Subgroups — C₃×#36262 #10654869

Order 768.

2630 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#551	C₂	1	2	yes	maximal, complemented
2	C₃×#2860	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2854	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2602	C₂	1	2	yes	maximal, complemented
6	C₃×#2601	C₂	1	2	yes	maximal, complemented
7	C₃×#2561	C₂	1	2	yes	maximal, complemented
8	C₃×#2560	C₂	1	2	yes	maximal, complemented
9	C₃×#2557	C₂	1	2	yes	maximal, complemented
10	C₃×#2534	C₂	1	2	yes	maximal, complemented
11	C₃×#2512	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2491	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2486	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2452	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2422	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2408	C₂	1	1	yes	maximal, characteristic
17	C₃×#2344	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2342	C₂	1	2	yes	maximal, complemented
19	C₃×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×C₄×#121	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×C₄²×D₄	C₂	1	1	yes	maximal, characteristic, complemented
24	#36262	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
26	C₃×#551	—	2	16	no	—
27	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×#126	C₂²	1	2	yes	complemented
29	C₂×C₃×#126	C₂²	1	2	yes	complemented
30	C₂×C₃×#124	C₂²	1	2	yes	complemented
31	C₂×C₃×#123	C₂²	1	2	yes	—
32	C₂×C₃×#123	C₂²	1	2	yes	complemented
33	C₂×C₃×#123	C₂²	1	2	yes	complemented
34	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
35	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₂×C₃×#121	C₂²	1	1	yes	characteristic
37	C₂×C₃×#121	C₂²	1	1	yes	characteristic
38	C₂×C₃×#120	C₂²	1	2	yes	—
39	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
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	2	yes	complemented
45	C₂×C₃×#117	C₂²	1	2	yes	—
46	C₂×C₃×#117	C₂²	1	2	yes	complemented
47	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
49	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
50	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
51	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
52	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
53	C₃×#398	C₂²	1	2	yes	complemented
54	C₃×#397	C₂²	1	2	yes	complemented
55	C₃×#397	C₂²	1	2	yes	complemented
56	C₃×#397	C₂²	1	2	yes	complemented
57	C₃×#396	C₂²	1	2	yes	complemented
58	C₃×#396	C₂²	1	2	yes	complemented
59	C₃×#394	C₂²	1	2	yes	—
60	C₃×#394	C₂²	1	2	yes	complemented
61	C₃×#394	C₂²	1	2	yes	complemented
62	C₃×#393	C₂²	1	2	yes	complemented
63	C₃×#393	C₂²	1	2	yes	complemented
64	C₃×#392	C₂²	1	2	yes	—
65	C₃×#391	C₂²	1	2	yes	complemented
66	C₃×#390	C₂²	1	1	yes	characteristic
67	C₃×#390	C₂²	1	1	yes	characteristic
68	C₃×#390	C₂²	1	1	yes	characteristic
69	C₃×#390	C₂²	1	1	yes	characteristic
70	C₃×#390	C₂²	1	1	yes	characteristic
71	C₃×#390	C₂²	1	1	yes	characteristic
72	C₃×#390	C₂²	1	1	yes	characteristic
73	C₃×#390	C₂²	1	2	yes	—
74	C₃×#390	C₂²	1	1	yes	characteristic
75	C₃×#390	C₂²	1	2	yes	—
76	C₃×#389	C₂²	1	1	yes	characteristic, complemented
77	C₃×#389	C₂²	1	1	yes	characteristic, complemented
78	C₃×#389	C₂²	1	1	yes	characteristic, complemented
79	C₃×#389	C₂²	1	1	yes	characteristic, complemented
80	C₃×#389	C₂²	1	1	yes	characteristic, complemented
81	C₃×#389	C₂²	1	1	yes	characteristic, complemented
82	C₃×#389	C₂²	1	2	yes	complemented
83	C₃×#388	C₂²	1	2	yes	complemented
84	C₃×#388	C₂²	1	2	yes	complemented
85	C₃×#388	C₂²	1	2	yes	complemented
86	C₃×#388	C₂²	1	2	yes	complemented
87	C₃×#388	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×#387	C₂²	1	2	yes	complemented
94	C₃×#387	C₂²	1	2	yes	complemented
95	C₃×#386	C₂²	1	2	yes	—
96	C₃×#386	C₂²	1	2	yes	—
97	C₃×#386	C₂²	1	2	yes	complemented
98	C₃×#386	C₂²	1	2	yes	complemented
99	C₃×#385	C₂²	1	2	yes	complemented
100	C₃×#385	C₂²	1	2	yes	complemented
101	C₃×#384	C₂²	1	1	yes	characteristic, complemented
102	C₃×#381	C₂²	1	2	yes	—
103	C₃×#381	C₂²	1	2	yes	—
104	C₃×#380	C₂²	1	1	yes	characteristic
105	C₃×#380	C₂²	1	1	yes	characteristic
106	C₃×#380	C₂²	1	2	yes	—
107	C₃×#380	C₂²	1	1	yes	characteristic, complemented
108	C₃×#380	C₂²	1	1	yes	characteristic, complemented
109	C₃×#379	C₂²	1	2	yes	—
110	C₃×#379	C₂²	1	2	yes	—
111	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
112	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
113	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
114	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
115	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
116	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
117	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
118	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
119	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
