Subgroups — C₃×#36258 #10654865

Order 768.

3732 conjugacy classes of subgroups.

The subgroup lattice has 936 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	2	yes	maximal, complemented
2	C₂×C₃×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2856	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2854	C₂	1	2	yes	maximal, complemented
6	C₃×#2548	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2538	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2426	C₂	1	2	yes	maximal, complemented
9	C₃×#2424	C₂	1	4	yes	maximal, complemented
10	C₃×#2416	C₂	1	2	yes	maximal, complemented
11	C₃×#2414	C₂	1	2	yes	maximal, complemented
12	C₃×#2411	C₂	1	4	yes	maximal, complemented
13	C₃×#2408	C₂	1	2	yes	maximal, complemented
14	C₃×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×D₄×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
16	C₃×C₄×#121	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₃×#390	C₂	1	2	yes	maximal, complemented
18	#36258	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
20	C₂³×C₃×D₄	C₂²	1	2	yes	—
21	C₂³×C₃×D₄	C₂²	1	2	yes	—
22	C₃×#546	—	2	16	no	—
23	C₃×D₄²	—	2	8	no	—
24	C₂×C₃×#127	C₂²	1	1	yes	characteristic
25	C₂×C₃×#124	C₂²	1	2	yes	complemented
26	C₂×C₃×#123	C₂²	1	4	yes	complemented
27	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₂×C₃×#121	C₂²	1	1	yes	characteristic
29	C₂×C₃×#121	C₂²	1	2	yes	—
30	C₂×C₃×#121	C₂²	1	2	yes	—
31	C₂×C₃×#121	C₂²	1	2	yes	complemented
32	C₂×C₃×#121	C₂²	1	4	yes	complemented
33	C₂×C₃×#121	C₂²	1	2	yes	complemented
34	C₂×C₃×#121	C₂²	1	2	yes	complemented
35	C₂×C₃×#120	C₂²	1	4	yes	—
36	C₂×C₃×#120	C₂²	1	4	yes	complemented
37	C₃×C₄×#41	—	2	8	no	—
38	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
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	2	yes	—
43	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
44	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
45	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
46	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
47	C₂×C₃×#117	C₂²	1	2	yes	complemented
48	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
49	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
50	C₂²×C₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
51	C₂²×C₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
52	C₂²×C₃×C₄²	C₂²	1	2	yes	complemented
53	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
54	C₃×#396	C₂²	1	4	yes	complemented
55	C₃×#396	C₂²	1	4	yes	complemented
56	C₃×#394	C₂²	1	4	yes	complemented
57	C₃×#394	C₂²	1	4	yes	complemented
58	C₃×#394	C₂²	1	4	yes	complemented
59	C₃×#392	C₂²	1	4	yes	complemented
60	C₃×#390	C₂²	1	2	yes	—
61	C₃×#390	C₂²	1	1	yes	characteristic
62	C₃×#390	C₂²	1	2	yes	complemented
63	C₃×#390	C₂²	1	2	yes	complemented
64	C₃×#390	C₂²	1	4	yes	complemented
65	C₃×#390	C₂²	1	2	yes	complemented
66	C₃×#390	C₂²	1	2	yes	complemented
67	C₃×#390	C₂²	1	4	yes	complemented
68	C₃×#390	C₂²	1	2	yes	complemented
69	C₃×#390	C₂²	1	2	yes	complemented
70	C₃×#389	C₂²	1	2	yes	complemented
71	C₃×#389	C₂²	1	2	yes	complemented
72	C₃×#389	C₂²	1	1	yes	characteristic, complemented
73	C₃×#388	C₂²	1	2	yes	complemented
74	C₃×#388	C₂²	1	4	yes	complemented
75	C₃×#388	C₂²	1	4	yes	complemented
76	C₃×#386	C₂²	1	4	yes	complemented
77	C₃×#386	C₂²	1	2	yes	complemented
78	C₃×#386	C₂²	1	4	yes	complemented
79	C₃×#385	C₂²	1	4	yes	complemented
80	C₃×#384	C₂²	1	1	yes	characteristic, complemented
81	C₃×#380	C₂²	1	2	yes	complemented
82	C₃×#380	C₂²	1	2	yes	complemented
83	C₃×#380	C₂²	1	1	yes	characteristic, complemented
84	C₃×#379	C₂²	1	4	yes	complemented
85	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
86	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
87	C₂×#546	C₂×C₃	1	2	yes	complemented
88	C₂×D₄²	C₂×C₃	1	1	yes	characteristic, complemented
89	C₂×C₄×#41	C₂×C₃	1	1	yes	characteristic, complemented
90	#2856	C₂×C₃	1	1	yes	characteristic, complemented
91	#2854	C₂×C₃	1	2	yes	complemented
92	#2548	C₂×C₃	1	1	yes	characteristic, complemented
93	#2538	C₂×C₃	1	1	yes	characteristic, complemented
