Subgroups — C₃×#35729 #10654336

Order 768.

2838 conjugacy classes of subgroups.

The subgroup lattice has 1162 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×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2635	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2632	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2627	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2610	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2598	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2591	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2564	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2476	C₂	1	2	yes	maximal, complemented
11	C₃×#2464	C₂	1	2	yes	maximal, complemented
12	C₃×#2458	C₂	1	2	yes	maximal, complemented
13	C₃×#2443	C₂	1	2	yes	maximal, complemented
14	C₃×#2418	C₂	1	2	yes	maximal, complemented
15	C₃×#2408	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2406	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2404	C₂	1	2	yes	maximal, complemented
18	C₃×#2398	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2388	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2358	C₂	1	2	yes	maximal, complemented
22	C₃×#2353	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2342	C₂	1	2	yes	maximal, complemented
24	#35729	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
27	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
28	C₃×#546	—	2	8	no	—
29	C₂×C₃×#124	C₂²	1	1	yes	characteristic
30	C₂×C₃×#123	C₂²	1	2	yes	—
31	C₂×C₃×#123	C₂²	1	2	yes	complemented
32	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₃×#121	C₂²	1	1	yes	characteristic
34	C₂×C₃×#121	C₂²	1	2	yes	—
35	C₂×C₃×#121	C₂²	1	2	yes	—
36	C₂×C₃×#120	C₂²	1	2	yes	—
37	C₂×C₃×#120	C₂²	1	2	yes	—
38	C₃×#520	—	2	8	no	—
39	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, 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	1	yes	characteristic
43	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
44	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
45	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
46	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
49	C₂×C₃×#117	C₂²	1	1	yes	characteristic
50	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
52	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
54	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
56	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
57	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
58	C₃×#400	C₂²	1	1	yes	characteristic, complemented
59	C₃×#400	C₂²	1	1	yes	characteristic, complemented
60	C₃×#400	C₂²	1	1	yes	characteristic, complemented
61	C₃×#399	C₂²	1	2	yes	complemented
62	C₃×#399	C₂²	1	1	yes	characteristic, complemented
63	C₃×#398	C₂²	1	2	yes	complemented
64	C₃×#398	C₂²	1	2	yes	complemented
65	C₃×#397	C₂²	1	2	yes	complemented
66	C₃×#395	C₂²	1	1	yes	characteristic, complemented
67	C₃×#395	C₂²	1	1	yes	characteristic, complemented
68	C₃×#395	C₂²	1	1	yes	characteristic, complemented
69	C₃×#394	C₂²	1	1	yes	characteristic
70	C₃×#394	C₂²	1	1	yes	characteristic
71	C₃×#394	C₂²	1	1	yes	characteristic
72	C₃×#394	C₂²	1	1	yes	characteristic
73	C₃×#394	C₂²	1	2	yes	—
74	C₃×#394	C₂²	1	2	yes	—
75	C₃×#394	C₂²	1	1	yes	characteristic
76	C₃×#394	C₂²	1	1	yes	characteristic
77	C₃×#394	C₂²	1	2	yes	complemented
78	C₃×#394	C₂²	1	2	yes	complemented
79	C₃×#393	C₂²	1	2	yes	complemented
80	C₃×#393	C₂²	1	1	yes	characteristic, complemented
81	C₃×#393	C₂²	1	2	yes	complemented
82	C₃×#392	C₂²	1	1	yes	characteristic
83	C₃×#392	C₂²	1	1	yes	characteristic
84	C₃×#392	C₂²	1	2	yes	complemented
85	C₃×#392	C₂²	1	2	yes	complemented
86	C₃×#390	C₂²	1	2	yes	—
87	C₃×#390	C₂²	1	2	yes	complemented
88	C₃×#388	C₂²	1	2	yes	complemented
89	C₃×#388	C₂²	1	2	yes	complemented
90	C₃×#388	C₂²	1	2	yes	complemented
91	C₃×#388	C₂²	1	2	yes	complemented
92	C₃×#388	C₂²	1	2	yes	complemented
93	C₃×#388	C₂²	1	2	yes	complemented
94	C₃×#388	C₂²	1	2	yes	complemented
95	C₃×#388	C₂²	1	2	yes	complemented
96	C₃×#388	C₂²	1	2	yes	complemented
97	C₃×#387	C₂²	1	2	yes	complemented
98	C₃×#387	C₂²	1	2	yes	complemented
99	C₃×#386	C₂²	1	2	yes	—
100	C₃×#386	C₂²	1	2	yes	—
101	C₃×#386	C₂²	1	2	yes	complemented
102	C₃×#386	C₂²	1	2	yes	complemented
103	C₃×#386	C₂²	1	2	yes	complemented
104	C₃×#386	C₂²	1	2	yes	complemented
105	C₃×#386	C₂²	1	2	yes	complemented
106	C₃×#386	C₂²	1	2	yes	complemented
107	C₃×#386	C₂²	1	2	yes	complemented
108	C₃×#385	C₂²	1	2	yes	—
109	C₃×#385	C₂²	1	2	yes	complemented
110	C₃×#385	C₂²	1	2	yes	complemented
111	C₃×#385	C₂²	1	2	yes	complemented
112	C₃×#385	C₂²	1	2	yes	complemented
113	C₃×#383	C₂²	1	1	yes	characteristic, complemented
114	C₃×#381	C₂²	1	2	yes	—
115	C₃×#381	C₂²	1	1	yes	characteristic, complemented
116	C₃×#380	C₂²	1	1	yes	characteristic
117	C₃×#380	C₂²	1	2	yes	—
118	C₃×#379	C₂²	1	2	yes	—
119	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
121	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
122	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
124	C₃×#376	C₂²	1	1	yes	characteristic, complemented
125	C₂×C₃×#95	C₂²	1	1	yes	characteristic
