Subgroups — C₃×#42457 #10661064

Order 768.

1688 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2838	C₂	1	2	yes	maximal, complemented
2	C₃×#2801	C₂	1	2	yes	maximal, complemented
3	C₃×#2777	C₂	1	2	yes	maximal, complemented
4	C₃×#2729	C₂	1	2	yes	maximal, complemented
5	C₃×#2674	C₂	1	2	yes	maximal, complemented
6	C₃×#2663	C₂	1	2	yes	maximal, complemented
7	C₃×#2632	C₂	1	2	yes	maximal, complemented
8	C₃×#2620	C₂	1	1	yes	maximal, characteristic
9	C₃×#2592	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2567	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2551	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2542	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2514	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2513	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2492	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2491	C₂	1	1	yes	maximal, characteristic
17	C₃×#2465	C₂	1	2	yes	maximal, complemented
18	C₃×#2423	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2422	C₂	1	1	yes	maximal, characteristic
20	C₃×#2396	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×Q₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2314	C₂	1	1	yes	maximal, characteristic, complemented
24	#42457	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×#124	C₂²	1	1	yes	characteristic
29	C₂×C₃×#124	C₂²	1	2	yes	—
30	C₂×C₃×#123	C₂²	1	2	yes	—
31	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
34	C₂×C₃×#121	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
38	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
39	C₂×C₃×#117	C₂²	1	1	yes	characteristic
40	C₃×#401	C₂²	1	2	yes	—
41	C₃×#400	C₂²	1	1	yes	characteristic
42	C₃×#400	C₂²	1	2	yes	—
43	C₃×#400	C₂²	1	2	yes	—
44	C₃×#399	C₂²	1	2	yes	—
45	C₃×#399	C₂²	1	2	yes	—
46	C₃×#399	C₂²	1	1	yes	characteristic
47	C₃×#399	C₂²	1	2	yes	—
48	C₃×#398	C₂²	1	1	yes	characteristic
49	C₃×#398	C₂²	1	1	yes	characteristic
50	C₃×#398	C₂²	1	2	yes	—
51	C₃×#397	C₂²	1	2	yes	—
52	C₃×#397	C₂²	1	2	yes	—
53	C₃×#397	C₂²	1	2	yes	—
54	C₃×#397	C₂²	1	2	yes	—
55	C₃×#396	C₂²	1	2	yes	—
56	C₃×#396	C₂²	1	2	yes	—
57	C₃×#396	C₂²	1	1	yes	characteristic
58	C₃×#396	C₂²	1	1	yes	characteristic
59	C₃×#395	C₂²	1	2	yes	—
60	C₃×#395	C₂²	1	2	yes	—
61	C₃×#395	C₂²	1	1	yes	characteristic
62	C₃×#395	C₂²	1	2	yes	—
63	C₃×#395	C₂²	1	2	yes	—
64	C₃×#394	C₂²	1	2	yes	—
65	C₃×#394	C₂²	1	2	yes	—
66	C₃×#394	C₂²	1	2	yes	—
67	C₃×#394	C₂²	1	2	yes	—
68	C₃×#393	C₂²	1	1	yes	characteristic
69	C₃×#393	C₂²	1	2	yes	—
70	C₃×#393	C₂²	1	2	yes	—
71	C₃×#393	C₂²	1	2	yes	—
72	C₃×#391	C₂²	1	1	yes	characteristic
73	C₃×#391	C₂²	1	1	yes	characteristic
74	C₃×#391	C₂²	1	1	yes	characteristic
75	C₃×#391	C₂²	1	2	yes	—
76	C₃×#391	C₂²	1	1	yes	characteristic
77	C₃×#390	C₂²	1	1	yes	characteristic
78	C₃×#390	C₂²	1	1	yes	characteristic
79	C₃×#390	C₂²	1	1	yes	characteristic
80	C₃×#390	C₂²	1	1	yes	characteristic
81	C₃×#389	C₂²	1	2	yes	—
82	C₃×#389	C₂²	1	2	yes	—
83	C₃×#389	C₂²	1	2	yes	—
84	C₃×#389	C₂²	1	1	yes	characteristic
85	C₃×#389	C₂²	1	1	yes	characteristic
86	C₃×#389	C₂²	1	2	yes	—
87	C₃×#389	C₂²	1	2	yes	—
88	C₃×#389	C₂²	1	2	yes	—
89	C₃×#388	C₂²	1	2	yes	—
90	C₃×#388	C₂²	1	2	yes	—
91	C₃×#388	C₂²	1	2	yes	—
92	C₃×#388	C₂²	1	2	yes	—
93	C₃×#388	C₂²	1	2	yes	—
