Subgroups — C₃×#35730 #10654337

Order 768.

2838 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2638	C₂	1	2	yes	maximal, complemented
4	C₃×#2628	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2563	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2561	C₂	1	2	yes	maximal, complemented
7	C₃×#2535	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2457	C₂	1	4	yes	maximal, complemented
9	C₃×#2420	C₂	1	2	yes	maximal, complemented
10	C₃×#2418	C₂	1	4	yes	maximal, complemented
11	C₃×#2408	C₂	1	2	yes	maximal, complemented
12	C₃×#2404	C₂	1	2	yes	maximal, complemented
13	C₃×#2392	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2388	C₂	1	2	yes	maximal, complemented
15	C₃×#2361	C₂	1	2	yes	maximal, complemented
16	C₃×#2357	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2352	C₂	1	2	yes	maximal, complemented
18	#35730	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₃×#41	C₂²	1	2	yes	complemented
20	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
21	C₃×#547	—	2	8	no	—
22	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×#123	C₂²	1	4	yes	complemented
24	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
25	C₂×C₃×#121	C₂²	1	2	yes	—
26	C₂×C₃×#121	C₂²	1	2	yes	—
27	C₂×C₃×#120	C₂²	1	4	yes	—
28	C₃×#518	—	2	8	no	—
29	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
31	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
33	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
35	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×C₄×D₄	C₂²	1	4	yes	complemented
38	C₂×C₃×#117	C₂²	1	1	yes	characteristic
39	C₂×C₃×#117	C₂²	1	1	yes	characteristic
40	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
41	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
42	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
43	C₃×#400	C₂²	1	2	yes	complemented
44	C₃×#399	C₂²	1	2	yes	—
45	C₃×#398	C₂²	1	1	yes	characteristic, complemented
46	C₃×#397	C₂²	1	1	yes	characteristic
47	C₃×#397	C₂²	1	4	yes	complemented
48	C₃×#397	C₂²	1	2	yes	complemented
49	C₃×#396	C₂²	1	2	yes	complemented
50	C₃×#395	C₂²	1	2	yes	complemented
51	C₃×#394	C₂²	1	4	yes	—
52	C₃×#394	C₂²	1	2	yes	—
53	C₃×#394	C₂²	1	1	yes	characteristic, complemented
54	C₃×#394	C₂²	1	4	yes	complemented
55	C₃×#393	C₂²	1	2	yes	—
56	C₃×#393	C₂²	1	2	yes	complemented
57	C₃×#393	C₂²	1	2	yes	complemented
58	C₃×#392	C₂²	1	4	yes	—
59	C₃×#392	C₂²	1	1	yes	characteristic
60	C₃×#392	C₂²	1	2	yes	complemented
61	C₃×#390	C₂²	1	2	yes	—
62	C₃×#390	C₂²	1	2	yes	—
63	C₃×#389	C₂²	1	2	yes	complemented
64	C₃×#388	C₂²	1	4	yes	—
65	C₃×#388	C₂²	1	4	yes	complemented
66	C₃×#388	C₂²	1	4	yes	complemented
67	C₃×#387	C₂²	1	4	yes	complemented
68	C₃×#386	C₂²	1	4	yes	—
69	C₃×#386	C₂²	1	4	yes	complemented
70	C₃×#386	C₂²	1	4	yes	complemented
71	C₃×#386	C₂²	1	4	yes	complemented
72	C₃×#385	C₂²	1	4	yes	complemented
73	C₃×#382	C₂²	1	1	yes	characteristic, complemented
74	C₃×#382	C₂²	1	2	yes	complemented
75	C₃×#381	C₂²	1	2	yes	complemented
76	C₃×#381	C₂²	1	4	yes	complemented
77	C₃×#380	C₂²	1	2	yes	—
78	C₃×#380	C₂²	1	4	yes	complemented
79	C₃×#380	C₂²	1	2	yes	complemented
80	C₃×#379	C₂²	1	4	yes	—
81	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
82	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
83	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