126	C₂×#546	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂×#520	C₂×C₃	1	1	yes	characteristic, complemented
128	#2635	C₂×C₃	1	1	yes	characteristic, complemented
129	#2632	C₂×C₃	1	1	yes	characteristic, complemented
130	#2627	C₂×C₃	1	1	yes	characteristic, complemented
131	#2610	C₂×C₃	1	1	yes	characteristic, complemented
132	#2598	C₂×C₃	1	1	yes	characteristic, complemented
133	#2591	C₂×C₃	1	1	yes	characteristic, complemented
134	#2564	C₂×C₃	1	1	yes	characteristic, complemented
135	#2476	C₂×C₃	1	2	yes	complemented
136	#2464	C₂×C₃	1	2	yes	complemented
137	#2458	C₂×C₃	1	2	yes	complemented
138	#2443	C₂×C₃	1	2	yes	complemented
139	#2418	C₂×C₃	1	2	yes	complemented
140	#2408	C₂×C₃	1	1	yes	characteristic, complemented
141	#2406	C₂×C₃	1	1	yes	characteristic, complemented
142	#2404	C₂×C₃	1	2	yes	complemented
143	#2398	C₂×C₃	1	1	yes	characteristic, complemented
144	#2388	C₂×C₃	1	1	yes	characteristic, complemented
145	C₂×#394	C₂×C₃	1	1	yes	characteristic, complemented
146	#2358	C₂×C₃	1	2	yes	complemented
147	#2353	C₂×C₃	1	1	yes	characteristic, complemented
148	#2342	C₂×C₃	1	2	yes	complemented
149	C₂⁵×C₃	C₂³	1	2	yes	—
150	C₂×C₃×#41	—	2	4	no	—
151	C₂×C₃×#41	—	2	4	no	—
152	C₂×C₃×#41	—	2	4	no	—
153	C₂×C₃×#41	—	2	4	no	—
154	C₂×C₃×#41	—	4	4	no	—
155	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
156	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
157	C₂²×C₃×D₄	—	2	4	no	—
158	C₂²×C₃×D₄	—	4	4	no	—
159	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
160	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
161	C₂²×C₃×D₄	C₂³	1	2	yes	—
162	C₂²×C₃×D₄	C₂³	1	2	yes	—
163	C₂²×C₃×D₄	C₂³	1	2	yes	—
164	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
165	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
166	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
167	C₂²×C₃×D₄	C₂³	1	2	yes	—
168	C₂²×C₃×D₄	C₂³	1	2	yes	—
169	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
170	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
171	C₂³×C₃×C₄	C₂³	1	2	yes	—
172	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
173	C₂³×C₃×C₄	C₂³	1	2	yes	—
174	C₂³×C₃×C₄	C₂³	1	2	yes	—
175	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
176	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
177	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
178	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
179	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
180	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
181	C₃×#124	—	2	4	no	—
182	C₃×#123	—	2	8	no	—
183	C₃×#123	—	4	4	no	—
184	C₃×C₂²⋊Q₈	—	2	4	no	—
185	C₃×#121	—	2	4	no	—
186	C₃×#121	—	2	8	no	—
187	C₃×#121	—	4	4	no	—
188	C₃×#120	—	2	8	no	—
189	C₃×#120	—	2	8	no	—
190	C₃×C₄×Q₈	—	2	4	no	—
191	C₃×C₄×Q₈	—	2	4	no	—
192	C₃×C₄×D₄	—	2	4	no	—
193	C₃×C₄×D₄	—	2	4	no	—
194	C₃×C₄×D₄	—	2	4	no	—
195	C₃×C₄×D₄	—	2	4	no	—
196	C₃×C₄×D₄	—	2	4	no	—
197	C₃×C₄×D₄	—	2	4	no	—
198	C₃×C₄×D₄	—	4	4	no	—
199	C₃×C₄×D₄	D₄	1	8	yes	complemented
200	C₃×#117	—	2	4	no	—
201	C₃×#117	—	2	4	no	—
202	C₃×#117	—	2	4	no	—
203	C₂×C₃×C₄⋊C₄	—	2	4	no	—
204	C₂×C₃×C₄⋊C₄	—	2	4	no	—
205	C₂×C₃×C₄⋊C₄	—	2	4	no	—
206	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
209	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
210	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
212	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
214	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
215	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
218	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
219	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
220	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
221	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
222	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
224	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
225	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
226	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
230	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
231	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
232	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
233	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
234	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
235	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
236	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
237	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
238	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
239	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
240	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
241	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
242	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
243	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
244	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
245	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
246	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
247	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
248	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
