Subgroups — C₃×#35731 #10654338

Order 768.

2054 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2651	C₂	1	2	yes	maximal, complemented
2	C₃×#2627	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2595	C₂	1	2	yes	maximal, complemented
4	C₃×#2593	C₂	1	2	yes	maximal, complemented
5	C₃×#2569	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2521	C₂	1	2	yes	maximal, complemented
7	C₃×#2516	C₂	1	2	yes	maximal, complemented
8	C₃×#2482	C₂	1	2	yes	maximal, complemented
9	C₃×#2480	C₂	1	2	yes	maximal, complemented
10	C₃×#2474	C₂	1	2	yes	maximal, complemented
11	C₃×#2468	C₂	1	2	yes	maximal, complemented
12	C₃×#2435	C₂	1	1	yes	maximal, characteristic
13	C₃×#2395	C₂	1	2	yes	maximal, complemented
14	C₂×C₃×#394	C₂	1	1	yes	maximal, characteristic
15	C₃×#2368	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2342	C₂	1	2	yes	maximal, complemented
17	C₃×#2342	C₂	1	2	yes	maximal, complemented
18	C₃×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
19	C₃×#2274	C₂	1	1	yes	maximal, characteristic, complemented
20	#35731	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×#126	C₂²	1	2	yes	complemented
23	C₂×C₃×#124	C₂²	1	2	yes	—
24	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
26	C₂×C₃×#117	C₂²	1	1	yes	characteristic
27	C₂×C₃×#117	C₂²	1	1	yes	characteristic
28	C₂×C₃×#117	C₂²	1	2	yes	complemented
29	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₃×#400	C₂²	1	1	yes	characteristic, complemented
34	C₃×#400	C₂²	1	1	yes	characteristic, complemented
35	C₃×#400	C₂²	1	2	yes	complemented
36	C₃×#399	C₂²	1	2	yes	complemented
37	C₃×#399	C₂²	1	2	yes	complemented
38	C₃×#398	C₂²	1	2	yes	complemented
39	C₃×#398	C₂²	1	2	yes	complemented
40	C₃×#398	C₂²	1	2	yes	complemented
41	C₃×#397	C₂²	1	2	yes	complemented
42	C₃×#397	C₂²	1	2	yes	complemented
43	C₃×#397	C₂²	1	2	yes	complemented
44	C₃×#397	C₂²	1	2	yes	complemented
45	C₃×#397	C₂²	1	2	yes	complemented
46	C₃×#396	C₂²	1	2	yes	complemented
47	C₃×#395	C₂²	1	1	yes	characteristic, complemented
48	C₃×#395	C₂²	1	1	yes	characteristic, complemented
49	C₃×#394	C₂²	1	1	yes	characteristic
50	C₃×#394	C₂²	1	1	yes	characteristic
51	C₃×#394	C₂²	1	1	yes	characteristic
52	C₃×#394	C₂²	1	2	yes	—
53	C₃×#394	C₂²	1	2	yes	—
54	C₃×#394	C₂²	1	1	yes	characteristic
55	C₃×#394	C₂²	1	2	yes	—
56	C₃×#394	C₂²	1	2	yes	—
57	C₃×#391	C₂²	1	2	yes	complemented
58	C₃×#390	C₂²	1	2	yes	—
59	C₃×#390	C₂²	1	2	yes	—
60	C₃×#388	C₂²	1	2	yes	complemented
61	C₃×#388	C₂²	1	2	yes	complemented
62	C₃×#388	C₂²	1	2	yes	complemented
63	C₃×#388	C₂²	1	2	yes	complemented
64	C₃×#388	C₂²	1	2	yes	complemented
65	C₃×#388	C₂²	1	2	yes	complemented
66	C₃×#388	C₂²	1	2	yes	complemented
67	C₃×#388	C₂²	1	2	yes	complemented
68	C₃×#388	C₂²	1	2	yes	complemented
69	C₃×#388	C₂²	1	2	yes	complemented
70	C₃×#388	C₂²	1	2	yes	complemented
71	C₃×#388	C₂²	1	2	yes	complemented
72	C₃×#388	C₂²	1	2	yes	complemented
73	C₃×#388	C₂²	1	2	yes	complemented
74	C₃×#388	C₂²	1	2	yes	complemented
75	C₃×#387	C₂²	1	2	yes	complemented
76	C₃×#387	C₂²	1	2	yes	complemented
77	C₃×#387	C₂²	1	2	yes	complemented
78	C₃×#387	C₂²	1	2	yes	complemented
79	C₃×#386	C₂²	1	2	yes	—
80	C₃×#386	C₂²	1	2	yes	—
81	C₃×#385	C₂²	1	2	yes	—
82	C₃×#385	C₂²	1	2	yes	—
83	C₃×#385	C₂²	1	2	yes	—
84	C₃×#385	C₂²	1	2	yes	complemented
85	C₃×#385	C₂²	1	2	yes	complemented
86	C₃×#381	C₂²	1	2	yes	—
87	C₃×#381	C₂²	1	2	yes	complemented
88	C₃×#380	C₂²	1	1	yes	characteristic