84	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	complemented
85	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
86	C₂×#547	C₂×C₃	1	1	yes	characteristic, complemented
87	C₂×#518	C₂×C₃	1	1	yes	characteristic, complemented
88	#2638	C₂×C₃	1	2	yes	complemented
89	#2628	C₂×C₃	1	1	yes	characteristic, complemented
90	#2563	C₂×C₃	1	1	yes	characteristic, complemented
91	#2561	C₂×C₃	1	2	yes	complemented
92	#2535	C₂×C₃	1	1	yes	characteristic, complemented
93	#2457	C₂×C₃	1	4	yes	complemented
94	#2420	C₂×C₃	1	2	yes	complemented
95	#2418	C₂×C₃	1	4	yes	complemented
96	#2408	C₂×C₃	1	2	yes	complemented
97	#2404	C₂×C₃	1	2	yes	complemented
98	#2392	C₂×C₃	1	1	yes	characteristic, complemented
99	#2388	C₂×C₃	1	2	yes	complemented
100	#2361	C₂×C₃	1	2	yes	complemented
101	#2357	C₂×C₃	1	1	yes	characteristic, complemented
102	#2352	C₂×C₃	1	2	yes	complemented
103	C₂⁵×C₃	C₂³	1	2	yes	—
104	C₂×C₃×#41	—	2	8	no	—
105	C₂×C₃×#41	—	4	8	no	—
106	C₂²×C₃×Q₈	C₂³	1	2	yes	—
107	C₂²×C₃×D₄	—	2	4	no	—
108	C₂²×C₃×D₄	—	2	4	no	—
109	C₂²×C₃×D₄	—	2	4	no	—
110	C₂²×C₃×D₄	C₂³	1	2	yes	—
111	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
112	C₂²×C₃×D₄	C₂³	1	4	yes	—
113	C₂²×C₃×D₄	C₂³	1	2	yes	—
114	C₂²×C₃×D₄	C₂³	1	4	yes	—
115	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
116	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
117	C₂³×C₃×C₄	C₂³	1	2	yes	—
118	C₂³×C₃×C₄	C₂³	1	4	yes	—
119	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
120	C₂³×C₃×C₄	C₂³	1	2	yes	—
121	C₂³×C₃×C₄	C₂³	1	2	yes	—
122	C₂³×C₃×C₄	C₂³	1	2	yes	—
123	C₂³×C₃×C₄	C₂³	1	2	yes	—
124	C₃×C₄⋊Q₈	—	2	4	no	—
125	C₃×#123	—	2	16	no	—
126	C₃×C₂²⋊Q₈	—	2	8	no	—
127	C₃×#121	—	2	8	no	—
128	C₃×#121	—	2	8	no	—
129	C₃×#120	—	4	8	no	—
130	C₃×C₄×D₄	—	2	4	no	—
131	C₃×C₄×D₄	—	2	8	no	—
132	C₃×C₄×D₄	—	2	8	no	—
133	C₃×C₄×D₄	—	2	4	no	—
134	C₃×C₄×D₄	—	2	8	no	—
135	C₃×C₄×D₄	—	2	4	no	—
136	C₃×C₄×D₄	—	2	4	no	—
137	C₃×C₄×D₄	—	4	8	no	—
138	C₃×C₄×D₄	D₄	1	8	yes	complemented
139	C₃×#117	—	2	4	no	—
140	C₃×#117	—	2	4	no	—
141	C₂×C₃×C₄⋊C₄	—	2	8	no	—
142	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
147	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
153	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
155	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
156	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
160	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
161	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
169	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
170	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
172	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
173	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
174	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
175	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₃×C₄²	C₂³	1	2	yes	—
177	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄²	C₂³	1	2	yes	—
179	C₂×C₃×C₄²	C₂³	1	4	yes	—
180	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
181	C₃×#95	C₂³	1	1	yes	characteristic
182	C₃×#95	C₂³	1	4	yes	—
183	C₃×#95	C₂³	1	4	yes	—
184	C₃×#95	C₂³	1	2	yes	—
185	C₃×#95	C₂³	1	2	yes	—
186	C₃×#95	C₂³	1	2	yes	—
187	C₃×#95	C₂³	1	1	yes	characteristic
188	C₃×#95	C₂³	1	4	yes	—
189	C₃×#95	C₂³	1	4	yes	—
190	C₃×#95	C₂³	1	4	yes	—
191	C₃×#95	C₂³	1	4	yes	—
192	C₃×#95	C₂³	1	2	yes	—
193	C₂²×#41	C₂²×C₃	1	2	yes	complemented