249	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
250	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
251	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
252	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
253	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
254	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
255	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
256	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
257	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
258	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
259	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
260	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
261	C₂×C₃×C₄²	C₂³	1	2	yes	—
262	C₂×C₃×C₄²	C₂³	1	2	yes	—
263	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
264	C₃×#95	C₂³	1	1	yes	characteristic
265	C₃×#95	C₂³	1	1	yes	characteristic
266	C₃×#95	C₂³	1	2	yes	—
267	C₃×#95	C₂³	1	1	yes	characteristic
268	C₃×#95	C₂³	1	2	yes	—
269	C₃×#95	C₂³	1	2	yes	—
270	C₃×#95	C₂³	1	2	yes	—
271	C₃×#95	C₂³	1	1	yes	characteristic
272	C₃×#95	C₂³	1	2	yes	—
273	C₃×#95	C₂³	1	2	yes	—
274	C₃×#95	C₂³	1	2	yes	—
275	C₃×#95	C₂³	1	2	yes	—
276	C₃×#95	C₂³	1	2	yes	—
277	C₃×#95	C₂³	1	2	yes	—
278	C₃×#95	C₂³	1	2	yes	—
279	C₃×#95	C₂³	1	2	yes	—
280	C₃×#95	C₂³	1	2	yes	—
281	C₃×#95	C₂³	1	2	yes	—
282	C₃×#95	C₂³	1	2	yes	—
283	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
284	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
285	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
286	#546	—	2	8	no	—
287	C₂×#124	C₂²×C₃	1	1	yes	characteristic
288	C₂×#123	C₂²×C₃	1	2	yes	—
289	C₂×#123	C₂²×C₃	1	2	yes	complemented
290	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
291	C₂×#121	C₂²×C₃	1	1	yes	characteristic
292	C₂×#121	C₂²×C₃	1	2	yes	—
293	C₂×#121	C₂²×C₃	1	2	yes	—
294	C₂×#120	C₂²×C₃	1	2	yes	—
295	C₂×#120	C₂²×C₃	1	2	yes	—
296	#520	—	2	8	no	—
297	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
298	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
299	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
300	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
301	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
302	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
303	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
304	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
305	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
306	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
307	C₂×#117	C₂²×C₃	1	1	yes	characteristic
308	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
309	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
310	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
311	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
312	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
313	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
314	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
315	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
316	#400	C₂²×C₃	1	1	yes	characteristic, complemented
317	#400	C₂²×C₃	1	1	yes	characteristic, complemented
318	#400	C₂²×C₃	1	1	yes	characteristic, complemented
319	#399	C₂²×C₃	1	1	yes	characteristic, complemented
320	#399	C₂²×C₃	1	2	yes	complemented
321	#398	C₂²×C₃	1	2	yes	complemented
322	#398	C₂²×C₃	1	2	yes	complemented
323	#397	C₂²×C₃	1	2	yes	complemented
324	#395	C₂²×C₃	1	1	yes	characteristic, complemented
325	#395	C₂²×C₃	1	1	yes	characteristic, complemented
326	#395	C₂²×C₃	1	1	yes	characteristic, complemented
327	#394	C₂²×C₃	1	1	yes	characteristic
328	#394	C₂²×C₃	1	1	yes	characteristic
329	#394	C₂²×C₃	1	1	yes	characteristic
330	#394	C₂²×C₃	1	1	yes	characteristic
331	#394	C₂²×C₃	1	1	yes	characteristic
332	#394	C₂²×C₃	1	2	yes	—
333	#394	C₂²×C₃	1	2	yes	—
334	#394	C₂²×C₃	1	1	yes	characteristic
335	#394	C₂²×C₃	1	2	yes	complemented
336	#394	C₂²×C₃	1	2	yes	complemented
337	#393	C₂²×C₃	1	1	yes	characteristic, complemented
338	#393	C₂²×C₃	1	2	yes	complemented
339	#393	C₂²×C₃	1	2	yes	complemented
340	#392	C₂²×C₃	1	1	yes	characteristic
341	#392	C₂²×C₃	1	1	yes	characteristic
342	#392	C₂²×C₃	1	2	yes	complemented
343	#392	C₂²×C₃	1	2	yes	complemented
344	#390	C₂²×C₃	1	2	yes	—
345	#390	C₂²×C₃	1	2	yes	complemented
346	#388	C₂²×C₃	1	2	yes	complemented
347	#388	C₂²×C₃	1	2	yes	complemented
348	#388	C₂²×C₃	1	2	yes	complemented
349	#388	C₂²×C₃	1	2	yes	complemented
350	#388	C₂²×C₃	1	2	yes	complemented
351	#388	C₂²×C₃	1	2	yes	complemented
352	#388	C₂²×C₃	1	2	yes	complemented
353	#388	C₂²×C₃	1	2	yes	complemented
354	#388	C₂²×C₃	1	2	yes	complemented
355	#387	C₂²×C₃	1	2	yes	complemented
356	#387	C₂²×C₃	1	2	yes	complemented
357	#386	C₂²×C₃	1	2	yes	—
358	#386	C₂²×C₃	1	2	yes	—
359	#386	C₂²×C₃	1	2	yes	complemented
360	#386	C₂²×C₃	1	2	yes	complemented
361	#386	C₂²×C₃	1	2	yes	complemented
362	#386	C₂²×C₃	1	2	yes	complemented
363	#386	C₂²×C₃	1	2	yes	complemented
364	#386	C₂²×C₃	1	2	yes	complemented
365	#386	C₂²×C₃	1	2	yes	complemented
366	#385	C₂²×C₃	1	2	yes	—
367	#385	C₂²×C₃	1	2	yes	complemented
368	#385	C₂²×C₃	1	2	yes	complemented
