Subgroups — C₃×#37688 #10656295

Order 768.

2200 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#543	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2729	C₂	1	2	yes	maximal, complemented
5	C₃×#2720	C₂	1	2	yes	maximal, complemented
6	C₃×#2704	C₂	1	2	yes	maximal, complemented
7	C₃×#2677	C₂	1	2	yes	maximal, complemented
8	C₃×#2659	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2626	C₂	1	1	yes	maximal, characteristic
10	C₃×#2465	C₂	1	2	yes	maximal, complemented
11	C₃×#2465	C₂	1	2	yes	maximal, complemented
12	C₃×#2440	C₂	1	2	yes	maximal, complemented
13	C₃×#2438	C₂	1	2	yes	maximal, complemented
14	C₃×#2437	C₂	1	2	yes	maximal
15	C₃×#2429	C₂	1	2	yes	maximal, complemented
16	C₃×#2423	C₂	1	2	yes	maximal, complemented
17	C₃×#2342	C₂	1	2	yes	maximal
18	C₃×#2329	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₃×#388	C₂	1	1	yes	maximal, characteristic
20	#37688	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₃×#543	—	2	8	no	—
22	C₃×#533	—	2	8	no	—
23	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
26	C₂×C₃×#125	C₂²	1	2	yes	complemented
27	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
32	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
34	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
35	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
36	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	complemented
39	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃×#117	C₂²	1	2	yes	—
41	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
44	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
47	C₃×#400	C₂²	1	2	yes	complemented
48	C₃×#399	C₂²	1	2	yes	—
49	C₃×#399	C₂²	1	2	yes	—
50	C₃×#398	C₂²	1	2	yes	complemented
51	C₃×#398	C₂²	1	2	yes	complemented
52	C₃×#398	C₂²	1	2	yes	complemented
53	C₃×#398	C₂²	1	2	yes	complemented
54	C₃×#398	C₂²	1	2	yes	complemented
55	C₃×#398	C₂²	1	2	yes	complemented
56	C₃×#396	C₂²	1	2	yes	—
57	C₃×#396	C₂²	1	2	yes	—
58	C₃×#396	C₂²	1	2	yes	—
59	C₃×#396	C₂²	1	2	yes	—
60	C₃×#395	C₂²	1	2	yes	complemented
61	C₃×#395	C₂²	1	2	yes	complemented
62	C₃×#395	C₂²	1	2	yes	complemented
63	C₃×#395	C₂²	1	2	yes	complemented
64	C₃×#395	C₂²	1	2	yes	complemented
65	C₃×#393	C₂²	1	2	yes	—
66	C₃×#393	C₂²	1	2	yes	—
67	C₃×#391	C₂²	1	2	yes	complemented
68	C₃×#391	C₂²	1	2	yes	complemented
69	C₃×#391	C₂²	1	1	yes	characteristic, complemented
70	C₃×#391	C₂²	1	1	yes	characteristic, complemented
71	C₃×#389	C₂²	1	2	yes	complemented
72	C₃×#389	C₂²	1	1	yes	characteristic, complemented
73	C₃×#389	C₂²	1	2	yes	complemented
74	C₃×#389	C₂²	1	2	yes	complemented
75	C₃×#389	C₂²	1	2	yes	complemented
76	C₃×#389	C₂²	1	1	yes	characteristic, complemented
77	C₃×#388	C₂²	1	2	yes	—
78	C₃×#388	C₂²	1	2	yes	—
79	C₃×#388	C₂²	1	2	yes	—
80	C₃×#388	C₂²	1	2	yes	—
81	C₃×#388	C₂²	1	2	yes	—
82	C₃×#388	C₂²	1	2	yes	—
83	C₃×#388	C₂²	1	2	yes	—
84	C₃×#388	C₂²	1	2	yes	—
85	C₃×#387	C₂²	1	2	yes	complemented
86	C₃×#387	C₂²	1	2	yes	complemented
87	C₃×#387	C₂²	1	2	yes	complemented
88	C₃×#387	C₂²	1	2	yes	complemented
89	C₃×#387	C₂²	1	2	yes	complemented
90	C₃×#387	C₂²	1	2	yes	complemented
91	C₃×#385	C₂²	1	2	yes	—
92	C₃×#385	C₂²	1	2	yes	—
93	C₃×#385	C₂²	1	2	yes	—
94	C₃×#385	C₂²	1	2	yes	—
95	C₃×#385	C₂²	1	2	yes	—
96	C₃×#385	C₂²	1	2	yes	—
97	C₃×#385	C₂²	1	2	yes	—
98	C₃×#384	C₂²	1	2	yes	complemented
99	C₃×#381	C₂²	1	2	yes	—
100	C₃×#380	C₂²	1	1	yes	characteristic
101	C₃×#380	C₂²	1	2	yes	—
102	C₃×#380	C₂²	1	2	yes	—
103	C₃×#380	C₂²	1	2	yes	—
104	C₃×#379	C₂²	1	2	yes	—
105	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