94	C₃×#388	C₂²	1	2	yes	—
95	C₃×#388	C₂²	1	2	yes	—
96	C₃×#388	C₂²	1	2	yes	—
97	C₃×#388	C₂²	1	2	yes	—
98	C₃×#388	C₂²	1	2	yes	—
99	C₃×#388	C₂²	1	2	yes	—
100	C₃×#387	C₂²	1	2	yes	—
101	C₃×#387	C₂²	1	2	yes	—
102	C₃×#387	C₂²	1	2	yes	—
103	C₃×#387	C₂²	1	2	yes	—
104	C₃×#385	C₂²	1	2	yes	—
105	C₃×#385	C₂²	1	2	yes	—
106	C₃×#384	C₂²	1	1	yes	characteristic
107	C₃×#384	C₂²	1	1	yes	characteristic
108	C₃×#384	C₂²	1	1	yes	characteristic
109	C₃×#384	C₂²	1	1	yes	characteristic
110	C₃×#383	C₂²	1	2	yes	—
111	C₃×#382	C₂²	1	1	yes	characteristic
112	C₃×#380	C₂²	1	1	yes	characteristic
113	C₃×#380	C₂²	1	1	yes	characteristic
114	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
115	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
116	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
117	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
118	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
119	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
120	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
121	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
123	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
124	#2838	C₂×C₃	1	2	yes	complemented
125	#2801	C₂×C₃	1	2	yes	complemented
126	#2777	C₂×C₃	1	2	yes	complemented
127	#2729	C₂×C₃	1	2	yes	complemented
128	#2674	C₂×C₃	1	2	yes	complemented
129	#2663	C₂×C₃	1	2	yes	complemented
130	#2632	C₂×C₃	1	2	yes	complemented
131	#2620	C₂×C₃	1	1	yes	characteristic
132	#2592	C₂×C₃	1	1	yes	characteristic, complemented
133	#2567	C₂×C₃	1	1	yes	characteristic, complemented
134	#2551	C₂×C₃	1	1	yes	characteristic, complemented
135	#2542	C₂×C₃	1	1	yes	characteristic, complemented
136	#2514	C₂×C₃	1	1	yes	characteristic, complemented
137	#2513	C₂×C₃	1	1	yes	characteristic, complemented
138	#2492	C₂×C₃	1	1	yes	characteristic, complemented
139	#2491	C₂×C₃	1	1	yes	characteristic
140	#2465	C₂×C₃	1	2	yes	complemented
141	#2423	C₂×C₃	1	1	yes	characteristic, complemented
142	#2422	C₂×C₃	1	1	yes	characteristic
143	#2396	C₂×C₃	1	1	yes	characteristic, complemented
144	#2367	C₂×C₃	1	1	yes	characteristic, complemented
145	Q₈×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
146	#2314	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
148	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
149	C₂²×C₃×Q₈	C₂³	1	2	yes	—
150	C₂²×C₃×Q₈	C₂³	1	2	yes	—
151	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
152	C₂²×C₃×D₄	C₂³	1	2	yes	—
153	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
154	C₂³×C₃×C₄	C₂³	1	2	yes	—
155	C₃×C₄⋊Q₈	—	4	2	no	—
156	C₃×C₄⋊Q₈	—	4	2	no	—
157	C₃×C₄⋊Q₈	—	4	4	no	—
158	C₃×#124	—	2	4	no	—
159	C₃×#124	—	4	4	no	—
160	C₃×#123	—	4	4	no	—
161	C₃×C₂²⋊Q₈	—	4	4	no	—
162	C₃×C₂²⋊Q₈	—	4	4	no	—
163	C₃×C₂²⋊Q₈	—	4	2	no	—
164	C₃×#121	—	4	2	no	—
165	C₃×C₄×Q₈	—	2	4	no	—
166	C₃×C₄×Q₈	—	4	4	no	—
167	C₃×C₄×Q₈	—	4	2	no	—
168	C₃×C₄×D₄	—	4	2	no	—
169	C₃×#117	—	2	4	no	—
170	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
185	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
194	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
195	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
200	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
201	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