94	#2426	C₂×C₃	1	2	yes	complemented
95	#2424	C₂×C₃	1	4	yes	complemented
96	#2416	C₂×C₃	1	2	yes	complemented
97	#2414	C₂×C₃	1	2	yes	complemented
98	#2411	C₂×C₃	1	4	yes	complemented
99	#2408	C₂×C₃	1	2	yes	complemented
100	D₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
101	D₄×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
102	C₄×#121	C₂×C₃	1	1	yes	characteristic, complemented
103	C₂×#390	C₂×C₃	1	2	yes	complemented
104	C₂⁵×C₃	C₂³	1	4	yes	—
105	C₂×C₃×#41	—	2	4	no	—
106	C₂×C₃×#41	—	2	4	no	—
107	C₂×C₃×#41	D₄	1	8	yes	complemented
108	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
109	C₂²×C₃×D₄	—	2	8	no	—
110	C₂²×C₃×D₄	—	2	8	no	—
111	C₂²×C₃×D₄	—	2	8	no	—
112	C₂²×C₃×D₄	—	2	8	no	—
113	C₂²×C₃×D₄	—	2	8	no	—
114	C₂²×C₃×D₄	—	4	4	no	—
115	C₂²×C₃×D₄	C₂³	1	4	yes	—
116	C₂²×C₃×D₄	C₂³	1	2	yes	—
117	C₂²×C₃×D₄	C₂³	1	2	yes	—
118	C₂²×C₃×D₄	C₂³	1	4	yes	—
119	C₂²×C₃×D₄	C₂³	1	2	yes	—
120	C₂²×C₃×D₄	C₂³	1	2	yes	—
121	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
122	C₂²×C₃×D₄	C₂³	1	2	yes	—
123	C₂²×C₃×D₄	C₂³	1	4	yes	—
124	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
125	C₂³×C₃×C₄	C₂³	1	2	yes	—
126	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
127	C₂³×C₃×C₄	C₂³	1	2	yes	—
128	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
129	C₂³×C₃×C₄	C₂³	1	2	yes	—
130	C₂³×C₃×C₄	C₂³	1	2	yes	—
131	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
132	C₂³×C₃×C₄	C₂³	1	4	yes	—
133	C₃×#127	—	2	4	no	—
134	C₃×#124	—	2	8	no	—
135	C₃×#123	—	2	16	no	—
136	C₃×C₂²⋊Q₈	—	2	8	no	—
137	C₃×#121	—	2	16	no	—
138	C₃×#121	—	2	4	no	—
139	C₃×#121	—	2	8	no	—
140	C₃×#121	—	2	8	no	—
141	C₃×#121	—	2	8	no	—
142	C₃×#121	—	4	4	no	—
143	C₃×#121	—	4	4	no	—
144	C₃×#120	—	2	16	no	—
145	C₃×#120	—	2	16	no	—
146	C₃×C₄×Q₈	—	2	4	no	—
147	C₃×C₄×Q₈	—	2	4	no	—
148	C₃×C₄×D₄	—	2	4	no	—
149	C₃×C₄×D₄	—	2	8	no	—
150	C₃×C₄×D₄	—	2	8	no	—
151	C₃×C₄×D₄	—	2	8	no	—
152	C₃×C₄×D₄	—	2	8	no	—
153	C₃×C₄×D₄	—	2	4	no	—
154	C₃×C₄×D₄	D₄	1	8	yes	complemented
155	C₃×#117	—	2	4	no	—
156	C₃×#117	—	2	8	no	—
157	C₂×C₃×C₄⋊C₄	—	4	4	no	—
158	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
166	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
170	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₃×C₂²⋊C₄	—	2	16	no	—
172	C₂×C₃×C₂²⋊C₄	—	4	8	no	—
173	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
177	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
179	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
181	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
183	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
184	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
185	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
186	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
188	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
189	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
190	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
191	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₄²	—	2	8	no	—
193	C₂×C₃×C₄²	—	2	4	no	—
194	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
195	C₂×C₃×C₄²	C₂³	1	2	yes	—
196	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
197	C₂×C₃×C₄²	C₂³	1	2	yes	—
198	C₂×C₃×C₄²	C₂³	1	2	yes	—
199	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
200	C₂×C₃×C₄²	C₂³	1	2	yes	—
201	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
202	C₃×#95	C₂³	1	2	yes	—
203	C₃×#95	C₂³	1	2	yes	—
204	C₃×#95	C₂³	1	2	yes	—
205	C₃×#95	C₂³	1	4	yes	—
206	C₃×#95	C₂³	1	4	yes	—
207	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
208	C₂³×D₄	C₂²×C₃	1	2	yes	—
209	C₂³×D₄	C₂²×C₃	1	2	yes	—
210	#546	—	2	16	no	—
211	D₄²	—	2	8	no	—
212	C₂×#127	C₂²×C₃	1	1	yes	characteristic
213	C₂×#124	C₂²×C₃	1	2	yes	complemented
214	C₂×#123	C₂²×C₃	1	4	yes	complemented
215	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
216	C₂×#121	C₂²×C₃	1	2	yes	—
217	C₂×#121	C₂²×C₃	1	1	yes	characteristic
218	C₂×#121	C₂²×C₃	1	2	yes	—
219	C₂×#121	C₂²×C₃	1	2	yes	complemented