194	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
195	#547	—	2	8	no	—
196	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
197	C₂×#123	C₂²×C₃	1	4	yes	complemented
198	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
199	C₂×#121	C₂²×C₃	1	2	yes	—
200	C₂×#121	C₂²×C₃	1	2	yes	—
201	C₂×#120	C₂²×C₃	1	4	yes	—
202	#518	—	2	8	no	—
203	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
204	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
205	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
206	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
207	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
208	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
209	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
210	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
211	C₂×C₄×D₄	C₂²×C₃	1	4	yes	complemented
212	C₂×#117	C₂²×C₃	1	1	yes	characteristic
213	C₂×#117	C₂²×C₃	1	1	yes	characteristic
214	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
215	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
216	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
217	#400	C₂²×C₃	1	2	yes	complemented
218	#399	C₂²×C₃	1	2	yes	—
219	#398	C₂²×C₃	1	1	yes	characteristic, complemented
220	#397	C₂²×C₃	1	1	yes	characteristic
221	#397	C₂²×C₃	1	2	yes	complemented
222	#397	C₂²×C₃	1	4	yes	complemented
223	#396	C₂²×C₃	1	2	yes	complemented
224	#395	C₂²×C₃	1	2	yes	complemented
225	#394	C₂²×C₃	1	4	yes	—
226	#394	C₂²×C₃	1	2	yes	—
227	#394	C₂²×C₃	1	1	yes	characteristic, complemented
228	#394	C₂²×C₃	1	4	yes	complemented
229	#393	C₂²×C₃	1	2	yes	—
230	#393	C₂²×C₃	1	2	yes	complemented
231	#393	C₂²×C₃	1	2	yes	complemented
232	#392	C₂²×C₃	1	4	yes	—
233	#392	C₂²×C₃	1	1	yes	characteristic
234	#392	C₂²×C₃	1	2	yes	complemented
235	#390	C₂²×C₃	1	2	yes	—
236	#390	C₂²×C₃	1	2	yes	—
237	#389	C₂²×C₃	1	2	yes	complemented
238	#388	C₂²×C₃	1	4	yes	—
239	#388	C₂²×C₃	1	4	yes	complemented
240	#388	C₂²×C₃	1	4	yes	complemented
241	#387	C₂²×C₃	1	4	yes	complemented
242	#386	C₂²×C₃	1	4	yes	—
243	#386	C₂²×C₃	1	4	yes	complemented
244	#386	C₂²×C₃	1	4	yes	complemented
245	#386	C₂²×C₃	1	4	yes	complemented
246	#385	C₂²×C₃	1	4	yes	complemented
247	#382	C₂²×C₃	1	2	yes	complemented
248	#382	C₂²×C₃	1	1	yes	characteristic, complemented
249	#381	C₂²×C₃	1	4	yes	complemented
250	#381	C₂²×C₃	1	2	yes	complemented
251	#380	C₂²×C₃	1	2	yes	—
252	#380	C₂²×C₃	1	4	yes	complemented
253	#380	C₂²×C₃	1	2	yes	complemented
254	#379	C₂²×C₃	1	4	yes	—
255	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
256	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
257	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
258	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
259	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
260	C₂⁴×C₃	—	2	4	no	—
261	C₂⁴×C₃	—	2	4	no	—
262	C₂⁴×C₃	—	2	4	no	—
263	C₂⁴×C₃	—	4	4	no	—
264	C₂⁴×C₃	—	4	4	no	—
265	C₂⁴×C₃	C₂⁴	1	2	yes	—
266	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
267	C₂⁴×C₃	C₂⁴	1	2	yes	—
268	C₂⁴×C₃	C₂⁴	1	2	yes	—
269	C₃×#41	—	4	32	no	—
270	C₂×C₃×Q₈	—	2	4	no	—
271	C₂×C₃×Q₈	—	4	4	no	—
272	C₂×C₃×D₄	—	2	32	no	—
273	C₂×C₃×D₄	—	2	4	no	—
274	C₂×C₃×D₄	—	2	4	no	—
275	C₂×C₃×D₄	—	2	4	no	—
276	C₂×C₃×D₄	—	2	8	no	—
277	C₂×C₃×D₄	—	2	4	no	—
278	C₂×C₃×D₄	—	2	8	no	—
279	C₂×C₃×D₄	—	2	8	no	—
280	C₂×C₃×D₄	—	2	4	no	—
281	C₂×C₃×D₄	—	2	8	no	—