120	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, 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×C₄³	C₂²	1	1	yes	characteristic, complemented
125	C₂×#551	C₂×C₃	1	2	yes	complemented
126	#2860	C₂×C₃	1	1	yes	characteristic, complemented
127	#2857	C₂×C₃	1	1	yes	characteristic, complemented
128	#2854	C₂×C₃	1	1	yes	characteristic, complemented
129	#2602	C₂×C₃	1	2	yes	complemented
130	#2601	C₂×C₃	1	2	yes	complemented
131	#2561	C₂×C₃	1	2	yes	complemented
132	#2560	C₂×C₃	1	2	yes	complemented
133	#2557	C₂×C₃	1	2	yes	complemented
134	#2534	C₂×C₃	1	2	yes	complemented
135	#2512	C₂×C₃	1	1	yes	characteristic, complemented
136	#2491	C₂×C₃	1	1	yes	characteristic, complemented
137	#2486	C₂×C₃	1	1	yes	characteristic, complemented
138	#2452	C₂×C₃	1	1	yes	characteristic, complemented
139	#2422	C₂×C₃	1	1	yes	characteristic, complemented
140	#2408	C₂×C₃	1	1	yes	characteristic
141	#2344	C₂×C₃	1	1	yes	characteristic, complemented
142	#2342	C₂×C₃	1	2	yes	complemented
143	D₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
144	C₄×#121	C₂×C₃	1	1	yes	characteristic, complemented
145	#2293	C₂×C₃	1	1	yes	characteristic, complemented
146	C₂×#390	C₂×C₃	1	1	yes	characteristic, complemented
147	C₄²×D₄	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂⁵×C₃	C₂³	1	2	yes	—
149	C₂²×C₃×Q₈	C₂³	1	2	yes	—
150	C₂²×C₃×D₄	—	2	4	no	—
151	C₂²×C₃×D₄	—	2	4	no	—
152	C₂²×C₃×D₄	—	4	2	no	—
153	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
154	C₂²×C₃×D₄	C₂³	1	2	yes	—
155	C₂²×C₃×D₄	C₂³	1	2	yes	—
156	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
157	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
158	C₂²×C₃×D₄	C₂³	1	2	yes	—
159	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
160	C₂³×C₃×C₄	C₂³	1	2	yes	—
161	C₂³×C₃×C₄	C₂³	1	2	yes	—
162	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
163	C₂³×C₃×C₄	C₂³	1	2	yes	—
164	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
165	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
166	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
167	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
168	C₃×C₄⋊Q₈	—	4	2	no	—
169	C₃×#126	—	2	8	no	—
170	C₃×#126	—	2	8	no	—
171	C₃×#124	—	2	8	no	—
172	C₃×#123	—	2	8	no	—
173	C₃×#123	—	2	8	no	—
174	C₃×#123	—	2	8	no	—
175	C₃×C₂²⋊Q₈	—	2	8	no	—
176	C₃×C₂²⋊Q₈	—	2	8	no	—
177	C₃×#121	—	2	4	no	—
178	C₃×#121	—	4	2	no	—
179	C₃×#120	—	2	8	no	—
180	C₃×C₄×D₄	—	2	4	no	—
181	C₃×C₄×D₄	—	2	8	no	—
182	C₃×C₄×D₄	—	2	4	no	—
183	C₃×C₄×D₄	—	2	4	no	—
184	C₃×C₄×D₄	—	4	2	no	—
185	C₃×C₄×D₄	D₄	1	8	yes	complemented
186	C₃×#117	—	2	8	no	—
187	C₃×#117	—	2	8	no	—
188	C₂×C₃×C₄⋊C₄	—	2	4	no	—
189	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
200	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
201	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
207	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
209	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
210	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
211	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
212	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
215	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
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	1	yes	characteristic
240	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
241	C₂×C₃×C₄²	—	4	2	no	—
242	C₂×C₃×C₄²	—	4	2	no	—
243	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
244	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
245	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
246	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
247	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
248	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
249	C₂×C₃×C₄²	C₂³	1	2	yes	—
250	C₂×C₃×C₄²	C₂³	1	2	yes	—
251	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
252	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
253	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
254	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
255	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
256	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
257	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
258	C₃×#95	C₂³	1	1	yes	characteristic
259	C₃×#95	C₂³	1	1	yes	characteristic
260	C₃×#95	C₂³	1	1	yes	characteristic
261	C₃×#95	C₂³	1	1	yes	characteristic
262	C₃×#95	C₂³	1	1	yes	characteristic
263	C₃×#95	C₂³	1	1	yes	characteristic
264	C₃×#95	C₂³	1	2	yes	—
265	C₃×#95	C₂³	1	2	yes	—
266	C₃×#95	C₂³	1	2	yes	—
267	C₃×#95	C₂³	1	2	yes	—
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	2	yes	—
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	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
277	#551	—	2	16	no	—
278	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