89	C₃×#380	C₂²	1	2	yes	—
90	C₃×#380	C₂²	1	2	yes	complemented
91	C₃×#379	C₂²	1	2	yes	—
92	C₃×#379	C₂²	1	2	yes	—
93	C₃×#379	C₂²	1	2	yes	—
94	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
95	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
96	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
97	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
98	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
99	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
100	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
102	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
103	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
104	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
105	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
106	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
107	C₂×C₃×#95	C₂²	1	1	yes	characteristic
108	#2651	C₂×C₃	1	2	yes	complemented
109	#2627	C₂×C₃	1	1	yes	characteristic, complemented
110	#2595	C₂×C₃	1	2	yes	complemented
111	#2593	C₂×C₃	1	2	yes	complemented
112	#2569	C₂×C₃	1	1	yes	characteristic, complemented
113	#2521	C₂×C₃	1	2	yes	complemented
114	#2516	C₂×C₃	1	2	yes	complemented
115	#2482	C₂×C₃	1	2	yes	complemented
116	#2480	C₂×C₃	1	2	yes	complemented
117	#2474	C₂×C₃	1	2	yes	complemented
118	#2468	C₂×C₃	1	2	yes	complemented
119	#2435	C₂×C₃	1	1	yes	characteristic
120	#2395	C₂×C₃	1	2	yes	complemented
121	C₂×#394	C₂×C₃	1	1	yes	characteristic
122	#2368	C₂×C₃	1	1	yes	characteristic, complemented
123	#2342	C₂×C₃	1	2	yes	complemented
124	#2342	C₂×C₃	1	2	yes	complemented
125	D₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
126	#2274	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂⁵×C₃	C₂³	1	2	yes	—
128	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
129	C₂²×C₃×D₄	—	2	4	no	—
130	C₂²×C₃×D₄	—	4	4	no	—
131	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
132	C₂²×C₃×D₄	C₂³	1	2	yes	—
133	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
134	C₂³×C₃×C₄	C₂³	1	2	yes	—
135	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
136	C₂³×C₃×C₄	C₂³	1	2	yes	—
137	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
138	C₂³×C₃×C₄	C₂³	1	2	yes	—
139	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
140	C₃×#126	—	4	4	no	—
141	C₃×#124	—	4	4	no	—
142	C₃×C₂²⋊Q₈	—	2	4	no	—
143	C₃×C₄×D₄	—	4	4	no	—
144	C₃×#117	—	2	4	no	—
145	C₃×#117	—	2	4	no	—
146	C₃×#117	—	4	4	no	—
147	C₂×C₃×C₄⋊C₄	—	2	4	no	—
148	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
152	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
164	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
166	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
167	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
168	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
177	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₃×C₄²	C₂³	1	2	yes	—
197	C₂×C₃×C₄²	C₂³	1	2	yes	—
198	C₂×C₃×C₄²	C₂³	1	2	yes	—
199	C₂×C₃×C₄²	C₂³	1	2	yes	—
200	C₂×C₃×C₄²	C₂³	1	2	yes	—
201	C₂×C₃×C₄²	C₂³	1	2	yes	—
202	C₂×C₃×C₄²	C₂³	1	2	yes	—
203	C₂×C₃×C₄²	C₂³	1	2	yes	—
204	C₃×#95	C₂³	1	1	yes	characteristic
205	C₃×#95	C₂³	1	2	yes	—
206	C₃×#95	C₂³	1	1	yes	characteristic
207	C₃×#95	C₂³	1	2	yes	—
208	C₃×#95	C₂³	1	2	yes	—
209	C₃×#95	C₂³	1	2	yes	—
210	C₃×#95	C₂³	1	2	yes	—
211	C₃×#95	C₂³	1	2	yes	—
212	C₃×#95	C₂³	1	2	yes	—
213	C₃×#95	C₂³	1	2	yes	—
214	C₃×#95	C₂³	1	2	yes	—
215	C₃×#95	C₂³	1	2	yes	—