282	C₂×C₃×D₄	—	2	2	no	—
283	C₂×C₃×D₄	—	2	2	no	—
284	C₂×C₃×D₄	—	2	4	no	—
285	C₂×C₃×D₄	—	2	2	no	—
286	C₂×C₃×D₄	—	2	2	no	—
287	C₂×C₃×D₄	—	2	2	no	—
288	C₂×C₃×D₄	—	4	4	no	—
289	C₂×C₃×D₄	—	4	2	no	—
290	C₂×C₃×D₄	—	4	4	no	—
291	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
292	C₂×C₃×D₄	#41	1	4	yes	complemented
293	C₂²×C₃×C₄	—	2	2	no	—
294	C₂²×C₃×C₄	—	2	2	no	—
295	C₂²×C₃×C₄	—	2	8	no	—
296	C₂²×C₃×C₄	—	2	4	no	—
297	C₂²×C₃×C₄	—	2	4	no	—
298	C₂²×C₃×C₄	—	2	8	no	—
299	C₂²×C₃×C₄	—	2	4	no	—
300	C₂²×C₃×C₄	—	2	4	no	—
301	C₂²×C₃×C₄	—	2	4	no	—
302	C₂²×C₃×C₄	—	2	4	no	—
303	C₂²×C₃×C₄	—	4	4	no	—
304	C₂²×C₃×C₄	—	4	4	no	—
305	C₂²×C₃×C₄	—	4	4	no	—
306	C₂²×C₃×C₄	—	4	4	no	—
307	C₂²×C₃×C₄	—	4	4	no	—
308	C₂²×C₃×C₄	C₂×D₄	1	8	yes	—
309	C₂²×C₃×C₄	#41	1	4	yes	complemented
310	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
311	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
312	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
313	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
314	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
315	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
316	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
317	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
318	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
319	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
320	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
321	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
322	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
323	C₃×C₄⋊C₄	—	2	4	no	—
324	C₃×C₄⋊C₄	—	2	8	no	—
325	C₃×C₄⋊C₄	—	2	2	no	—
326	C₃×C₄⋊C₄	—	2	2	no	—
327	C₃×C₄⋊C₄	—	2	2	no	—
328	C₃×C₄⋊C₄	—	2	2	no	—
329	C₃×C₄⋊C₄	—	2	4	no	—
330	C₃×C₄⋊C₄	—	2	4	no	—
331	C₃×C₄⋊C₄	—	2	4	no	—
332	C₃×C₄⋊C₄	—	4	2	no	—
333	C₃×C₄⋊C₄	—	4	4	no	—
334	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
335	C₃×C₂²⋊C₄	—	2	4	no	—
336	C₃×C₂²⋊C₄	—	2	8	no	—
337	C₃×C₂²⋊C₄	—	2	4	no	—
338	C₃×C₂²⋊C₄	—	2	8	no	—
339	C₃×C₂²⋊C₄	—	2	4	no	—
340	C₃×C₂²⋊C₄	—	2	4	no	—
341	C₃×C₂²⋊C₄	—	2	2	no	—
342	C₃×C₂²⋊C₄	—	2	2	no	—
343	C₃×C₂²⋊C₄	—	2	4	no	—
344	C₃×C₂²⋊C₄	—	2	4	no	—
345	C₃×C₂²⋊C₄	—	2	4	no	—
346	C₃×C₂²⋊C₄	—	2	4	no	—
347	C₃×C₂²⋊C₄	—	4	4	no	—
348	C₃×C₂²⋊C₄	—	4	4	no	—
349	C₃×C₂²⋊C₄	—	4	2	no	—
350	C₃×C₂²⋊C₄	—	4	4	no	—
351	C₃×C₂²⋊C₄	—	4	4	no	—
352	C₃×C₂²⋊C₄	—	4	4	no	—
353	C₃×C₂²⋊C₄	—	4	4	no	—
354	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
355	C₃×C₄²	—	2	4	no	—
356	C₃×C₄²	—	2	2	no	—
357	C₃×C₄²	—	2	4	no	—
358	C₃×C₄²	—	4	4	no	—
359	C₃×C₄²	C₂×D₄	1	4	yes	—
360	C₂⁵	C₂³×C₃	1	2	yes	—
361	C₂×#41	—	2	8	no	—
362	C₂×#41	—	4	8	no	—
363	C₂²×Q₈	C₂³×C₃	1	2	yes	—
364	C₂²×D₄	—	2	4	no	—
365	C₂²×D₄	—	2	4	no	—
366	C₂²×D₄	—	2	4	no	—
367	C₂²×D₄	C₂³×C₃	1	2	yes	—
368	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
369	C₂²×D₄	C₂³×C₃	1	2	yes	—
370	C₂²×D₄	C₂³×C₃	1	4	yes	—
371	C₂²×D₄	C₂³×C₃	1	4	yes	—
372	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
373	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
374	C₂³×C₄	C₂³×C₃	1	2	yes	—
375	C₂³×C₄	C₂³×C₃	1	4	yes	—
376	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
377	C₂³×C₄	C₂³×C₃	1	2	yes	—
378	C₂³×C₄	C₂³×C₃	1	2	yes	—
379	C₂³×C₄	C₂³×C₃	1	2	yes	—
380	C₂³×C₄	C₂³×C₃	1	2	yes	—
381	C₄⋊Q₈	—	2	4	no	—
382	#123	—	2	16	no	—
383	C₂²⋊Q₈	—	2	8	no	—
384	#121	—	2	8	no	—
385	#121	—	2	8	no	—
386	#120	—	4	8	no	—