106	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
107	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
108	C₂×C₃×#95	C₂²	1	1	yes	characteristic
109	C₂×C₃×#95	C₂²	1	1	yes	characteristic
110	C₂×#543	C₂×C₃	1	1	yes	characteristic
111	C₂×#533	C₂×C₃	1	1	yes	characteristic, complemented
112	#2855	C₂×C₃	1	1	yes	characteristic, complemented
113	#2729	C₂×C₃	1	2	yes	complemented
114	#2720	C₂×C₃	1	2	yes	complemented
115	#2704	C₂×C₃	1	2	yes	complemented
116	#2677	C₂×C₃	1	2	yes	complemented
117	#2659	C₂×C₃	1	1	yes	characteristic, complemented
118	#2626	C₂×C₃	1	1	yes	characteristic
119	#2465	C₂×C₃	1	2	yes	complemented
120	#2465	C₂×C₃	1	2	yes	complemented
121	#2440	C₂×C₃	1	2	yes	complemented
122	#2438	C₂×C₃	1	2	yes	complemented
123	#2437	C₂×C₃	1	2	yes	—
124	#2429	C₂×C₃	1	2	yes	complemented
125	#2423	C₂×C₃	1	2	yes	complemented
126	#2342	C₂×C₃	1	2	yes	—
127	#2329	C₂×C₃	1	1	yes	characteristic, complemented
128	C₂×#388	C₂×C₃	1	1	yes	characteristic
129	C₂⁵×C₃	C₂³	1	1	yes	characteristic
130	C₂²×C₃×Q₈	C₂³	1	2	yes	—
131	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
132	C₂²×C₃×Q₈	C₂³	1	2	yes	—
133	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
134	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
135	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
136	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
137	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
138	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
139	C₂³×C₃×C₄	C₂³	1	2	yes	—
140	C₂³×C₃×C₄	C₂³	1	2	yes	—
141	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
142	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
143	C₃×C₄⋊Q₈	—	2	4	no	—
144	C₃×C₄⋊Q₈	—	2	4	no	—
145	C₃×C₄⋊Q₈	—	4	4	no	—
146	C₃×#125	—	2	8	no	—
147	C₃×C₂²⋊Q₈	—	2	8	no	—
148	C₃×C₂²⋊Q₈	—	2	4	no	—
149	C₃×C₂²⋊Q₈	—	2	4	no	—
150	C₃×C₂²⋊Q₈	—	2	8	no	—
151	C₃×C₂²⋊Q₈	—	2	8	no	—
152	C₃×C₂²⋊Q₈	—	2	8	no	—
153	C₃×C₂²⋊Q₈	—	2	8	no	—
154	C₃×C₂²⋊Q₈	—	2	8	no	—
155	C₃×C₂²⋊Q₈	—	4	4	no	—
156	C₃×C₂²⋊Q₈	D₄	1	8	yes	—
157	C₃×C₄×Q₈	—	2	4	no	—
158	C₃×C₄×Q₈	—	2	4	no	—
159	C₃×C₄×Q₈	—	2	8	no	—
160	C₃×#117	—	2	8	no	—
161	C₂×C₃×C₄⋊C₄	—	4	2	no	—
162	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₃×C₄⋊C₄	C₂³	1	2	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	2	yes	—
170	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
185	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
188	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
191	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
192	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
193	C₂×C₃×C₂²⋊C₄	Q₈	1	8	yes	complemented
194	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₃×C₄²	—	2	4	no	—
211	C₂×C₃×C₄²	C₂³	1	2	yes	—
212	C₂×C₃×C₄²	C₂³	1	2	yes	—
213	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
214	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
215	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₄²	C₂³	1	2	yes	—
218	C₂×C₃×C₄²	C₂³	1	2	yes	—
219	C₃×#95	C₂³	1	2	yes	—
220	C₃×#95	C₂³	1	2	yes	—
221	C₃×#95	C₂³	1	2	yes	—
222	C₃×#95	C₂³	1	2	yes	—
223	C₃×#95	C₂³	1	2	yes	—
224	C₃×#95	C₂³	1	2	yes	—
225	C₃×#95	C₂³	1	2	yes	—
226	C₃×#95	C₂³	1	2	yes	—
227	C₃×#95	C₂³	1	2	yes	—
228	C₃×#95	C₂³	1	2	yes	—
229	C₃×#95	C₂³	1	2	yes	—
230	C₃×#95	C₂³	1	2	yes	—
231	C₃×#95	C₂³	1	2	yes	—
232	C₃×#95	C₂³	1	2	yes	—
233	C₃×#95	C₂³	1	2	yes	—
234	C₃×#95	C₂³	1	2	yes	—
235	C₃×#95	C₂³	1	2	yes	—
236	C₃×#95	C₂³	1	2	yes	—
237	C₃×#95	C₂³	1	2	yes	—
238	C₃×#95	C₂³	1	2	yes	—