216	C₃×#95	C₂³	1	2	yes	—
217	C₃×#95	C₂³	1	2	yes	—
218	C₃×#95	C₂³	1	2	yes	—
219	C₃×#95	C₂³	1	2	yes	—
220	C₃×#95	C₂³	1	1	yes	characteristic
221	C₃×#95	C₂³	1	1	yes	characteristic
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	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
228	C₂×#126	C₂²×C₃	1	2	yes	complemented
229	C₂×#124	C₂²×C₃	1	2	yes	—
230	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
231	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
232	C₂×#117	C₂²×C₃	1	1	yes	characteristic
233	C₂×#117	C₂²×C₃	1	1	yes	characteristic
234	C₂×#117	C₂²×C₃	1	2	yes	complemented
235	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
236	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
237	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
238	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
239	#400	C₂²×C₃	1	2	yes	complemented
240	#400	C₂²×C₃	1	1	yes	characteristic, complemented
241	#400	C₂²×C₃	1	1	yes	characteristic, complemented
242	#399	C₂²×C₃	1	2	yes	complemented
243	#399	C₂²×C₃	1	2	yes	complemented
244	#398	C₂²×C₃	1	2	yes	complemented
245	#398	C₂²×C₃	1	2	yes	complemented
246	#398	C₂²×C₃	1	2	yes	complemented
247	#397	C₂²×C₃	1	2	yes	complemented
248	#397	C₂²×C₃	1	2	yes	complemented
249	#397	C₂²×C₃	1	2	yes	complemented
250	#397	C₂²×C₃	1	2	yes	complemented
251	#397	C₂²×C₃	1	2	yes	complemented
252	#396	C₂²×C₃	1	2	yes	complemented
253	#395	C₂²×C₃	1	1	yes	characteristic, complemented
254	#395	C₂²×C₃	1	1	yes	characteristic, complemented
255	#394	C₂²×C₃	1	1	yes	characteristic
256	#394	C₂²×C₃	1	2	yes	—
257	#394	C₂²×C₃	1	2	yes	—
258	#394	C₂²×C₃	1	1	yes	characteristic
259	#394	C₂²×C₃	1	1	yes	characteristic
260	#394	C₂²×C₃	1	1	yes	characteristic
261	#394	C₂²×C₃	1	2	yes	—
262	#394	C₂²×C₃	1	2	yes	—
263	#391	C₂²×C₃	1	2	yes	complemented
264	#390	C₂²×C₃	1	2	yes	—
265	#390	C₂²×C₃	1	2	yes	—
266	#388	C₂²×C₃	1	2	yes	complemented
267	#388	C₂²×C₃	1	2	yes	complemented
268	#388	C₂²×C₃	1	2	yes	complemented
269	#388	C₂²×C₃	1	2	yes	complemented
270	#388	C₂²×C₃	1	2	yes	complemented
271	#388	C₂²×C₃	1	2	yes	complemented
272	#388	C₂²×C₃	1	2	yes	complemented
273	#388	C₂²×C₃	1	2	yes	complemented
274	#388	C₂²×C₃	1	2	yes	complemented
275	#388	C₂²×C₃	1	2	yes	complemented
276	#388	C₂²×C₃	1	2	yes	complemented
277	#388	C₂²×C₃	1	2	yes	complemented
278	#388	C₂²×C₃	1	2	yes	complemented
279	#388	C₂²×C₃	1	2	yes	complemented
280	#388	C₂²×C₃	1	2	yes	complemented
281	#387	C₂²×C₃	1	2	yes	complemented
282	#387	C₂²×C₃	1	2	yes	complemented
283	#387	C₂²×C₃	1	2	yes	complemented
284	#387	C₂²×C₃	1	2	yes	complemented
285	#386	C₂²×C₃	1	2	yes	—
286	#386	C₂²×C₃	1	2	yes	—
287	#385	C₂²×C₃	1	2	yes	—
288	#385	C₂²×C₃	1	2	yes	—
289	#385	C₂²×C₃	1	2	yes	—
290	#385	C₂²×C₃	1	2	yes	complemented
291	#385	C₂²×C₃	1	2	yes	complemented
292	#381	C₂²×C₃	1	2	yes	—
293	#381	C₂²×C₃	1	2	yes	complemented
294	#380	C₂²×C₃	1	1	yes	characteristic
295	#380	C₂²×C₃	1	2	yes	—
296	#380	C₂²×C₃	1	2	yes	complemented
297	#379	C₂²×C₃	1	2	yes	—
298	#379	C₂²×C₃	1	2	yes	—
299	#379	C₂²×C₃	1	2	yes	—
300	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
301	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
302	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
303	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
304	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
305	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