220	C₂×#121	C₂²×C₃	1	4	yes	complemented
221	C₂×#121	C₂²×C₃	1	2	yes	complemented
222	C₂×#121	C₂²×C₃	1	2	yes	complemented
223	C₂×#120	C₂²×C₃	1	4	yes	—
224	C₂×#120	C₂²×C₃	1	4	yes	complemented
225	C₄×#41	—	2	8	no	—
226	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
227	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
228	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
229	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
230	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
231	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
232	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
233	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
234	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
235	C₂×#117	C₂²×C₃	1	2	yes	complemented
236	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
237	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
238	C₂²×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
239	C₂²×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
240	C₂²×C₄²	C₂²×C₃	1	2	yes	complemented
241	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
242	#396	C₂²×C₃	1	4	yes	complemented
243	#396	C₂²×C₃	1	4	yes	complemented
244	#394	C₂²×C₃	1	4	yes	complemented
245	#394	C₂²×C₃	1	4	yes	complemented
246	#394	C₂²×C₃	1	4	yes	complemented
247	#392	C₂²×C₃	1	4	yes	complemented
248	#390	C₂²×C₃	1	2	yes	—
249	#390	C₂²×C₃	1	1	yes	characteristic
250	#390	C₂²×C₃	1	2	yes	complemented
251	#390	C₂²×C₃	1	2	yes	complemented
252	#390	C₂²×C₃	1	2	yes	complemented
253	#390	C₂²×C₃	1	2	yes	complemented
254	#390	C₂²×C₃	1	2	yes	complemented
255	#390	C₂²×C₃	1	4	yes	complemented
256	#390	C₂²×C₃	1	2	yes	complemented
257	#390	C₂²×C₃	1	4	yes	complemented
258	#389	C₂²×C₃	1	1	yes	characteristic, complemented
259	#389	C₂²×C₃	1	2	yes	complemented
260	#389	C₂²×C₃	1	2	yes	complemented
261	#388	C₂²×C₃	1	4	yes	complemented
262	#388	C₂²×C₃	1	4	yes	complemented
263	#388	C₂²×C₃	1	2	yes	complemented
264	#386	C₂²×C₃	1	4	yes	complemented
265	#386	C₂²×C₃	1	4	yes	complemented
266	#386	C₂²×C₃	1	2	yes	complemented
267	#385	C₂²×C₃	1	4	yes	complemented
268	#384	C₂²×C₃	1	1	yes	characteristic, complemented
269	#380	C₂²×C₃	1	2	yes	complemented
270	#380	C₂²×C₃	1	2	yes	complemented
271	#380	C₂²×C₃	1	1	yes	characteristic, complemented
272	#379	C₂²×C₃	1	4	yes	complemented
273	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
274	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
275	C₂⁴×C₃	—	2	8	no	—
276	C₂⁴×C₃	—	2	8	no	—
277	C₂⁴×C₃	—	2	8	no	—
278	C₂⁴×C₃	—	2	8	no	—
279	C₂⁴×C₃	—	4	4	no	—
280	C₂⁴×C₃	—	4	4	no	—
281	C₂⁴×C₃	—	4	4	no	—
282	C₂⁴×C₃	C₂⁴	1	4	yes	—
283	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
284	C₂⁴×C₃	C₂⁴	1	2	yes	—
285	C₂⁴×C₃	C₂⁴	1	2	yes	—
286	C₃×#41	—	2	32	no	—
287	C₂×C₃×Q₈	—	2	2	no	—
288	C₂×C₃×Q₈	—	2	2	no	—
289	C₂×C₃×Q₈	C₂×D₄	1	4	yes	complemented
290	C₂×C₃×D₄	—	2	4	no	—
291	C₂×C₃×D₄	—	2	4	no	—
292	C₂×C₃×D₄	—	2	4	no	—
293	C₂×C₃×D₄	—	2	8	no	—
294	C₂×C₃×D₄	—	2	8	no	—
295	C₂×C₃×D₄	—	2	4	no	—
296	C₂×C₃×D₄	—	2	8	no	—
297	C₂×C₃×D₄	—	2	8	no	—
298	C₂×C₃×D₄	—	2	8	no	—
299	C₂×C₃×D₄	—	2	2	no	—
300	C₂×C₃×D₄	—	2	8	no	—
301	C₂×C₃×D₄	—	2	4	no	—
302	C₂×C₃×D₄	—	2	4	no	—
303	C₂×C₃×D₄	—	2	4	no	—
304	C₂×C₃×D₄	—	2	4	no	—
305	C₂×C₃×D₄	—	2	4	no	—
306	C₂×C₃×D₄	—	2	4	no	—
307	C₂×C₃×D₄	—	2	2	no	—
308	C₂×C₃×D₄	—	2	4	no	—
309	C₂×C₃×D₄	—	4	32	no	—
310	C₂×C₃×D₄	—	4	4	no	—
311	C₂×C₃×D₄	—	4	2	no	—
312	C₂×C₃×D₄	—	4	2	no	—
313	C₂×C₃×D₄	—	4	4	no	—
314	C₂×C₃×D₄	—	4	4	no	—
315	C₂×C₃×D₄	—	4	2	no	—
316	C₂×C₃×D₄	—	4	32	no	—
317	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
318	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
319	C₂×C₃×D₄	C₂×D₄	1	8	yes	complemented
320	C₂×C₃×D₄	#41	1	4	yes	—
321	C₂×C₃×D₄	#41	1	4	yes	complemented
322	C₂²×C₃×C₄	—	2	4	no	—
323	C₂²×C₃×C₄	—	2	4	no	—
324	C₂²×C₃×C₄	—	2	2	no	—
325	C₂²×C₃×C₄	—	2	4	no	—
326	C₂²×C₃×C₄	—	2	2	no	—
327	C₂²×C₃×C₄	—	2	4	no	—
328	C₂²×C₃×C₄	—	2	4	no	—
329	C₂²×C₃×C₄	—	2	8	no	—
330	C₂²×C₃×C₄	—	2	2	no	—
331	C₂²×C₃×C₄	—	2	2	no	—