387	C₄×D₄	—	2	4	no	—
388	C₄×D₄	—	2	8	no	—
389	C₄×D₄	—	2	8	no	—
390	C₄×D₄	—	2	4	no	—
391	C₄×D₄	—	2	8	no	—
392	C₄×D₄	—	2	4	no	—
393	C₄×D₄	—	2	4	no	—
394	C₄×D₄	—	4	8	no	—
395	C₄×D₄	C₃×D₄	1	8	yes	complemented
396	#117	—	2	4	no	—
397	#117	—	2	4	no	—
398	C₂×C₄⋊C₄	—	2	8	no	—
399	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
400	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
401	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
405	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
407	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
409	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
410	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
411	C₂×C₂²⋊C₄	—	2	8	no	—
412	C₂×C₂²⋊C₄	—	2	8	no	—
413	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
415	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
433	C₂×C₄²	C₂³×C₃	1	2	yes	—
434	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₃	1	2	yes	—
436	C₂×C₄²	C₂³×C₃	1	4	yes	—
437	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
438	#95	C₂³×C₃	1	1	yes	characteristic
439	#95	C₂³×C₃	1	4	yes	—
440	#95	C₂³×C₃	1	4	yes	—
441	#95	C₂³×C₃	1	2	yes	—
442	#95	C₂³×C₃	1	2	yes	—
443	#95	C₂³×C₃	1	2	yes	—
444	#95	C₂³×C₃	1	1	yes	characteristic
445	#95	C₂³×C₃	1	4	yes	—
446	#95	C₂³×C₃	1	4	yes	—
447	#95	C₂³×C₃	1	4	yes	—
448	#95	C₂³×C₃	1	4	yes	—
449	#95	C₂³×C₃	1	2	yes	—
450	C₂³×C₃	—	2	16	no	—
451	C₂³×C₃	—	2	1	no	—
452	C₂³×C₃	—	2	2	no	—
453	C₂³×C₃	—	2	2	no	—
454	C₂³×C₃	—	2	2	no	—
455	C₂³×C₃	—	2	2	no	—
456	C₂³×C₃	—	2	1	no	—
457	C₂³×C₃	—	2	2	no	—
458	C₂³×C₃	—	2	2	no	—
459	C₂³×C₃	—	2	2	no	—
460	C₂³×C₃	—	2	4	no	—
461	C₂³×C₃	—	2	2	no	—
462	C₂³×C₃	—	2	4	no	—
463	C₂³×C₃	—	2	2	no	—
464	C₂³×C₃	—	2	2	no	—
465	C₂³×C₃	—	2	4	no	—
466	C₂³×C₃	—	2	2	no	—
467	C₂³×C₃	—	2	4	no	—
468	C₂³×C₃	—	2	2	no	—
469	C₂³×C₃	—	8	4	no	—
470	C₂³×C₃	—	8	8	no	—
471	C₂³×C₃	—	8	4	no	—
472	C₂³×C₃	—	8	8	no	—
473	C₂³×C₃	C₂²×D₄	1	4	yes	—
474	C₂³×C₃	C₂×#41	1	2	yes	—
475	C₂³×C₃	C₂×#41	1	4	yes	—
476	C₂³×C₃	H(5,𝔽₂)	1	4	yes	—
477	C₂³×C₃	C₂⁵	1	1	yes	characteristic
478	C₃×Q₈	—	4	8	no	—
479	C₃×D₄	—	2	16	no	—
480	C₃×D₄	—	2	8	no	—
481	C₃×D₄	—	2	8	no	—
482	C₃×D₄	—	2	8	no	—
483	C₃×D₄	—	4	8	no	—
484	C₃×D₄	—	4	16	no	—
485	C₃×D₄	—	4	16	no	—
486	C₂×C₃×C₄	—	2	1	no	—
487	C₂×C₃×C₄	—	2	1	no	—
488	C₂×C₃×C₄	—	2	4	no	—
489	C₂×C₃×C₄	—	2	2	no	—
490	C₂×C₃×C₄	—	2	2	no	—
491	C₂×C₃×C₄	—	2	8	no	—
492	C₂×C₃×C₄	—	2	1	no	—
493	C₂×C₃×C₄	—	2	2	no	—
494	C₂×C₃×C₄	—	2	1	no	—
495	C₂×C₃×C₄	—	2	2	no	—
496	C₂×C₃×C₄	—	2	4	no	—
497	C₂×C₃×C₄	—	2	2	no	—
498	C₂×C₃×C₄	—	2	2	no	—
499	C₂×C₃×C₄	—	2	2	no	—
500	C₂×C₃×C₄	—	2	2	no	—
501	C₂×C₃×C₄	—	2	4	no	—
502	C₂×C₃×C₄	—	2	2	no	—
503	C₂×C₃×C₄	—	2	4	no	—
504	C₂×C₃×C₄	—	2	2	no	—
505	C₂×C₃×C₄	—	2	2	no	—
506	C₂×C₃×C₄	—	2	4	no	—
507	C₂×C₃×C₄	—	2	4	no	—
508	C₂×C₃×C₄	—	2	2	no	—
509	C₂×C₃×C₄	—	2	4	no	—
510	C₂×C₃×C₄	—	2	2	no	—
511	C₂×C₃×C₄	—	2	4	no	—
512	C₂×C₃×C₄	—	2	2	no	—
513	C₂×C₃×C₄	—	4	8	no	—
514	C₂×C₃×C₄	—	4	16	no	—
515	C₂×C₃×C₄	—	4	8	no	—
516	C₂×C₃×C₄	—	8	4	no	—
517	C₂×C₃×C₄	—	8	4	no	—
518	C₂×C₃×C₄	—	8	4	no	—
519	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
520	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
521	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
522	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
523	C₂×C₃×C₄	C₂×#41	1	2	yes	—
524	C₂×C₃×C₄	C₂×#41	1	2	yes	—