306	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
307	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
308	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
309	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
310	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
311	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
312	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
313	C₂×#95	C₂²×C₃	1	1	yes	characteristic
314	C₂⁴×C₃	—	2	4	no	—
315	C₂⁴×C₃	—	2	4	no	—
316	C₂⁴×C₃	—	2	4	no	—
317	C₂⁴×C₃	—	2	4	no	—
318	C₂⁴×C₃	—	4	2	no	—
319	C₂⁴×C₃	—	4	2	no	—
320	C₂⁴×C₃	—	4	2	no	—
321	C₂⁴×C₃	C₂⁴	1	2	yes	—
322	C₂⁴×C₃	C₂⁴	1	2	yes	—
323	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
324	C₂×C₃×Q₈	—	2	2	no	—
325	C₂×C₃×Q₈	—	4	2	no	—
326	C₂×C₃×D₄	—	2	4	no	—
327	C₂×C₃×D₄	—	2	4	no	—
328	C₂×C₃×D₄	—	2	2	no	—
329	C₂×C₃×D₄	—	2	2	no	—
330	C₂×C₃×D₄	—	2	4	no	—
331	C₂×C₃×D₄	—	4	2	no	—
332	C₂×C₃×D₄	—	4	2	no	—
333	C₂×C₃×D₄	—	4	16	no	—
334	C₂²×C₃×C₄	—	2	2	no	—
335	C₂²×C₃×C₄	—	2	2	no	—
336	C₂²×C₃×C₄	—	2	4	no	—
337	C₂²×C₃×C₄	—	2	4	no	—
338	C₂²×C₃×C₄	—	2	2	no	—
339	C₂²×C₃×C₄	—	2	4	no	—
340	C₂²×C₃×C₄	—	2	4	no	—
341	C₂²×C₃×C₄	—	4	2	no	—
342	C₂²×C₃×C₄	—	4	2	no	—
343	C₂²×C₃×C₄	—	4	2	no	—
344	C₂²×C₃×C₄	—	4	2	no	—
345	C₂²×C₃×C₄	—	4	2	no	—
346	C₂²×C₃×C₄	—	4	2	no	—
347	C₂²×C₃×C₄	—	4	2	no	—
348	C₂²×C₃×C₄	#41	1	4	yes	—
349	C₂²×C₃×C₄	#41	1	4	yes	—
350	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
351	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
352	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
353	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
354	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
355	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
356	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
357	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
358	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
359	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
360	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
361	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
362	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
363	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
364	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
365	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
366	C₃×C₄⋊C₄	—	2	2	no	—
367	C₃×C₄⋊C₄	—	2	2	no	—
368	C₃×C₄⋊C₄	—	2	2	no	—
369	C₃×C₄⋊C₄	—	2	2	no	—
370	C₃×C₄⋊C₄	—	2	4	no	—
371	C₃×C₄⋊C₄	—	2	4	no	—
372	C₃×C₄⋊C₄	—	2	2	no	—
373	C₃×C₄⋊C₄	—	2	4	no	—
374	C₃×C₄⋊C₄	—	4	2	no	—
375	C₃×C₄⋊C₄	—	4	2	no	—
376	C₃×C₄⋊C₄	—	4	2	no	—
377	C₃×C₄⋊C₄	—	4	2	no	—
378	C₃×C₄⋊C₄	—	4	2	no	—
379	C₃×C₄⋊C₄	—	4	2	no	—
380	C₃×C₄⋊C₄	—	4	2	no	—
381	C₃×C₄⋊C₄	—	4	2	no	—
382	C₃×C₄⋊C₄	—	4	2	no	—
383	C₃×C₂²⋊C₄	—	2	4	no	—
384	C₃×C₂²⋊C₄	—	2	2	no	—
385	C₃×C₂²⋊C₄	—	2	2	no	—
386	C₃×C₂²⋊C₄	—	2	2	no	—
387	C₃×C₂²⋊C₄	—	2	4	no	—
388	C₃×C₂²⋊C₄	—	2	4	no	—
389	C₃×C₂²⋊C₄	—	2	4	no	—
390	C₃×C₂²⋊C₄	—	2	4	no	—
391	C₃×C₂²⋊C₄	—	2	4	no	—
392	C₃×C₂²⋊C₄	—	2	4	no	—
393	C₃×C₂²⋊C₄	—	2	4	no	—
394	C₃×C₂²⋊C₄	—	2	4	no	—
395	C₃×C₂²⋊C₄	—	2	4	no	—
396	C₃×C₂²⋊C₄	—	2	4	no	—
397	C₃×C₂²⋊C₄	—	2	4	no	—
398	C₃×C₂²⋊C₄	—	2	4	no	—
399	C₃×C₂²⋊C₄	—	4	2	no	—
400	C₃×C₂²⋊C₄	—	4	2	no	—
401	C₃×C₂²⋊C₄	—	4	2	no	—
402	C₃×C₂²⋊C₄	—	4	2	no	—
403	C₃×C₂²⋊C₄	—	4	2	no	—
404	C₃×C₂²⋊C₄	—	4	2	no	—
405	C₃×C₂²⋊C₄	—	4	2	no	—
406	C₃×C₂²⋊C₄	—	4	2	no	—
407	C₃×C₂²⋊C₄	—	4	2	no	—
408	C₃×C₂²⋊C₄	—	4	2	no	—