369	#385	C₂²×C₃	1	2	yes	complemented
370	#385	C₂²×C₃	1	2	yes	complemented
371	#383	C₂²×C₃	1	1	yes	characteristic, complemented
372	#381	C₂²×C₃	1	2	yes	—
373	#381	C₂²×C₃	1	1	yes	characteristic, complemented
374	#380	C₂²×C₃	1	2	yes	—
375	#380	C₂²×C₃	1	1	yes	characteristic
376	#379	C₂²×C₃	1	2	yes	—
377	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
378	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
379	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
380	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
381	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
382	#376	C₂²×C₃	1	1	yes	characteristic, complemented
383	C₂×#95	C₂²×C₃	1	1	yes	characteristic
384	C₂⁴×C₃	—	2	4	no	—
385	C₂⁴×C₃	—	2	4	no	—
386	C₂⁴×C₃	—	2	4	no	—
387	C₂⁴×C₃	—	2	4	no	—
388	C₂⁴×C₃	—	4	2	no	—
389	C₂⁴×C₃	—	4	2	no	—
390	C₂⁴×C₃	—	4	2	no	—
391	C₂⁴×C₃	C₂⁴	1	2	yes	—
392	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
393	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
394	C₂⁴×C₃	C₂⁴	1	2	yes	—
395	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
396	C₃×#41	—	2	32	no	—
397	C₃×#41	—	4	16	no	—
398	C₂×C₃×Q₈	—	2	2	no	—
399	C₂×C₃×Q₈	—	2	2	no	—
400	C₂×C₃×Q₈	—	2	2	no	—
401	C₂×C₃×Q₈	—	2	2	no	—
402	C₂×C₃×Q₈	—	4	2	no	—
403	C₂×C₃×D₄	—	2	2	no	—
404	C₂×C₃×D₄	—	2	2	no	—
405	C₂×C₃×D₄	—	2	2	no	—
406	C₂×C₃×D₄	—	2	2	no	—
407	C₂×C₃×D₄	—	2	2	no	—
408	C₂×C₃×D₄	—	2	2	no	—
409	C₂×C₃×D₄	—	2	4	no	—
410	C₂×C₃×D₄	—	2	4	no	—
411	C₂×C₃×D₄	—	2	4	no	—
412	C₂×C₃×D₄	—	2	4	no	—
413	C₂×C₃×D₄	—	2	4	no	—
414	C₂×C₃×D₄	—	2	4	no	—
415	C₂×C₃×D₄	—	2	4	no	—
416	C₂×C₃×D₄	—	2	4	no	—
417	C₂×C₃×D₄	—	2	2	no	—
418	C₂×C₃×D₄	—	2	4	no	—
419	C₂×C₃×D₄	—	2	2	no	—
420	C₂×C₃×D₄	—	2	2	no	—
421	C₂×C₃×D₄	—	4	2	no	—
422	C₂×C₃×D₄	—	4	2	no	—
423	C₂×C₃×D₄	—	4	2	no	—
424	C₂×C₃×D₄	—	4	2	no	—
425	C₂×C₃×D₄	—	4	2	no	—
426	C₂×C₃×D₄	—	4	2	no	—
427	C₂×C₃×D₄	—	4	2	no	—
428	C₂×C₃×D₄	—	4	2	no	—
429	C₂×C₃×D₄	—	4	16	no	—
430	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
431	C₂×C₃×D₄	#41	1	4	yes	complemented
432	C₂²×C₃×C₄	—	2	2	no	—
433	C₂²×C₃×C₄	—	2	2	no	—
434	C₂²×C₃×C₄	—	2	2	no	—
435	C₂²×C₃×C₄	—	2	2	no	—
436	C₂²×C₃×C₄	—	2	2	no	—
437	C₂²×C₃×C₄	—	2	2	no	—
438	C₂²×C₃×C₄	—	2	2	no	—
439	C₂²×C₃×C₄	—	2	2	no	—
440	C₂²×C₃×C₄	—	2	4	no	—
441	C₂²×C₃×C₄	—	2	2	no	—
442	C₂²×C₃×C₄	—	2	2	no	—
443	C₂²×C₃×C₄	—	2	4	no	—
444	C₂²×C₃×C₄	—	2	4	no	—
445	C₂²×C₃×C₄	—	2	4	no	—
446	C₂²×C₃×C₄	—	2	2	no	—
447	C₂²×C₃×C₄	—	2	2	no	—
448	C₂²×C₃×C₄	—	4	2	no	—
449	C₂²×C₃×C₄	—	4	2	no	—
450	C₂²×C₃×C₄	—	4	2	no	—
451	C₂²×C₃×C₄	—	4	2	no	—
452	C₂²×C₃×C₄	—	4	2	no	—
453	C₂²×C₃×C₄	—	4	2	no	—
454	C₂²×C₃×C₄	—	4	2	no	—
455	C₂²×C₃×C₄	—	4	2	no	—
456	C₂²×C₃×C₄	—	4	2	no	—
457	C₂²×C₃×C₄	—	4	2	no	—
458	C₂²×C₃×C₄	—	4	2	no	—
459	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
460	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
461	C₂²×C₃×C₄	#41	1	4	yes	complemented
462	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
463	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
464	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
465	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
466	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
467	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
468	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
469	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
470	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
471	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
472	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
473	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
474	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
475	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
476	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
477	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
478	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
479	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
480	C₃×C₄⋊C₄	—	2	2	no	—
481	C₃×C₄⋊C₄	—	2	2	no	—
482	C₃×C₄⋊C₄	—	2	2	no	—
483	C₃×C₄⋊C₄	—	2	2	no	—
484	C₃×C₄⋊C₄	—	2	2	no	—
485	C₃×C₄⋊C₄	—	2	2	no	—
486	C₃×C₄⋊C₄	—	2	2	no	—
487	C₃×C₄⋊C₄	—	2	2	no	—
488	C₃×C₄⋊C₄	—	2	2	no	—
489	C₃×C₄⋊C₄	—	2	2	no	—
490	C₃×C₄⋊C₄	—	2	4	no	—
491	C₃×C₄⋊C₄	—	4	2	no	—
492	C₃×C₄⋊C₄	—	4	2	no	—
493	C₃×C₄⋊C₄	—	4	2	no	—
494	C₃×C₄⋊C₄	—	4	2	no	—
495	C₃×C₄⋊C₄	—	4	2	no	—
496	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
497	C₃×C₂²⋊C₄	—	2	4	no	—
498	C₃×C₂²⋊C₄	—	2	2	no	—
499	C₃×C₂²⋊C₄	—	2	2	no	—
500	C₃×C₂²⋊C₄	—	2	4	no	—
501	C₃×C₂²⋊C₄	—	2	4	no	—
502	C₃×C₂²⋊C₄	—	2	4	no	—
503	C₃×C₂²⋊C₄	—	2	4	no	—
504	C₃×C₂²⋊C₄	—	2	4	no	—
505	C₃×C₂²⋊C₄	—	2	4	no	—
506	C₃×C₂²⋊C₄	—	2	2	no	—
507	C₃×C₂²⋊C₄	—	2	2	no	—
508	C₃×C₂²⋊C₄	—	2	4	no	—
509	C₃×C₂²⋊C₄	—	2	4	no	—
510	C₃×C₂²⋊C₄	—	2	4	no	—
511	C₃×C₂²⋊C₄	—	2	4	no	—
512	C₃×C₂²⋊C₄	—	2	4	no	—
513	C₃×C₂²⋊C₄	—	2	4	no	—
514	C₃×C₂²⋊C₄	—	2	4	no	—
515	C₃×C₂²⋊C₄	—	2	4	no	—
516	C₃×C₂²⋊C₄	—	4	2	no	—
517	C₃×C₂²⋊C₄	—	4	2	no	—
518	C₃×C₂²⋊C₄	—	4	2	no	—
519	C₃×C₂²⋊C₄	—	4	2	no	—
520	C₃×C₂²⋊C₄	—	4	2	no	—
521	C₃×C₂²⋊C₄	—	4	2	no	—
522	C₃×C₂²⋊C₄	—	4	2	no	—
523	C₃×C₂²⋊C₄	—	4	2	no	—
524	C₃×C₂²⋊C₄	—	4	2	no	—
525	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
