	6	yes	—
235	C₃×C₄×D₄	C₂³	1	12	yes	—
236	C₃×C₄×D₄	C₂³	1	24	yes	—
237	C₃×C₄×D₄	C₂³	1	12	yes	—
238	C₃×C₄×D₄	C₂³	1	24	yes	—
239	C₃×C₄×D₄	C₂³	1	3	yes	—
240	C₃×C₄×D₄	C₂³	1	3	yes	—
241	C₃×C₄×D₄	C₂³	1	12	yes	—
242	C₃×C₄×D₄	C₂³	1	12	yes	—
243	C₃×C₄×D₄	C₂³	1	6	yes	—
244	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
245	C₃×C₄×D₄	C₂³	1	12	yes	—
246	C₃×C₄×D₄	C₂³	1	3	yes	—
247	C₃×C₄×D₄	C₂³	1	6	yes	—
248	C₃×C₄×D₄	C₂³	1	6	yes	—
249	C₃×C₄×D₄	C₂³	1	12	yes	—
250	C₃×#117	C₂³	1	3	yes	—
251	C₃×#117	C₂³	1	6	yes	—
252	C₃×#117	C₂³	1	12	yes	—
253	C₃×#117	C₂³	1	12	yes	—
254	C₃×#117	C₂³	1	6	yes	—
255	C₃×#117	C₂³	1	6	yes	—
256	C₃×#117	C₂³	1	3	yes	—
257	C₃×#117	C₂³	1	12	yes	—
258	C₃×#117	C₂³	1	6	yes	—
259	C₃×#117	C₂³	1	6	yes	—
260	C₃×#117	C₂³	1	12	yes	—
261	C₃×#117	C₂³	1	6	yes	—
262	C₃×#117	C₂³	1	24	yes	—
263	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
264	C₂×C₃×C₄⋊C₄	C₂³	1	3	yes	—
265	C₂×C₃×C₄⋊C₄	C₂³	1	12	yes	—
266	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
267	C₂×C₃×C₄⋊C₄	C₂³	1	12	yes	—
268	C₂×C₃×C₄⋊C₄	C₂³	1	12	yes	—
269	C₂×C₃×C₄⋊C₄	C₂³	1	12	yes	—
270	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
271	C₂×C₃×C₄⋊C₄	C₂³	1	3	yes	—
272	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
273	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
274	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
275	C₂×C₃×C₄⋊C₄	C₂³	1	12	yes	—
276	C₂×C₃×C₂²⋊C₄	C₂³	1	12	yes	—
277	C₂×C₃×C₂²⋊C₄	C₂³	1	6	yes	—
278	C₂×C₃×C₂²⋊C₄	C₂³	1	12	yes	—
279	C₂×C₃×C₄²	C₂³	1	12	yes	—
280	C₂×C₃×C₄²	C₂³	1	3	yes	—
281	C₂×C₃×C₄²	C₂³	1	6	yes	—
282	C₂×C₃×C₄²	C₂³	1	6	yes	—
283	C₂×2₋¹⁺⁴	C₂²×C₃	1	1	yes	characteristic
284	C₂²×#41	C₂²×C₃	1	2	yes	—
285	#559	C₂²×C₃	1	6	yes	complemented
286	Q₈²	C₂²×C₃	1	2	yes	complemented
287	#557	C₂²×C₃	1	6	yes	complemented
288	#557	C₂²×C₃	1	2	yes	complemented
289	#556	C₂²×C₃	1	3	yes	complemented
290	#556	C₂²×C₃	1	6	yes	complemented
291	#556	C₂²×C₃	1	12	yes	complemented
292	#555	C₂²×C₃	1	3	yes	complemented
293	#554	C₂²×C₃	1	3	yes	—
294	#554	C₂²×C₃	1	6	yes	—
295	#554	C₂²×C₃	1	12	yes	complemented
296	#554	C₂²×C₃	1	6	yes	complemented
297	#554	C₂²×C₃	1	6	yes	complemented
298	#554	C₂²×C₃	1	12	yes	complemented
299	#554	C₂²×C₃	1	12	yes	complemented
300	#554	C₂²×C₃	1	6	yes	complemented
301	#553	C₂²×C₃	1	6	yes	complemented
302	#553	C₂²×C₃	1	12	yes	complemented
303	#553	C₂²×C₃	1	12	yes	complemented
304	#552	C₂²×C₃	1	6	yes	complemented
305	#552	C₂²×C₃	1	6	yes	complemented
306	#552	C₂²×C₃	1	12	yes	complemented
307	#552	C₂²×C₃	1	12	yes	complemented
308	#552	C₂²×C₃	1	24	yes	complemented
309	#551	C₂²×C₃	1	12	yes	complemented
310	#551	C₂²×C₃	1	24	yes	complemented
311	#550	C₂²×C₃	1	1	yes	characteristic
312	D₄×Q₈	C₂²×C₃	1	1	yes	characteristic
313	D₄×Q₈	C₂²×C₃	1	4	yes	complemented
314	D₄×Q₈	C₂²×C₃	1	6	yes	complemented
315	#548	C₂²×C₃	1	2	yes	—
316	#548	C₂²×C₃	1	4	yes	complemented
317	#548	C₂²×C₃	1	12	yes	complemented
318	#547	C₂²×C₃	1	3	yes	—
319	#547	C₂²×C₃	1	1	yes	characteristic
320	#547	C₂²×C₃	1	12	yes	complemented
321	#547	C₂²×C₃	1	6	yes	complemented
322	#547	C₂²×C₃	1	12	yes	complemented
323	#546	C₂²×C₃	1	6	yes	—
324	#546	C₂²×C₃	1	6	yes	—
325	#546	C₂²×C₃	1	12	yes	complemented
326	D₄²	C₂²×C₃	1	3	yes	—
327	#544	C₂²×C₃	1	6	yes	complemented
328	#542	C₂²×C₃	1	12	yes	complemented
329	#542	C₂²×C₃	1	12	yes	complemented
330	#541	C₂²×C₃	1	12	yes	complemented
331	#539	C₂²×C₃	1	24	yes	complemented
332	#539	C₂²×C₃	1	12	yes	complemented
333	#537	C₂²×C₃	1	6	yes	complemented
334	#536	C₂²×C₃	1	6	yes	complemented
335	#533	C₂²×C₃	1	3	yes	complemented
336	#533	C₂²×C₃	1	12	yes	complemented
337	#533	C₂²×C₃	1	6	yes	complemented
338	#532	C₂²×C₃	1	3	yes	—
339	#532	C₂²×C₃	1	6	yes	complemented