409	C₃×C₂²⋊C₄	—	4	2	no	—
410	C₃×C₂²⋊C₄	#41	1	4	yes	—
411	C₃×C₄²	—	2	4	no	—
412	C₃×C₄²	—	2	4	no	—
413	C₃×C₄²	—	4	2	no	—
414	C₃×C₄²	—	4	2	no	—
415	C₃×C₄²	—	4	2	no	—
416	C₃×C₄²	—	4	2	no	—
417	C₃×C₄²	—	4	2	no	—
418	C₃×C₄²	—	4	2	no	—
419	C₂⁵	C₂³×C₃	1	2	yes	—
420	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
421	C₂²×D₄	—	2	4	no	—
422	C₂²×D₄	—	4	4	no	—
423	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
424	C₂²×D₄	C₂³×C₃	1	2	yes	—
425	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
426	C₂³×C₄	C₂³×C₃	1	2	yes	—
427	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
429	C₂³×C₄	C₂³×C₃	1	2	yes	—
430	C₂³×C₄	C₂³×C₃	1	2	yes	—
431	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
432	#126	—	4	4	no	—
433	#124	—	4	4	no	—
434	C₂²⋊Q₈	—	2	4	no	—
435	C₄×D₄	—	4	4	no	—
436	#117	—	2	4	no	—
437	#117	—	2	4	no	—
438	#117	—	4	4	no	—
439	C₂×C₄⋊C₄	—	2	4	no	—
440	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
453	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
454	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
456	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
457	C₂×C₂²⋊C₄	—	2	8	no	—
458	C₂×C₂²⋊C₄	—	2	8	no	—
459	C₂×C₂²⋊C₄	—	4	4	no	—
460	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
471	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
472	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₃	1	2	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	2	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
488	C₂×C₄²	C₂³×C₃	1	2	yes	—
489	C₂×C₄²	C₂³×C₃	1	2	yes	—
490	C₂×C₄²	C₂³×C₃	1	2	yes	—
491	C₂×C₄²	C₂³×C₃	1	2	yes	—
492	C₂×C₄²	C₂³×C₃	1	2	yes	—
493	C₂×C₄²	C₂³×C₃	1	2	yes	—
494	C₂×C₄²	C₂³×C₃	1	2	yes	—
495	C₂×C₄²	C₂³×C₃	1	2	yes	—
496	#95	C₂³×C₃	1	1	yes	characteristic
497	#95	C₂³×C₃	1	2	yes	—
498	#95	C₂³×C₃	1	1	yes	characteristic
499	#95	C₂³×C₃	1	2	yes	—
500	#95	C₂³×C₃	1	2	yes	—
501	#95	C₂³×C₃	1	2	yes	—
502	#95	C₂³×C₃	1	2	yes	—
503	#95	C₂³×C₃	1	2	yes	—
504	#95	C₂³×C₃	1	2	yes	—
505	#95	C₂³×C₃	1	2	yes	—
506	#95	C₂³×C₃	1	2	yes	—
507	#95	C₂³×C₃	1	2	yes	—
508	#95	C₂³×C₃	1	2	yes	—
509	#95	C₂³×C₃	1	2	yes	—
510	#95	C₂³×C₃	1	2	yes	—
511	#95	C₂³×C₃	1	2	yes	—
512	#95	C₂³×C₃	1	1	yes	characteristic
513	#95	C₂³×C₃	1	1	yes	characteristic
514	#95	C₂³×C₃	1	2	yes	—
515	#95	C₂³×C₃	1	2	yes	—
516	#95	C₂³×C₃	1	2	yes	—
517	#95	C₂³×C₃	1	2	yes	—
518	#95	C₂³×C₃	1	2	yes	—
519	C₂³×C₃	—	2	2	no	—
520	C₂³×C₃	—	2	2	no	—
521	C₂³×C₃	—	2	2	no	—
522	C₂³×C₃	—	2	2	no	—
523	C₂³×C₃	—	2	2	no	—
524	C₂³×C₃	—	2	2	no	—
525	C₂³×C₃	—	2	2	no	—
526	C₂³×C₃	—	2	2	no	—
527	C₂³×C₃	—	2	2	no	—
528	C₂³×C₃	—	2	2	no	—
529	C₂³×C₃	—	2	2	no	—
530	C₂³×C₃	—	2	2	no	—
531	C₂³×C₃	—	2	2	no	—
532	C₂³×C₃	—	2	2	no	—
533	C₂³×C₃	—	2	2	no	—
534	C₂³×C₃	—	4	8	no	—
535	C₂³×C₃	—	4	8	no	—
536	C₂³×C₃	—	4	8	no	—
537	C₂³×C₃	—	4	8	no	—
538	C₂³×C₃	—	8	4	no	—
539	C₂³×C₃	—	8	4	no	—
540	C₂³×C₃	—	8	4	no	—
541	C₂³×C₃	C₂×#41	1	2	yes	—
542	C₂³×C₃	C₂×#41	1	2	yes	—
543	C₂³×C₃	C₂×#41	1	2	yes	—
544	C₂³×C₃	H(5,𝔽₂)	1	4	yes	—
545	C₂³×C₃	C₂⁵	1	1	yes	characteristic
546	C₃×Q₈	—	8	2	no	—
547	C₃×D₄	—	2	8	no	—
548	C₃×D₄	—	4	8	no	—
549	C₃×D₄	—	4	4	no	—
550	C₂×C₃×C₄	—	2	8	no	—
551	C₂×C₃×C₄	—	2	1	no	—
552	C₂×C₃×C₄	—	2	1	no	—
553	C₂×C₃×C₄	—	2	1	no	—
554	C₂×C₃×C₄	—	2	1	no	—
555	C₂×C₃×C₄	—	2	2	no	—
556	C₂×C₃×C₄	—	2	2	no	—
557	C₂×C₃×C₄	—	2	2	no	—
558	C₂×C₃×C₄	—	2	2	no	—
559	C₂×C₃×C₄	—	2	2	no	—
560	C₂×C₃×C₄	—	2	2	no	—
561	C₂×C₃×C₄	—	2	2	no	—