526	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
527	C₃×C₄²	—	2	2	no	—
528	C₃×C₄²	—	2	2	no	—
529	C₃×C₄²	—	2	2	no	—
530	C₃×C₄²	—	2	2	no	—
531	C₃×C₄²	—	2	2	no	—
532	C₃×C₄²	—	4	2	no	—
533	C₃×C₄²	—	4	2	no	—
534	C₃×C₄²	C₂×D₄	1	4	yes	—
535	C₂⁵	C₂³×C₃	1	2	yes	—
536	C₂×#41	—	2	4	no	—
537	C₂×#41	—	2	4	no	—
538	C₂×#41	—	2	4	no	—
539	C₂×#41	—	2	4	no	—
540	C₂×#41	—	4	4	no	—
541	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
542	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
543	C₂²×D₄	—	2	4	no	—
544	C₂²×D₄	—	4	4	no	—
545	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
546	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
547	C₂²×D₄	C₂³×C₃	1	2	yes	—
548	C₂²×D₄	C₂³×C₃	1	2	yes	—
549	C₂²×D₄	C₂³×C₃	1	2	yes	—
550	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
551	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
552	C₂²×D₄	C₂³×C₃	1	2	yes	—
553	C₂²×D₄	C₂³×C₃	1	2	yes	—
554	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
555	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
556	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
557	C₂³×C₄	C₂³×C₃	1	2	yes	—
558	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
559	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
560	C₂³×C₄	C₂³×C₃	1	2	yes	—
561	C₂³×C₄	C₂³×C₃	1	2	yes	—
562	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
563	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
564	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
566	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
567	#124	—	2	4	no	—
568	#123	—	2	8	no	—
569	#123	—	4	4	no	—
570	C₂²⋊Q₈	—	2	4	no	—
571	#121	—	2	4	no	—
572	#121	—	2	8	no	—
573	#121	—	4	4	no	—
574	#120	—	2	8	no	—
575	#120	—	2	8	no	—
576	C₄×Q₈	—	2	4	no	—
577	C₄×Q₈	—	2	4	no	—
578	C₄×D₄	—	2	4	no	—
579	C₄×D₄	—	2	4	no	—
580	C₄×D₄	—	2	4	no	—
581	C₄×D₄	—	2	4	no	—
582	C₄×D₄	—	2	4	no	—
583	C₄×D₄	—	2	4	no	—
584	C₄×D₄	—	4	4	no	—
585	C₄×D₄	C₃×D₄	1	8	yes	complemented
586	#117	—	2	4	no	—
587	#117	—	2	4	no	—
588	#117	—	2	4	no	—
589	C₂×C₄⋊C₄	—	2	4	no	—
590	C₂×C₄⋊C₄	—	2	4	no	—
591	C₂×C₄⋊C₄	—	2	4	no	—
592	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
609	C₂×C₂²⋊C₄	—	2	8	no	—
610	C₂×C₂²⋊C₄	—	2	8	no	—
611	C₂×C₂²⋊C₄	—	4	4	no	—
612	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
622	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
623	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
625	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
641	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₃	1	2	yes	—
648	C₂×C₄²	C₂³×C₃	1	2	yes	—
649	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
650	#95	C₂³×C₃	1	1	yes	characteristic
651	#95	C₂³×C₃	1	1	yes	characteristic
652	#95	C₂³×C₃	1	2	yes	—
653	#95	C₂³×C₃	1	1	yes	characteristic
654	#95	C₂³×C₃	1	2	yes	—
655	#95	C₂³×C₃	1	2	yes	—
656	#95	C₂³×C₃	1	2	yes	—
657	#95	C₂³×C₃	1	1	yes	characteristic
658	#95	C₂³×C₃	1	2	yes	—
659	#95	C₂³×C₃	1	2	yes	—
660	#95	C₂³×C₃	1	2	yes	—
661	#95	C₂³×C₃	1	2	yes	—
662	#95	C₂³×C₃	1	2	yes	—
663	#95	C₂³×C₃	1	2	yes	—
664	#95	C₂³×C₃	1	2	yes	—
665	#95	C₂³×C₃	1	2	yes	—
666	#95	C₂³×C₃	1	2	yes	—
667	#95	C₂³×C₃	1	2	yes	—
668	#95	C₂³×C₃	1	2	yes	—
669	C₂³×C₃	—	2	2	no	—
670	C₂³×C₃	—	2	2	no	—
671	C₂³×C₃	—	2	1	no	—
672	C₂³×C₃	—	2	2	no	—
673	C₂³×C₃	—	2	2	no	—
674	C₂³×C₃	—	2	2	no	—
675	C₂³×C₃	—	2	1	no	—
676	C₂³×C₃	—	2	1	no	—
677	C₂³×C₃	—	2	1	no	—
678	C₂³×C₃	—	2	2	no	—
679	C₂³×C₃	—	2	2	no	—
680	C₂³×C₃	—	2	2	no	—
681	C₂³×C₃	—	2	2	no	—
682	C₂³×C₃	—	2	2	no	—
683	C₂³×C₃	—	2	2	no	—
684	C₂³×C₃	—	2	2	no	—
685	C₂³×C₃	—	2	2	no	—
686	C₂³×C₃	—	2	2	no	—
687	C₂³×C₃	—	2	2	no	—
688	C₂³×C₃	—	2	2	no	—
689	C₂³×C₃	—	2	2	no	—
690	C₂³×C₃	—	2	2	no	—
691	C₂³×C₃	—	2	2	no	—
692	C₂³×C₃	—	4	8	no	—
693	C₂³×C₃	—	4	8	no	—
694	C₂³×C₃	—	4	8	no	—
695	C₂³×C₃	—	4	8	no	—
696	C₂³×C₃	—	8	4	no	—
697	C₂³×C₃	—	8	4	no	—
698	C₂³×C₃	—	8	4	no	—
699	C₂³×C₃	C₂²×D₄	1	2	yes	—
700	C₂³×C₃	C₂²×D₄	1	2	yes	—
701	C₂³×C₃	C₂×#41	1	2	yes	—
702	C₂³×C₃	C₂×#41	1	2	yes	—
703	C₂³×C₃	C₂×#41	1	2	yes	—
704	C₂³×C₃	H(5,𝔽₂)	1	4	yes	—
705	C₂³×C₃	C₂⁵	1	1	yes	characteristic
706	C₃×Q₈	—	2	8	no	—
707	C₃×Q₈	—	4	4	no	—
708	C₃×D₄	—	2	8	no	—
709	C₃×D₄	—	2	8	no	—
710	C₃×D₄	—	2	8	no	—
711	C₃×D₄	—	2	8	no	—
712	C₃×D₄	—	4	8	no	—
713	C₃×D₄	—	4	4	no	—
714	C₃×D₄	—	4	8	no	—
715	C₃×D₄	—	4	8	no	—
716	C₃×D₄	—	8	4	no	—
717	C₃×D₄	—	8	4	no	—
718	C₂×C₃×C₄	—	2	8	no	—
719	C₂×C₃×C₄	—	2	8	no	—
720	C₂×C₃×C₄	—	2	8	no	—
721	C₂×C₃×C₄	—	2	1	no	—
722	C₂×C₃×C₄	—	2	1	no	—
723	C₂×C₃×C₄	—	2	1	no	—
724	C₂×C₃×C₄	—	2	1	no	—
725	C₂×C₃×C₄	—	2	1	no	—
726	C₂×C₃×C₄	—	2	1	no	—
727	C₂×C₃×C₄	—	2	1	no	—
728	C₂×C₃×C₄	—	2	1	no	—
729	C₂×C₃×C₄	—	2	2	no	—
730	C₂×C₃×C₄	—	2	2	no	—
731	C₂×C₃×C₄	—	2	2	no	—
732	C₂×C₃×C₄	—	2	2	no	—
733	C₂×C₃×C₄	—	2	1	no	—
734	C₂×C₃×C₄	—	2	1	no	—
735	C₂×C₃×C₄	—	2	1	no	—
736	C₂×C₃×C₄	—	2	1	no	—
737	C₂×C₃×C₄	—	2	2	no	—
738	C₂×C₃×C₄	—	2	2	no	—
739	C₂×C₃×C₄	—	2	2	no	—
740	C₂×C₃×C₄	—	2	2	no	—
741	C₂×C₃×C₄	—	2	2	no	—
742	C₂×C₃×C₄	—	2	2	no	—
743	C₂×C₃×C₄	—	2	2	no	—
744	C₂×C₃×C₄	—	2	2	no	—
745	C₂×C₃×C₄	—	2	2	no	—
746	C₂×C₃×C₄	—	2	2	no	—
747	C₂×C₃×C₄	—	2	2	no	—
748	C₂×C₃×C₄	—	2	2	no	—