332	C₂²×C₃×C₄	—	2	4	no	—
333	C₂²×C₃×C₄	—	2	4	no	—
334	C₂²×C₃×C₄	—	2	2	no	—
335	C₂²×C₃×C₄	—	2	4	no	—
336	C₂²×C₃×C₄	—	2	4	no	—
337	C₂²×C₃×C₄	—	2	2	no	—
338	C₂²×C₃×C₄	—	2	2	no	—
339	C₂²×C₃×C₄	—	4	1	no	—
340	C₂²×C₃×C₄	—	4	2	no	—
341	C₂²×C₃×C₄	—	4	4	no	—
342	C₂²×C₃×C₄	—	4	4	no	—
343	C₂²×C₃×C₄	C₂×D₄	1	8	yes	—
344	C₂²×C₃×C₄	C₂×D₄	1	8	yes	complemented
345	C₂²×C₃×C₄	C₂×D₄	1	4	yes	complemented
346	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
347	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
348	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
349	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
350	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
351	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
352	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
353	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
354	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
355	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
356	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
357	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
358	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
359	C₃×C₄⋊C₄	—	2	4	no	—
360	C₃×C₄⋊C₄	—	2	4	no	—
361	C₃×C₄⋊C₄	—	2	2	no	—
362	C₃×C₄⋊C₄	—	2	2	no	—
363	C₃×C₄⋊C₄	—	2	4	no	—
364	C₃×C₄⋊C₄	—	2	4	no	—
365	C₃×C₄⋊C₄	—	2	8	no	—
366	C₃×C₄⋊C₄	—	2	2	no	—
367	C₃×C₄⋊C₄	—	2	2	no	—
368	C₃×C₄⋊C₄	—	2	4	no	—
369	C₃×C₄⋊C₄	—	4	4	no	—
370	C₃×C₄⋊C₄	—	4	2	no	—
371	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
372	C₃×C₂²⋊C₄	—	2	4	no	—
373	C₃×C₂²⋊C₄	—	2	8	no	—
374	C₃×C₂²⋊C₄	—	2	4	no	—
375	C₃×C₂²⋊C₄	—	2	4	no	—
376	C₃×C₂²⋊C₄	—	2	4	no	—
377	C₃×C₂²⋊C₄	—	2	8	no	—
378	C₃×C₂²⋊C₄	—	2	8	no	—
379	C₃×C₂²⋊C₄	—	2	8	no	—
380	C₃×C₂²⋊C₄	—	2	4	no	—
381	C₃×C₂²⋊C₄	—	2	4	no	—
382	C₃×C₂²⋊C₄	—	2	8	no	—
383	C₃×C₂²⋊C₄	—	2	8	no	—
384	C₃×C₂²⋊C₄	—	2	4	no	—
385	C₃×C₂²⋊C₄	—	2	8	no	—
386	C₃×C₂²⋊C₄	—	4	4	no	—
387	C₃×C₂²⋊C₄	—	4	4	no	—
388	C₃×C₂²⋊C₄	—	4	4	no	—
389	C₃×C₂²⋊C₄	—	4	4	no	—
390	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
391	C₃×C₄²	—	2	2	no	—
392	C₃×C₄²	—	2	4	no	—
393	C₃×C₄²	—	2	2	no	—
394	C₃×C₄²	—	2	4	no	—
395	C₃×C₄²	—	2	2	no	—
396	C₃×C₄²	—	2	4	no	—
397	C₃×C₄²	—	2	4	no	—
398	C₃×C₄²	C₂×D₄	1	4	yes	—
399	C₂⁵	C₂³×C₃	1	4	yes	—
400	C₂×#41	—	2	4	no	—
401	C₂×#41	—	2	4	no	—
402	C₂×#41	C₃×D₄	1	8	yes	complemented
403	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
404	C₂²×D₄	—	2	8	no	—
405	C₂²×D₄	—	2	8	no	—
406	C₂²×D₄	—	2	8	no	—
407	C₂²×D₄	—	2	8	no	—
408	C₂²×D₄	—	2	8	no	—
409	C₂²×D₄	—	4	4	no	—
410	C₂²×D₄	C₂³×C₃	1	4	yes	—
411	C₂²×D₄	C₂³×C₃	1	2	yes	—
412	C₂²×D₄	C₂³×C₃	1	2	yes	—
413	C₂²×D₄	C₂³×C₃	1	2	yes	—
414	C₂²×D₄	C₂³×C₃	1	4	yes	—
415	C₂²×D₄	C₂³×C₃	1	2	yes	—
416	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
417	C₂²×D₄	C₂³×C₃	1	2	yes	—
418	C₂²×D₄	C₂³×C₃	1	4	yes	—
419	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
420	C₂³×C₄	C₂³×C₃	1	2	yes	—
421	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
422	C₂³×C₄	C₂³×C₃	1	2	yes	—
423	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
424	C₂³×C₄	C₂³×C₃	1	2	yes	—
425	C₂³×C₄	C₂³×C₃	1	2	yes	—
426	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
427	C₂³×C₄	C₂³×C₃	1	4	yes	—
428	#127	—	2	4	no	—
429	#124	—	2	8	no	—
430	#123	—	2	16	no	—
431	C₂²⋊Q₈	—	2	8	no	—
432	#121	—	2	16	no	—
433	#121	—	2	4	no	—
434	#121	—	2	8	no	—
435	#121	—	2	8	no	—
436	#121	—	2	8	no	—
437	#121	—	4	4	no	—
438	#121	—	4	4	no	—
439	#120	—	2	16	no	—
440	#120	—	2	16	no	—
441	C₄×Q₈	—	2	4	no	—
442	C₄×Q₈	—	2	4	no	—
443	C₄×D₄	—	2	4	no	—
444	C₄×D₄	—	2	8	no	—
445	C₄×D₄	—	2	8	no	—
446	C₄×D₄	—	2	8	no	—
447	C₄×D₄	—	2	8	no	—
448	C₄×D₄	—	2	4	no	—
449	C₄×D₄	C₃×D₄	1	8	yes	complemented
450	#117	—	2	4	no	—
451	#117	—	2	8	no	—
452	C₂×C₄⋊C₄	—	4	4	no	—
453	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
461	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
463	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
464	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
466	C₂×C₂²⋊C₄	—	2	16	no	—
467	C₂×C₂²⋊C₄	—	4	8	no	—