562	C₂×C₃×C₄	—	2	2	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	2	no	—
567	C₂×C₃×C₄	—	2	2	no	—
568	C₂×C₃×C₄	—	2	1	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	2	no	—
574	C₂×C₃×C₄	—	2	2	no	—
575	C₂×C₃×C₄	—	2	2	no	—
576	C₂×C₃×C₄	—	2	2	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	—	2	2	no	—
581	C₂×C₃×C₄	—	2	2	no	—
582	C₂×C₃×C₄	—	2	2	no	—
583	C₂×C₃×C₄	—	2	2	no	—
584	C₂×C₃×C₄	—	2	2	no	—
585	C₂×C₃×C₄	—	2	2	no	—
586	C₂×C₃×C₄	—	2	2	no	—
587	C₂×C₃×C₄	—	2	2	no	—
588	C₂×C₃×C₄	—	2	2	no	—
589	C₂×C₃×C₄	—	2	2	no	—
590	C₂×C₃×C₄	—	4	4	no	—
591	C₂×C₃×C₄	—	4	8	no	—
592	C₂×C₃×C₄	—	8	4	no	—
593	C₂×C₃×C₄	—	8	2	no	—
594	C₂×C₃×C₄	—	8	4	no	—
595	C₂×C₃×C₄	C₂×#41	1	2	yes	—
596	C₂×C₃×C₄	C₂×#41	1	4	yes	—
597	C₂×C₃×C₄	C₂×#41	1	2	yes	—
598	C₂×C₃×C₄	C₂×#41	1	2	yes	—
599	C₂×C₃×C₄	C₂×#41	1	2	yes	—
600	C₂⁴	—	2	4	no	—
601	C₂⁴	—	2	4	no	—
602	C₂⁴	—	2	4	no	—
603	C₂⁴	—	2	4	no	—
604	C₂⁴	—	4	2	no	—
605	C₂⁴	—	4	2	no	—
606	C₂⁴	—	4	2	no	—
607	C₂⁴	C₂⁴×C₃	1	2	yes	—
608	C₂⁴	C₂⁴×C₃	1	2	yes	—
609	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
610	C₂×Q₈	—	2	2	no	—
611	C₂×Q₈	—	4	2	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	2	2	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	4	2	no	—
618	C₂×D₄	—	4	2	no	—
619	C₂×D₄	—	4	16	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	4	2	no	—
628	C₂²×C₄	—	4	2	no	—
629	C₂²×C₄	—	4	2	no	—
630	C₂²×C₄	—	4	2	no	—
631	C₂²×C₄	—	4	2	no	—
632	C₂²×C₄	—	4	2	no	—
633	C₂²×C₄	—	4	2	no	—
634	C₂²×C₄	C₃×#41	1	4	yes	—
635	C₂²×C₄	C₃×#41	1	4	yes	—
636	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
645	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
646	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
649	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
650	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
651	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	4	2	no	—
661	C₄⋊C₄	—	4	2	no	—
662	C₄⋊C₄	—	4	2	no	—
663	C₄⋊C₄	—	4	2	no	—
664	C₄⋊C₄	—	4	2	no	—
665	C₄⋊C₄	—	4	2	no	—
666	C₄⋊C₄	—	4	2	no	—
667	C₄⋊C₄	—	4	2	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₂²⋊C₄	—	2	4	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	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	4	2	no	—
686	C₂²⋊C₄	—	4	2	no	—
687	C₂²⋊C₄	—	4	2	no	—
688	C₂²⋊C₄	—	4	2	no	—
689	C₂²⋊C₄	—	4	2	no	—
690	C₂²⋊C₄	—	4	2	no	—
691	C₂²⋊C₄	—	4	2	no	—
692	C₂²⋊C₄	—	4	2	no	—
693	C₂²⋊C₄	—	4	2	no	—
694	C₂²⋊C₄	—	4	2	no	—
695	C₂²⋊C₄	—	4	2	no	—
696	C₂²⋊C₄	C₃×#41	1	4	yes	—
697	C₄²	—	2	4	no	—
698	C₄²	—	2	4	no	—
699	C₄²	—	4	2	no	—
700	C₄²	—	4	2	no	—
701	C₄²	—	4	2	no	—
702	C₄²	—	4	2	no	—
703	C₄²	—	4	2	no	—
704	C₄²	—	4	2	no	—
705	C₂²×C₃	—	2	2	no	—
706	C₂²×C₃	—	2	4	no	—
707	C₂²×C₃	—	2	2	no	—
708	C₂²×C₃	—	2	4	no	—
709	C₂²×C₃	—	2	4	no	—
710	C₂²×C₃	—	2	4	no	—
711	C₂²×C₃	—	2	4	no	—
712	C₂²×C₃	—	4	2	no	—
713	C₂²×C₃	—	4	2	no	—
714	C₂²×C₃	—	4	2	no	—
715	C₂²×C₃	—	4	2	no	—
716	C₂²×C₃	—	4	2	no	—
717	C₂²×C₃	—	4	2	no	—
718	C₂²×C₃	—	4	2	no	—
719	C₂²×C₃	—	4	2	no	—
720	C₂²×C₃	—	4	2	no	—
721	C₂²×C₃	—	4	2	no	—
722	C₂²×C₃	—	4	2	no	—
723	C₂²×C₃	—	8	16	no	—
724	C₂²×C₃	#529	1	4	yes	—
725	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
726	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
727	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
728	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
729	C₂²×C₃	#585	1	2	yes	—
730	C₃×C₄	—	2	2	no	—
731	C₃×C₄	—	2	2	no	—
732	C₃×C₄	—	2	2	no	—
733	C₃×C₄	—	2	2	no	—