239	C₃×#95	C₂³	1	2	yes	—
240	#543	—	2	8	no	—
241	#533	—	2	8	no	—
242	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
243	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
244	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
245	C₂×#125	C₂²×C₃	1	2	yes	complemented
246	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
247	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
248	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
249	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
250	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
251	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
252	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
253	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
254	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
255	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
256	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
257	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
258	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
259	C₂×#117	C₂²×C₃	1	2	yes	—
260	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
261	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
262	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
263	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
264	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
265	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
266	#400	C₂²×C₃	1	2	yes	complemented
267	#399	C₂²×C₃	1	2	yes	—
268	#399	C₂²×C₃	1	2	yes	—
269	#398	C₂²×C₃	1	2	yes	complemented
270	#398	C₂²×C₃	1	2	yes	complemented
271	#398	C₂²×C₃	1	2	yes	complemented
272	#398	C₂²×C₃	1	2	yes	complemented
273	#398	C₂²×C₃	1	2	yes	complemented
274	#398	C₂²×C₃	1	2	yes	complemented
275	#396	C₂²×C₃	1	2	yes	—
276	#396	C₂²×C₃	1	2	yes	—
277	#396	C₂²×C₃	1	2	yes	—
278	#396	C₂²×C₃	1	2	yes	—
279	#395	C₂²×C₃	1	2	yes	complemented
280	#395	C₂²×C₃	1	2	yes	complemented
281	#395	C₂²×C₃	1	2	yes	complemented
282	#395	C₂²×C₃	1	2	yes	complemented
283	#395	C₂²×C₃	1	2	yes	complemented
284	#393	C₂²×C₃	1	2	yes	—
285	#393	C₂²×C₃	1	2	yes	—
286	#391	C₂²×C₃	1	2	yes	complemented
287	#391	C₂²×C₃	1	1	yes	characteristic, complemented
288	#391	C₂²×C₃	1	1	yes	characteristic, complemented
289	#391	C₂²×C₃	1	2	yes	complemented
290	#389	C₂²×C₃	1	2	yes	complemented
291	#389	C₂²×C₃	1	1	yes	characteristic, complemented
292	#389	C₂²×C₃	1	1	yes	characteristic, complemented
293	#389	C₂²×C₃	1	2	yes	complemented
294	#389	C₂²×C₃	1	2	yes	complemented
295	#389	C₂²×C₃	1	2	yes	complemented
296	#388	C₂²×C₃	1	2	yes	—
297	#388	C₂²×C₃	1	2	yes	—
298	#388	C₂²×C₃	1	2	yes	—
299	#388	C₂²×C₃	1	2	yes	—
300	#388	C₂²×C₃	1	2	yes	—
301	#388	C₂²×C₃	1	2	yes	—
302	#388	C₂²×C₃	1	2	yes	—
303	#388	C₂²×C₃	1	2	yes	—
304	#387	C₂²×C₃	1	2	yes	complemented
305	#387	C₂²×C₃	1	2	yes	complemented
306	#387	C₂²×C₃	1	2	yes	complemented
307	#387	C₂²×C₃	1	2	yes	complemented
308	#387	C₂²×C₃	1	2	yes	complemented
309	#387	C₂²×C₃	1	2	yes	complemented
310	#385	C₂²×C₃	1	2	yes	—
311	#385	C₂²×C₃	1	2	yes	—
312	#385	C₂²×C₃	1	2	yes	—
313	#385	C₂²×C₃	1	2	yes	—
314	#385	C₂²×C₃	1	2	yes	—
315	#385	C₂²×C₃	1	2	yes	—
316	#385	C₂²×C₃	1	2	yes	—
317	#384	C₂²×C₃	1	2	yes	complemented
318	#381	C₂²×C₃	1	2	yes	—
319	#380	C₂²×C₃	1	1	yes	characteristic
320	#380	C₂²×C₃	1	2	yes	—
321	#380	C₂²×C₃	1	2	yes	—
322	#380	C₂²×C₃	1	2	yes	—
323	#379	C₂²×C₃	1	2	yes	—
324	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
325	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