468	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
487	C₂×C₄²	—	2	8	no	—
488	C₂×C₄²	—	2	4	no	—
489	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
490	C₂×C₄²	C₂³×C₃	1	2	yes	—
491	C₂×C₄²	C₂³×C₃	1	2	yes	—
492	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
493	C₂×C₄²	C₂³×C₃	1	2	yes	—
494	C₂×C₄²	C₂³×C₃	1	2	yes	—
495	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
497	#95	C₂³×C₃	1	2	yes	—
498	#95	C₂³×C₃	1	2	yes	—
499	#95	C₂³×C₃	1	2	yes	—
500	#95	C₂³×C₃	1	4	yes	—
501	#95	C₂³×C₃	1	4	yes	—
502	C₂³×C₃	—	2	2	no	—
503	C₂³×C₃	—	2	2	no	—
504	C₂³×C₃	—	2	2	no	—
505	C₂³×C₃	—	2	2	no	—
506	C₂³×C₃	—	2	2	no	—
507	C₂³×C₃	—	2	1	no	—
508	C₂³×C₃	—	2	2	no	—
509	C₂³×C₃	—	2	1	no	—
510	C₂³×C₃	—	2	1	no	—
511	C₂³×C₃	—	2	2	no	—
512	C₂³×C₃	—	2	2	no	—
513	C₂³×C₃	—	2	1	no	—
514	C₂³×C₃	—	2	1	no	—
515	C₂³×C₃	—	2	2	no	—
516	C₂³×C₃	—	2	1	no	—
517	C₂³×C₃	—	2	2	no	—
518	C₂³×C₃	—	2	4	no	—
519	C₂³×C₃	—	2	4	no	—
520	C₂³×C₃	—	2	4	no	—
521	C₂³×C₃	—	2	4	no	—
522	C₂³×C₃	—	2	4	no	—
523	C₂³×C₃	—	2	4	no	—
524	C₂³×C₃	—	2	4	no	—
525	C₂³×C₃	—	4	16	no	—
526	C₂³×C₃	—	4	16	no	—
527	C₂³×C₃	—	4	16	no	—
528	C₂³×C₃	—	4	16	no	—
529	C₂³×C₃	—	8	8	no	—
530	C₂³×C₃	—	8	8	no	—
531	C₂³×C₃	—	8	8	no	—
532	C₂³×C₃	C₂²×D₄	1	2	yes	—
533	C₂³×C₃	C₂²×D₄	1	4	yes	—
534	C₂³×C₃	C₂²×D₄	1	4	yes	—
535	C₂³×C₃	C₂×#41	1	4	yes	—
536	C₂³×C₃	C₂×#41	1	4	yes	—
537	C₂³×C₃	C₂⁵	1	1	yes	characteristic
538	C₃×Q₈	—	2	8	no	—
539	C₃×D₄	—	2	16	no	—
540	C₃×D₄	—	2	8	no	—
541	C₃×D₄	—	4	16	no	—
542	C₃×D₄	—	4	8	no	—
543	C₃×D₄	—	4	16	no	—
544	C₃×D₄	—	4	8	no	—
545	C₃×D₄	—	4	8	no	—
546	C₃×D₄	—	8	4	no	—
547	C₃×D₄	—	8	8	no	—
548	C₃×D₄	#121	1	16	yes	complemented
549	C₂×C₃×C₄	—	2	16	no	—
550	C₂×C₃×C₄	—	2	1	no	—
551	C₂×C₃×C₄	—	2	1	no	—
552	C₂×C₃×C₄	—	2	2	no	—
553	C₂×C₃×C₄	—	2	1	no	—
554	C₂×C₃×C₄	—	2	2	no	—
555	C₂×C₃×C₄	—	2	2	no	—
556	C₂×C₃×C₄	—	2	2	no	—
557	C₂×C₃×C₄	—	2	1	no	—
558	C₂×C₃×C₄	—	2	1	no	—
559	C₂×C₃×C₄	—	2	1	no	—
560	C₂×C₃×C₄	—	2	8	no	—
561	C₂×C₃×C₄	—	2	16	no	—
562	C₂×C₃×C₄	—	2	1	no	—
563	C₂×C₃×C₄	—	2	2	no	—
564	C₂×C₃×C₄	—	2	2	no	—
565	C₂×C₃×C₄	—	2	2	no	—
566	C₂×C₃×C₄	—	2	4	no	—
567	C₂×C₃×C₄	—	2	2	no	—
568	C₂×C₃×C₄	—	2	2	no	—
569	C₂×C₃×C₄	—	2	1	no	—
570	C₂×C₃×C₄	—	2	2	no	—
571	C₂×C₃×C₄	—	2	2	no	—
572	C₂×C₃×C₄	—	2	2	no	—
573	C₂×C₃×C₄	—	2	4	no	—
574	C₂×C₃×C₄	—	2	1	no	—
575	C₂×C₃×C₄	—	2	2	no	—
576	C₂×C₃×C₄	—	2	4	no	—
577	C₂×C₃×C₄	—	2	2	no	—
578	C₂×C₃×C₄	—	2	2	no	—
579	C₂×C₃×C₄	—	2	2	no	—
580	C₂×C₃×C₄	—	4	4	no	—
581	C₂×C₃×C₄	—	4	8	no	—
582	C₂×C₃×C₄	—	4	8	no	—
583	C₂×C₃×C₄	—	4	4	no	—
584	C₂×C₃×C₄	—	8	8	no	—
585	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
586	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
587	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
588	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
589	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
590	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
591	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
592	C₂×C₃×C₄	C₂×#41	1	2	yes	—
593	C₂×C₃×C₄	C₂×#41	1	2	yes	—
594	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
595	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
596	C₂⁴	—	2	8	no	—
597	C₂⁴	—	2	8	no	—
598	C₂⁴	—	2	8	no	—
599	C₂⁴	—	2	8	no	—
600	C₂⁴	—	4	4	no	—
601	C₂⁴	—	4	4	no	—
602	C₂⁴	—	4	4	no	—
603	C₂⁴	C₂⁴×C₃	1	4	yes	—
604	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
605	C₂⁴	C₂⁴×C₃	1	2	yes	—
606	C₂⁴	C₂⁴×C₃	1	2	yes	—
607	#41	—	2	32	no	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	C₂×C₃×D₄	1	4	yes	complemented
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	8	no	—
615	C₂×D₄	—	2	8	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	8	no	—
618	C₂×D₄	—	2	8	no	—
619	C₂×D₄	—	2	8	no	—
620	C₂×D₄	—	2	2	no	—
621	C₂×D₄	—	2	8	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	2	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	4	32	no	—
631	C₂×D₄	—	4	4	no	—
632	C₂×D₄	—	4	2	no	—
633	C₂×D₄	—	4	2	no	—
634	C₂×D₄	—	4	4	no	—
635	C₂×D₄	—	4	4	no	—
636	C₂×D₄	—	4	2	no	—
637	C₂×D₄	—	4	32	no	—
638	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