279	C₂×#126	C₂²×C₃	1	2	yes	complemented
280	C₂×#126	C₂²×C₃	1	2	yes	complemented
281	C₂×#124	C₂²×C₃	1	2	yes	complemented
282	C₂×#123	C₂²×C₃	1	2	yes	—
283	C₂×#123	C₂²×C₃	1	2	yes	complemented
284	C₂×#123	C₂²×C₃	1	2	yes	complemented
285	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
286	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
287	C₂×#121	C₂²×C₃	1	1	yes	characteristic
288	C₂×#121	C₂²×C₃	1	1	yes	characteristic
289	C₂×#120	C₂²×C₃	1	2	yes	—
290	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
291	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
292	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
293	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
294	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
295	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
296	C₂×#117	C₂²×C₃	1	2	yes	—
297	C₂×#117	C₂²×C₃	1	2	yes	complemented
298	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
299	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
300	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
301	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
302	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
303	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
304	#398	C₂²×C₃	1	2	yes	complemented
305	#397	C₂²×C₃	1	2	yes	complemented
306	#397	C₂²×C₃	1	2	yes	complemented
307	#397	C₂²×C₃	1	2	yes	complemented
308	#396	C₂²×C₃	1	2	yes	complemented
309	#396	C₂²×C₃	1	2	yes	complemented
310	#394	C₂²×C₃	1	2	yes	—
311	#394	C₂²×C₃	1	2	yes	complemented
312	#394	C₂²×C₃	1	2	yes	complemented
313	#393	C₂²×C₃	1	2	yes	complemented
314	#393	C₂²×C₃	1	2	yes	complemented
315	#392	C₂²×C₃	1	2	yes	—
316	#391	C₂²×C₃	1	2	yes	complemented
317	#390	C₂²×C₃	1	2	yes	—
318	#390	C₂²×C₃	1	1	yes	characteristic
319	#390	C₂²×C₃	1	1	yes	characteristic
320	#390	C₂²×C₃	1	1	yes	characteristic
321	#390	C₂²×C₃	1	2	yes	—
322	#390	C₂²×C₃	1	1	yes	characteristic
323	#390	C₂²×C₃	1	1	yes	characteristic
324	#390	C₂²×C₃	1	1	yes	characteristic
325	#390	C₂²×C₃	1	1	yes	characteristic
326	#390	C₂²×C₃	1	1	yes	characteristic
327	#389	C₂²×C₃	1	1	yes	characteristic, complemented
328	#389	C₂²×C₃	1	1	yes	characteristic, complemented
329	#389	C₂²×C₃	1	1	yes	characteristic, complemented
330	#389	C₂²×C₃	1	2	yes	complemented
331	#389	C₂²×C₃	1	1	yes	characteristic, complemented
332	#389	C₂²×C₃	1	1	yes	characteristic, complemented
333	#389	C₂²×C₃	1	1	yes	characteristic, complemented
334	#388	C₂²×C₃	1	2	yes	complemented
335	#388	C₂²×C₃	1	2	yes	complemented
336	#388	C₂²×C₃	1	2	yes	complemented
337	#388	C₂²×C₃	1	2	yes	complemented
338	#388	C₂²×C₃	1	2	yes	complemented
339	#388	C₂²×C₃	1	2	yes	complemented
340	#388	C₂²×C₃	1	2	yes	complemented
341	#388	C₂²×C₃	1	2	yes	complemented
342	#388	C₂²×C₃	1	2	yes	complemented
343	#388	C₂²×C₃	1	2	yes	complemented
344	#387	C₂²×C₃	1	2	yes	complemented
345	#387	C₂²×C₃	1	2	yes	complemented
346	#386	C₂²×C₃	1	2	yes	—
347	#386	C₂²×C₃	1	2	yes	—
348	#386	C₂²×C₃	1	2	yes	complemented
349	#386	C₂²×C₃	1	2	yes	complemented
350	#385	C₂²×C₃	1	2	yes	complemented
351	#385	C₂²×C₃	1	2	yes	complemented
352	#384	C₂²×C₃	1	1	yes	characteristic, complemented
353	#381	C₂²×C₃	1	2	yes	—
354	#381	C₂²×C₃	1	2	yes	—
355	#380	C₂²×C₃	1	1	yes	characteristic
356	#380	C₂²×C₃	1	2	yes	—
357	#380	C₂²×C₃	1	1	yes	characteristic
358	#380	C₂²×C₃	1	1	yes	characteristic, complemented
359	#380	C₂²×C₃	1	1	yes	characteristic, complemented
360	#379	C₂²×C₃	1	2	yes	—
361	#379	C₂²×C₃	1	2	yes	—
362	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
363	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
364	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
365	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
366	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
367	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
368	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
369	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
370	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
371	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
372	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
373	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
374	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
375	C₄³	C₂²×C₃	1	1	yes	characteristic, complemented
376	C₂⁴×C₃	—	2	4	no	—
377	C₂⁴×C₃	—	2	4	no	—
378	C₂⁴×C₃	—	2	4	no	—
379	C₂⁴×C₃	—	2	4	no	—
380	C₂⁴×C₃	—	4	2	no	—
381	C₂⁴×C₃	—	4	2	no	—
382	C₂⁴×C₃	—	4	2	no	—
383	C₂⁴×C₃	C₂⁴	1	2	yes	—
384	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
385	C₂⁴×C₃	C₂⁴	1	2	yes	—
386	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
387	C₂×C₃×Q₈	—	2	4	no	—
388	C₂×C₃×Q₈	—	4	2	no	—
389	C₂×C₃×Q₈	—	4	2	no	—
390	C₂×C₃×D₄	—	2	2	no	—
391	C₂×C₃×D₄	—	2	2	no	—