326	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
327	C₂×#95	C₂²×C₃	1	1	yes	characteristic
328	C₂×#95	C₂²×C₃	1	1	yes	characteristic
329	C₂⁴×C₃	—	2	2	no	—
330	C₂⁴×C₃	—	2	2	no	—
331	C₂⁴×C₃	—	4	1	no	—
332	C₂⁴×C₃	—	4	1	no	—
333	C₂⁴×C₃	—	4	1	no	—
334	C₂⁴×C₃	—	4	1	no	—
335	C₂⁴×C₃	C₂×Q₈	1	4	yes	—
336	C₂⁴×C₃	C₂⁴	1	2	yes	—
337	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
338	C₂×C₃×Q₈	—	2	4	no	—
339	C₂×C₃×Q₈	—	2	2	no	—
340	C₂×C₃×Q₈	—	2	2	no	—
341	C₂×C₃×Q₈	—	2	4	no	—
342	C₂×C₃×Q₈	—	2	4	no	—
343	C₂×C₃×Q₈	—	4	1	no	—
344	C₂×C₃×Q₈	—	4	1	no	—
345	C₂×C₃×Q₈	—	4	2	no	—
346	C₂×C₃×Q₈	—	4	1	no	—
347	C₂×C₃×Q₈	—	4	1	no	—
348	C₂×C₃×Q₈	—	4	2	no	—
349	C₂×C₃×Q₈	—	4	1	no	—
350	C₂×C₃×Q₈	—	4	1	no	—
351	C₂×C₃×Q₈	—	4	2	no	—
352	C₂×C₃×Q₈	C₂×D₄	1	4	yes	—
353	C₂²×C₃×C₄	—	2	2	no	—
354	C₂²×C₃×C₄	—	2	2	no	—
355	C₂²×C₃×C₄	—	2	2	no	—
356	C₂²×C₃×C₄	—	2	2	no	—
357	C₂²×C₃×C₄	—	2	2	no	—
358	C₂²×C₃×C₄	—	2	2	no	—
359	C₂²×C₃×C₄	—	2	4	no	—
360	C₂²×C₃×C₄	—	2	4	no	—
361	C₂²×C₃×C₄	—	4	1	no	—
362	C₂²×C₃×C₄	—	4	1	no	—
363	C₂²×C₃×C₄	—	4	1	no	—
364	C₂²×C₃×C₄	—	4	1	no	—
365	C₂²×C₃×C₄	—	4	1	no	—
366	C₂²×C₃×C₄	—	4	1	no	—
367	C₂²×C₃×C₄	—	4	1	no	—
368	C₂²×C₃×C₄	—	4	2	no	—
369	C₂²×C₃×C₄	—	4	2	no	—
370	C₂²×C₃×C₄	—	4	2	no	—
371	C₂²×C₃×C₄	—	4	2	no	—
372	C₂²×C₃×C₄	—	4	1	no	—
373	C₂²×C₃×C₄	—	4	1	no	—
374	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
375	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
376	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
377	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
378	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
379	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
380	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
381	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
382	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
383	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
384	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
385	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
386	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
387	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
388	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
389	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
390	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
391	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
392	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
393	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
394	C₃×C₄⋊C₄	—	2	4	no	—
395	C₃×C₄⋊C₄	—	2	4	no	—
396	C₃×C₄⋊C₄	—	2	4	no	—
397	C₃×C₄⋊C₄	—	2	4	no	—
398	C₃×C₄⋊C₄	—	2	4	no	—
399	C₃×C₄⋊C₄	—	2	4	no	—
400	C₃×C₄⋊C₄	—	2	2	no	—
401	C₃×C₄⋊C₄	—	2	2	no	—
402	C₃×C₄⋊C₄	—	2	4	no	—
403	C₃×C₄⋊C₄	—	2	4	no	—
404	C₃×C₄⋊C₄	—	2	4	no	—
405	C₃×C₄⋊C₄	—	2	4	no	—
406	C₃×C₄⋊C₄	—	2	4	no	—
407	C₃×C₄⋊C₄	—	2	4	no	—
408	C₃×C₄⋊C₄	—	4	2	no	—
409	C₃×C₄⋊C₄	—	4	2	no	—
410	C₃×C₄⋊C₄	—	4	1	no	—
411	C₃×C₄⋊C₄	—	4	1	no	—
412	C₃×C₄⋊C₄	—	4	2	no	—
413	C₃×C₄⋊C₄	—	4	2	no	—
414	C₃×C₄⋊C₄	—	4	2	no	—
415	C₃×C₄⋊C₄	—	4	2	no	—
416	C₃×C₄⋊C₄	—	4	2	no	—
417	C₃×C₄⋊C₄	—	4	2	no	—
418	C₃×C₄⋊C₄	—	4	2	no	—
419	C₃×C₄⋊C₄	—	4	2	no	—
420	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
421	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
422	C₃×C₂²⋊C₄	—	2	4	no	—
423	C₃×C₂²⋊C₄	—	2	4	no	—
424	C₃×C₂²⋊C₄	—	2	4	no	—
425	C₃×C₂²⋊C₄	—	2	4	no	—
426	C₃×C₂²⋊C₄	—	2	4	no	—
427	C₃×C₂²⋊C₄	—	2	4	no	—
428	C₃×C₂²⋊C₄	—	2	4	no	—
429	C₃×C₂²⋊C₄	—	2	4	no	—
430	C₃×C₂²⋊C₄	—	4	2	no	—
431	C₃×C₂²⋊C₄	—	4	2	no	—
432	C₃×C₂²⋊C₄	—	4	2	no	—
433	C₃×C₂²⋊C₄	—	4	2	no	—