340	C₂×C₄⋊Q₈	C₂²×C₃	1	3	yes	complemented
341	#529	C₂²×C₃	1	6	yes	complemented
342	#529	C₂²×C₃	1	12	yes	complemented
343	#529	C₂²×C₃	1	12	yes	complemented
344	#529	C₂²×C₃	1	12	yes	complemented
345	C₂×#125	C₂²×C₃	1	6	yes	complemented
346	#525	C₂²×C₃	1	6	yes	—
347	#525	C₂²×C₃	1	6	yes	complemented
348	#525	C₂²×C₃	1	24	yes	complemented
349	C₂×C₂²⋊Q₈	C₂²×C₃	1	6	yes	complemented
350	C₂×C₂²⋊Q₈	C₂²×C₃	1	12	yes	complemented
351	#520	C₂²×C₃	1	1	yes	characteristic
352	#520	C₂²×C₃	1	2	yes	—
353	#520	C₂²×C₃	1	6	yes	complemented
354	#520	C₂²×C₃	1	6	yes	complemented
355	#520	C₂²×C₃	1	12	yes	complemented
356	#520	C₂²×C₃	1	4	yes	complemented
357	#520	C₂²×C₃	1	3	yes	complemented
358	#520	C₂²×C₃	1	6	yes	complemented
359	#519	C₂²×C₃	1	3	yes	complemented
360	#519	C₂²×C₃	1	2	yes	complemented
361	C₄×#41	C₂²×C₃	1	1	yes	characteristic
362	C₄×#41	C₂²×C₃	1	6	yes	—
363	C₄×#41	C₂²×C₃	1	3	yes	complemented
364	C₄×#41	C₂²×C₃	1	6	yes	complemented
365	C₂×C₄×Q₈	C₂²×C₃	1	4	yes	complemented
366	C₂×C₄×Q₈	C₂²×C₃	1	3	yes	complemented
367	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
368	C₂×C₄×D₄	C₂²×C₃	1	3	yes	—
369	C₂×C₄×D₄	C₂²×C₃	1	6	yes	—
370	C₂×C₄×D₄	C₂²×C₃	1	12	yes	complemented
371	C₂×#117	C₂²×C₃	1	6	yes	complemented
372	C₂²×C₄⋊C₄	C₂²×C₃	1	6	yes	complemented
373	C₂⁴×C₃	C₂⁴	1	6	yes	—
374	C₃×#41	—	2	8	no	—
375	C₃×#41	—	2	24	no	—
376	C₃×#41	—	2	24	no	—
377	C₃×#41	—	2	8	no	—
378	C₃×#41	—	2	24	no	—
379	C₃×#41	—	2	12	no	—
380	C₃×#41	—	8	12	no	—
381	C₃×#41	#41	1	8	yes	complemented
382	C₂×C₃×Q₈	—	2	8	no	—
383	C₂×C₃×Q₈	—	2	8	no	—
384	C₂×C₃×Q₈	—	2	12	no	—
385	C₂×C₃×Q₈	—	8	6	no	—
386	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
387	C₂×C₃×Q₈	C₂⁴	1	3	yes	—
388	C₂×C₃×Q₈	C₂⁴	1	6	yes	—
389	C₂×C₃×Q₈	C₂⁴	1	6	yes	—
390	C₂×C₃×Q₈	C₂⁴	1	6	yes	—
391	C₂×C₃×Q₈	C₂⁴	1	12	yes	—
392	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
393	C₂×C₃×D₄	—	2	24	no	—
394	C₂×C₃×D₄	—	2	12	no	—
395	C₂×C₃×D₄	C₂⁴	1	4	yes	—
396	C₂×C₃×D₄	C₂⁴	1	6	yes	—
397	C₂×C₃×D₄	C₂⁴	1	3	yes	—
398	C₂×C₃×D₄	C₂⁴	1	6	yes	—
399	C₂×C₃×D₄	C₂⁴	1	12	yes	—
400	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
401	C₂×C₃×D₄	C₂⁴	1	6	yes	—
402	C₂×C₃×D₄	C₂⁴	1	6	yes	—
403	C₂×C₃×D₄	C₂⁴	1	12	yes	—
404	C₂×C₃×D₄	C₂⁴	1	3	yes	—
405	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
406	C₂²×C₃×C₄	—	2	24	no	—
407	C₂²×C₃×C₄	—	8	12	no	—
408	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
409	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
410	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
411	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
412	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
413	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
414	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
415	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
416	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
417	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
418	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
419	C₂²×C₃×C₄	C₂⁴	1	12	yes	—
420	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
421	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
422	C₂²×C₃×C₄	C₂⁴	1	12	yes	—
423	C₂²×C₃×C₄	C₂⁴	1	24	yes	—
424	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
425	C₃×C₄⋊C₄	C₂⁴	1	3	yes	—
426	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
427	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
428	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
429	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
430	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
431	C₃×C₄⋊C₄	C₂⁴	1	24	yes	—
432	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
433	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