734	C₃×C₄	—	2	4	no	—
735	C₃×C₄	—	4	1	no	—
736	C₃×C₄	—	4	1	no	—
737	C₃×C₄	—	4	2	no	—
738	C₃×C₄	—	4	2	no	—
739	C₃×C₄	—	4	2	no	—
740	C₃×C₄	—	4	2	no	—
741	C₃×C₄	—	4	2	no	—
742	C₃×C₄	—	4	2	no	—
743	C₃×C₄	—	4	2	no	—
744	C₃×C₄	—	4	2	no	—
745	C₃×C₄	—	4	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	4	8	no	—
762	C₂³	—	4	8	no	—
763	C₂³	—	4	8	no	—
764	C₂³	—	4	8	no	—
765	C₂³	—	8	4	no	—
766	C₂³	—	8	4	no	—
767	C₂³	—	8	4	no	—
768	C₂³	C₂×C₃×#41	1	2	yes	—
769	C₂³	C₂×C₃×#41	1	2	yes	—
770	C₂³	C₂×C₃×#41	1	2	yes	—
771	C₂³	C₃×H(5,𝔽₂)	1	4	yes	—
772	C₂³	C₂⁵×C₃	1	1	yes	characteristic
773	Q₈	—	8	2	no	—
774	D₄	—	2	8	no	—
775	D₄	—	4	8	no	—
776	D₄	—	4	4	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	8	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	4	8	no	—
819	C₂×C₄	—	8	4	no	—
820	C₂×C₄	—	8	2	no	—
821	C₂×C₄	—	8	4	no	—
822	C₂×C₄	C₂×C₃×#41	1	2	yes	—
823	C₂×C₄	C₂×C₃×#41	1	4	yes	—
824	C₂×C₄	C₂×C₃×#41	1	2	yes	—
825	C₂×C₄	C₂×C₃×#41	1	2	yes	—
826	C₂×C₄	C₂×C₃×#41	1	2	yes	—
827	C₂×C₃	—	2	4	no	—
828	C₂×C₃	—	4	4	no	—
829	C₂×C₃	—	8	2	no	—
830	C₂×C₃	C₂×#529	1	1	yes	characteristic
831	C₂×C₃	#3490	1	1	yes	characteristic
832	C₂×C₃	#3494	1	2	yes	—
833	C₂×C₃	#3510	1	1	yes	characteristic
834	C₂×C₃	#3513	1	2	yes	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	4	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	4	no	—
839	C₂²	—	2	4	no	—
840	C₂²	—	2	4	no	—
841	C₂²	—	2	4	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	8	16	no	—
854	C₂²	C₃×#529	1	4	yes	—
855	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
856	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
857	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
858	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
859	C₂²	C₃×#585	1	2	yes	—
860	C₄	—	2	2	no	—
861	C₄	—	2	2	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	4	no	—
865	C₄	—	4	1	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	2	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	2	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	2	no	—
876	C₃	#35731	1	1	yes	characteristic, direct product factor, Sylow
877	C₂	—	2	4	no	—
878	C₂	—	4	4	no	—
879	C₂	—	8	2	no	—
880	C₂	C₂×C₃×#529	1	1	yes	characteristic
881	C₂	C₃×#3490	1	1	yes	characteristic
882	C₂	C₃×#3494	1	2	yes	—
883	C₂	C₃×#3510	1	1	yes	characteristic
884	C₂	C₃×#3513	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂³×C₃×D₄	C₂²
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. C₃×#2651	C₂	semidirect
2. C₃×#2627	C₂	semidirect
3. C₃×#2595	C₂	semidirect
4. C₃×#2593	C₂	semidirect
5. C₃×#2569	C₂	semidirect
6. C₃×#2521	C₂	semidirect
7. C₃×#2516	C₂	semidirect
8. C₃×#2482	C₂	semidirect
9. C₃×#2480	C₂	semidirect
10. C₃×#2474	C₂	semidirect
11. C₃×#2468	C₂	semidirect
13. C₃×#2395	C₂	semidirect
15. C₃×#2368	C₂	semidirect
16. C₃×#2342	C₂	semidirect
17. C₃×#2342	C₂	semidirect
19. C₃×#2274	C₂	semidirect
20. #35731	C₃	direct (N × H)
22. C₂×C₃×#126	C₂²	semidirect
28. C₂×C₃×#117	C₂²	semidirect
33. C₃×#400	C₂²	semidirect
34. C₃×#400	C₂²	semidirect
35. C₃×#400	C₂²	semidirect
36. C₃×#399	C₂²	semidirect
37. C₃×#399	C₂²	semidirect
38. C₃×#398	C₂²	semidirect
39. C₃×#398	C₂²	semidirect
40. C₃×#398	C₂²	semidirect
41. C₃×#397	C₂²	semidirect
42. C₃×#397	C₂²	semidirect
43. C₃×#397	C₂²	semidirect
44. C₃×#397	C₂²	semidirect
45. C₃×#397	C₂²	semidirect
46. C₃×#396	C₂²	semidirect
47. C₃×#395	C₂²	semidirect