392	C₂×C₃×D₄	—	2	4	no	—
393	C₂×C₃×D₄	—	2	4	no	—
394	C₂×C₃×D₄	—	2	4	no	—
395	C₂×C₃×D₄	—	2	4	no	—
396	C₂×C₃×D₄	—	2	2	no	—
397	C₂×C₃×D₄	—	2	4	no	—
398	C₂×C₃×D₄	—	2	2	no	—
399	C₂×C₃×D₄	—	2	2	no	—
400	C₂×C₃×D₄	—	2	2	no	—
401	C₂×C₃×D₄	—	2	2	no	—
402	C₂×C₃×D₄	—	4	16	no	—
403	C₂×C₃×D₄	—	4	2	no	—
404	C₂×C₃×D₄	—	4	2	no	—
405	C₂×C₃×D₄	—	4	2	no	—
406	C₂×C₃×D₄	—	4	2	no	—
407	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
408	C₂×C₃×D₄	#41	1	4	yes	—
409	C₂²×C₃×C₄	—	2	2	no	—
410	C₂²×C₃×C₄	—	2	2	no	—
411	C₂²×C₃×C₄	—	2	4	no	—
412	C₂²×C₃×C₄	—	2	4	no	—
413	C₂²×C₃×C₄	—	2	4	no	—
414	C₂²×C₃×C₄	—	2	4	no	—
415	C₂²×C₃×C₄	—	2	4	no	—
416	C₂²×C₃×C₄	—	2	2	no	—
417	C₂²×C₃×C₄	—	2	2	no	—
418	C₂²×C₃×C₄	—	2	2	no	—
419	C₂²×C₃×C₄	—	2	2	no	—
420	C₂²×C₃×C₄	—	2	4	no	—
421	C₂²×C₃×C₄	—	4	1	no	—
422	C₂²×C₃×C₄	—	4	1	no	—
423	C₂²×C₃×C₄	—	4	1	no	—
424	C₂²×C₃×C₄	—	4	1	no	—
425	C₂²×C₃×C₄	—	4	1	no	—
426	C₂²×C₃×C₄	—	4	1	no	—
427	C₂²×C₃×C₄	—	4	1	no	—
428	C₂²×C₃×C₄	—	4	1	no	—
429	C₂²×C₃×C₄	—	4	2	no	—
430	C₂²×C₃×C₄	—	4	2	no	—
431	C₂²×C₃×C₄	—	4	2	no	—
432	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
433	C₂²×C₃×C₄	C₂×D₄	1	4	yes	complemented
434	C₂²×C₃×C₄	#41	1	4	yes	—
435	C₂²×C₃×C₄	#41	1	4	yes	—
436	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
437	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
438	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
439	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
440	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
441	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
442	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
443	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
444	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
445	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
446	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
447	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
448	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
449	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
450	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
451	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
452	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
453	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
454	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
455	C₃×C₄⋊C₄	—	2	4	no	—
456	C₃×C₄⋊C₄	—	2	4	no	—
457	C₃×C₄⋊C₄	—	2	4	no	—
458	C₃×C₄⋊C₄	—	2	4	no	—
459	C₃×C₄⋊C₄	—	2	4	no	—
460	C₃×C₄⋊C₄	—	2	4	no	—
461	C₃×C₄⋊C₄	—	2	4	no	—
462	C₃×C₄⋊C₄	—	2	4	no	—
463	C₃×C₄⋊C₄	—	2	2	no	—
464	C₃×C₄⋊C₄	—	2	2	no	—
465	C₃×C₄⋊C₄	—	2	2	no	—
466	C₃×C₄⋊C₄	—	2	2	no	—
467	C₃×C₄⋊C₄	—	2	2	no	—
468	C₃×C₄⋊C₄	—	2	2	no	—
469	C₃×C₄⋊C₄	—	2	2	no	—
470	C₃×C₄⋊C₄	—	2	2	no	—
471	C₃×C₄⋊C₄	—	4	2	no	—
472	C₃×C₄⋊C₄	—	4	2	no	—
473	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	complemented
474	C₃×C₂²⋊C₄	—	2	4	no	—
475	C₃×C₂²⋊C₄	—	2	4	no	—
476	C₃×C₂²⋊C₄	—	2	4	no	—
477	C₃×C₂²⋊C₄	—	2	4	no	—
478	C₃×C₂²⋊C₄	—	2	4	no	—
479	C₃×C₂²⋊C₄	—	2	2	no	—
480	C₃×C₂²⋊C₄	—	2	2	no	—
481	C₃×C₂²⋊C₄	—	2	4	no	—
482	C₃×C₂²⋊C₄	—	2	4	no	—
483	C₃×C₂²⋊C₄	—	2	4	no	—
484	C₃×C₂²⋊C₄	—	2	4	no	—
485	C₃×C₂²⋊C₄	—	2	4	no	—
486	C₃×C₂²⋊C₄	—	2	4	no	—
487	C₃×C₂²⋊C₄	—	2	4	no	—
488	C₃×C₂²⋊C₄	—	2	4	no	—
489	C₃×C₂²⋊C₄	—	2	4	no	—
490	C₃×C₂²⋊C₄	—	2	4	no	—
491	C₃×C₂²⋊C₄	—	2	4	no	—
492	C₃×C₂²⋊C₄	—	2	4	no	—
493	C₃×C₂²⋊C₄	—	2	4	no	—
494	C₃×C₂²⋊C₄	—	2	2	no	—
495	C₃×C₂²⋊C₄	—	2	2	no	—
496	C₃×C₂²⋊C₄	—	4	2	no	—
497	C₃×C₂²⋊C₄	—	4	2	no	—
498	C₃×C₂²⋊C₄	—	4	2	no	—
499	C₃×C₂²⋊C₄	—	4	2	no	—
500	C₃×C₂²⋊C₄	—	4	2	no	—
501	C₃×C₂²⋊C₄	—	4	2	no	—
502	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
503	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
504	C₃×C₄²	—	2	4	no	—
505	C₃×C₄²	—	2	4	no	—
506	C₃×C₄²	—	2	2	no	—
507	C₃×C₄²	—	2	2	no	—
508	C₃×C₄²	—	2	2	no	—
509	C₃×C₄²	—	2	2	no	—
510	C₃×C₄²	—	2	2	no	—
511	C₃×C₄²	—	2	2	no	—
512	C₃×C₄²	—	4	1	no	—
513	C₃×C₄²	—	4	1	no	—
514	C₃×C₄²	—	4	1	no	—
515	C₃×C₄²	—	4	1	no	—
516	C₃×C₄²	—	4	1	no	—
517	C₃×C₄²	—	4	1	no	—
518	C₃×C₄²	C₂×D₄	1	4	yes	complemented
519	C₂⁵	C₂³×C₃	1	2	yes	—
520	C₂²×Q₈	C₂³×C₃	1	2	yes	—
521	C₂²×D₄	—	2	4	no	—
522	C₂²×D₄	—	2	4	no	—
523	C₂²×D₄	—	4	2	no	—
524	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
525	C₂²×D₄	C₂³×C₃	1	2	yes	—
526	C₂²×D₄	C₂³×C₃	1	2	yes	—
527	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
528	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
529	C₂²×D₄	C₂³×C₃	1	2	yes	—
530	C₂³×C₄	C₂³×C₃	1	2	yes	—
531	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
532	C₂³×C₄	C₂³×C₃	1	2	yes	—
533	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₃	1	2	yes	—
535	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
536	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
537	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
539	C₄⋊Q₈	—	4	2	no	—