525	C₂×C₃×C₄	C₂×#41	1	2	yes	—
526	C₂⁴	—	2	4	no	—
527	C₂⁴	—	2	4	no	—
528	C₂⁴	—	2	4	no	—
529	C₂⁴	—	4	4	no	—
530	C₂⁴	—	4	4	no	—
531	C₂⁴	C₂⁴×C₃	1	2	yes	—
532	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
533	C₂⁴	C₂⁴×C₃	1	2	yes	—
534	C₂⁴	C₂⁴×C₃	1	2	yes	—
535	#41	—	4	32	no	—
536	C₂×Q₈	—	2	4	no	—
537	C₂×Q₈	—	4	4	no	—
538	C₂×D₄	—	2	32	no	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	2	4	no	—
541	C₂×D₄	—	2	4	no	—
542	C₂×D₄	—	2	8	no	—
543	C₂×D₄	—	2	4	no	—
544	C₂×D₄	—	2	8	no	—
545	C₂×D₄	—	2	8	no	—
546	C₂×D₄	—	2	4	no	—
547	C₂×D₄	—	2	8	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	4	4	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂×D₄	—	4	2	no	—
557	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
558	C₂×D₄	C₃×#41	1	4	yes	complemented
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	8	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	2	8	no	—
565	C₂²×C₄	—	2	4	no	—
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	4	4	no	—
570	C₂²×C₄	—	4	4	no	—
571	C₂²×C₄	—	4	4	no	—
572	C₂²×C₄	—	4	4	no	—
573	C₂²×C₄	—	4	4	no	—
574	C₂²×C₄	C₂×C₃×D₄	1	8	yes	—
575	C₂²×C₄	C₃×#41	1	4	yes	complemented
576	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
578	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
583	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
584	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
585	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
589	C₄⋊C₄	—	2	4	no	—
590	C₄⋊C₄	—	2	8	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	4	4	no	—
599	C₄⋊C₄	—	4	2	no	—
600	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	8	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	8	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	4	4	no	—
614	C₂²⋊C₄	—	4	4	no	—
615	C₂²⋊C₄	—	4	4	no	—
616	C₂²⋊C₄	—	4	4	no	—
617	C₂²⋊C₄	—	4	4	no	—
618	C₂²⋊C₄	—	4	4	no	—
619	C₂²⋊C₄	—	4	2	no	—
620	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
621	C₄²	—	2	4	no	—
622	C₄²	—	2	2	no	—
623	C₄²	—	2	4	no	—
624	C₄²	—	4	4	no	—
625	C₄²	C₂×C₃×D₄	1	4	yes	—
626	C₂²×C₃	—	2	2	no	—
627	C₂²×C₃	—	2	4	no	—
628	C₂²×C₃	—	2	4	no	—
629	C₂²×C₃	—	2	4	no	—
630	C₂²×C₃	—	2	4	no	—
631	C₂²×C₃	—	2	4	no	—
632	C₂²×C₃	—	2	4	no	—
633	C₂²×C₃	—	2	4	no	—
634	C₂²×C₃	—	2	4	no	—
635	C₂²×C₃	—	2	8	no	—
636	C₂²×C₃	—	4	2	no	—
637	C₂²×C₃	—	4	2	no	—
638	C₂²×C₃	—	4	1	no	—
639	C₂²×C₃	—	4	2	no	—
640	C₂²×C₃	—	4	4	no	—
641	C₂²×C₃	—	4	4	no	—
642	C₂²×C₃	—	4	2	no	—
643	C₂²×C₃	—	4	2	no	—
644	C₂²×C₃	—	4	1	no	—
645	C₂²×C₃	—	4	2	no	—
646	C₂²×C₃	—	4	4	no	—
647	C₂²×C₃	—	4	2	no	—
648	C₂²×C₃	—	8	16	no	—
649	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
650	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
651	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
652	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
653	C₂²×C₃	#585	1	2	yes	—
654	C₃×C₄	—	2	2	no	—
655	C₃×C₄	—	2	4	no	—
656	C₃×C₄	—	2	2	no	—
657	C₃×C₄	—	2	2	no	—
658	C₃×C₄	—	4	2	no	—
659	C₃×C₄	—	4	4	no	—
660	C₃×C₄	—	4	1	no	—
661	C₃×C₄	—	4	2	no	—
662	C₃×C₄	—	4	2	no	—
663	C₃×C₄	—	4	2	no	—
664	C₃×C₄	—	4	1	no	—
665	C₃×C₄	—	4	4	no	—
666	C₃×C₄	#525	1	4	yes	—
667	C₂³	—	2	16	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	4	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	4	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	4	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	4	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	8	4	no	—