212	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
225	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
226	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
227	C₂×C₃×C₄²	C₂³	1	2	yes	—
228	C₂×C₃×C₄²	C₂³	1	2	yes	—
229	C₂×C₃×C₄²	C₂³	1	2	yes	—
230	C₂×C₃×C₄²	C₂³	1	2	yes	—
231	C₂×C₃×C₄²	C₂³	1	2	yes	—
232	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
233	C₃×#95	C₂³	1	1	yes	characteristic
234	C₃×#95	C₂³	1	1	yes	characteristic
235	C₃×#95	C₂³	1	2	yes	—
236	C₃×#95	C₂³	1	1	yes	characteristic
237	C₃×#95	C₂³	1	1	yes	characteristic
238	C₃×#95	C₂³	1	1	yes	characteristic
239	C₃×#95	C₂³	1	1	yes	characteristic
240	C₃×#95	C₂³	1	2	yes	—
241	C₃×#95	C₂³	1	2	yes	—
242	C₃×#95	C₂³	1	1	yes	characteristic
243	C₃×#95	C₂³	1	1	yes	characteristic
244	C₃×#95	C₂³	1	2	yes	—
245	C₃×#95	C₂³	1	2	yes	—
246	C₃×#95	C₂³	1	1	yes	characteristic
247	C₃×#95	C₂³	1	1	yes	characteristic
248	C₃×#95	C₂³	1	2	yes	—
249	C₃×#95	C₂³	1	2	yes	—
250	C₃×#95	C₂³	1	2	yes	—
251	C₃×#95	C₂³	1	2	yes	—
252	C₃×#95	C₂³	1	2	yes	—
253	C₃×#95	C₂³	1	2	yes	—
254	C₃×#95	C₂³	1	2	yes	—
255	C₃×#95	C₂³	1	2	yes	—
256	C₃×#95	C₂³	1	2	yes	—
257	C₃×#95	C₂³	1	2	yes	—
258	C₃×#95	C₂³	1	2	yes	—
259	C₃×#95	C₂³	1	2	yes	—
260	C₃×#95	C₂³	1	2	yes	—
261	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
262	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
263	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
264	C₂×#124	C₂²×C₃	1	1	yes	characteristic
265	C₂×#124	C₂²×C₃	1	2	yes	—
266	C₂×#123	C₂²×C₃	1	2	yes	—
267	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
268	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
269	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
270	C₂×#121	C₂²×C₃	1	1	yes	characteristic
271	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
272	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
273	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
274	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
275	C₂×#117	C₂²×C₃	1	1	yes	characteristic
276	#401	C₂²×C₃	1	2	yes	—
277	#400	C₂²×C₃	1	1	yes	characteristic
278	#400	C₂²×C₃	1	2	yes	—
279	#400	C₂²×C₃	1	2	yes	—
280	#399	C₂²×C₃	1	2	yes	—
281	#399	C₂²×C₃	1	2	yes	—
282	#399	C₂²×C₃	1	2	yes	—
283	#399	C₂²×C₃	1	1	yes	characteristic
284	#398	C₂²×C₃	1	2	yes	—
285	#398	C₂²×C₃	1	1	yes	characteristic
286	#398	C₂²×C₃	1	1	yes	characteristic
287	#397	C₂²×C₃	1	2	yes	—
288	#397	C₂²×C₃	1	2	yes	—
289	#397	C₂²×C₃	1	2	yes	—
290	#397	C₂²×C₃	1	2	yes	—
291	#396	C₂²×C₃	1	2	yes	—
292	#396	C₂²×C₃	1	2	yes	—
293	#396	C₂²×C₃	1	1	yes	characteristic
294	#396	C₂²×C₃	1	1	yes	characteristic
295	#395	C₂²×C₃	1	2	yes	—
296	#395	C₂²×C₃	1	2	yes	—
297	#395	C₂²×C₃	1	2	yes	—
298	#395	C₂²×C₃	1	1	yes	characteristic
299	#395	C₂²×C₃	1	2	yes	—
300	#394	C₂²×C₃	1	2	yes	—
301	#394	C₂²×C₃	1	2	yes	—
302	#394	C₂²×C₃	1	2	yes	—
303	#394	C₂²×C₃	1	2	yes	—
304	#393	C₂²×C₃	1	2	yes	—
305	#393	C₂²×C₃	1	2	yes	—
306	#393	C₂²×C₃	1	1	yes	characteristic
307	#393	C₂²×C₃	1	2	yes	—
308	#391	C₂²×C₃	1	1	yes	characteristic
309	#391	C₂²×C₃	1	1	yes	characteristic
310	#391	C₂²×C₃	1	1	yes	characteristic
311	#391	C₂²×C₃	1	1	yes	characteristic
312	#391	C₂²×C₃	1	2	yes	—
313	#390	C₂²×C₃	1	1	yes	characteristic
314	#390	C₂²×C₃	1	1	yes	characteristic
315	#390	C₂²×C₃	1	1	yes	characteristic