540	#126	—	2	8	no	—
541	#126	—	2	8	no	—
542	#124	—	2	8	no	—
543	#123	—	2	8	no	—
544	#123	—	2	8	no	—
545	#123	—	2	8	no	—
546	C₂²⋊Q₈	—	2	8	no	—
547	C₂²⋊Q₈	—	2	8	no	—
548	#121	—	2	4	no	—
549	#121	—	4	2	no	—
550	#120	—	2	8	no	—
551	C₄×D₄	—	2	4	no	—
552	C₄×D₄	—	2	8	no	—
553	C₄×D₄	—	2	4	no	—
554	C₄×D₄	—	2	4	no	—
555	C₄×D₄	—	4	2	no	—
556	C₄×D₄	C₃×D₄	1	8	yes	complemented
557	#117	—	2	8	no	—
558	#117	—	2	8	no	—
559	C₂×C₄⋊C₄	—	2	4	no	—
560	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
579	C₂×C₂²⋊C₄	—	2	8	no	—
580	C₂×C₂²⋊C₄	—	2	8	no	—
581	C₂×C₂²⋊C₄	—	2	8	no	—
582	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
596	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
598	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
599	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
611	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
612	C₂×C₄²	—	4	2	no	—
613	C₂×C₄²	—	4	2	no	—
614	C₂×C₄²	C₂³×C₃	1	2	yes	—
615	C₂×C₄²	C₂³×C₃	1	2	yes	—
616	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
618	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
629	#95	C₂³×C₃	1	1	yes	characteristic
630	#95	C₂³×C₃	1	1	yes	characteristic
631	#95	C₂³×C₃	1	1	yes	characteristic
632	#95	C₂³×C₃	1	1	yes	characteristic
633	#95	C₂³×C₃	1	1	yes	characteristic
634	#95	C₂³×C₃	1	1	yes	characteristic
635	#95	C₂³×C₃	1	2	yes	—
636	#95	C₂³×C₃	1	2	yes	—
637	#95	C₂³×C₃	1	2	yes	—
638	#95	C₂³×C₃	1	2	yes	—
639	#95	C₂³×C₃	1	2	yes	—
640	#95	C₂³×C₃	1	2	yes	—
641	#95	C₂³×C₃	1	2	yes	—
642	#95	C₂³×C₃	1	2	yes	—
643	#95	C₂³×C₃	1	2	yes	—
644	#95	C₂³×C₃	1	2	yes	—
645	#95	C₂³×C₃	1	2	yes	—
646	#95	C₂³×C₃	1	2	yes	—
647	C₂³×C₃	—	2	1	no	—
648	C₂³×C₃	—	2	1	no	—
649	C₂³×C₃	—	2	1	no	—
650	C₂³×C₃	—	2	1	no	—
651	C₂³×C₃	—	2	2	no	—
652	C₂³×C₃	—	2	2	no	—
653	C₂³×C₃	—	2	1	no	—
654	C₂³×C₃	—	2	1	no	—
655	C₂³×C₃	—	2	1	no	—
656	C₂³×C₃	—	2	2	no	—
657	C₂³×C₃	—	2	2	no	—
658	C₂³×C₃	—	2	1	no	—
659	C₂³×C₃	—	2	2	no	—
660	C₂³×C₃	—	2	1	no	—
661	C₂³×C₃	—	2	1	no	—
662	C₂³×C₃	—	2	2	no	—
663	C₂³×C₃	—	2	2	no	—
664	C₂³×C₃	—	2	2	no	—
665	C₂³×C₃	—	2	2	no	—
666	C₂³×C₃	—	2	2	no	—
667	C₂³×C₃	—	2	2	no	—
668	C₂³×C₃	—	2	2	no	—
669	C₂³×C₃	—	2	2	no	—
670	C₂³×C₃	—	4	8	no	—
671	C₂³×C₃	—	4	8	no	—
672	C₂³×C₃	—	4	8	no	—
673	C₂³×C₃	—	4	8	no	—
674	C₂³×C₃	—	8	4	no	—
675	C₂³×C₃	—	8	4	no	—
676	C₂³×C₃	—	8	4	no	—
677	C₂³×C₃	C₂²×D₄	1	2	yes	—
678	C₂³×C₃	C₂²×D₄	1	2	yes	—
679	C₂³×C₃	C₂×#41	1	4	yes	—
680	C₂³×C₃	C₂×#41	1	2	yes	—
681	C₂³×C₃	C₂×#41	1	2	yes	—
682	C₂³×C₃	C₂⁵	1	1	yes	characteristic
683	C₃×Q₈	—	8	4	no	—
684	C₃×D₄	—	2	8	no	—
685	C₃×D₄	—	2	8	no	—
686	C₃×D₄	—	4	8	no	—
687	C₃×D₄	—	4	8	no	—
688	C₃×D₄	—	4	4	no	—
689	C₃×D₄	—	8	4	no	—
690	C₂×C₃×C₄	—	2	1	no	—
691	C₂×C₃×C₄	—	2	1	no	—
692	C₂×C₃×C₄	—	2	1	no	—
693	C₂×C₃×C₄	—	2	1	no	—
694	C₂×C₃×C₄	—	2	1	no	—
695	C₂×C₃×C₄	—	2	1	no	—
696	C₂×C₃×C₄	—	2	1	no	—
697	C₂×C₃×C₄	—	2	1	no	—
698	C₂×C₃×C₄	—	2	1	no	—
699	C₂×C₃×C₄	—	2	1	no	—
700	C₂×C₃×C₄	—	2	1	no	—
701	C₂×C₃×C₄	—	2	1	no	—
702	C₂×C₃×C₄	—	2	1	no	—
703	C₂×C₃×C₄	—	2	1	no	—
704	C₂×C₃×C₄	—	2	1	no	—
705	C₂×C₃×C₄	—	2	1	no	—
706	C₂×C₃×C₄	—	2	8	no	—
707	C₂×C₃×C₄	—	2	2	no	—
708	C₂×C₃×C₄	—	2	2	no	—
709	C₂×C₃×C₄	—	2	2	no	—
710	C₂×C₃×C₄	—	2	2	no	—
711	C₂×C₃×C₄	—	2	2	no	—
712	C₂×C₃×C₄	—	2	2	no	—
713	C₂×C₃×C₄	—	2	1	no	—
714	C₂×C₃×C₄	—	2	1	no	—
715	C₂×C₃×C₄	—	2	1	no	—
716	C₂×C₃×C₄	—	2	2	no	—
717	C₂×C₃×C₄	—	2	2	no	—
718	C₂×C₃×C₄	—	2	1	no	—
719	C₂×C₃×C₄	—	2	2	no	—
720	C₂×C₃×C₄	—	2	1	no	—
721	C₂×C₃×C₄	—	2	1	no	—
722	C₂×C₃×C₄	—	2	2	no	—
723	C₂×C₃×C₄	—	2	2	no	—
724	C₂×C₃×C₄	—	2	2	no	—
725	C₂×C₃×C₄	—	2	1	no	—
726	C₂×C₃×C₄	—	2	1	no	—
727	C₂×C₃×C₄	—	2	2	no	—
728	C₂×C₃×C₄	—	2	2	no	—
729	C₂×C₃×C₄	—	2	1	no	—
730	C₂×C₃×C₄	—	2	1	no	—
731	C₂×C₃×C₄	—	2	1	no	—
732	C₂×C₃×C₄	—	2	1	no	—
733	C₂×C₃×C₄	—	2	2	no	—
734	C₂×C₃×C₄	—	2	2	no	—
735	C₂×C₃×C₄	—	2	2	no	—
736	C₂×C₃×C₄	—	2	2	no	—
737	C₂×C₃×C₄	—	4	4	no	—
738	C₂×C₃×C₄	—	4	4	no	—
739	C₂×C₃×C₄	—	4	4	no	—
740	C₂×C₃×C₄	—	4	8	no	—
741	C₂×C₃×C₄	—	4	4	no	—
742	C₂×C₃×C₄	—	4	8	no	—
743	C₂×C₃×C₄	—	4	4	no	—
744	C₂×C₃×C₄	—	8	4	no	—
745	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
746	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
747	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
748	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
749	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
750	C₂×C₃×C₄	C₂×#41	1	2	yes	—
751	C₂×C₃×C₄	C₂×#41	1	2	yes	—
752	C₂×C₃×C₄	C₂×#41	1	2	yes	—
753	C₂×C₃×C₄	C₂×#41	1	2	yes	—
754	C₂×C₃×C₄	C₂×#41	1	2	yes	—
755	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
756	C₂⁴	—	2	4	no	—
757	C₂⁴	—	2	4	no	—
758	C₂⁴	—	2	4	no	—
759	C₂⁴	—	2	4	no	—
760	C₂⁴	—	4	2	no	—
761	C₂⁴	—	4	2	no	—
762	C₂⁴	—	4	2	no	—
763	C₂⁴	C₂⁴×C₃	1	2	yes	—
764	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
765	C₂⁴	C₂⁴×C₃	1	2	yes	—
766	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