434	C₃×C₄⋊C₄	C₂⁴	1	3	yes	—
435	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
436	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
437	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
438	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
439	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
440	C₃×C₄⋊C₄	C₂⁴	1	3	yes	—
441	C₃×C₄⋊C₄	C₂⁴	1	24	yes	—
442	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
443	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
444	C₃×C₄⋊C₄	C₂⁴	1	3	yes	—
445	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
446	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
447	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
448	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
449	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
450	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
451	C₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
452	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
453	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
454	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
455	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
456	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
457	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
458	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
459	C₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
460	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
461	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
462	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
463	C₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
464	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
465	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
466	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
467	C₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
468	C₃×C₄²	C₂⁴	1	6	yes	—
469	C₃×C₄²	C₂⁴	1	1	yes	characteristic
470	C₃×C₄²	C₂⁴	1	6	yes	—
471	C₃×C₄²	C₂⁴	1	3	yes	—
472	C₃×C₄²	C₂⁴	1	12	yes	—
473	C₃×C₄²	C₂⁴	1	12	yes	—
474	C₃×C₄²	C₂⁴	1	12	yes	—
475	C₃×C₄²	C₂⁴	1	6	yes	—
476	C₃×C₄²	C₂⁴	1	3	yes	—
477	C₃×C₄²	C₂⁴	1	12	yes	—
478	C₃×C₄²	C₂⁴	1	3	yes	—
479	2₋¹⁺⁴	—	2	8	no	—
480	C₂×#41	—	2	16	no	—
481	C₂×#41	C₂³×C₃	1	2	yes	—
482	C₂×#41	C₂³×C₃	1	3	yes	—
483	C₂×#41	C₂³×C₃	1	6	yes	—
484	C₂×#41	C₂³×C₃	1	6	yes	—
485	C₂×#41	C₂³×C₃	1	6	yes	—
486	C₂×#41	C₂³×C₃	1	2	yes	—
487	C₂×#41	C₂³×C₃	1	12	yes	—
488	C₂×#41	C₂³×C₃	1	1	yes	characteristic
489	C₂²×Q₈	C₂³×C₃	1	2	yes	—
490	C₂²×Q₈	C₂³×C₃	1	3	yes	—
491	C₂²×Q₈	C₂³×C₃	1	2	yes	—
492	C₂²×Q₈	C₂³×C₃	1	6	yes	—
493	C₂²×D₄	C₂³×C₃	1	3	yes	—
494	C₂²×D₄	C₂³×C₃	1	6	yes	—
495	C₂³×C₄	C₂³×C₃	1	6	yes	—
496	C₂³×C₄	C₂³×C₃	1	12	yes	—
497	C₄⋊Q₈	C₂³×C₃	1	3	yes	—
498	C₄⋊Q₈	C₂³×C₃	1	6	yes	—
499	C₄⋊Q₈	C₂³×C₃	1	6	yes	—
500	C₄⋊Q₈	C₂³×C₃	1	6	yes	—
501	C₄⋊Q₈	C₂³×C₃	1	3	yes	—
502	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
503	C₄⋊Q₈	C₂³×C₃	1	12	yes	—
504	C₄⋊Q₈	C₂³×C₃	1	12	yes	—
505	#127	C₂³×C₃	1	3	yes	—
506	#126	C₂³×C₃	1	12	yes	—
507	#126	C₂³×C₃	1	12	yes	—
508	#126	C₂³×C₃	1	24	yes	—
509	#126	C₂³×C₃	1	24	yes	—
510	#126	C₂³×C₃	1	12	yes	—
511	#125	C₂³×C₃	1	6	yes	—
512	#125	C₂³×C₃	1	12	yes	—
513	#125	C₂³×C₃	1	24	yes	—
514	#125	C₂³×C₃	1	12	yes	—
515	#125	C₂³×C₃	1	12	yes	—
516	#125	C₂³×C₃	1	24	yes	—
517	#125	C₂³×C₃	1	6	yes	—
518	#124	C₂³×C₃	1	6	yes	—
519	#124	C₂³×C₃	1	12	yes	—
520	#124	C₂³×C₃	1	12	yes	—
521	#124	C₂³×C₃	1	6	yes	—
522	#124	C₂³×C₃	1	12	yes	—
523	#123	C₂³×C₃	1	12	yes	—
524	#123	C₂³×C₃	1	12	yes	—
525	#123	C₂³×C₃	1	24	yes	—
526	#123	C₂³×C₃	1	24	yes	—
527	#123	C₂³×C₃	1	12	yes	—
528	#123	C₂³×C₃	1	4	yes	—
529	#123	C₂³×C₃	1	24	yes	—
530	#123	C₂³×C₃	1	12	yes	—