749	C₂×C₃×C₄	—	2	2	no	—
750	C₂×C₃×C₄	—	2	2	no	—
751	C₂×C₃×C₄	—	2	2	no	—
752	C₂×C₃×C₄	—	2	2	no	—
753	C₂×C₃×C₄	—	2	2	no	—
754	C₂×C₃×C₄	—	2	2	no	—
755	C₂×C₃×C₄	—	2	2	no	—
756	C₂×C₃×C₄	—	2	2	no	—
757	C₂×C₃×C₄	—	2	2	no	—
758	C₂×C₃×C₄	—	2	2	no	—
759	C₂×C₃×C₄	—	4	4	no	—
760	C₂×C₃×C₄	—	4	4	no	—
761	C₂×C₃×C₄	—	4	8	no	—
762	C₂×C₃×C₄	—	8	2	no	—
763	C₂×C₃×C₄	—	8	2	no	—
764	C₂×C₃×C₄	—	8	4	no	—
765	C₂×C₃×C₄	—	8	2	no	—
766	C₂×C₃×C₄	—	8	2	no	—
767	C₂×C₃×C₄	—	8	4	no	—
768	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
769	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
770	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
771	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
772	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
773	C₂×C₃×C₄	C₂×#41	1	2	yes	—
774	C₂×C₃×C₄	C₂×#41	1	2	yes	—
775	C₂×C₃×C₄	C₂×#41	1	2	yes	—
776	C₂⁴	—	2	4	no	—
777	C₂⁴	—	2	4	no	—
778	C₂⁴	—	2	4	no	—
779	C₂⁴	—	2	4	no	—
780	C₂⁴	—	4	2	no	—
781	C₂⁴	—	4	2	no	—
782	C₂⁴	—	4	2	no	—
783	C₂⁴	C₂⁴×C₃	1	2	yes	—
784	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
785	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
786	C₂⁴	C₂⁴×C₃	1	2	yes	—
787	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
788	#41	—	2	32	no	—
789	#41	—	4	16	no	—
790	C₂×Q₈	—	2	2	no	—
791	C₂×Q₈	—	2	2	no	—
792	C₂×Q₈	—	2	2	no	—
793	C₂×Q₈	—	2	2	no	—
794	C₂×Q₈	—	4	2	no	—
795	C₂×D₄	—	2	2	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	—	2	2	no	—
799	C₂×D₄	—	2	2	no	—
800	C₂×D₄	—	2	2	no	—
801	C₂×D₄	—	2	4	no	—
802	C₂×D₄	—	2	4	no	—
803	C₂×D₄	—	2	4	no	—
804	C₂×D₄	—	2	4	no	—
805	C₂×D₄	—	2	4	no	—
806	C₂×D₄	—	2	4	no	—
807	C₂×D₄	—	2	4	no	—
808	C₂×D₄	—	2	4	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	4	no	—
811	C₂×D₄	—	2	2	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	4	2	no	—
814	C₂×D₄	—	4	2	no	—
815	C₂×D₄	—	4	2	no	—
816	C₂×D₄	—	4	2	no	—
817	C₂×D₄	—	4	2	no	—
818	C₂×D₄	—	4	2	no	—
819	C₂×D₄	—	4	2	no	—
820	C₂×D₄	—	4	2	no	—
821	C₂×D₄	—	4	16	no	—
822	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
823	C₂×D₄	C₃×#41	1	4	yes	complemented
824	C₂²×C₄	—	2	2	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	2	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	2	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	4	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	4	no	—
836	C₂²×C₄	—	2	4	no	—
837	C₂²×C₄	—	2	4	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	4	2	no	—
841	C₂²×C₄	—	4	2	no	—
842	C₂²×C₄	—	4	2	no	—
843	C₂²×C₄	—	4	2	no	—
844	C₂²×C₄	—	4	2	no	—
845	C₂²×C₄	—	4	2	no	—
846	C₂²×C₄	—	4	2	no	—
847	C₂²×C₄	—	4	2	no	—
848	C₂²×C₄	—	4	2	no	—
849	C₂²×C₄	—	4	2	no	—
850	C₂²×C₄	—	4	2	no	—
851	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
852	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
853	C₂²×C₄	C₃×#41	1	4	yes	complemented
854	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
855	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
856	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
857	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
858	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
859	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
860	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
861	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
862	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
863	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
864	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
865	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
868	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	4	no	—
883	C₄⋊C₄	—	4	2	no	—
884	C₄⋊C₄	—	4	2	no	—
885	C₄⋊C₄	—	4	2	no	—
886	C₄⋊C₄	—	4	2	no	—
887	C₄⋊C₄	—	4	2	no	—
888	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
889	C₂²⋊C₄	—	2	4	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	4	no	—
893	C₂²⋊C₄	—	2	4	no	—
894	C₂²⋊C₄	—	2	4	no	—
895	C₂²⋊C₄	—	2	4	no	—
896	C₂²⋊C₄	—	2	4	no	—
897	C₂²⋊C₄	—	2	4	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	4	no	—
901	C₂²⋊C₄	—	2	4	no	—
902	C₂²⋊C₄	—	2	4	no	—
903	C₂²⋊C₄	—	2	4	no	—
904	C₂²⋊C₄	—	2	4	no	—
905	C₂²⋊C₄	—	2	4	no	—
906	C₂²⋊C₄	—	2	4	no	—
907	C₂²⋊C₄	—	2	4	no	—
908	C₂²⋊C₄	—	4	2	no	—
909	C₂²⋊C₄	—	4	2	no	—
910	C₂²⋊C₄	—	4	2	no	—
911	C₂²⋊C₄	—	4	2	no	—
912	C₂²⋊C₄	—	4	2	no	—
913	C₂²⋊C₄	—	4	2	no	—
914	C₂²⋊C₄	—	4	2	no	—
915	C₂²⋊C₄	—	4	2	no	—
916	C₂²⋊C₄	—	4	2	no	—
917	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
918	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
919	C₄²	—	2	2	no	—
920	C₄²	—	2	2	no	—
921	C₄²	—	2	2	no	—
922	C₄²	—	2	2	no	—
923	C₄²	—	2	2	no	—
924	C₄²	—	4	2	no	—
925	C₄²	—	4	2	no	—
926	C₄²	C₂×C₃×D₄	1	4	yes	—
927	C₂²×C₃	—	2	2	no	—
928	C₂²×C₃	—	2	4	no	—
929	C₂²×C₃	—	2	2	no	—
930	C₂²×C₃	—	2	4	no	—
931	C₂²×C₃	—	2	2	no	—
932	C₂²×C₃	—	2	2	no	—
933	C₂²×C₃	—	2	2	no	—
934	C₂²×C₃	—	2	4	no	—
935	C₂²×C₃	—	2	4	no	—
936	C₂²×C₃	—	2	2	no	—
937	C₂²×C₃	—	2	4	no	—
938	C₂²×C₃	—	2	4	no	—
939	C₂²×C₃	—	4	2	no	—
940	C₂²×C₃	—	4	1	no	—
941	C₂²×C₃	—	4	2	no	—
942	C₂²×C₃	—	4	2	no	—
943	C₂²×C₃	—	4	2	no	—
944	C₂²×C₃	—	4	2	no	—
945	C₂²×C₃	—	4	1	no	—
946	C₂²×C₃	—	4	2	no	—
947	C₂²×C₃	—	4	2	no	—