767	C₂×Q₈	—	2	4	no	—
768	C₂×Q₈	—	4	2	no	—
769	C₂×Q₈	—	4	2	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	4	no	—
773	C₂×D₄	—	2	4	no	—
774	C₂×D₄	—	2	4	no	—
775	C₂×D₄	—	2	4	no	—
776	C₂×D₄	—	2	2	no	—
777	C₂×D₄	—	2	4	no	—
778	C₂×D₄	—	2	2	no	—
779	C₂×D₄	—	2	2	no	—
780	C₂×D₄	—	2	2	no	—
781	C₂×D₄	—	2	2	no	—
782	C₂×D₄	—	4	16	no	—
783	C₂×D₄	—	4	2	no	—
784	C₂×D₄	—	4	2	no	—
785	C₂×D₄	—	4	2	no	—
786	C₂×D₄	—	4	2	no	—
787	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
788	C₂×D₄	C₃×#41	1	4	yes	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	4	no	—
792	C₂²×C₄	—	2	4	no	—
793	C₂²×C₄	—	2	4	no	—
794	C₂²×C₄	—	2	4	no	—
795	C₂²×C₄	—	2	4	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	2	2	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	4	no	—
801	C₂²×C₄	—	4	1	no	—
802	C₂²×C₄	—	4	1	no	—
803	C₂²×C₄	—	4	1	no	—
804	C₂²×C₄	—	4	1	no	—
805	C₂²×C₄	—	4	1	no	—
806	C₂²×C₄	—	4	1	no	—
807	C₂²×C₄	—	4	1	no	—
808	C₂²×C₄	—	4	1	no	—
809	C₂²×C₄	—	4	2	no	—
810	C₂²×C₄	—	4	2	no	—
811	C₂²×C₄	—	4	2	no	—
812	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
813	C₂²×C₄	C₂×C₃×D₄	1	4	yes	complemented
814	C₂²×C₄	C₃×#41	1	4	yes	—
815	C₂²×C₄	C₃×#41	1	4	yes	—
816	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
817	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
819	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
821	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
822	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
823	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
824	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
825	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
832	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
835	C₄⋊C₄	—	2	4	no	—
836	C₄⋊C₄	—	2	4	no	—
837	C₄⋊C₄	—	2	4	no	—
838	C₄⋊C₄	—	2	4	no	—
839	C₄⋊C₄	—	2	4	no	—
840	C₄⋊C₄	—	2	4	no	—
841	C₄⋊C₄	—	2	4	no	—
842	C₄⋊C₄	—	2	4	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	4	2	no	—
852	C₄⋊C₄	—	4	2	no	—
853	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	complemented
854	C₂²⋊C₄	—	2	4	no	—
855	C₂²⋊C₄	—	2	4	no	—
856	C₂²⋊C₄	—	2	4	no	—
857	C₂²⋊C₄	—	2	4	no	—
858	C₂²⋊C₄	—	2	4	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	4	no	—
862	C₂²⋊C₄	—	2	4	no	—
863	C₂²⋊C₄	—	2	4	no	—
864	C₂²⋊C₄	—	2	4	no	—
865	C₂²⋊C₄	—	2	4	no	—
866	C₂²⋊C₄	—	2	4	no	—
867	C₂²⋊C₄	—	2	4	no	—
868	C₂²⋊C₄	—	2	4	no	—
869	C₂²⋊C₄	—	2	4	no	—
870	C₂²⋊C₄	—	2	4	no	—
871	C₂²⋊C₄	—	2	4	no	—
872	C₂²⋊C₄	—	2	4	no	—
873	C₂²⋊C₄	—	2	4	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	4	2	no	—
877	C₂²⋊C₄	—	4	2	no	—
878	C₂²⋊C₄	—	4	2	no	—
879	C₂²⋊C₄	—	4	2	no	—
880	C₂²⋊C₄	—	4	2	no	—
881	C₂²⋊C₄	—	4	2	no	—
882	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
883	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	complemented
884	C₄²	—	2	4	no	—
885	C₄²	—	2	4	no	—
886	C₄²	—	2	2	no	—
887	C₄²	—	2	2	no	—
888	C₄²	—	2	2	no	—
889	C₄²	—	2	2	no	—
890	C₄²	—	2	2	no	—
891	C₄²	—	2	2	no	—
892	C₄²	—	4	1	no	—
893	C₄²	—	4	1	no	—
894	C₄²	—	4	1	no	—
895	C₄²	—	4	1	no	—
896	C₄²	—	4	1	no	—
897	C₄²	—	4	1	no	—
898	C₄²	C₂×C₃×D₄	1	4	yes	complemented
899	C₂²×C₃	—	2	2	no	—
900	C₂²×C₃	—	2	2	no	—
901	C₂²×C₃	—	2	2	no	—
902	C₂²×C₃	—	2	2	no	—
903	C₂²×C₃	—	2	2	no	—
904	C₂²×C₃	—	2	2	no	—
905	C₂²×C₃	—	2	2	no	—
906	C₂²×C₃	—	2	4	no	—
907	C₂²×C₃	—	2	2	no	—
908	C₂²×C₃	—	2	4	no	—
909	C₂²×C₃	—	2	4	no	—
910	C₂²×C₃	—	2	2	no	—
911	C₂²×C₃	—	4	2	no	—
912	C₂²×C₃	—	4	1	no	—
913	C₂²×C₃	—	4	1	no	—
914	C₂²×C₃	—	4	2	no	—
915	C₂²×C₃	—	4	1	no	—
916	C₂²×C₃	—	4	2	no	—
917	C₂²×C₃	—	4	1	no	—
918	C₂²×C₃	—	4	2	no	—
919	C₂²×C₃	—	4	2	no	—
920	C₂²×C₃	—	4	2	no	—
921	C₂²×C₃	—	4	2	no	—
922	C₂²×C₃	—	4	2	no	—
923	C₂²×C₃	—	4	2	no	—
924	C₂²×C₃	—	4	2	no	—
925	C₂²×C₃	—	4	2	no	—
926	C₂²×C₃	—	8	16	no	—
927	C₂²×C₃	#532	1	4	yes	—
928	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
929	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
930	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
931	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
932	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
933	C₂²×C₃	#585	1	1	yes	characteristic
934	C₂²×C₃	#585	1	1	yes	characteristic
935	C₃×C₄	—	2	2	no	—
936	C₃×C₄	—	2	2	no	—
937	C₃×C₄	—	2	2	no	—
938	C₃×C₄	—	2	2	no	—
939	C₃×C₄	—	2	2	no	—
940	C₃×C₄	—	2	2	no	—
941	C₃×C₄	—	2	2	no	—
942	C₃×C₄	—	2	2	no	—
943	C₃×C₄	—	4	2	no	—
944	C₃×C₄	—	4	2	no	—
945	C₃×C₄	—	4	2	no	—
946	C₃×C₄	—	4	2	no	—
947	C₃×C₄	—	4	1	no	—
948	C₃×C₄	—	4	1	no	—
949	C₃×C₄	—	4	2	no	—
950	C₃×C₄	—	4	2	no	—
951	C₃×C₄	—	4	1	no	—
952	C₃×C₄	—	4	1	no	—
953	C₃×C₄	#551	1	4	yes	complemented
954	C₂³	—	2	1	no	—
955	C₂³	—	2	1	no	—
956	C₂³	—	2	1	no	—
957	C₂³	—	2	1	no	—
958	C₂³	—	2	2	no	—
959	C₂³	—	2	2	no	—
960	C₂³	—	2	1	no	—
961	C₂³	—	2	1	no	—
962	C₂³	—	2	1	no	—
963	C₂³	—	2	2	no	—
964	C₂³	—	2	2	no	—