316	#390	C₂²×C₃	1	1	yes	characteristic
317	#389	C₂²×C₃	1	2	yes	—
318	#389	C₂²×C₃	1	2	yes	—
319	#389	C₂²×C₃	1	2	yes	—
320	#389	C₂²×C₃	1	2	yes	—
321	#389	C₂²×C₃	1	2	yes	—
322	#389	C₂²×C₃	1	1	yes	characteristic
323	#389	C₂²×C₃	1	1	yes	characteristic
324	#389	C₂²×C₃	1	2	yes	—
325	#388	C₂²×C₃	1	2	yes	—
326	#388	C₂²×C₃	1	2	yes	—
327	#388	C₂²×C₃	1	2	yes	—
328	#388	C₂²×C₃	1	2	yes	—
329	#388	C₂²×C₃	1	2	yes	—
330	#388	C₂²×C₃	1	2	yes	—
331	#388	C₂²×C₃	1	2	yes	—
332	#388	C₂²×C₃	1	2	yes	—
333	#388	C₂²×C₃	1	2	yes	—
334	#388	C₂²×C₃	1	2	yes	—
335	#388	C₂²×C₃	1	2	yes	—
336	#387	C₂²×C₃	1	2	yes	—
337	#387	C₂²×C₃	1	2	yes	—
338	#387	C₂²×C₃	1	2	yes	—
339	#387	C₂²×C₃	1	2	yes	—
340	#385	C₂²×C₃	1	2	yes	—
341	#385	C₂²×C₃	1	2	yes	—
342	#384	C₂²×C₃	1	1	yes	characteristic
343	#384	C₂²×C₃	1	1	yes	characteristic
344	#384	C₂²×C₃	1	1	yes	characteristic
345	#384	C₂²×C₃	1	1	yes	characteristic
346	#383	C₂²×C₃	1	2	yes	—
347	#382	C₂²×C₃	1	1	yes	characteristic
348	#380	C₂²×C₃	1	1	yes	characteristic
349	#380	C₂²×C₃	1	1	yes	characteristic
350	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
351	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
352	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
353	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
354	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
355	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
356	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
357	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
358	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
359	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
360	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
361	C₂⁴×C₃	C₂⁴	1	2	yes	—
362	C₂×C₃×Q₈	—	2	2	no	—
363	C₂×C₃×Q₈	—	2	2	no	—
364	C₂×C₃×Q₈	—	2	2	no	—
365	C₂×C₃×Q₈	—	2	2	no	—
366	C₂×C₃×Q₈	—	2	4	no	—
367	C₂×C₃×Q₈	—	2	2	no	—
368	C₂×C₃×Q₈	—	2	2	no	—
369	C₂×C₃×Q₈	—	4	2	no	—
370	C₂×C₃×Q₈	—	4	2	no	—
371	C₂×C₃×Q₈	—	4	2	no	—
372	C₂×C₃×Q₈	—	4	2	no	—
373	C₂×C₃×Q₈	—	4	2	no	—
374	C₂×C₃×D₄	—	2	2	no	—
375	C₂×C₃×D₄	—	2	2	no	—
376	C₂×C₃×D₄	—	2	2	no	—
377	C₂×C₃×D₄	—	4	2	no	—
378	C₂×C₃×D₄	—	4	2	no	—
379	C₂×C₃×D₄	—	4	2	no	—
380	C₂²×C₃×C₄	—	2	2	no	—
381	C₂²×C₃×C₄	—	2	2	no	—
382	C₂²×C₃×C₄	—	2	2	no	—
383	C₂²×C₃×C₄	—	2	4	no	—
384	C₂²×C₃×C₄	—	4	2	no	—
385	C₂²×C₃×C₄	—	4	2	no	—
386	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
387	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
388	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
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	1	yes	characteristic
393	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
394	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
395	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
396	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
397	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
398	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
399	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
400	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
401	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
402	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
403	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