434	C₃×C₂²⋊C₄	—	4	2	no	—
435	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
436	C₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
437	C₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
438	C₃×C₄²	—	2	2	no	—
439	C₃×C₄²	—	2	2	no	—
440	C₃×C₄²	—	2	2	no	—
441	C₃×C₄²	—	2	2	no	—
442	C₃×C₄²	—	2	4	no	—
443	C₃×C₄²	—	2	4	no	—
444	C₃×C₄²	—	4	2	no	—
445	C₃×C₄²	—	4	2	no	—
446	C₂⁵	C₂³×C₃	1	1	yes	characteristic
447	C₂²×Q₈	C₂³×C₃	1	2	yes	—
448	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
449	C₂²×Q₈	C₂³×C₃	1	2	yes	—
450	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
451	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
452	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
454	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
455	C₂³×C₄	C₂³×C₃	1	2	yes	—
456	C₂³×C₄	C₂³×C₃	1	2	yes	—
457	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
458	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
460	C₄⋊Q₈	—	2	4	no	—
461	C₄⋊Q₈	—	2	4	no	—
462	C₄⋊Q₈	—	4	4	no	—
463	#125	—	2	8	no	—
464	C₂²⋊Q₈	—	2	8	no	—
465	C₂²⋊Q₈	—	2	4	no	—
466	C₂²⋊Q₈	—	2	4	no	—
467	C₂²⋊Q₈	—	2	8	no	—
468	C₂²⋊Q₈	—	2	8	no	—
469	C₂²⋊Q₈	—	2	8	no	—
470	C₂²⋊Q₈	—	2	8	no	—
471	C₂²⋊Q₈	—	2	8	no	—
472	C₂²⋊Q₈	—	4	4	no	—
473	C₂²⋊Q₈	C₃×D₄	1	8	yes	—
474	C₄×Q₈	—	2	4	no	—
475	C₄×Q₈	—	2	4	no	—
476	C₄×Q₈	—	2	8	no	—
477	#117	—	2	8	no	—
478	C₂×C₄⋊C₄	—	4	2	no	—
479	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
507	C₂×C₂²⋊C₄	—	2	4	no	—
508	C₂×C₂²⋊C₄	—	2	8	no	—
509	C₂×C₂²⋊C₄	—	4	2	no	—
510	C₂×C₂²⋊C₄	C₃×Q₈	1	8	yes	complemented
511	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
527	C₂×C₄²	—	2	4	no	—
528	C₂×C₄²	C₂³×C₃	1	2	yes	—
529	C₂×C₄²	C₂³×C₃	1	2	yes	—
530	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
533	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
534	C₂×C₄²	C₂³×C₃	1	2	yes	—
535	C₂×C₄²	C₂³×C₃	1	2	yes	—
536	#95	C₂³×C₃	1	2	yes	—
537	#95	C₂³×C₃	1	2	yes	—
538	#95	C₂³×C₃	1	2	yes	—
539	#95	C₂³×C₃	1	2	yes	—
540	#95	C₂³×C₃	1	2	yes	—
541	#95	C₂³×C₃	1	2	yes	—
542	#95	C₂³×C₃	1	2	yes	—
543	#95	C₂³×C₃	1	2	yes	—
544	#95	C₂³×C₃	1	2	yes	—
545	#95	C₂³×C₃	1	2	yes	—
546	#95	C₂³×C₃	1	2	yes	—
547	#95	C₂³×C₃	1	2	yes	—
548	#95	C₂³×C₃	1	2	yes	—
549	#95	C₂³×C₃	1	2	yes	—
550	#95	C₂³×C₃	1	2	yes	—
551	#95	C₂³×C₃	1	2	yes	—
552	#95	C₂³×C₃	1	2	yes	—
553	#95	C₂³×C₃	1	2	yes	—
554	#95	C₂³×C₃	1	2	yes	—
555	#95	C₂³×C₃	1	2	yes	—
556	#95	C₂³×C₃	1	2	yes	—
557	C₂³×C₃	—	2	1	no	—
558	C₂³×C₃	—	2	1	no	—
559	C₂³×C₃	—	2	1	no	—
560	C₂³×C₃	—	2	1	no	—
561	C₂³×C₃	—	2	2	no	—
562	C₂³×C₃	—	2	2	no	—
563	C₂³×C₃	—	2	2	no	—
564	C₂³×C₃	—	2	2	no	—
565	C₂³×C₃	—	2	2	no	—
566	C₂³×C₃	—	2	2	no	—
567	C₂³×C₃	—	2	8	no	—
568	C₂³×C₃	—	4	4	no	—
569	C₂³×C₃	—	4	4	no	—
570	C₂³×C₃	—	8	2	no	—
571	C₂³×C₃	—	8	2	no	—
572	C₂³×C₃	—	8	2	no	—
573	C₂³×C₃	—	8	2	no	—
574	C₂³×C₃	C₂²×D₄	1	2	yes	—
575	C₂³×C₃	C₂²×Q₈	1	4	yes	—
576	C₂³×C₃	C₂²×Q₈	1	2	yes	—
577	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
578	C₂³×C₃	C₂⁵	1	1	yes	characteristic
579	C₃×Q₈	—	4	4	no	—
580	C₃×Q₈	—	4	8	no	—
581	C₃×Q₈	—	4	4	no	—
582	C₃×Q₈	—	8	2	no	—
583	C₃×Q₈	—	8	4	no	—
584	C₂×C₃×C₄	—	2	8	no	—
585	C₂×C₃×C₄	—	2	1	no	—
586	C₂×C₃×C₄	—	2	1	no	—
587	C₂×C₃×C₄	—	2	1	no	—
588	C₂×C₃×C₄	—	2	2	no	—
589	C₂×C₃×C₄	—	2	2	no	—
590	C₂×C₃×C₄	—	2	1	no	—
591	C₂×C₃×C₄	—	2	1	no	—
592	C₂×C₃×C₄	—	2	2	no	—
593	C₂×C₃×C₄	—	2	2	no	—
594	C₂×C₃×C₄	—	2	1	no	—
595	C₂×C₃×C₄	—	2	1	no	—
596	C₂×C₃×C₄	—	2	2	no	—
597	C₂×C₃×C₄	—	2	1	no	—
598	C₂×C₃×C₄	—	2	1	no	—
599	C₂×C₃×C₄	—	2	1	no	—
600	C₂×C₃×C₄	—	2	2	no	—
601	C₂×C₃×C₄	—	2	1	no	—