48. C₃×#395	C₂²	semidirect
57. C₃×#391	C₂²	semidirect
60. C₃×#388	C₂²	semidirect
61. C₃×#388	C₂²	semidirect
62. C₃×#388	C₂²	semidirect
63. C₃×#388	C₂²	semidirect
64. C₃×#388	C₂²	semidirect
65. C₃×#388	C₂²	semidirect
66. C₃×#388	C₂²	semidirect
67. C₃×#388	C₂²	semidirect
68. C₃×#388	C₂²	semidirect
69. C₃×#388	C₂²	semidirect
70. C₃×#388	C₂²	semidirect
71. C₃×#388	C₂²	semidirect
72. C₃×#388	C₂²	semidirect
73. C₃×#388	C₂²	semidirect
74. C₃×#388	C₂²	semidirect
75. C₃×#387	C₂²	semidirect
76. C₃×#387	C₂²	semidirect
77. C₃×#387	C₂²	semidirect
78. C₃×#387	C₂²	semidirect
84. C₃×#385	C₂²	semidirect
85. C₃×#385	C₂²	semidirect
87. C₃×#381	C₂²	semidirect
90. C₃×#380	C₂²	semidirect
94. C₃×C₄×C₄⋊C₄	C₂²	semidirect
95. C₃×C₄×C₄⋊C₄	C₂²	semidirect
96. C₃×C₄×C₄⋊C₄	C₂²	semidirect
97. C₃×C₄×C₄⋊C₄	C₂²	semidirect
98. C₃×C₄×C₄⋊C₄	C₂²	semidirect
104. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
105. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
106. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
108. #2651	C₂×C₃	semidirect
109. #2627	C₂×C₃	semidirect
110. #2595	C₂×C₃	semidirect
111. #2593	C₂×C₃	semidirect
112. #2569	C₂×C₃	semidirect
113. #2521	C₂×C₃	semidirect
114. #2516	C₂×C₃	semidirect
115. #2482	C₂×C₃	semidirect
116. #2480	C₂×C₃	semidirect
117. #2474	C₂×C₃	semidirect
118. #2468	C₂×C₃	semidirect
120. #2395	C₂×C₃	semidirect
122. #2368	C₂×C₃	semidirect
123. #2342	C₂×C₃	semidirect
124. #2342	C₂×C₃	semidirect
126. #2274	C₂×C₃	semidirect
228. C₂×#126	C₂²×C₃	semidirect
234. C₂×#117	C₂²×C₃	semidirect
239. #400	C₂²×C₃	semidirect
240. #400	C₂²×C₃	semidirect
241. #400	C₂²×C₃	semidirect
242. #399	C₂²×C₃	semidirect
243. #399	C₂²×C₃	semidirect
244. #398	C₂²×C₃	semidirect
245. #398	C₂²×C₃	semidirect
246. #398	C₂²×C₃	semidirect
247. #397	C₂²×C₃	semidirect
248. #397	C₂²×C₃	semidirect
249. #397	C₂²×C₃	semidirect
250. #397	C₂²×C₃	semidirect
251. #397	C₂²×C₃	semidirect
252. #396	C₂²×C₃	semidirect
253. #395	C₂²×C₃	semidirect
254. #395	C₂²×C₃	semidirect
263. #391	C₂²×C₃	semidirect
266. #388	C₂²×C₃	semidirect
267. #388	C₂²×C₃	semidirect
268. #388	C₂²×C₃	semidirect
269. #388	C₂²×C₃	semidirect
270. #388	C₂²×C₃	semidirect
271. #388	C₂²×C₃	semidirect
272. #388	C₂²×C₃	semidirect
273. #388	C₂²×C₃	semidirect
274. #388	C₂²×C₃	semidirect
275. #388	C₂²×C₃	semidirect
276. #388	C₂²×C₃	semidirect
277. #388	C₂²×C₃	semidirect
278. #388	C₂²×C₃	semidirect
279. #388	C₂²×C₃	semidirect
280. #388	C₂²×C₃	semidirect
281. #387	C₂²×C₃	semidirect
282. #387	C₂²×C₃	semidirect
283. #387	C₂²×C₃	semidirect
284. #387	C₂²×C₃	semidirect
290. #385	C₂²×C₃	semidirect
291. #385	C₂²×C₃	semidirect
293. #381	C₂²×C₃	semidirect
296. #380	C₂²×C₃	semidirect
300. C₄×C₄⋊C₄	C₂²×C₃	semidirect
301. C₄×C₄⋊C₄	C₂²×C₃	semidirect
302. C₄×C₄⋊C₄	C₂²×C₃	semidirect
303. C₄×C₄⋊C₄	C₂²×C₃	semidirect
304. C₄×C₄⋊C₄	C₂²×C₃	semidirect
310. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
311. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
312. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
876. C₃	#35731	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#2651	2
C₃×#2627	2
C₃×#2595	2
C₃×#2593	2
C₃×#2569	2
C₃×#2521	2
C₃×#2516	2
C₃×#2482	2
C₃×#2480	2
C₃×#2474	2
C₃×#2468	2
C₃×#2435	2
C₃×#2395	2
C₂×C₃×#394	2
C₃×#2368	2
C₃×#2342	2
C₃×D₄×C₂²⋊C₄	2
C₃×#2274	2
#35731	3

Subgroups — C3×#35731 #10654338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35731 #10654338