531	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
532	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
533	C₂²⋊Q₈	C₂³×C₃	1	24	yes	—
534	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
535	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
536	C₂²⋊Q₈	C₂³×C₃	1	24	yes	—
537	C₂²⋊Q₈	C₂³×C₃	1	24	yes	—
538	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
539	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
540	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
541	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
542	C₂²⋊Q₈	C₂³×C₃	1	24	yes	—
543	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
544	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
545	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
546	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
547	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
548	#121	C₂³×C₃	1	6	yes	—
549	#121	C₂³×C₃	1	6	yes	—
550	#121	C₂³×C₃	1	2	yes	—
551	#121	C₂³×C₃	1	12	yes	—
552	#121	C₂³×C₃	1	6	yes	—
553	#121	C₂³×C₃	1	24	yes	—
554	#121	C₂³×C₃	1	6	yes	—
555	#121	C₂³×C₃	1	6	yes	—
556	#121	C₂³×C₃	1	6	yes	—
557	#121	C₂³×C₃	1	12	yes	—
558	#120	C₂³×C₃	1	12	yes	—
559	#120	C₂³×C₃	1	12	yes	—
560	C₄×Q₈	C₂³×C₃	1	2	yes	—
561	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
562	C₄×Q₈	C₂³×C₃	1	3	yes	—
563	C₄×Q₈	C₂³×C₃	1	6	yes	—
564	C₄×Q₈	C₂³×C₃	1	6	yes	—
565	C₄×Q₈	C₂³×C₃	1	6	yes	—
566	C₄×Q₈	C₂³×C₃	1	6	yes	—
567	C₄×Q₈	C₂³×C₃	1	4	yes	—
568	C₄×Q₈	C₂³×C₃	1	12	yes	—
569	C₄×Q₈	C₂³×C₃	1	12	yes	—
570	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
571	C₄×Q₈	C₂³×C₃	1	6	yes	—
572	C₄×Q₈	C₂³×C₃	1	6	yes	—
573	C₄×Q₈	C₂³×C₃	1	6	yes	—
574	C₄×Q₈	C₂³×C₃	1	3	yes	—
575	C₄×Q₈	C₂³×C₃	1	6	yes	—
576	C₄×Q₈	C₂³×C₃	1	12	yes	—
577	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
578	C₄×D₄	C₂³×C₃	1	6	yes	—
579	C₄×D₄	C₂³×C₃	1	3	yes	—
580	C₄×D₄	C₂³×C₃	1	6	yes	—
581	C₄×D₄	C₂³×C₃	1	24	yes	—
582	C₄×D₄	C₂³×C₃	1	6	yes	—
583	C₄×D₄	C₂³×C₃	1	3	yes	—
584	C₄×D₄	C₂³×C₃	1	12	yes	—
585	C₄×D₄	C₂³×C₃	1	3	yes	—
586	C₄×D₄	C₂³×C₃	1	6	yes	—
587	C₄×D₄	C₂³×C₃	1	12	yes	—
588	C₄×D₄	C₂³×C₃	1	24	yes	—
589	C₄×D₄	C₂³×C₃	1	12	yes	—
590	C₄×D₄	C₂³×C₃	1	12	yes	—
591	C₄×D₄	C₂³×C₃	1	24	yes	—
592	C₄×D₄	C₂³×C₃	1	3	yes	—
593	C₄×D₄	C₂³×C₃	1	3	yes	—
594	C₄×D₄	C₂³×C₃	1	12	yes	—
595	C₄×D₄	C₂³×C₃	1	12	yes	—
596	C₄×D₄	C₂³×C₃	1	6	yes	—
597	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
598	C₄×D₄	C₂³×C₃	1	12	yes	—
599	C₄×D₄	C₂³×C₃	1	3	yes	—
600	C₄×D₄	C₂³×C₃	1	6	yes	—
601	C₄×D₄	C₂³×C₃	1	6	yes	—
602	C₄×D₄	C₂³×C₃	1	12	yes	—
603	#117	C₂³×C₃	1	3	yes	—
604	#117	C₂³×C₃	1	6	yes	—
605	#117	C₂³×C₃	1	12	yes	—
606	#117	C₂³×C₃	1	12	yes	—
607	#117	C₂³×C₃	1	6	yes	—
608	#117	C₂³×C₃	1	6	yes	—
609	#117	C₂³×C₃	1	3	yes	—
610	#117	C₂³×C₃	1	12	yes	—
611	#117	C₂³×C₃	1	6	yes	—
612	#117	C₂³×C₃	1	6	yes	—
613	#117	C₂³×C₃	1	12	yes	—
614	#117	C₂³×C₃	1	6	yes	—
615	#117	C₂³×C₃	1	24	yes	—
616	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
617	C₂×C₄⋊C₄	C₂³×C₃	1	3	yes	—
618	C₂×C₄⋊C₄	C₂³×C₃	1	12	yes	—
619	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
620	C₂×C₄⋊C₄	C₂³×C₃	1	12	yes	—
621	C₂×C₄⋊C₄	C₂³×C₃	1	12	yes	—
622	C₂×C₄⋊C₄	C₂³×C₃	1	12	yes	—
623	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₃	1	3	yes	—
625	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
626	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
627	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
628	C₂×C₄⋊C₄	C₂³×C₃	1	12	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₃	1	12	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₃	1	12	yes	—
632	C₂×C₄²	C₂³×C₃	1	12	yes	—
633	C₂×C₄²	C₂³×C₃	1	3	yes	—
634	C₂×C₄²	C₂³×C₃	1	6	yes	—
635	C₂×C₄²	C₂³×C₃	1	6	yes	—