639	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
640	C₂×D₄	C₂×C₃×D₄	1	8	yes	complemented
641	C₂×D₄	C₃×#41	1	4	yes	—
642	C₂×D₄	C₃×#41	1	4	yes	complemented
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	8	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	4	no	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	4	1	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	4	no	—
663	C₂²×C₄	—	4	4	no	—
664	C₂²×C₄	C₂×C₃×D₄	1	8	yes	—
665	C₂²×C₄	C₂×C₃×D₄	1	8	yes	complemented
666	C₂²×C₄	C₂×C₃×D₄	1	4	yes	complemented
667	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
670	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
673	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
679	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	8	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	4	4	no	—
691	C₄⋊C₄	—	4	2	no	—
692	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	8	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	8	no	—
699	C₂²⋊C₄	—	2	8	no	—
700	C₂²⋊C₄	—	2	8	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	8	no	—
704	C₂²⋊C₄	—	2	8	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	8	no	—
707	C₂²⋊C₄	—	4	4	no	—
708	C₂²⋊C₄	—	4	4	no	—
709	C₂²⋊C₄	—	4	4	no	—
710	C₂²⋊C₄	—	4	4	no	—
711	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
712	C₄²	—	2	2	no	—
713	C₄²	—	2	4	no	—
714	C₄²	—	2	2	no	—
715	C₄²	—	2	4	no	—
716	C₄²	—	2	2	no	—
717	C₄²	—	2	4	no	—
718	C₄²	—	2	4	no	—
719	C₄²	C₂×C₃×D₄	1	4	yes	—
720	C₂²×C₃	—	2	4	no	—
721	C₂²×C₃	—	2	4	no	—
722	C₂²×C₃	—	2	4	no	—
723	C₂²×C₃	—	2	4	no	—
724	C₂²×C₃	—	2	4	no	—
725	C₂²×C₃	—	2	4	no	—
726	C₂²×C₃	—	2	2	no	—
727	C₂²×C₃	—	2	4	no	—
728	C₂²×C₃	—	2	2	no	—
729	C₂²×C₃	—	2	4	no	—
730	C₂²×C₃	—	2	4	no	—
731	C₂²×C₃	—	2	2	no	—
732	C₂²×C₃	—	4	2	no	—
733	C₂²×C₃	—	4	1	no	—
734	C₂²×C₃	—	4	1	no	—
735	C₂²×C₃	—	4	1	no	—
736	C₂²×C₃	—	4	2	no	—
737	C₂²×C₃	—	4	2	no	—
738	C₂²×C₃	—	4	1	no	—
739	C₂²×C₃	—	4	2	no	—
740	C₂²×C₃	—	4	4	no	—
741	C₂²×C₃	—	4	4	no	—
742	C₂²×C₃	—	4	4	no	—
743	C₂²×C₃	—	4	4	no	—
744	C₂²×C₃	—	4	4	no	—
745	C₂²×C₃	—	4	4	no	—
746	C₂²×C₃	—	4	4	no	—
747	C₂²×C₃	—	8	32	no	—
748	C₂²×C₃	C₂×#121	1	8	yes	—
749	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
750	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
751	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
752	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
753	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
754	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
755	C₂²×C₃	#585	1	1	yes	characteristic
756	C₃×C₄	—	2	2	no	—
757	C₃×C₄	—	2	4	no	—
758	C₃×C₄	—	2	4	no	—
759	C₃×C₄	—	2	2	no	—
760	C₃×C₄	—	2	2	no	—
761	C₃×C₄	—	4	2	no	—
762	C₃×C₄	—	4	1	no	—
763	C₃×C₄	—	4	2	no	—
764	C₃×C₄	—	4	2	no	—
765	C₃×C₄	—	4	2	no	—
766	C₃×C₄	—	4	4	no	—
767	C₃×C₄	C₂×#121	1	4	yes	—
768	C₃×C₄	#546	1	4	yes	complemented
769	C₂³	—	2	2	no	—
770	C₂³	—	2	2	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	2	1	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	1	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	1	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	4	no	—
786	C₂³	—	2	4	no	—
787	C₂³	—	2	4	no	—
788	C₂³	—	2	4	no	—
789	C₂³	—	2	4	no	—
790	C₂³	—	2	4	no	—
791	C₂³	—	2	4	no	—
792	C₂³	—	4	16	no	—
793	C₂³	—	4	16	no	—
794	C₂³	—	4	16	no	—
795	C₂³	—	4	16	no	—
796	C₂³	—	8	8	no	—
797	C₂³	—	8	8	no	—
798	C₂³	—	8	8	no	—
799	C₂³	C₂²×C₃×D₄	1	2	yes	—
800	C₂³	C₂²×C₃×D₄	1	4	yes	—
801	C₂³	C₂²×C₃×D₄	1	4	yes	—
802	C₂³	C₂×C₃×#41	1	4	yes	—
803	C₂³	C₂×C₃×#41	1	4	yes	—
804	C₂³	C₂⁵×C₃	1	1	yes	characteristic
805	Q₈	—	2	8	no	—
806	D₄	—	2	16	no	—
807	D₄	—	2	8	no	—
808	D₄	—	4	16	no	—
809	D₄	—	4	8	no	—
810	D₄	—	4	16	no	—
811	D₄	—	4	8	no	—
812	D₄	—	4	8	no	—
813	D₄	—	8	4	no	—
814	D₄	—	8	8	no	—
815	D₄	C₃×#121	1	16	yes	complemented
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	16	no	—
827	C₂×C₄	—	2	8	no	—
828	C₂×C₄	—	2	16	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	4	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	4	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	4	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	4	4	no	—