404	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
405	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
406	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
407	C₃×C₄⋊C₄	—	2	2	no	—
408	C₃×C₄⋊C₄	—	2	2	no	—
409	C₃×C₄⋊C₄	—	2	2	no	—
410	C₃×C₄⋊C₄	—	2	2	no	—
411	C₃×C₄⋊C₄	—	2	2	no	—
412	C₃×C₄⋊C₄	—	2	2	no	—
413	C₃×C₄⋊C₄	—	2	4	no	—
414	C₃×C₄⋊C₄	—	2	2	no	—
415	C₃×C₄⋊C₄	—	2	2	no	—
416	C₃×C₄⋊C₄	—	2	2	no	—
417	C₃×C₄⋊C₄	—	2	2	no	—
418	C₃×C₄⋊C₄	—	2	4	no	—
419	C₃×C₄⋊C₄	—	2	2	no	—
420	C₃×C₄⋊C₄	—	2	2	no	—
421	C₃×C₄⋊C₄	—	2	2	no	—
422	C₃×C₄⋊C₄	—	2	2	no	—
423	C₃×C₄⋊C₄	—	2	2	no	—
424	C₃×C₄⋊C₄	—	2	2	no	—
425	C₃×C₄⋊C₄	—	2	2	no	—
426	C₃×C₄⋊C₄	—	4	2	no	—
427	C₃×C₄⋊C₄	—	4	2	no	—
428	C₃×C₄⋊C₄	—	4	2	no	—
429	C₃×C₄⋊C₄	—	4	2	no	—
430	C₃×C₄⋊C₄	—	4	2	no	—
431	C₃×C₄⋊C₄	—	4	2	no	—
432	C₃×C₄⋊C₄	—	4	2	no	—
433	C₃×C₄⋊C₄	—	4	2	no	—
434	C₃×C₄⋊C₄	—	4	2	no	—
435	C₃×C₄⋊C₄	—	4	2	no	—
436	C₃×C₄⋊C₄	—	4	2	no	—
437	C₃×C₄⋊C₄	—	4	2	no	—
438	C₃×C₂²⋊C₄	—	2	2	no	—
439	C₃×C₂²⋊C₄	—	2	2	no	—
440	C₃×C₂²⋊C₄	—	2	4	no	—
441	C₃×C₂²⋊C₄	—	2	4	no	—
442	C₃×C₂²⋊C₄	—	2	4	no	—
443	C₃×C₂²⋊C₄	—	2	2	no	—
444	C₃×C₂²⋊C₄	—	2	2	no	—
445	C₃×C₂²⋊C₄	—	2	4	no	—
446	C₃×C₂²⋊C₄	—	2	2	no	—
447	C₃×C₂²⋊C₄	—	2	2	no	—
448	C₃×C₂²⋊C₄	—	2	4	no	—
449	C₃×C₂²⋊C₄	—	4	2	no	—
450	C₃×C₂²⋊C₄	—	4	2	no	—
451	C₃×C₂²⋊C₄	—	4	2	no	—
452	C₃×C₂²⋊C₄	—	4	2	no	—
453	C₃×C₂²⋊C₄	—	4	2	no	—
454	C₃×C₂²⋊C₄	—	4	2	no	—
455	C₃×C₂²⋊C₄	—	4	2	no	—
456	C₃×C₂²⋊C₄	—	4	2	no	—
457	C₃×C₂²⋊C₄	—	4	2	no	—
458	C₃×C₂²⋊C₄	—	4	2	no	—
459	C₃×C₄²	—	2	2	no	—
460	C₃×C₄²	—	2	2	no	—
461	C₃×C₄²	—	2	2	no	—
462	C₃×C₄²	—	2	2	no	—
463	C₃×C₄²	—	2	4	no	—
464	C₃×C₄²	—	2	2	no	—
465	C₃×C₄²	—	4	2	no	—
466	C₃×C₄²	—	4	2	no	—
467	C₃×C₄²	—	4	2	no	—
468	C₃×C₄²	—	4	2	no	—
469	C₃×C₄²	#41	1	4	yes	—
470	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
471	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
472	C₂²×Q₈	C₂³×C₃	1	2	yes	—
473	C₂²×Q₈	C₂³×C₃	1	2	yes	—
474	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
475	C₂²×D₄	C₂³×C₃	1	2	yes	—
476	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
477	C₂³×C₄	C₂³×C₃	1	2	yes	—
478	C₄⋊Q₈	—	4	2	no	—
479	C₄⋊Q₈	—	4	2	no	—
480	C₄⋊Q₈	—	4	4	no	—
481	#124	—	2	4	no	—
482	#124	—	4	4	no	—
483	#123	—	4	4	no	—
484	C₂²⋊Q₈	—	4	4	no	—
485	C₂²⋊Q₈	—	4	4	no	—
486	C₂²⋊Q₈	—	4	2	no	—
487	#121	—	4	2	no	—
488	C₄×Q₈	—	2	4	no	—
489	C₄×Q₈	—	4	4	no	—
490	C₄×Q₈	—	4	2	no	—
491	C₄×D₄	—	4	2	no	—
492	#117	—	2	4	no	—
493	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
525	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
526	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
533	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
534	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
545	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₃	1	2	yes	—
548	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
550	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
551	C₂×C₄²	C₂³×C₃	1	2	yes	—
552	C₂×C₄²	C₂³×C₃	1	2	yes	—
553	C₂×C₄²	C₂³×C₃	1	2	yes	—
554	C₂×C₄²	C₂³×C₃	1	2	yes	—
555	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
556	#95	C₂³×C₃	1	1	yes	characteristic
557	#95	C₂³×C₃	1	1	yes	characteristic
558	#95	C₂³×C₃	1	2	yes	—
559	#95	C₂³×C₃	1	1	yes	characteristic
560	#95	C₂³×C₃	1	1	yes	characteristic
561	#95	C₂³×C₃	1	1	yes	characteristic