602	C₂×C₃×C₄	—	2	2	no	—
603	C₂×C₃×C₄	—	2	2	no	—
604	C₂×C₃×C₄	—	2	2	no	—
605	C₂×C₃×C₄	—	2	2	no	—
606	C₂×C₃×C₄	—	2	2	no	—
607	C₂×C₃×C₄	—	2	2	no	—
608	C₂×C₃×C₄	—	2	2	no	—
609	C₂×C₃×C₄	—	2	1	no	—
610	C₂×C₃×C₄	—	2	2	no	—
611	C₂×C₃×C₄	—	2	2	no	—
612	C₂×C₃×C₄	—	2	2	no	—
613	C₂×C₃×C₄	—	2	2	no	—
614	C₂×C₃×C₄	—	2	2	no	—
615	C₂×C₃×C₄	—	2	2	no	—
616	C₂×C₃×C₄	—	2	2	no	—
617	C₂×C₃×C₄	—	2	2	no	—
618	C₂×C₃×C₄	—	2	2	no	—
619	C₂×C₃×C₄	—	2	2	no	—
620	C₂×C₃×C₄	—	2	2	no	—
621	C₂×C₃×C₄	—	2	2	no	—
622	C₂×C₃×C₄	—	2	1	no	—
623	C₂×C₃×C₄	—	2	2	no	—
624	C₂×C₃×C₄	—	2	2	no	—
625	C₂×C₃×C₄	—	2	2	no	—
626	C₂×C₃×C₄	—	2	2	no	—
627	C₂×C₃×C₄	—	2	2	no	—
628	C₂×C₃×C₄	—	4	4	no	—
629	C₂×C₃×C₄	—	4	4	no	—
630	C₂×C₃×C₄	—	4	4	no	—
631	C₂×C₃×C₄	—	8	4	no	—
632	C₂×C₃×C₄	—	8	4	no	—
633	C₂×C₃×C₄	—	8	2	no	—
634	C₂×C₃×C₄	—	8	2	no	—
635	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
636	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
637	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
638	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
639	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
640	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
641	C₂×C₃×C₄	C₂²×Q₈	1	4	yes	—
642	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
643	C₂⁴	—	2	2	no	—
644	C₂⁴	—	2	2	no	—
645	C₂⁴	—	4	1	no	—
646	C₂⁴	—	4	1	no	—
647	C₂⁴	—	4	1	no	—
648	C₂⁴	—	4	1	no	—
649	C₂⁴	C₂×C₃×Q₈	1	4	yes	—
650	C₂⁴	C₂⁴×C₃	1	2	yes	—
651	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
652	C₂×Q₈	—	2	4	no	—
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	4	no	—
656	C₂×Q₈	—	2	4	no	—
657	C₂×Q₈	—	4	1	no	—
658	C₂×Q₈	—	4	1	no	—
659	C₂×Q₈	—	4	2	no	—
660	C₂×Q₈	—	4	1	no	—
661	C₂×Q₈	—	4	1	no	—
662	C₂×Q₈	—	4	2	no	—
663	C₂×Q₈	—	4	1	no	—
664	C₂×Q₈	—	4	1	no	—
665	C₂×Q₈	—	4	2	no	—
666	C₂×Q₈	C₂×C₃×D₄	1	4	yes	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	2	4	no	—
675	C₂²×C₄	—	4	1	no	—
676	C₂²×C₄	—	4	1	no	—
677	C₂²×C₄	—	4	1	no	—
678	C₂²×C₄	—	4	1	no	—
679	C₂²×C₄	—	4	1	no	—
680	C₂²×C₄	—	4	1	no	—
681	C₂²×C₄	—	4	1	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	—	4	2	no	—
684	C₂²×C₄	—	4	2	no	—
685	C₂²×C₄	—	4	2	no	—
686	C₂²×C₄	—	4	1	no	—
687	C₂²×C₄	—	4	1	no	—
688	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
689	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
690	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
691	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	4	2	no	—
723	C₄⋊C₄	—	4	2	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	—	4	2	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	1	no	—
729	C₄⋊C₄	—	4	1	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
735	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	4	2	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	—	4	2	no	—
747	C₂²⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
750	C₂²⋊C₄	C₂×C₃×Q₈	1	8	yes	—
751	C₂²⋊C₄	C₂×C₃×Q₈	1	8	yes	—
752	C₄²	—	2	2	no	—
753	C₄²	—	2	2	no	—
754	C₄²	—	2	2	no	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	4	no	—
757	C₄²	—	2	4	no	—
758	C₄²	—	4	2	no	—
759	C₄²	—	4	2	no	—
760	C₂²×C₃	—	2	2	no	—
761	C₂²×C₃	—	2	2	no	—
762	C₂²×C₃	—	2	2	no	—
763	C₂²×C₃	—	2	2	no	—
764	C₂²×C₃	—	2	2	no	—
765	C₂²×C₃	—	2	2	no	—
766	C₂²×C₃	—	2	4	no	—
767	C₂²×C₃	—	2	4	no	—
768	C₂²×C₃	—	2	4	no	—
769	C₂²×C₃	—	4	2	no	—
770	C₂²×C₃	—	4	2	no	—
771	C₂²×C₃	—	4	2	no	—
772	C₂²×C₃	—	4	2	no	—
773	C₂²×C₃	—	8	8	no	—
774	C₂²×C₃	D₄×Q₈	1	4	yes	—
775	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
776	C₂²×C₃	C₂³×Q₈	1	1	yes	characteristic