948	C₂²×C₃	—	4	2	no	—
949	C₂²×C₃	—	4	2	no	—
950	C₂²×C₃	—	4	2	no	—
951	C₂²×C₃	—	4	2	no	—
952	C₂²×C₃	—	4	2	no	—
953	C₂²×C₃	—	4	2	no	—
954	C₂²×C₃	—	4	2	no	—
955	C₂²×C₃	—	8	16	no	—
956	C₂²×C₃	#525	1	4	yes	—
957	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
958	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
959	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
960	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
961	C₂²×C₃	#585	1	2	yes	—
962	C₃×C₄	—	2	2	no	—
963	C₃×C₄	—	2	2	no	—
964	C₃×C₄	—	2	2	no	—
965	C₃×C₄	—	2	2	no	—
966	C₃×C₄	—	2	2	no	—
967	C₃×C₄	—	2	2	no	—
968	C₃×C₄	—	2	2	no	—
969	C₃×C₄	—	2	2	no	—
970	C₃×C₄	—	4	2	no	—
971	C₃×C₄	—	4	1	no	—
972	C₃×C₄	—	4	1	no	—
973	C₃×C₄	—	4	1	no	—
974	C₃×C₄	—	4	2	no	—
975	C₃×C₄	—	4	2	no	—
976	C₃×C₄	—	4	1	no	—
977	C₃×C₄	—	4	2	no	—
978	C₃×C₄	—	4	2	no	—
979	C₃×C₄	—	4	2	no	—
980	C₂³	—	2	2	no	—
981	C₂³	—	2	2	no	—
982	C₂³	—	2	1	no	—
983	C₂³	—	2	2	no	—
984	C₂³	—	2	2	no	—
985	C₂³	—	2	2	no	—
986	C₂³	—	2	1	no	—
987	C₂³	—	2	1	no	—
988	C₂³	—	2	1	no	—
989	C₂³	—	2	2	no	—
990	C₂³	—	2	2	no	—
991	C₂³	—	2	2	no	—
992	C₂³	—	2	2	no	—
993	C₂³	—	2	2	no	—
994	C₂³	—	2	2	no	—
995	C₂³	—	2	2	no	—
996	C₂³	—	2	2	no	—
997	C₂³	—	2	2	no	—
998	C₂³	—	2	2	no	—
999	C₂³	—	2	2	no	—
1000	C₂³	—	2	2	no	—
1001	C₂³	—	2	2	no	—
1002	C₂³	—	2	2	no	—
1003	C₂³	—	4	8	no	—
1004	C₂³	—	4	8	no	—
1005	C₂³	—	4	8	no	—
1006	C₂³	—	4	8	no	—
1007	C₂³	—	8	4	no	—
1008	C₂³	—	8	4	no	—
1009	C₂³	—	8	4	no	—
1010	C₂³	C₂²×C₃×D₄	1	2	yes	—
1011	C₂³	C₂²×C₃×D₄	1	2	yes	—
1012	C₂³	C₂×C₃×#41	1	2	yes	—
1013	C₂³	C₂×C₃×#41	1	2	yes	—
1014	C₂³	C₂×C₃×#41	1	2	yes	—
1015	C₂³	C₃×H(5,𝔽₂)	1	4	yes	—
1016	C₂³	C₂⁵×C₃	1	1	yes	characteristic
1017	Q₈	—	2	8	no	—
1018	Q₈	—	4	4	no	—
1019	D₄	—	2	8	no	—
1020	D₄	—	2	8	no	—
1021	D₄	—	2	8	no	—
1022	D₄	—	2	8	no	—
1023	D₄	—	4	8	no	—
1024	D₄	—	4	4	no	—
1025	D₄	—	4	8	no	—
1026	D₄	—	4	8	no	—
1027	D₄	—	8	4	no	—
1028	D₄	—	8	4	no	—
1029	C₂×C₄	—	2	8	no	—
1030	C₂×C₄	—	2	8	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	8	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	4	4	no	—
1071	C₂×C₄	—	4	4	no	—
1072	C₂×C₄	—	4	8	no	—
1073	C₂×C₄	—	8	2	no	—
1074	C₂×C₄	—	8	2	no	—
1075	C₂×C₄	—	8	4	no	—
1076	C₂×C₄	—	8	2	no	—
1077	C₂×C₄	—	8	2	no	—
1078	C₂×C₄	—	8	4	no	—
1079	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1080	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1081	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1082	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1083	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1084	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1085	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1086	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1087	C₂×C₃	—	2	4	no	—
1088	C₂×C₃	—	4	2	no	—
1089	C₂×C₃	—	4	2	no	—
1090	C₂×C₃	—	4	4	no	—
1091	C₂×C₃	—	8	2	no	—
1092	C₂×C₃	C₂×#525	1	1	yes	characteristic
1093	C₂×C₃	#3484	1	1	yes	characteristic
1094	C₂×C₃	#3494	1	2	yes	—
1095	C₂×C₃	#3500	1	1	yes	characteristic
1096	C₂×C₃	#3513	1	2	yes	—
1097	C₂²	—	2	2	no	—
1098	C₂²	—	2	4	no	—
1099	C₂²	—	2	2	no	—
1100	C₂²	—	2	4	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	4	no	—
1105	C₂²	—	2	4	no	—
1106	C₂²	—	2	2	no	—
1107	C₂²	—	2	4	no	—
1108	C₂²	—	2	4	no	—
1109	C₂²	—	4	2	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	4	2	no	—
1113	C₂²	—	4	2	no	—
1114	C₂²	—	4	2	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	2	no	—
1117	C₂²	—	4	2	no	—
1118	C₂²	—	4	2	no	—
1119	C₂²	—	4	2	no	—
1120	C₂²	—	4	2	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	2	no	—
1123	C₂²	—	4	2	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	8	16	no	—
1126	C₂²	C₃×#525	1	4	yes	—
1127	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1128	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1129	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1130	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
1131	C₂²	C₃×#585	1	2	yes	—
1132	C₄	—	2	2	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	2	2	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	2	2	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	2	no	—
1145	C₄	—	4	2	no	—
1146	C₄	—	4	2	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	2	no	—
1149	C₄	—	4	2	no	—
1150	C₃	#35729	1	1	yes	characteristic, direct product factor, Sylow
1151	C₂	—	2	4	no	—
1152	C₂	—	4	4	no	—
1153	C₂	—	4	2	no	—
1154	C₂	—	4	2	no	—
1155	C₂	—	8	2	no	—
1156	C₂	C₂×C₃×#525	1	1	yes	characteristic
1157	C₂	C₃×#3484	1	1	yes	characteristic
1158	C₂	C₃×#3494	1	2	yes	—
1159	C₂	C₃×#3500	1	1	yes	characteristic
1160	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×#520	C₂	semidirect
3. C₃×#2635	C₂	semidirect
4. C₃×#2632	C₂	semidirect
5. C₃×#2627	C₂	semidirect
6. C₃×#2610	C₂	semidirect
7. C₃×#2598	C₂	semidirect
8. C₃×#2591	C₂	semidirect
9. C₃×#2564	C₂	semidirect
10. C₃×#2476	C₂	semidirect
11. C₃×#2464	C₂	semidirect
12. C₃×#2458	C₂	semidirect
13. C₃×#2443	C₂	semidirect
14. C₃×#2418	C₂	semidirect
15. C₃×#2408	C₂	semidirect
16. C₃×#2406	C₂	semidirect
17. C₃×#2404	C₂	semidirect
18. C₃×#2398	C₂	semidirect
19. C₃×#2388	C₂	semidirect