562	#95	C₂³×C₃	1	1	yes	characteristic
563	#95	C₂³×C₃	1	2	yes	—
564	#95	C₂³×C₃	1	2	yes	—
565	#95	C₂³×C₃	1	1	yes	characteristic
566	#95	C₂³×C₃	1	1	yes	characteristic
567	#95	C₂³×C₃	1	2	yes	—
568	#95	C₂³×C₃	1	2	yes	—
569	#95	C₂³×C₃	1	1	yes	characteristic
570	#95	C₂³×C₃	1	1	yes	characteristic
571	#95	C₂³×C₃	1	2	yes	—
572	#95	C₂³×C₃	1	2	yes	—
573	#95	C₂³×C₃	1	2	yes	—
574	#95	C₂³×C₃	1	2	yes	—
575	#95	C₂³×C₃	1	2	yes	—
576	#95	C₂³×C₃	1	2	yes	—
577	#95	C₂³×C₃	1	2	yes	—
578	#95	C₂³×C₃	1	2	yes	—
579	#95	C₂³×C₃	1	2	yes	—
580	#95	C₂³×C₃	1	2	yes	—
581	#95	C₂³×C₃	1	2	yes	—
582	#95	C₂³×C₃	1	2	yes	—
583	#95	C₂³×C₃	1	2	yes	—
584	C₂³×C₃	—	2	1	no	—
585	C₂³×C₃	—	2	2	no	—
586	C₂³×C₃	—	2	2	no	—
587	C₂³×C₃	—	2	1	no	—
588	C₂³×C₃	—	2	1	no	—
589	C₂³×C₃	—	2	2	no	—
590	C₂³×C₃	—	2	1	no	—
591	C₂³×C₃	—	2	2	no	—
592	C₂³×C₃	—	2	1	no	—
593	C₂³×C₃	—	2	2	no	—
594	C₂³×C₃	—	2	1	no	—
595	C₂³×C₃	—	2	2	no	—
596	C₂³×C₃	—	2	1	no	—
597	C₂³×C₃	—	2	2	no	—
598	C₂³×C₃	C₂⁵	1	1	yes	characteristic
599	C₃×Q₈	—	2	8	no	—
600	C₃×Q₈	—	4	4	no	—
601	C₃×Q₈	—	8	4	no	—
602	C₃×Q₈	—	8	4	no	—
603	C₃×D₄	—	4	4	no	—
604	C₃×D₄	—	8	4	no	—
605	C₂×C₃×C₄	—	2	1	no	—
606	C₂×C₃×C₄	—	2	1	no	—
607	C₂×C₃×C₄	—	2	1	no	—
608	C₂×C₃×C₄	—	2	1	no	—
609	C₂×C₃×C₄	—	2	1	no	—
610	C₂×C₃×C₄	—	2	1	no	—
611	C₂×C₃×C₄	—	2	1	no	—
612	C₂×C₃×C₄	—	2	1	no	—
613	C₂×C₃×C₄	—	2	1	no	—
614	C₂×C₃×C₄	—	2	1	no	—
615	C₂×C₃×C₄	—	2	1	no	—
616	C₂×C₃×C₄	—	2	1	no	—
617	C₂×C₃×C₄	—	2	1	no	—
618	C₂×C₃×C₄	—	2	1	no	—
619	C₂×C₃×C₄	—	2	1	no	—
620	C₂×C₃×C₄	—	2	1	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	1	no	—
625	C₂×C₃×C₄	—	2	2	no	—
626	C₂×C₃×C₄	—	2	1	no	—
627	C₂×C₃×C₄	—	2	2	no	—
628	C₂×C₃×C₄	—	2	2	no	—
629	C₂×C₃×C₄	—	2	2	no	—
630	C₂×C₃×C₄	—	2	2	no	—
631	C₂×C₃×C₄	—	2	2	no	—
632	C₂×C₃×C₄	—	2	2	no	—
633	C₂×C₃×C₄	—	2	1	no	—
634	C₂×C₃×C₄	—	2	1	no	—
635	C₂×C₃×C₄	—	2	2	no	—
636	C₂×C₃×C₄	—	2	1	no	—
637	C₂×C₃×C₄	—	2	1	no	—
638	C₂×C₃×C₄	—	2	1	no	—
639	C₂×C₃×C₄	—	2	1	no	—
640	C₂×C₃×C₄	—	2	2	no	—
641	C₂×C₃×C₄	—	2	2	no	—
642	C₂×C₃×C₄	—	2	2	no	—
643	C₂×C₃×C₄	—	2	2	no	—
644	C₂×C₃×C₄	—	2	2	no	—
645	C₂×C₃×C₄	—	2	2	no	—
646	C₂×C₃×C₄	—	2	1	no	—
647	C₂×C₃×C₄	—	2	1	no	—
648	C₂×C₃×C₄	—	2	2	no	—
649	C₂×C₃×C₄	—	2	2	no	—
650	C₂×C₃×C₄	—	2	1	no	—
651	C₂×C₃×C₄	—	2	1	no	—
652	C₂×C₃×C₄	—	2	1	no	—
653	C₂×C₃×C₄	—	2	1	no	—
654	C₂×C₃×C₄	—	2	2	no	—
655	C₂×C₃×C₄	—	2	2	no	—
656	C₂×C₃×C₄	—	2	1	no	—
657	C₂×C₃×C₄	—	2	1	no	—
658	C₂×C₃×C₄	—	2	2	no	—
659	C₂×C₃×C₄	—	4	4	no	—
660	C₂×C₃×C₄	—	8	4	no	—
661	C₂×C₃×C₄	C₂×#41	1	2	yes	—
662	C₂×C₃×C₄	C₂×#41	1	2	yes	—
663	C₂×C₃×C₄	C₂×#41	1	2	yes	—
664	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
665	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
666	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
667	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
668	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
669	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
670	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
671	C₂⁴	C₂⁴×C₃	1	2	yes	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	2	no	—
676	C₂×Q₈	—	2	4	no	—
677	C₂×Q₈	—	2	2	no	—
678	C₂×Q₈	—	2	2	no	—
679	C₂×Q₈	—	4	2	no	—
680	C₂×Q₈	—	4	2	no	—
681	C₂×Q₈	—	4	2	no	—
682	C₂×Q₈	—	4	2	no	—
683	C₂×Q₈	—	4	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	4	2	no	—