777	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
778	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
779	C₂²×C₃	#585	1	1	yes	characteristic
780	C₂²×C₃	#585	1	1	yes	characteristic
781	C₂²×C₃	#585	1	1	yes	characteristic
782	C₃×C₄	—	2	2	no	—
783	C₃×C₄	—	2	2	no	—
784	C₃×C₄	—	2	2	no	—
785	C₃×C₄	—	2	2	no	—
786	C₃×C₄	—	2	4	no	—
787	C₃×C₄	—	2	2	no	—
788	C₃×C₄	—	2	4	no	—
789	C₃×C₄	—	2	4	no	—
790	C₃×C₄	—	4	2	no	—
791	C₃×C₄	—	4	2	no	—
792	C₃×C₄	—	4	1	no	—
793	C₃×C₄	—	4	2	no	—
794	C₃×C₄	—	4	2	no	—
795	C₃×C₄	—	4	2	no	—
796	C₃×C₄	—	4	2	no	—
797	C₃×C₄	—	4	2	no	—
798	C₃×C₄	—	4	2	no	—
799	C₂³	—	2	1	no	—
800	C₂³	—	2	1	no	—
801	C₂³	—	2	1	no	—
802	C₂³	—	2	1	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	8	no	—
810	C₂³	—	4	4	no	—
811	C₂³	—	4	4	no	—
812	C₂³	—	8	2	no	—
813	C₂³	—	8	2	no	—
814	C₂³	—	8	2	no	—
815	C₂³	—	8	2	no	—
816	C₂³	C₂²×C₃×D₄	1	2	yes	—
817	C₂³	C₂²×C₃×Q₈	1	4	yes	—
818	C₂³	C₂²×C₃×Q₈	1	2	yes	—
819	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
820	C₂³	C₂⁵×C₃	1	1	yes	characteristic
821	Q₈	—	4	4	no	—
822	Q₈	—	4	8	no	—
823	Q₈	—	4	4	no	—
824	Q₈	—	8	2	no	—
825	Q₈	—	8	4	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	8	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	4	4	no	—
871	C₂×C₄	—	4	4	no	—
872	C₂×C₄	—	4	4	no	—
873	C₂×C₄	—	8	4	no	—
874	C₂×C₄	—	8	4	no	—
875	C₂×C₄	—	8	2	no	—
876	C₂×C₄	—	8	2	no	—
877	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
878	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
879	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
880	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
881	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
882	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
883	C₂×C₄	C₂²×C₃×Q₈	1	4	yes	—
884	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
885	C₂×C₃	—	2	4	no	—
886	C₂×C₃	—	4	4	no	—
887	C₂×C₃	#3458	1	1	yes	characteristic
888	C₂×C₃	C₂×D₄×Q₈	1	1	yes	characteristic
889	C₂×C₃	#3485	1	1	yes	characteristic
890	C₂×C₃	#3488	1	1	yes	characteristic
891	C₂×C₃	#3501	1	1	yes	characteristic
892	C₂×C₃	#3561	1	1	yes	characteristic
893	C₂×C₃	#3564	1	1	yes	characteristic
894	C₂²	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	2	no	—
898	C₂²	—	2	2	no	—
899	C₂²	—	2	2	no	—
900	C₂²	—	2	4	no	—
901	C₂²	—	2	4	no	—
902	C₂²	—	2	4	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	8	8	no	—
908	C₂²	C₃×D₄×Q₈	1	4	yes	—
909	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
910	C₂²	C₂³×C₃×Q₈	1	1	yes	characteristic
911	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
912	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
913	C₂²	C₃×#585	1	1	yes	characteristic
914	C₂²	C₃×#585	1	1	yes	characteristic
915	C₂²	C₃×#585	1	1	yes	characteristic
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	2	4	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	4	no	—
923	C₄	—	2	4	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	1	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	2	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	2	no	—
933	C₃	#37688	1	1	yes	characteristic, direct product factor, Sylow
934	C₂	—	2	4	no	—
935	C₂	—	4	4	no	—
936	C₂	C₃×#3458	1	1	yes	characteristic
937	C₂	C₂×C₃×D₄×Q₈	1	1	yes	characteristic
938	C₂	C₃×#3485	1	1	yes	characteristic
939	C₂	C₃×#3488	1	1	yes	characteristic
940	C₂	C₃×#3501	1	1	yes	characteristic
941	C₂	C₃×#3561	1	1	yes	characteristic
942	C₂	C₃×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂⁵×C₃	C₂³
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