965	C₂³	—	2	1	no	—
966	C₂³	—	2	2	no	—
967	C₂³	—	2	1	no	—
968	C₂³	—	2	1	no	—
969	C₂³	—	2	2	no	—
970	C₂³	—	2	2	no	—
971	C₂³	—	2	2	no	—
972	C₂³	—	2	2	no	—
973	C₂³	—	2	2	no	—
974	C₂³	—	2	2	no	—
975	C₂³	—	2	2	no	—
976	C₂³	—	2	2	no	—
977	C₂³	—	4	8	no	—
978	C₂³	—	4	8	no	—
979	C₂³	—	4	8	no	—
980	C₂³	—	4	8	no	—
981	C₂³	—	8	4	no	—
982	C₂³	—	8	4	no	—
983	C₂³	—	8	4	no	—
984	C₂³	C₂²×C₃×D₄	1	2	yes	—
985	C₂³	C₂²×C₃×D₄	1	2	yes	—
986	C₂³	C₂×C₃×#41	1	4	yes	—
987	C₂³	C₂×C₃×#41	1	2	yes	—
988	C₂³	C₂×C₃×#41	1	2	yes	—
989	C₂³	C₂⁵×C₃	1	1	yes	characteristic
990	Q₈	—	8	4	no	—
991	D₄	—	2	8	no	—
992	D₄	—	2	8	no	—
993	D₄	—	4	8	no	—
994	D₄	—	4	8	no	—
995	D₄	—	4	4	no	—
996	D₄	—	8	4	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	8	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	4	4	no	—
1045	C₂×C₄	—	4	4	no	—
1046	C₂×C₄	—	4	4	no	—
1047	C₂×C₄	—	4	8	no	—
1048	C₂×C₄	—	4	4	no	—
1049	C₂×C₄	—	4	8	no	—
1050	C₂×C₄	—	4	4	no	—
1051	C₂×C₄	—	8	4	no	—
1052	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1053	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1054	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1055	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1056	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1057	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1058	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1059	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1060	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1061	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1062	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1063	C₂×C₃	—	2	4	no	—
1064	C₂×C₃	—	4	2	no	—
1065	C₂×C₃	—	4	4	no	—
1066	C₂×C₃	—	8	2	no	—
1067	C₂×C₃	C₂×#532	1	1	yes	characteristic
1068	C₂×C₃	D₄×#41	1	1	yes	characteristic
1069	C₂×C₃	C₂×#551	1	1	yes	characteristic
1070	C₂×C₃	#3475	1	1	yes	characteristic
1071	C₂×C₃	#3496	1	1	yes	characteristic
1072	C₂×C₃	#3505	1	1	yes	characteristic
1073	C₂×C₃	#3510	1	1	yes	characteristic
1074	C₂²	—	2	2	no	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	2	2	no	—
1077	C₂²	—	2	2	no	—
1078	C₂²	—	2	2	no	—
1079	C₂²	—	2	2	no	—
1080	C₂²	—	2	2	no	—
1081	C₂²	—	2	4	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	4	no	—
1084	C₂²	—	2	4	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	4	2	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	2	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	2	no	—
1092	C₂²	—	4	2	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	2	no	—
1095	C₂²	—	4	2	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	2	no	—
1098	C₂²	—	4	2	no	—
1099	C₂²	—	4	2	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	—	8	16	no	—
1102	C₂²	C₃×#532	1	4	yes	—
1103	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1104	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1105	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1106	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1107	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1108	C₂²	C₃×#585	1	1	yes	characteristic
1109	C₂²	C₃×#585	1	1	yes	characteristic
1110	C₄	—	2	2	no	—
1111	C₄	—	2	2	no	—
1112	C₄	—	2	2	no	—
1113	C₄	—	2	2	no	—
1114	C₄	—	2	2	no	—
1115	C₄	—	2	2	no	—
1116	C₄	—	2	2	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	2	no	—
1120	C₄	—	4	2	no	—
1121	C₄	—	4	2	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	2	no	—
1125	C₄	—	4	2	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	1	no	—
1128	C₄	C₃×#551	1	4	yes	complemented
1129	C₃	#36262	1	1	yes	characteristic, direct product factor, Sylow
1130	C₂	—	2	4	no	—
1131	C₂	—	4	4	no	—
1132	C₂	—	4	2	no	—
1133	C₂	—	8	2	no	—
1134	C₂	C₂×C₃×#532	1	1	yes	characteristic
1135	C₂	C₃×D₄×#41	1	1	yes	characteristic
1136	C₂	C₂×C₃×#551	1	1	yes	characteristic
1137	C₂	C₃×#3475	1	1	yes	characteristic
1138	C₂	C₃×#3496	1	1	yes	characteristic
1139	C₂	C₃×#3505	1	1	yes	characteristic
1140	C₂	C₃×#3510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₃×#2408	C₂
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×#551	C₂	semidirect
2. C₃×#2860	C₂	semidirect
3. C₃×#2857	C₂	semidirect
4. C₃×#2854	C₂	semidirect
5. C₃×#2602	C₂	semidirect
6. C₃×#2601	C₂	semidirect
7. C₃×#2561	C₂	semidirect
8. C₃×#2560	C₂	semidirect
9. C₃×#2557	C₂	semidirect
10. C₃×#2534	C₂	semidirect
11. C₃×#2512	C₂	semidirect
12. C₃×#2491	C₂	semidirect
13. C₃×#2486	C₂	semidirect
14. C₃×#2452	C₂	semidirect
15. C₃×#2422	C₂	semidirect
17. C₃×#2344	C₂	semidirect
18. C₃×#2342	C₂	semidirect
19. C₃×D₄×C₂²⋊C₄	C₂	semidirect
20. C₃×C₄×#121	C₂	semidirect
21. C₃×#2293	C₂	semidirect
22. C₂×C₃×#390	C₂	semidirect
23. C₃×C₄²×D₄	C₂	semidirect
24. #36262	C₃	direct (N × H)
27. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
28. C₂×C₃×#126	C₂²	semidirect
29. C₂×C₃×#126	C₂²	semidirect