636	C₂³×C₃	—	2	12	no	—
637	C₂³×C₃	—	2	12	no	—
638	C₂³×C₃	—	4	6	no	—
639	C₂³×C₃	C₂⁵	1	6	yes	—
640	C₂³×C₃	C₂⁵	1	2	yes	—
641	C₂³×C₃	C₂⁵	1	3	yes	—
642	C₂³×C₃	C₂⁵	1	2	yes	—
643	C₃×Q₈	—	2	6	no	—
644	C₃×Q₈	—	2	12	no	—
645	C₃×Q₈	—	2	12	no	—
646	C₃×Q₈	—	2	4	no	—
647	C₃×Q₈	—	4	6	no	—
648	C₃×Q₈	—	4	12	no	—
649	C₃×Q₈	C₂×#41	1	4	yes	—
650	C₃×D₄	—	2	24	no	—
651	C₃×D₄	—	2	12	no	—
652	C₃×D₄	—	2	12	no	—
653	C₃×D₄	—	2	8	no	—
654	C₃×D₄	—	2	12	no	—
655	C₃×D₄	—	2	2	no	—
656	C₃×D₄	—	2	6	no	—
657	C₃×D₄	—	4	12	no	—
658	C₃×D₄	—	4	6	no	—
659	C₃×D₄	C₂×#41	1	12	yes	—
660	C₃×D₄	2₋¹⁺⁴	1	4	yes	complemented
661	C₂×C₃×C₄	—	2	12	no	—
662	C₂×C₃×C₄	—	2	12	no	—
663	C₂×C₃×C₄	—	2	8	no	—
664	C₂×C₃×C₄	—	2	4	no	—
665	C₂×C₃×C₄	—	2	12	no	—
666	C₂×C₃×C₄	—	2	12	no	—
667	C₂×C₃×C₄	—	2	12	no	—
668	C₂×C₃×C₄	—	2	12	no	—
669	C₂×C₃×C₄	—	2	6	no	—
670	C₂×C₃×C₄	—	2	4	no	—
671	C₂×C₃×C₄	—	4	6	no	—
672	C₂×C₃×C₄	—	4	12	no	—
673	C₂×C₃×C₄	—	4	12	no	—
674	C₂×C₃×C₄	—	4	24	no	—
675	C₂×C₃×C₄	—	4	3	no	—
676	C₂×C₃×C₄	—	4	6	no	—
677	C₂×C₃×C₄	C₂×#41	1	12	yes	—
678	C₂×C₃×C₄	C₂⁵	1	2	yes	—
679	C₂×C₃×C₄	C₂⁵	1	4	yes	—
680	C₂×C₃×C₄	C₂⁵	1	3	yes	—
681	C₂×C₃×C₄	C₂⁵	1	6	yes	—
682	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
683	C₂×C₃×C₄	C₂⁵	1	6	yes	—
684	C₂×C₃×C₄	C₂⁵	1	6	yes	—
685	C₂×C₃×C₄	C₂⁵	1	3	yes	—
686	C₂×C₃×C₄	C₂⁵	1	12	yes	—
687	C₂×C₃×C₄	C₂⁵	1	2	yes	—
688	C₂×C₃×C₄	C₂⁵	1	3	yes	—
689	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
690	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
691	C₂⁴	C₂⁴×C₃	1	6	yes	—
692	#41	—	2	8	no	—
693	#41	—	2	24	no	—
694	#41	—	2	24	no	—
695	#41	—	2	8	no	—
696	#41	—	2	24	no	—
697	#41	—	2	12	no	—
698	#41	—	8	12	no	—
699	#41	C₃×#41	1	8	yes	complemented
700	C₂×Q₈	—	2	8	no	—
701	C₂×Q₈	—	2	8	no	—
702	C₂×Q₈	—	2	12	no	—
703	C₂×Q₈	—	8	6	no	—
704	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
705	C₂×Q₈	C₂⁴×C₃	1	3	yes	—
706	C₂×Q₈	C₂⁴×C₃	1	6	yes	—
707	C₂×Q₈	C₂⁴×C₃	1	6	yes	—
708	C₂×Q₈	C₂⁴×C₃	1	6	yes	—
709	C₂×Q₈	C₂⁴×C₃	1	12	yes	—
710	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
711	C₂×D₄	—	2	24	no	—
712	C₂×D₄	—	2	12	no	—
713	C₂×D₄	C₂⁴×C₃	1	4	yes	—
714	C₂×D₄	C₂⁴×C₃	1	6	yes	—
715	C₂×D₄	C₂⁴×C₃	1	3	yes	—
716	C₂×D₄	C₂⁴×C₃	1	6	yes	—
717	C₂×D₄	C₂⁴×C₃	1	12	yes	—
718	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
719	C₂×D₄	C₂⁴×C₃	1	6	yes	—
720	C₂×D₄	C₂⁴×C₃	1	6	yes	—
721	C₂×D₄	C₂⁴×C₃	1	12	yes	—
722	C₂×D₄	C₂⁴×C₃	1	3	yes	—
723	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
724	C₂²×C₄	—	2	24	no	—
725	C₂²×C₄	—	8	12	no	—
726	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
727	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
728	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
730	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
731	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
732	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
733	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
735	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
736	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
737	C₂²×C₄	C₂⁴×C₃	1	12	yes	—
738	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
739	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
740	C₂²×C₄	C₂⁴×C₃	1	12	yes	—
741	C₂²×C₄	C₂⁴×C₃	1	24	yes	—
742	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
743	C₄⋊C₄	C₂⁴×C₃	1	3	yes	—
744	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
745	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
746	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
747	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
748	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
749	C₄⋊C₄	C₂⁴×C₃	1	24	yes	—
750	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