2. C₂×C₃×#533	C₂	semidirect
3. C₃×#2855	C₂	semidirect
4. C₃×#2729	C₂	semidirect
5. C₃×#2720	C₂	semidirect
6. C₃×#2704	C₂	semidirect
7. C₃×#2677	C₂	semidirect
8. C₃×#2659	C₂	semidirect
10. C₃×#2465	C₂	semidirect
11. C₃×#2465	C₂	semidirect
12. C₃×#2440	C₂	semidirect
13. C₃×#2438	C₂	semidirect
15. C₃×#2429	C₂	semidirect
16. C₃×#2423	C₂	semidirect
18. C₃×#2329	C₂	semidirect
20. #37688	C₃	direct (N × H)
23. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
24. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
25. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
26. C₂×C₃×#125	C₂²	semidirect
37. C₂×C₃×C₄×Q₈	C₂²	semidirect
38. C₂×C₃×C₄×Q₈	C₂²	semidirect
39. C₂×C₃×C₄×Q₈	C₂²	semidirect
47. C₃×#400	C₂²	semidirect
50. C₃×#398	C₂²	semidirect
51. C₃×#398	C₂²	semidirect
52. C₃×#398	C₂²	semidirect
53. C₃×#398	C₂²	semidirect
54. C₃×#398	C₂²	semidirect
55. C₃×#398	C₂²	semidirect
60. C₃×#395	C₂²	semidirect
61. C₃×#395	C₂²	semidirect
62. C₃×#395	C₂²	semidirect
63. C₃×#395	C₂²	semidirect
64. C₃×#395	C₂²	semidirect
67. C₃×#391	C₂²	semidirect
68. C₃×#391	C₂²	semidirect
69. C₃×#391	C₂²	semidirect
70. C₃×#391	C₂²	semidirect
71. C₃×#389	C₂²	semidirect
72. C₃×#389	C₂²	semidirect
73. C₃×#389	C₂²	semidirect
74. C₃×#389	C₂²	semidirect
75. C₃×#389	C₂²	semidirect
76. C₃×#389	C₂²	semidirect
85. C₃×#387	C₂²	semidirect
86. C₃×#387	C₂²	semidirect
87. C₃×#387	C₂²	semidirect
88. C₃×#387	C₂²	semidirect
89. C₃×#387	C₂²	semidirect
90. C₃×#387	C₂²	semidirect
98. C₃×#384	C₂²	semidirect
111. C₂×#533	C₂×C₃	semidirect
112. #2855	C₂×C₃	semidirect
113. #2729	C₂×C₃	semidirect
114. #2720	C₂×C₃	semidirect
115. #2704	C₂×C₃	semidirect
116. #2677	C₂×C₃	semidirect
117. #2659	C₂×C₃	semidirect
119. #2465	C₂×C₃	semidirect
120. #2465	C₂×C₃	semidirect
121. #2440	C₂×C₃	semidirect
122. #2438	C₂×C₃	semidirect
124. #2429	C₂×C₃	semidirect
125. #2423	C₂×C₃	semidirect
127. #2329	C₂×C₃	semidirect
193. C₂×C₃×C₂²⋊C₄	Q₈	semidirect
242. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
243. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
244. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
245. C₂×#125	C₂²×C₃	semidirect
256. C₂×C₄×Q₈	C₂²×C₃	semidirect
257. C₂×C₄×Q₈	C₂²×C₃	semidirect
258. C₂×C₄×Q₈	C₂²×C₃	semidirect
266. #400	C₂²×C₃	semidirect
269. #398	C₂²×C₃	semidirect
270. #398	C₂²×C₃	semidirect
271. #398	C₂²×C₃	semidirect
272. #398	C₂²×C₃	semidirect
273. #398	C₂²×C₃	semidirect
274. #398	C₂²×C₃	semidirect
279. #395	C₂²×C₃	semidirect
280. #395	C₂²×C₃	semidirect
281. #395	C₂²×C₃	semidirect
282. #395	C₂²×C₃	semidirect
283. #395	C₂²×C₃	semidirect
286. #391	C₂²×C₃	semidirect
287. #391	C₂²×C₃	semidirect
288. #391	C₂²×C₃	semidirect
289. #391	C₂²×C₃	semidirect
290. #389	C₂²×C₃	semidirect
291. #389	C₂²×C₃	semidirect
292. #389	C₂²×C₃	semidirect
293. #389	C₂²×C₃	semidirect
294. #389	C₂²×C₃	semidirect
295. #389	C₂²×C₃	semidirect
304. #387	C₂²×C₃	semidirect
305. #387	C₂²×C₃	semidirect
306. #387	C₂²×C₃	semidirect
307. #387	C₂²×C₃	semidirect
308. #387	C₂²×C₃	semidirect
309. #387	C₂²×C₃	semidirect
317. #384	C₂²×C₃	semidirect
510. C₂×C₂²⋊C₄	C₃×Q₈	semidirect
933. C₃	#37688	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×#543	2
C₂×C₃×#533	2
C₃×#2855	2
C₃×#2729	2
C₃×#2720	2
C₃×#2704	2
C₃×#2677	2
C₃×#2659	2
C₃×#2626	2
C₃×#2465	2
C₃×#2440	2
C₃×#2438	2
C₃×#2437	2
C₃×#2429	2
C₃×#2423	2
C₃×#2342	2
C₃×#2329	2
C₂×C₃×#388	2
#37688	3

Subgroups — C3×#37688 #10656295

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37688 #10656295