687	C₂³	—	8	8	no	—
688	C₂³	—	8	4	no	—
689	C₂³	—	8	8	no	—
690	C₂³	C₂²×C₃×D₄	1	4	yes	—
691	C₂³	C₂×C₃×#41	1	2	yes	—
692	C₂³	C₂×C₃×#41	1	4	yes	—
693	C₂³	C₃×H(5,𝔽₂)	1	4	yes	—
694	C₂³	C₂⁵×C₃	1	1	yes	characteristic
695	Q₈	—	4	8	no	—
696	D₄	—	2	16	no	—
697	D₄	—	2	8	no	—
698	D₄	—	2	8	no	—
699	D₄	—	2	8	no	—
700	D₄	—	4	16	no	—
701	D₄	—	4	8	no	—
702	D₄	—	4	16	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	8	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	4	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	4	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	4	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	4	8	no	—
731	C₂×C₄	—	4	16	no	—
732	C₂×C₄	—	4	8	no	—
733	C₂×C₄	—	8	4	no	—
734	C₂×C₄	—	8	4	no	—
735	C₂×C₄	—	8	4	no	—
736	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
737	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
738	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
739	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
740	C₂×C₄	C₂×C₃×#41	1	2	yes	—
741	C₂×C₄	C₂×C₃×#41	1	2	yes	—
742	C₂×C₄	C₂×C₃×#41	1	2	yes	—
743	C₂×C₃	—	4	4	no	—
744	C₂×C₃	—	4	4	no	—
745	C₂×C₃	—	4	4	no	—
746	C₂×C₃	—	4	2	no	—
747	C₂×C₃	C₂×#525	1	1	yes	characteristic
748	C₂×C₃	#3484	1	1	yes	characteristic
749	C₂×C₃	#3494	1	2	yes	—
750	C₂×C₃	#3500	1	1	yes	characteristic
751	C₂×C₃	#3513	1	2	yes	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	4	no	—
754	C₂²	—	2	4	no	—
755	C₂²	—	2	4	no	—
756	C₂²	—	2	4	no	—
757	C₂²	—	2	4	no	—
758	C₂²	—	2	4	no	—
759	C₂²	—	2	4	no	—
760	C₂²	—	2	4	no	—
761	C₂²	—	2	8	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	4	no	—
766	C₂²	—	4	4	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	4	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	8	16	no	—
775	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
776	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
777	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
778	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
779	C₂²	C₃×#585	1	2	yes	—
780	C₄	—	2	2	no	—
781	C₄	—	2	4	no	—
782	C₄	—	2	2	no	—
783	C₄	—	2	2	no	—
784	C₄	—	4	2	no	—
785	C₄	—	4	4	no	—
786	C₄	—	4	1	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	1	no	—
791	C₄	—	4	4	no	—
792	C₄	C₃×#525	1	4	yes	—
793	C₃	#35730	1	1	yes	characteristic, direct product factor, Sylow
794	C₂	—	4	2	no	—
795	C₂	—	4	4	no	—
796	C₂	—	4	4	no	—
797	C₂	—	4	4	no	—
798	C₂	C₂×C₃×#525	1	1	yes	characteristic
799	C₂	C₃×#3484	1	1	yes	characteristic
800	C₂	C₃×#3494	1	2	yes	—
801	C₂	C₃×#3500	1	1	yes	characteristic
802	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×#547	C₂	semidirect
2. C₂×C₃×#518	C₂	semidirect
3. C₃×#2638	C₂	semidirect
4. C₃×#2628	C₂	semidirect
5. C₃×#2563	C₂	semidirect
6. C₃×#2561	C₂	semidirect
7. C₃×#2535	C₂	semidirect
8. C₃×#2457	C₂	semidirect
9. C₃×#2420	C₂	semidirect
10. C₃×#2418	C₂	semidirect
11. C₃×#2408	C₂	semidirect
12. C₃×#2404	C₂	semidirect
13. C₃×#2392	C₂	semidirect
14. C₃×#2388	C₂	semidirect
15. C₃×#2361	C₂	semidirect
16. C₃×#2357	C₂	semidirect
17. C₃×#2352	C₂	semidirect
18. #35730	C₃	direct (N × H)
19. C₂²×C₃×#41	C₂²	semidirect
22. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
23. C₂×C₃×#123	C₂²	semidirect
24. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