751	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
752	C₄⋊C₄	C₂⁴×C₃	1	3	yes	—
753	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
754	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
755	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
756	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
757	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
758	C₄⋊C₄	C₂⁴×C₃	1	3	yes	—
759	C₄⋊C₄	C₂⁴×C₃	1	24	yes	—
760	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
761	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
762	C₄⋊C₄	C₂⁴×C₃	1	3	yes	—
763	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
764	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
765	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
766	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
767	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
768	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
769	C₂²⋊C₄	C₂⁴×C₃	1	2	yes	—
770	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
771	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
772	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
773	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
774	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
775	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
776	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
777	C₂²⋊C₄	C₂⁴×C₃	1	24	yes	—
778	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
779	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
780	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
781	C₂²⋊C₄	C₂⁴×C₃	1	2	yes	—
782	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
783	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
784	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
785	C₂²⋊C₄	C₂⁴×C₃	1	4	yes	—
786	C₄²	C₂⁴×C₃	1	6	yes	—
787	C₄²	C₂⁴×C₃	1	1	yes	characteristic
788	C₄²	C₂⁴×C₃	1	6	yes	—
789	C₄²	C₂⁴×C₃	1	3	yes	—
790	C₄²	C₂⁴×C₃	1	12	yes	—
791	C₄²	C₂⁴×C₃	1	12	yes	—
792	C₄²	C₂⁴×C₃	1	12	yes	—
793	C₄²	C₂⁴×C₃	1	6	yes	—
794	C₄²	C₂⁴×C₃	1	3	yes	—
795	C₄²	C₂⁴×C₃	1	12	yes	—
796	C₄²	C₂⁴×C₃	1	3	yes	—
797	C₂²×C₃	—	2	2	no	—
798	C₂²×C₃	—	2	3	no	—
799	C₂²×C₃	—	2	3	no	—
800	C₂²×C₃	—	2	2	no	—
801	C₂²×C₃	—	2	2	no	—
802	C₂²×C₃	—	2	6	no	—
803	C₂²×C₃	—	2	2	no	—
804	C₂²×C₃	—	2	6	no	—
805	C₂²×C₃	—	2	6	no	—
806	C₂²×C₃	—	2	2	no	—
807	C₂²×C₃	—	4	24	no	—
808	C₂²×C₃	C₂²×#41	1	6	yes	—
809	C₂²×C₃	C₂×2₋¹⁺⁴	1	4	yes	—
810	C₂²×C₃	C₂⁶	1	1	yes	characteristic
811	C₃×C₄	—	2	2	no	—
812	C₃×C₄	—	2	6	no	—
813	C₃×C₄	—	2	6	no	—
814	C₃×C₄	—	2	2	no	—
815	C₃×C₄	—	2	3	no	—
816	C₃×C₄	—	2	4	no	—
817	C₃×C₄	—	2	6	no	—
818	C₃×C₄	—	2	12	no	—
819	C₃×C₄	—	2	3	no	—
820	C₃×C₄	—	2	1	no	—
821	C₃×C₄	C₂²×#41	1	2	yes	—
822	C₃×C₄	C₂²×#41	1	6	yes	—
823	C₃×C₄	C₂×2₋¹⁺⁴	1	2	yes	—
824	C₂³	—	2	12	no	—
825	C₂³	—	2	12	no	—
826	C₂³	—	4	6	no	—
827	C₂³	C₂⁵×C₃	1	6	yes	—
828	C₂³	C₂⁵×C₃	1	2	yes	—
829	C₂³	C₂⁵×C₃	1	3	yes	—
830	C₂³	C₂⁵×C₃	1	2	yes	—
831	Q₈	—	2	6	no	—
832	Q₈	—	2	12	no	—
833	Q₈	—	2	12	no	—
834	Q₈	—	2	4	no	—
835	Q₈	—	4	6	no	—
836	Q₈	—	4	12	no	—
837	Q₈	C₂×C₃×#41	1	4	yes	—
838	D₄	—	2	24	no	—
839	D₄	—	2	12	no	—
840	D₄	—	2	12	no	—
841	D₄	—	2	8	no	—
842	D₄	—	2	12	no	—
843	D₄	—	2	2	no	—
844	D₄	—	2	6	no	—
845	D₄	—	4	12	no	—
846	D₄	—	4	6	no	—
847	D₄	C₂×C₃×#41	1	12	yes	—
848	D₄	C₃×2₋¹⁺⁴	1	4	yes	complemented
849	C₂×C₄	—	2	12	no	—
850	C₂×C₄	—	2	12	no	—
851	C₂×C₄	—	2	8	no	—
852	C₂×C₄	—	2	4	no	—
853	C₂×C₄	—	2	12	no	—
854	C₂×C₄	—	2	12	no	—
855	C₂×C₄	—	2	12	no	—
856	C₂×C₄	—	2	12	no	—
857	C₂×C₄	—	2	6	no	—
858	C₂×C₄	—	2	4	no	—
859	C₂×C₄	—	4	6	no	—
860	C₂×C₄	—	4	12	no	—
861	C₂×C₄	—	4	12	no	—
862	C₂×C₄	—	4	24	no	—
863	C₂×C₄	—	4	3	no	—
864	C₂×C₄	—	4	6	no	—
865	C₂×C₄	C₂×C₃×#41	1	12	yes	—