848	C₂×C₄	—	4	8	no	—
849	C₂×C₄	—	4	8	no	—
850	C₂×C₄	—	4	4	no	—
851	C₂×C₄	—	8	8	no	—
852	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
853	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
854	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
855	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
856	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
857	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
858	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
859	C₂×C₄	C₂×C₃×#41	1	2	yes	—
860	C₂×C₄	C₂×C₃×#41	1	2	yes	—
861	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
862	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
863	C₂×C₃	—	2	8	no	—
864	C₂×C₃	—	4	2	no	—
865	C₂×C₃	—	4	4	no	—
866	C₂×C₃	—	8	4	no	—
867	C₂×C₃	C₂²×#121	1	1	yes	characteristic
868	C₂×C₃	C₂×#546	1	1	yes	characteristic
869	C₂×C₃	D₄×#41	1	1	yes	characteristic
870	C₂×C₃	#3481	1	1	yes	characteristic
871	C₂×C₃	#3488	1	1	yes	characteristic
872	C₂×C₃	#3498	1	1	yes	characteristic
873	C₂×C₃	#3514	1	1	yes	characteristic
874	C₂²	—	2	4	no	—
875	C₂²	—	2	4	no	—
876	C₂²	—	2	4	no	—
877	C₂²	—	2	4	no	—
878	C₂²	—	2	4	no	—
879	C₂²	—	2	4	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	4	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	2	4	no	—
884	C₂²	—	2	4	no	—
885	C₂²	—	2	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	1	no	—
888	C₂²	—	4	1	no	—
889	C₂²	—	4	1	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	4	no	—
895	C₂²	—	4	4	no	—
896	C₂²	—	4	4	no	—
897	C₂²	—	4	4	no	—
898	C₂²	—	4	4	no	—
899	C₂²	—	4	4	no	—
900	C₂²	—	4	4	no	—
901	C₂²	—	8	32	no	—
902	C₂²	C₂×C₃×#121	1	8	yes	—
903	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
904	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
905	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
906	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
907	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
908	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
909	C₂²	C₃×#585	1	1	yes	characteristic
910	C₄	—	2	2	no	—
911	C₄	—	2	4	no	—
912	C₄	—	2	4	no	—
913	C₄	—	2	2	no	—
914	C₄	—	2	2	no	—
915	C₄	—	4	2	no	—
916	C₄	—	4	1	no	—
917	C₄	—	4	2	no	—
918	C₄	—	4	2	no	—
919	C₄	—	4	2	no	—
920	C₄	—	4	4	no	—
921	C₄	C₂×C₃×#121	1	4	yes	—
922	C₄	C₃×#546	1	4	yes	complemented
923	C₃	#36258	1	1	yes	characteristic, direct product factor, Sylow
924	C₂	—	2	8	no	—
925	C₂	—	4	4	no	—
926	C₂	—	4	2	no	—
927	C₂	—	8	4	no	—
928	C₂	C₂²×C₃×#121	1	1	yes	characteristic
929	C₂	C₂×C₃×#546	1	1	yes	characteristic
930	C₂	C₃×D₄×#41	1	1	yes	characteristic
931	C₂	C₃×#3481	1	1	yes	characteristic
932	C₂	C₃×#3488	1	1	yes	characteristic
933	C₂	C₃×#3498	1	1	yes	characteristic
934	C₂	C₃×#3514	1	1	yes	characteristic

	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×D₄²	C₂	semidirect
3. C₂×C₃×C₄×#41	C₂	semidirect
4. C₃×#2856	C₂	semidirect
5. C₃×#2854	C₂	semidirect
6. C₃×#2548	C₂	semidirect
7. C₃×#2538	C₂	semidirect
8. C₃×#2426	C₂	semidirect
9. C₃×#2424	C₂	semidirect
10. C₃×#2416	C₂	semidirect
11. C₃×#2414	C₂	semidirect
12. C₃×#2411	C₂	semidirect
13. C₃×#2408	C₂	semidirect
14. C₃×D₄×C₄⋊C₄	C₂	semidirect
15. C₃×D₄×C₂²⋊C₄	C₂	semidirect
16. C₃×C₄×#121	C₂	semidirect
17. C₂×C₃×#390	C₂	semidirect
18. #36258	C₃	direct (N × H)
25. C₂×C₃×#124	C₂²	semidirect
26. C₂×C₃×#123	C₂²	semidirect
27. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₃×#121	C₂²	semidirect
32. C₂×C₃×#121	C₂²	semidirect
33. C₂×C₃×#121	C₂²	semidirect
34. C₂×C₃×#121	C₂²	semidirect
36. C₂×C₃×#120	C₂²	semidirect
38. C₂×C₃×C₄×Q₈	C₂²	semidirect
39. C₂×C₃×C₄×Q₈	C₂²	semidirect
44. C₂×C₃×C₄×D₄	C₂²	semidirect
45. C₂×C₃×C₄×D₄	C₂²	semidirect
46. C₂×C₃×C₄×D₄	C₂²	semidirect
47. C₂×C₃×#117	C₂²	semidirect
48. C₂×C₃×#117	C₂²	semidirect
49. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
50. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
51. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