36. C₂×C₃×C₄×D₄	C₂²	semidirect
37. C₂×C₃×C₄×D₄	C₂²	semidirect
40. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
43. C₃×#400	C₂²	semidirect
45. C₃×#398	C₂²	semidirect
47. C₃×#397	C₂²	semidirect
48. C₃×#397	C₂²	semidirect
49. C₃×#396	C₂²	semidirect
50. C₃×#395	C₂²	semidirect
53. C₃×#394	C₂²	semidirect
54. C₃×#394	C₂²	semidirect
56. C₃×#393	C₂²	semidirect
57. C₃×#393	C₂²	semidirect
60. C₃×#392	C₂²	semidirect
63. C₃×#389	C₂²	semidirect
65. C₃×#388	C₂²	semidirect
66. C₃×#388	C₂²	semidirect
67. C₃×#387	C₂²	semidirect
69. C₃×#386	C₂²	semidirect
70. C₃×#386	C₂²	semidirect
71. C₃×#386	C₂²	semidirect
72. C₃×#385	C₂²	semidirect
73. C₃×#382	C₂²	semidirect
74. C₃×#382	C₂²	semidirect
75. C₃×#381	C₂²	semidirect
76. C₃×#381	C₂²	semidirect
78. C₃×#380	C₂²	semidirect
79. C₃×#380	C₂²	semidirect
81. C₃×C₄×C₄⋊C₄	C₂²	semidirect
82. C₃×C₄×C₄⋊C₄	C₂²	semidirect
83. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
84. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
85. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
86. C₂×#547	C₂×C₃	semidirect
87. C₂×#518	C₂×C₃	semidirect
88. #2638	C₂×C₃	semidirect
89. #2628	C₂×C₃	semidirect
90. #2563	C₂×C₃	semidirect
91. #2561	C₂×C₃	semidirect
92. #2535	C₂×C₃	semidirect
93. #2457	C₂×C₃	semidirect
94. #2420	C₂×C₃	semidirect
95. #2418	C₂×C₃	semidirect
96. #2408	C₂×C₃	semidirect
97. #2404	C₂×C₃	semidirect
98. #2392	C₂×C₃	semidirect
99. #2388	C₂×C₃	semidirect
100. #2361	C₂×C₃	semidirect
101. #2357	C₂×C₃	semidirect
102. #2352	C₂×C₃	semidirect
138. C₃×C₄×D₄	D₄	semidirect
193. C₂²×#41	C₂²×C₃	semidirect
196. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
197. C₂×#123	C₂²×C₃	semidirect
198. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
210. C₂×C₄×D₄	C₂²×C₃	semidirect
211. C₂×C₄×D₄	C₂²×C₃	semidirect
214. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
217. #400	C₂²×C₃	semidirect
219. #398	C₂²×C₃	semidirect
221. #397	C₂²×C₃	semidirect
222. #397	C₂²×C₃	semidirect
223. #396	C₂²×C₃	semidirect
224. #395	C₂²×C₃	semidirect
227. #394	C₂²×C₃	semidirect
228. #394	C₂²×C₃	semidirect
230. #393	C₂²×C₃	semidirect
231. #393	C₂²×C₃	semidirect
234. #392	C₂²×C₃	semidirect
237. #389	C₂²×C₃	semidirect
239. #388	C₂²×C₃	semidirect
240. #388	C₂²×C₃	semidirect
241. #387	C₂²×C₃	semidirect
243. #386	C₂²×C₃	semidirect
244. #386	C₂²×C₃	semidirect
245. #386	C₂²×C₃	semidirect
246. #385	C₂²×C₃	semidirect
247. #382	C₂²×C₃	semidirect
248. #382	C₂²×C₃	semidirect
249. #381	C₂²×C₃	semidirect
250. #381	C₂²×C₃	semidirect
252. #380	C₂²×C₃	semidirect
253. #380	C₂²×C₃	semidirect
255. C₄×C₄⋊C₄	C₂²×C₃	semidirect
256. C₄×C₄⋊C₄	C₂²×C₃	semidirect
257. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
258. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
259. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
292. C₂×C₃×D₄	#41	semidirect
309. C₂²×C₃×C₄	#41	semidirect
395. C₄×D₄	C₃×D₄	semidirect
558. C₂×D₄	C₃×#41	semidirect
575. C₂²×C₄	C₃×#41	semidirect
793. C₃	#35730	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×#547	2
C₂×C₃×#518	2
C₃×#2638	2
C₃×#2628	2
C₃×#2563	2
C₃×#2561	2
C₃×#2535	2
C₃×#2457	2
C₃×#2420	2
C₃×#2418	2
C₃×#2408	2
C₃×#2404	2
C₃×#2392	2
C₃×#2388	2
C₃×#2361	2
C₃×#2357	2
C₃×#2352	2
#35730	3

Subgroups — C3×#35730 #10654337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35730 #10654337