866	C₂×C₄	C₂⁵×C₃	1	2	yes	—
867	C₂×C₄	C₂⁵×C₃	1	4	yes	—
868	C₂×C₄	C₂⁵×C₃	1	3	yes	—
869	C₂×C₄	C₂⁵×C₃	1	6	yes	—
870	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
871	C₂×C₄	C₂⁵×C₃	1	6	yes	—
872	C₂×C₄	C₂⁵×C₃	1	6	yes	—
873	C₂×C₄	C₂⁵×C₃	1	3	yes	—
874	C₂×C₄	C₂⁵×C₃	1	12	yes	—
875	C₂×C₄	C₂⁵×C₃	1	2	yes	—
876	C₂×C₄	C₂⁵×C₃	1	3	yes	—
877	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
878	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
879	C₂×C₃	—	2	4	no	—
880	C₂×C₃	—	2	6	no	—
881	C₂×C₃	—	4	2	no	—
882	C₂×C₃	—	4	6	no	—
883	C₂×C₃	C₂³×#41	1	1	yes	characteristic
884	C₂×C₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
885	C₂×C₃	H(7,𝔽₂)	1	1	yes	characteristic
886	C₂²	—	2	2	no	—
887	C₂²	—	2	3	no	—
888	C₂²	—	2	3	no	—
889	C₂²	—	2	2	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	6	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	2	6	no	—
894	C₂²	—	2	6	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	4	24	no	—
897	C₂²	C₂²×C₃×#41	1	6	yes	—
898	C₂²	C₂×C₃×2₋¹⁺⁴	1	4	yes	—
899	C₂²	C₂⁶×C₃	1	1	yes	characteristic
900	C₄	—	2	2	no	—
901	C₄	—	2	6	no	—
902	C₄	—	2	6	no	—
903	C₄	—	2	2	no	—
904	C₄	—	2	3	no	—
905	C₄	—	2	4	no	—
906	C₄	—	2	6	no	—
907	C₄	—	2	12	no	—
908	C₄	—	2	3	no	—
909	C₄	—	2	1	no	—
910	C₄	C₂²×C₃×#41	1	2	yes	—
911	C₄	C₂²×C₃×#41	1	6	yes	—
912	C₄	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
913	C₃	#63000	1	1	yes	characteristic, direct product factor, Sylow
914	C₂	—	2	4	no	—
915	C₂	—	2	6	no	—
916	C₂	—	4	6	no	—
917	C₂	—	4	2	no	—
918	C₂	C₂³×C₃×#41	1	1	yes	characteristic
919	C₂	C₂²×C₃×2₋¹⁺⁴	1	1	yes	characteristic
920	C₂	C₃×H(7,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3522	C₂	semidirect
2. C₃×#3520	C₂	semidirect
3. C₃×#3516	C₂	semidirect
4. C₃×#3515	C₂	semidirect
5. C₃×#3511	C₂	semidirect
6. C₃×#3507	C₂	semidirect
7. C₃×#3503	C₂	semidirect
8. C₃×#3495	C₂	semidirect
9. C₃×#3492	C₂	semidirect
10. C₃×#3489	C₂	semidirect
11. C₃×#3481	C₂	semidirect
12. C₃×Q₈×#41	C₂	semidirect
13. C₃×#3475	C₂	semidirect
14. C₂×C₃×#554	C₂	semidirect
15. C₃×D₄×#41	C₂	semidirect
16. C₃×C₄×2₋¹⁺⁴	C₂	semidirect
17. C₂×C₃×#520	C₂	semidirect
18. #63000	C₃	direct (N × H)
21. C₃×#559	C₂²	semidirect
22. C₃×Q₈²	C₂²	semidirect
23. C₃×#557	C₂²	semidirect
24. C₃×#557	C₂²	semidirect
25. C₃×#556	C₂²	semidirect
26. C₃×#556	C₂²	semidirect
27. C₃×#556	C₂²	semidirect
28. C₃×#555	C₂²	semidirect
31. C₃×#554	C₂²	semidirect
32. C₃×#554	C₂²	semidirect
33. C₃×#554	C₂²	semidirect
34. C₃×#554	C₂²	semidirect
35. C₃×#554	C₂²	semidirect
36. C₃×#554	C₂²	semidirect
37. C₃×#553	C₂²	semidirect
38. C₃×#553	C₂²	semidirect
39. C₃×#553	C₂²	semidirect
40. C₃×#552	C₂²	semidirect
41. C₃×#552	C₂²	semidirect
42. C₃×#552	C₂²	semidirect
43. C₃×#552	C₂²	semidirect
44. C₃×#552	C₂²	semidirect
45. C₃×#551	C₂²	semidirect
46. C₃×#551	C₂²	semidirect
49. C₃×D₄×Q₈	C₂²	semidirect
50. C₃×D₄×Q₈	C₂²	semidirect
52. C₃×#548	C₂²	semidirect
53. C₃×#548	C₂²	semidirect
56. C₃×#547	C₂²	semidirect
57. C₃×#547	C₂²	semidirect
58. C₃×#547	C₂²	semidirect
61. C₃×#546	C₂²	semidirect
63. C₃×#544	C₂²	semidirect
64. C₃×#542	C₂²	semidirect
65. C₃×#542	C₂²	semidirect
66. C₃×#541	C₂²	semidirect
67. C₃×#539	C₂²	semidirect
68. C₃×#539	C₂²	semidirect
69. C₃×#537	C₂²	semidirect
70. C₃×#536	C₂²	semidirect
71. C₃×#533	C₂²	semidirect
72. C₃×#533	C₂²	semidirect
73. C₃×#533	C₂²	semidirect
75. C₃×#532	C₂²	semidirect
76. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
77. C₃×#529	C₂²	semidirect
78. C₃×#529	C₂²	semidirect
79. C₃×#529	C₂²	semidirect
80. C₃×#529	C₂²	semidirect
81. C₂×C₃×#125	C₂²	semidirect
83. C₃×#525	C₂²	semidirect
84. C₃×#525	C₂²	semidirect
85. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
86. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
89. C₃×#520	C₂²	semidirect
90. C₃×#520	C₂²	semidirect
91. C₃×#520	C₂²	semidirect
92. C₃×#520	C₂²	semidirect
93. C₃×#520	C₂²	semidirect
94. C₃×#520	C₂²	semidirect
95. C₃×#519	C₂²	semidirect
96. C₃×#519	C₂²	semidirect
99. C₃×C₄×#41	C₂²	semidirect
100. C₃×C₄×#41	C₂²	semidirect
101. C₂×C₃×C₄×Q₈	C₂²	semidirect
102. C₂×C₃×C₄×Q₈	C₂²	semidirect
103. C₂×C₃×C₄×Q₈	C₂²	semidirect
106. C₂×C₃×C₄×D₄	C₂²	semidirect
107. C₂×C₃×#117	C₂²	semidirect
108. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
109. #3522	C₂×C₃	semidirect
110. #3520	C₂×C₃	semidirect
111. #3516	C₂×C₃	semidirect
112. #3515	C₂×C₃	semidirect
113. #3511	C₂×C₃	semidirect
114. #3507	C₂×C₃	semidirect
115. #3503	C₂×C₃	semidirect
116. #3495	C₂×C₃	semidirect
117. #3492	C₂×C₃	semidirect
118. #3489	C₂×C₃	semidirect
119. #3481	C₂×C₃	semidirect
120. Q₈×#41	C₂×C₃	semidirect
121. #3475	C₂×C₃	semidirect
122. C₂×#554	C₂×C₃	semidirect
123. D₄×#41	C₂×C₃	semidirect
124. C₄×2₋¹⁺⁴	C₂×C₃	semidirect
125. C₂×#520	C₂×C₃	semidirect
285. #559	C₂²×C₃	semidirect
286. Q₈²	C₂²×C₃	semidirect
287. #557	C₂²×C₃	semidirect
288. #557	C₂²×C₃	semidirect
289. #556	C₂²×C₃	semidirect
290. #556	C₂²×C₃	semidirect
291. #556	C₂²×C₃	semidirect
292. #555	C₂²×C₃	semidirect
295. #554	C₂²×C₃	semidirect
296. #554	C₂²×C₃	semidirect
297. #554	C₂²×C₃	semidirect
298. #554	C₂²×C₃	semidirect
299. #554	C₂²×C₃	semidirect
300. #554	C₂²×C₃	semidirect
301. #553	C₂²×C₃	semidirect
302. #553	C₂²×C₃	semidirect
303. #553	C₂²×C₃	semidirect
304. #552	C₂²×C₃	semidirect
305. #552	C₂²×C₃	semidirect
306. #552	C₂²×C₃	semidirect
307. #552	C₂²×C₃	semidirect
308. #552	C₂²×C₃	semidirect
309. #551	C₂²×C₃	semidirect
310. #551	C₂²×C₃	semidirect
313. D₄×Q₈	C₂²×C₃	semidirect
314. D₄×Q₈	C₂²×C₃	semidirect
316. #548	C₂²×C₃	semidirect
317. #548	C₂²×C₃	semidirect
320. #547	C₂²×C₃	semidirect
321. #547	C₂²×C₃	semidirect
322. #547	C₂²×C₃	semidirect
325. #546	C₂²×C₃	semidirect
327. #544	C₂²×C₃	semidirect
328. #542	C₂²×C₃	semidirect
329. #542	C₂²×C₃	semidirect
330. #541	C₂²×C₃	semidirect
331. #539	C₂²×C₃	semidirect
332. #539	C₂²×C₃	semidirect
333. #537	C₂²×C₃	semidirect
334. #536	C₂²×C₃	semidirect
335. #533	C₂²×C₃	semidirect
336. #533	C₂²×C₃	semidirect
337. #533	C₂²×C₃	semidirect
339. #532	C₂²×C₃	semidirect
340. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
341. #529	C₂²×C₃	semidirect
342. #529	C₂²×C₃	semidirect
343. #529	C₂²×C₃	semidirect
344. #529	C₂²×C₃	semidirect
345. C₂×#125	C₂²×C₃	semidirect
347. #525	C₂²×C₃	semidirect
348. #525	C₂²×C₃	semidirect
349. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
350. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
353. #520	C₂²×C₃	semidirect
354. #520	C₂²×C₃	semidirect
355. #520	C₂²×C₃	semidirect
356. #520	C₂²×C₃	semidirect
357. #520	C₂²×C₃	semidirect
358. #520	C₂²×C₃	semidirect
359. #519	C₂²×C₃	semidirect
360. #519	C₂²×C₃	semidirect
363. C₄×#41	C₂²×C₃	semidirect
364. C₄×#41	C₂²×C₃	semidirect
365. C₂×C₄×Q₈	C₂²×C₃	semidirect
366. C₂×C₄×Q₈	C₂²×C₃	semidirect
367. C₂×C₄×Q₈	C₂²×C₃	semidirect
370. C₂×C₄×D₄	C₂²×C₃	semidirect
371. C₂×#117	C₂²×C₃	semidirect
372. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
381. C₃×#41	#41	semidirect
660. C₃×D₄	2₋¹⁺⁴	semidirect
699. #41	C₃×#41	semidirect
848. D₄	C₃×2₋¹⁺⁴	semidirect
913. C₃	#63000	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#3522	2
C₃×#3520	2
C₃×#3516	2
C₃×#3515	2
C₃×#3511	2
C₃×#3507	2
C₃×#3503	2
C₃×#3495	2
C₃×#3492	2
C₃×#3489	2
C₃×#3481	2
C₃×Q₈×#41	2
C₃×#3475	2
C₂×C₃×#554	2
C₃×D₄×#41	2
C₃×C₄×2₋¹⁺⁴	2
C₂×C₃×#520	2
#63000	3

Subgroups — C3×#63000 #10681607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#63000 #10681607