688	C₂×D₄	—	4	2	no	—
689	C₂×D₄	—	4	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	—	4	2	no	—
695	C₂²×C₄	—	4	2	no	—
696	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
702	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
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	2	yes	—
708	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₄⋊C₄	—	4	2	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₄⋊C₄	—	4	2	no	—
747	C₄⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	4	2	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₂²⋊C₄	—	4	2	no	—
767	C₂²⋊C₄	—	4	2	no	—
768	C₂²⋊C₄	—	4	2	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	2	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	2	no	—
773	C₄²	—	2	4	no	—
774	C₄²	—	2	2	no	—
775	C₄²	—	4	2	no	—
776	C₄²	—	4	2	no	—
777	C₄²	—	4	2	no	—
778	C₄²	—	4	2	no	—
779	C₄²	C₃×#41	1	4	yes	—
780	C₂²×C₃	—	4	1	no	—
781	C₂²×C₃	—	4	2	no	—
782	C₂²×C₃	—	4	1	no	—
783	C₂²×C₃	—	4	2	no	—
784	C₂²×C₃	—	4	1	no	—
785	C₂²×C₃	—	4	2	no	—
786	C₂²×C₃	—	4	2	no	—
787	C₂²×C₃	—	4	1	no	—
788	C₂²×C₃	—	4	2	no	—
789	C₂²×C₃	—	4	1	no	—
790	C₂²×C₃	—	4	1	no	—
791	C₂²×C₃	—	4	2	no	—
792	C₂²×C₃	—	4	1	no	—
793	C₂²×C₃	—	4	2	no	—
794	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
795	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
796	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
797	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
798	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
799	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
800	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
801	C₃×C₄	—	2	2	no	—
802	C₃×C₄	—	2	2	no	—
803	C₃×C₄	—	2	2	no	—
804	C₃×C₄	—	2	2	no	—
805	C₃×C₄	—	2	2	no	—
806	C₃×C₄	—	2	2	no	—
807	C₃×C₄	—	4	1	no	—
808	C₃×C₄	—	4	2	no	—
809	C₃×C₄	—	4	1	no	—
810	C₃×C₄	—	4	1	no	—
811	C₃×C₄	—	4	1	no	—
812	C₃×C₄	—	4	1	no	—
813	C₃×C₄	—	4	2	no	—
814	C₃×C₄	—	4	2	no	—
815	C₃×C₄	—	4	2	no	—
816	C₃×C₄	—	4	1	no	—
817	C₃×C₄	—	4	2	no	—
818	C₃×C₄	—	4	2	no	—
819	C₃×C₄	—	4	2	no	—
820	C₃×C₄	—	4	1	no	—
821	C₃×C₄	#542	1	4	yes	—
822	C₂³	—	2	1	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	2	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	2	no	—
836	C₂³	C₂⁵×C₃	1	1	yes	characteristic
837	Q₈	—	2	8	no	—
838	Q₈	—	4	4	no	—
839	Q₈	—	8	4	no	—
840	Q₈	—	8	4	no	—
841	D₄	—	4	4	no	—
842	D₄	—	8	4	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	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	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	4	4	no	—
898	C₂×C₄	—	8	4	no	—
899	C₂×C₄	C₂×C₃×#41	1	2	yes	—
900	C₂×C₄	C₂×C₃×#41	1	2	yes	—
901	C₂×C₄	C₂×C₃×#41	1	2	yes	—
902	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
903	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
904	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
905	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
906	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
907	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
908	C₂×C₃	—	8	1	no	—
909	C₂×C₃	—	8	2	no	—
910	C₂×C₃	C₂×#542	1	1	yes	characteristic
911	C₂×C₃	#3492	1	1	yes	characteristic
912	C₂×C₃	#3511	1	1	yes	characteristic
913	C₂×C₃	#3543	1	1	yes	characteristic
914	C₂×C₃	#3550	1	1	yes	characteristic