30. C₂×C₃×#124	C₂²	semidirect
32. C₂×C₃×#123	C₂²	semidirect
33. C₂×C₃×#123	C₂²	semidirect
35. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
44. C₂×C₃×C₄×D₄	C₂²	semidirect
46. C₂×C₃×#117	C₂²	semidirect
52. C₂²×C₃×C₄²	C₂²	semidirect
53. C₃×#398	C₂²	semidirect
54. C₃×#397	C₂²	semidirect
55. C₃×#397	C₂²	semidirect
56. C₃×#397	C₂²	semidirect
57. C₃×#396	C₂²	semidirect
58. C₃×#396	C₂²	semidirect
60. C₃×#394	C₂²	semidirect
61. C₃×#394	C₂²	semidirect
62. C₃×#393	C₂²	semidirect
63. C₃×#393	C₂²	semidirect
65. C₃×#391	C₂²	semidirect
76. C₃×#389	C₂²	semidirect
77. C₃×#389	C₂²	semidirect
78. C₃×#389	C₂²	semidirect
79. C₃×#389	C₂²	semidirect
80. C₃×#389	C₂²	semidirect
81. C₃×#389	C₂²	semidirect
82. C₃×#389	C₂²	semidirect
83. C₃×#388	C₂²	semidirect
84. C₃×#388	C₂²	semidirect
85. C₃×#388	C₂²	semidirect
86. C₃×#388	C₂²	semidirect
87. C₃×#388	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×#387	C₂²	semidirect
94. C₃×#387	C₂²	semidirect
97. C₃×#386	C₂²	semidirect
98. C₃×#386	C₂²	semidirect
99. C₃×#385	C₂²	semidirect
100. C₃×#385	C₂²	semidirect
101. C₃×#384	C₂²	semidirect
107. C₃×#380	C₂²	semidirect
108. C₃×#380	C₂²	semidirect
111. C₃×C₄×C₄⋊C₄	C₂²	semidirect
112. C₃×C₄×C₄⋊C₄	C₂²	semidirect
113. C₃×C₄×C₄⋊C₄	C₂²	semidirect
114. C₃×C₄×C₄⋊C₄	C₂²	semidirect
115. C₃×C₄×C₄⋊C₄	C₂²	semidirect
119. C₃×C₄×C₂²⋊C₄	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×C₄³	C₂²	semidirect
125. C₂×#551	C₂×C₃	semidirect
126. #2860	C₂×C₃	semidirect
127. #2857	C₂×C₃	semidirect
128. #2854	C₂×C₃	semidirect
129. #2602	C₂×C₃	semidirect
130. #2601	C₂×C₃	semidirect
131. #2561	C₂×C₃	semidirect
132. #2560	C₂×C₃	semidirect
133. #2557	C₂×C₃	semidirect
134. #2534	C₂×C₃	semidirect
135. #2512	C₂×C₃	semidirect
136. #2491	C₂×C₃	semidirect
137. #2486	C₂×C₃	semidirect
138. #2452	C₂×C₃	semidirect
139. #2422	C₂×C₃	semidirect
141. #2344	C₂×C₃	semidirect
142. #2342	C₂×C₃	semidirect
143. D₄×C₂²⋊C₄	C₂×C₃	semidirect
144. C₄×#121	C₂×C₃	semidirect
145. #2293	C₂×C₃	semidirect
146. C₂×#390	C₂×C₃	semidirect
147. C₄²×D₄	C₂×C₃	semidirect
185. C₃×C₄×D₄	D₄	semidirect
278. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
279. C₂×#126	C₂²×C₃	semidirect
280. C₂×#126	C₂²×C₃	semidirect
281. C₂×#124	C₂²×C₃	semidirect
283. C₂×#123	C₂²×C₃	semidirect
284. C₂×#123	C₂²×C₃	semidirect
286. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
295. C₂×C₄×D₄	C₂²×C₃	semidirect
297. C₂×#117	C₂²×C₃	semidirect
303. C₂²×C₄²	C₂²×C₃	semidirect
304. #398	C₂²×C₃	semidirect
305. #397	C₂²×C₃	semidirect
306. #397	C₂²×C₃	semidirect
307. #397	C₂²×C₃	semidirect
308. #396	C₂²×C₃	semidirect
309. #396	C₂²×C₃	semidirect
311. #394	C₂²×C₃	semidirect
312. #394	C₂²×C₃	semidirect
313. #393	C₂²×C₃	semidirect
314. #393	C₂²×C₃	semidirect
316. #391	C₂²×C₃	semidirect
327. #389	C₂²×C₃	semidirect
328. #389	C₂²×C₃	semidirect
329. #389	C₂²×C₃	semidirect
330. #389	C₂²×C₃	semidirect
331. #389	C₂²×C₃	semidirect
332. #389	C₂²×C₃	semidirect
333. #389	C₂²×C₃	semidirect
334. #388	C₂²×C₃	semidirect
335. #388	C₂²×C₃	semidirect
336. #388	C₂²×C₃	semidirect
337. #388	C₂²×C₃	semidirect
338. #388	C₂²×C₃	semidirect
339. #388	C₂²×C₃	semidirect
340. #388	C₂²×C₃	semidirect
341. #388	C₂²×C₃	semidirect
342. #388	C₂²×C₃	semidirect
343. #388	C₂²×C₃	semidirect
344. #387	C₂²×C₃	semidirect
345. #387	C₂²×C₃	semidirect
348. #386	C₂²×C₃	semidirect
349. #386	C₂²×C₃	semidirect
350. #385	C₂²×C₃	semidirect
351. #385	C₂²×C₃	semidirect
352. #384	C₂²×C₃	semidirect
358. #380	C₂²×C₃	semidirect
359. #380	C₂²×C₃	semidirect
362. C₄×C₄⋊C₄	C₂²×C₃	semidirect
363. C₄×C₄⋊C₄	C₂²×C₃	semidirect
364. C₄×C₄⋊C₄	C₂²×C₃	semidirect
365. C₄×C₄⋊C₄	C₂²×C₃	semidirect
366. C₄×C₄⋊C₄	C₂²×C₃	semidirect
370. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
371. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
372. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
373. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
374. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
375. C₄³	C₂²×C₃	semidirect
433. C₂²×C₃×C₄	C₂×D₄	semidirect
473. C₃×C₄⋊C₄	C₂×D₄	semidirect
503. C₃×C₂²⋊C₄	C₂×D₄	semidirect
518. C₃×C₄²	C₂×D₄	semidirect
556. C₄×D₄	C₃×D₄	semidirect
813. C₂²×C₄	C₂×C₃×D₄	semidirect
853. C₄⋊C₄	C₂×C₃×D₄	semidirect
883. C₂²⋊C₄	C₂×C₃×D₄	semidirect
898. C₄²	C₂×C₃×D₄	semidirect
953. C₃×C₄	#551	semidirect
1128. C₄	C₃×#551	semidirect
1129. C₃	#36262	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×#551	2
C₃×#2860	2
C₃×#2857	2
C₃×#2854	2
C₃×#2602	2
C₃×#2601	2
C₃×#2561	2
C₃×#2560	2
C₃×#2557	2
C₃×#2534	2
C₃×#2512	2
C₃×#2491	2
C₃×#2486	2
C₃×#2452	2
C₃×#2422	2
C₃×#2408	2
C₃×#2344	2
C₃×#2342	2
C₃×D₄×C₂²⋊C₄	2
C₃×C₄×#121	2
C₃×#2293	2
C₂×C₃×#390	2
C₃×C₄²×D₄	2
#36262	3

Subgroups — C3×#36262 #10654869

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#36262 #10654869