20. C₂×C₃×#394	C₂	semidirect
21. C₃×#2358	C₂	semidirect
22. C₃×#2353	C₂	semidirect
23. C₃×#2342	C₂	semidirect
24. #35729	C₃	direct (N × H)
31. C₂×C₃×#123	C₂²	semidirect
39. C₂×C₃×C₄×Q₈	C₂²	semidirect
40. C₂×C₃×C₄×Q₈	C₂²	semidirect
46. C₂×C₃×C₄×D₄	C₂²	semidirect
47. C₂×C₃×C₄×D₄	C₂²	semidirect
48. C₂×C₃×C₄×D₄	C₂²	semidirect
50. C₂×C₃×#117	C₂²	semidirect
51. C₂×C₃×#117	C₂²	semidirect
53. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
54. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
58. C₃×#400	C₂²	semidirect
59. C₃×#400	C₂²	semidirect
60. C₃×#400	C₂²	semidirect
61. C₃×#399	C₂²	semidirect
62. C₃×#399	C₂²	semidirect
63. C₃×#398	C₂²	semidirect
64. C₃×#398	C₂²	semidirect
65. C₃×#397	C₂²	semidirect
66. C₃×#395	C₂²	semidirect
67. C₃×#395	C₂²	semidirect
68. C₃×#395	C₂²	semidirect
77. C₃×#394	C₂²	semidirect
78. C₃×#394	C₂²	semidirect
79. C₃×#393	C₂²	semidirect
80. C₃×#393	C₂²	semidirect
81. C₃×#393	C₂²	semidirect
84. C₃×#392	C₂²	semidirect
85. C₃×#392	C₂²	semidirect
87. C₃×#390	C₂²	semidirect
88. C₃×#388	C₂²	semidirect
89. C₃×#388	C₂²	semidirect
90. C₃×#388	C₂²	semidirect
91. C₃×#388	C₂²	semidirect
92. C₃×#388	C₂²	semidirect
93. C₃×#388	C₂²	semidirect
94. C₃×#388	C₂²	semidirect
95. C₃×#388	C₂²	semidirect
96. C₃×#388	C₂²	semidirect
97. C₃×#387	C₂²	semidirect
98. C₃×#387	C₂²	semidirect
101. C₃×#386	C₂²	semidirect
102. C₃×#386	C₂²	semidirect
103. C₃×#386	C₂²	semidirect
104. C₃×#386	C₂²	semidirect
105. C₃×#386	C₂²	semidirect
106. C₃×#386	C₂²	semidirect
107. C₃×#386	C₂²	semidirect
109. C₃×#385	C₂²	semidirect
110. C₃×#385	C₂²	semidirect
111. C₃×#385	C₂²	semidirect
112. C₃×#385	C₂²	semidirect
113. C₃×#383	C₂²	semidirect
115. C₃×#381	C₂²	semidirect
120. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
121. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
122. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
123. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
124. C₃×#376	C₂²	semidirect
126. C₂×#546	C₂×C₃	semidirect
127. C₂×#520	C₂×C₃	semidirect
128. #2635	C₂×C₃	semidirect
129. #2632	C₂×C₃	semidirect
130. #2627	C₂×C₃	semidirect
131. #2610	C₂×C₃	semidirect
132. #2598	C₂×C₃	semidirect
133. #2591	C₂×C₃	semidirect
134. #2564	C₂×C₃	semidirect
135. #2476	C₂×C₃	semidirect
136. #2464	C₂×C₃	semidirect
137. #2458	C₂×C₃	semidirect
138. #2443	C₂×C₃	semidirect
139. #2418	C₂×C₃	semidirect
140. #2408	C₂×C₃	semidirect
141. #2406	C₂×C₃	semidirect
142. #2404	C₂×C₃	semidirect
143. #2398	C₂×C₃	semidirect
144. #2388	C₂×C₃	semidirect
145. C₂×#394	C₂×C₃	semidirect
146. #2358	C₂×C₃	semidirect
147. #2353	C₂×C₃	semidirect
148. #2342	C₂×C₃	semidirect
199. C₃×C₄×D₄	D₄	semidirect
289. C₂×#123	C₂²×C₃	semidirect
297. C₂×C₄×Q₈	C₂²×C₃	semidirect
298. C₂×C₄×Q₈	C₂²×C₃	semidirect
304. C₂×C₄×D₄	C₂²×C₃	semidirect
305. C₂×C₄×D₄	C₂²×C₃	semidirect
306. C₂×C₄×D₄	C₂²×C₃	semidirect
308. C₂×#117	C₂²×C₃	semidirect
309. C₂×#117	C₂²×C₃	semidirect
311. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
312. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
316. #400	C₂²×C₃	semidirect
317. #400	C₂²×C₃	semidirect
318. #400	C₂²×C₃	semidirect
319. #399	C₂²×C₃	semidirect
320. #399	C₂²×C₃	semidirect
321. #398	C₂²×C₃	semidirect
322. #398	C₂²×C₃	semidirect
323. #397	C₂²×C₃	semidirect
324. #395	C₂²×C₃	semidirect
325. #395	C₂²×C₃	semidirect
326. #395	C₂²×C₃	semidirect
335. #394	C₂²×C₃	semidirect
336. #394	C₂²×C₃	semidirect
337. #393	C₂²×C₃	semidirect
338. #393	C₂²×C₃	semidirect
339. #393	C₂²×C₃	semidirect
342. #392	C₂²×C₃	semidirect
343. #392	C₂²×C₃	semidirect
345. #390	C₂²×C₃	semidirect
346. #388	C₂²×C₃	semidirect
347. #388	C₂²×C₃	semidirect
348. #388	C₂²×C₃	semidirect
349. #388	C₂²×C₃	semidirect
350. #388	C₂²×C₃	semidirect
351. #388	C₂²×C₃	semidirect
352. #388	C₂²×C₃	semidirect
353. #388	C₂²×C₃	semidirect
354. #388	C₂²×C₃	semidirect
355. #387	C₂²×C₃	semidirect
356. #387	C₂²×C₃	semidirect
359. #386	C₂²×C₃	semidirect
360. #386	C₂²×C₃	semidirect
361. #386	C₂²×C₃	semidirect
362. #386	C₂²×C₃	semidirect
363. #386	C₂²×C₃	semidirect
364. #386	C₂²×C₃	semidirect
365. #386	C₂²×C₃	semidirect
367. #385	C₂²×C₃	semidirect
368. #385	C₂²×C₃	semidirect
369. #385	C₂²×C₃	semidirect
370. #385	C₂²×C₃	semidirect
371. #383	C₂²×C₃	semidirect
373. #381	C₂²×C₃	semidirect
378. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
379. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
380. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
381. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
382. #376	C₂²×C₃	semidirect
431. C₂×C₃×D₄	#41	semidirect
461. C₂²×C₃×C₄	#41	semidirect
585. C₄×D₄	C₃×D₄	semidirect
823. C₂×D₄	C₃×#41	semidirect
853. C₂²×C₄	C₃×#41	semidirect
1150. C₃	#35729	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×#520	2
C₃×#2635	2
C₃×#2632	2
C₃×#2627	2
C₃×#2610	2
C₃×#2598	2
C₃×#2591	2
C₃×#2564	2
C₃×#2476	2
C₃×#2464	2
C₃×#2458	2
C₃×#2443	2
C₃×#2418	2
C₃×#2408	2
C₃×#2406	2
C₃×#2404	2
C₃×#2398	2
C₃×#2388	2
C₂×C₃×#394	2
C₃×#2358	2
C₃×#2353	2
C₃×#2342	2
#35729	3

Subgroups — C3×#35729 #10654336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35729 #10654336