52. C₂²×C₃×C₄²	C₂²	semidirect
53. C₂²×C₃×C₄²	C₂²	semidirect
54. C₃×#396	C₂²	semidirect
55. C₃×#396	C₂²	semidirect
56. C₃×#394	C₂²	semidirect
57. C₃×#394	C₂²	semidirect
58. C₃×#394	C₂²	semidirect
59. C₃×#392	C₂²	semidirect
62. C₃×#390	C₂²	semidirect
63. C₃×#390	C₂²	semidirect
64. C₃×#390	C₂²	semidirect
65. C₃×#390	C₂²	semidirect
66. C₃×#390	C₂²	semidirect
67. C₃×#390	C₂²	semidirect
68. C₃×#390	C₂²	semidirect
69. C₃×#390	C₂²	semidirect
70. C₃×#389	C₂²	semidirect
71. C₃×#389	C₂²	semidirect
72. C₃×#389	C₂²	semidirect
73. C₃×#388	C₂²	semidirect
74. C₃×#388	C₂²	semidirect
75. C₃×#388	C₂²	semidirect
76. C₃×#386	C₂²	semidirect
77. C₃×#386	C₂²	semidirect
78. C₃×#386	C₂²	semidirect
79. C₃×#385	C₂²	semidirect
80. C₃×#384	C₂²	semidirect
81. C₃×#380	C₂²	semidirect
82. C₃×#380	C₂²	semidirect
83. C₃×#380	C₂²	semidirect
84. C₃×#379	C₂²	semidirect
85. C₃×C₄×C₄⋊C₄	C₂²	semidirect
86. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
87. C₂×#546	C₂×C₃	semidirect
88. C₂×D₄²	C₂×C₃	semidirect
89. C₂×C₄×#41	C₂×C₃	semidirect
90. #2856	C₂×C₃	semidirect
91. #2854	C₂×C₃	semidirect
92. #2548	C₂×C₃	semidirect
93. #2538	C₂×C₃	semidirect
94. #2426	C₂×C₃	semidirect
95. #2424	C₂×C₃	semidirect
96. #2416	C₂×C₃	semidirect
97. #2414	C₂×C₃	semidirect
98. #2411	C₂×C₃	semidirect
99. #2408	C₂×C₃	semidirect
100. D₄×C₄⋊C₄	C₂×C₃	semidirect
101. D₄×C₂²⋊C₄	C₂×C₃	semidirect
102. C₄×#121	C₂×C₃	semidirect
103. C₂×#390	C₂×C₃	semidirect
107. C₂×C₃×#41	D₄	semidirect
154. C₃×C₄×D₄	D₄	semidirect
213. C₂×#124	C₂²×C₃	semidirect
214. C₂×#123	C₂²×C₃	semidirect
215. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
219. C₂×#121	C₂²×C₃	semidirect
220. C₂×#121	C₂²×C₃	semidirect
221. C₂×#121	C₂²×C₃	semidirect
222. C₂×#121	C₂²×C₃	semidirect
224. C₂×#120	C₂²×C₃	semidirect
226. C₂×C₄×Q₈	C₂²×C₃	semidirect
227. C₂×C₄×Q₈	C₂²×C₃	semidirect
232. C₂×C₄×D₄	C₂²×C₃	semidirect
233. C₂×C₄×D₄	C₂²×C₃	semidirect
234. C₂×C₄×D₄	C₂²×C₃	semidirect
235. C₂×#117	C₂²×C₃	semidirect
236. C₂×#117	C₂²×C₃	semidirect
237. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
238. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
239. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
240. C₂²×C₄²	C₂²×C₃	semidirect
241. C₂²×C₄²	C₂²×C₃	semidirect
242. #396	C₂²×C₃	semidirect
243. #396	C₂²×C₃	semidirect
244. #394	C₂²×C₃	semidirect
245. #394	C₂²×C₃	semidirect
246. #394	C₂²×C₃	semidirect
247. #392	C₂²×C₃	semidirect
250. #390	C₂²×C₃	semidirect
251. #390	C₂²×C₃	semidirect
252. #390	C₂²×C₃	semidirect
253. #390	C₂²×C₃	semidirect
254. #390	C₂²×C₃	semidirect
255. #390	C₂²×C₃	semidirect
256. #390	C₂²×C₃	semidirect
257. #390	C₂²×C₃	semidirect
258. #389	C₂²×C₃	semidirect
259. #389	C₂²×C₃	semidirect
260. #389	C₂²×C₃	semidirect
261. #388	C₂²×C₃	semidirect
262. #388	C₂²×C₃	semidirect
263. #388	C₂²×C₃	semidirect
264. #386	C₂²×C₃	semidirect
265. #386	C₂²×C₃	semidirect
266. #386	C₂²×C₃	semidirect
267. #385	C₂²×C₃	semidirect
268. #384	C₂²×C₃	semidirect
269. #380	C₂²×C₃	semidirect
270. #380	C₂²×C₃	semidirect
271. #380	C₂²×C₃	semidirect
272. #379	C₂²×C₃	semidirect
273. C₄×C₄⋊C₄	C₂²×C₃	semidirect
274. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
289. C₂×C₃×Q₈	C₂×D₄	semidirect
319. C₂×C₃×D₄	C₂×D₄	semidirect
321. C₂×C₃×D₄	#41	semidirect
344. C₂²×C₃×C₄	C₂×D₄	semidirect
345. C₂²×C₃×C₄	C₂×D₄	semidirect
402. C₂×#41	C₃×D₄	semidirect
449. C₄×D₄	C₃×D₄	semidirect
548. C₃×D₄	#121	semidirect
610. C₂×Q₈	C₂×C₃×D₄	semidirect
640. C₂×D₄	C₂×C₃×D₄	semidirect
642. C₂×D₄	C₃×#41	semidirect
665. C₂²×C₄	C₂×C₃×D₄	semidirect
666. C₂²×C₄	C₂×C₃×D₄	semidirect
768. C₃×C₄	#546	semidirect
815. D₄	C₃×#121	semidirect
922. C₄	C₃×#546	semidirect
923. C₃	#36258	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×D₄²	2
C₂×C₃×C₄×#41	2
C₃×#2856	2
C₃×#2854	2
C₃×#2548	2
C₃×#2538	2
C₃×#2426	2
C₃×#2424	2
C₃×#2416	2
C₃×#2414	2
C₃×#2411	2
C₃×#2408	2
C₃×D₄×C₄⋊C₄	2
C₃×D₄×C₂²⋊C₄	2
C₃×C₄×#121	2
C₂×C₃×#390	2
#36258	3

Subgroups — C3×#36258 #10654865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#36258 #10654865