915	C₂×C₃	#3550	1	1	yes	characteristic
916	C₂×C₃	#3552	1	1	yes	characteristic
917	C₂²	—	4	1	no	—
918	C₂²	—	4	2	no	—
919	C₂²	—	4	1	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	1	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	1	no	—
927	C₂²	—	4	1	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	4	1	no	—
930	C₂²	—	4	2	no	—
931	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
932	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
933	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
934	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
935	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
936	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
937	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
938	C₄	—	2	2	no	—
939	C₄	—	2	2	no	—
940	C₄	—	2	2	no	—
941	C₄	—	2	2	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	2	no	—
944	C₄	—	4	1	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	1	no	—
947	C₄	—	4	1	no	—
948	C₄	—	4	1	no	—
949	C₄	—	4	1	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	1	no	—
953	C₄	—	4	2	no	—
954	C₄	—	4	2	no	—
955	C₄	—	4	2	no	—
956	C₄	—	4	2	no	—
957	C₄	—	4	1	no	—
958	C₄	C₃×#542	1	4	yes	—
959	C₃	#42457	1	1	yes	characteristic, direct product factor, Sylow
960	C₂	—	8	1	no	—
961	C₂	—	8	2	no	—
962	C₂	C₂×C₃×#542	1	1	yes	characteristic
963	C₂	C₃×#3492	1	1	yes	characteristic
964	C₂	C₃×#3511	1	1	yes	characteristic
965	C₂	C₃×#3543	1	1	yes	characteristic
966	C₂	C₃×#3550	1	1	yes	characteristic
967	C₂	C₃×#3550	1	1	yes	characteristic
968	C₂	C₃×#3552	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#121	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×#2838	C₂	semidirect
2. C₃×#2801	C₂	semidirect
3. C₃×#2777	C₂	semidirect
4. C₃×#2729	C₂	semidirect
5. C₃×#2674	C₂	semidirect
6. C₃×#2663	C₂	semidirect
7. C₃×#2632	C₂	semidirect
9. C₃×#2592	C₂	semidirect
10. C₃×#2567	C₂	semidirect
11. C₃×#2551	C₂	semidirect
12. C₃×#2542	C₂	semidirect
13. C₃×#2514	C₂	semidirect
14. C₃×#2513	C₂	semidirect
15. C₃×#2492	C₂	semidirect
17. C₃×#2465	C₂	semidirect
18. C₃×#2423	C₂	semidirect
20. C₃×#2396	C₂	semidirect
21. C₃×#2367	C₂	semidirect
22. C₃×Q₈×C₄⋊C₄	C₂	semidirect
23. C₃×#2314	C₂	semidirect
24. #42457	C₃	direct (N × H)
124. #2838	C₂×C₃	semidirect
125. #2801	C₂×C₃	semidirect
126. #2777	C₂×C₃	semidirect
127. #2729	C₂×C₃	semidirect
128. #2674	C₂×C₃	semidirect
129. #2663	C₂×C₃	semidirect
130. #2632	C₂×C₃	semidirect
132. #2592	C₂×C₃	semidirect
133. #2567	C₂×C₃	semidirect
134. #2551	C₂×C₃	semidirect
135. #2542	C₂×C₃	semidirect
136. #2514	C₂×C₃	semidirect
137. #2513	C₂×C₃	semidirect
138. #2492	C₂×C₃	semidirect
140. #2465	C₂×C₃	semidirect
141. #2423	C₂×C₃	semidirect
143. #2396	C₂×C₃	semidirect
144. #2367	C₂×C₃	semidirect
145. Q₈×C₄⋊C₄	C₂×C₃	semidirect
146. #2314	C₂×C₃	semidirect
959. C₃	#42457	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×#2838	2
C₃×#2801	2
C₃×#2777	2
C₃×#2729	2
C₃×#2674	2
C₃×#2663	2
C₃×#2632	2
C₃×#2620	2
C₃×#2592	2
C₃×#2567	2
C₃×#2551	2
C₃×#2542	2
C₃×#2514	2
C₃×#2513	2
C₃×#2492	2
C₃×#2491	2
C₃×#2465	2
C₃×#2423	2
C₃×#2422	2
C₃×#2396	2
C₃×#2367	2
C₃×Q₈×C₄⋊C₄	2
C₃×#2314	2
#42457	3

Subgroups — C3×#42457 #10661064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#42457 #10661064