Subgroups — C₃×#37773 #10656380

Order 768.

2156 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2732	C₂	1	2	yes	maximal, complemented
5	C₃×#2730	C₂	1	2	yes	maximal, complemented
6	C₃×#2721	C₂	1	2	yes	maximal, complemented
7	C₃×#2694	C₂	1	2	yes	maximal, complemented
8	C₃×#2658	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2621	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2542	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2540	C₂	1	1	yes	maximal, characteristic
12	C₃×#2479	C₂	1	2	yes	maximal, complemented
13	C₃×#2471	C₂	1	2	yes	maximal, complemented
14	C₃×#2448	C₂	1	2	yes	maximal, complemented
15	C₃×#2429	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2429	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2427	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2426	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2423	C₂	1	2	yes	maximal, complemented
20	C₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2331	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	#37773	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃×#542	—	2	8	no	—
26	C₃×#533	—	2	8	no	—
27	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃×#126	C₂²	1	2	yes	—
32	C₂×C₃×#125	C₂²	1	2	yes	—
33	C₂×C₃×#124	C₂²	1	1	yes	characteristic
34	C₂×C₃×#124	C₂²	1	1	yes	characteristic
35	C₂×C₃×#124	C₂²	1	2	yes	—
36	C₂×C₃×#124	C₂²	1	1	yes	characteristic
37	C₂×C₃×#123	C₂²	1	2	yes	—
38	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
41	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
42	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
45	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₃×#121	C₂²	1	1	yes	characteristic
47	C₂×C₃×#121	C₂²	1	1	yes	characteristic
48	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
49	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
50	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
51	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
52	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
53	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
54	C₂×C₃×#117	C₂²	1	1	yes	characteristic
55	C₂×C₃×#117	C₂²	1	2	yes	—
56	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
57	C₃×#399	C₂²	1	2	yes	—
58	C₃×#399	C₂²	1	2	yes	—
59	C₃×#399	C₂²	1	2	yes	—
60	C₃×#399	C₂²	1	2	yes	—
61	C₃×#399	C₂²	1	2	yes	—
62	C₃×#399	C₂²	1	2	yes	—
63	C₃×#399	C₂²	1	2	yes	—
64	C₃×#398	C₂²	1	2	yes	—
65	C₃×#398	C₂²	1	2	yes	—
66	C₃×#398	C₂²	1	2	yes	—
67	C₃×#398	C₂²	1	2	yes	—
68	C₃×#397	C₂²	1	2	yes	—
69	C₃×#397	C₂²	1	2	yes	—
70	C₃×#397	C₂²	1	2	yes	—
71	C₃×#396	C₂²	1	2	yes	—
72	C₃×#396	C₂²	1	2	yes	—
73	C₃×#396	C₂²	1	2	yes	—
74	C₃×#394	C₂²	1	2	yes	—
75	C₃×#394	C₂²	1	2	yes	—
76	C₃×#392	C₂²	1	2	yes	—
77	C₃×#391	C₂²	1	1	yes	characteristic
78	C₃×#391	C₂²	1	1	yes	characteristic
79	C₃×#391	C₂²	1	1	yes	characteristic
80	C₃×#391	C₂²	1	2	yes	—
81	C₃×#391	C₂²	1	2	yes	—
82	C₃×#390	C₂²	1	1	yes	characteristic
83	C₃×#390	C₂²	1	2	yes	—
84	C₃×#390	C₂²	1	2	yes	—
85	C₃×#390	C₂²	1	2	yes	—
86	C₃×#390	C₂²	1	2	yes	—
87	C₃×#389	C₂²	1	2	yes	—
88	C₃×#389	C₂²	1	2	yes	—
89	C₃×#389	C₂²	1	1	yes	characteristic
90	C₃×#389	C₂²	1	1	yes	characteristic
91	C₃×#389	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	1	yes	characteristic
99	C₃×#388	C₂²	1	2	yes	—
100	C₃×#388	C₂²	1	1	yes	characteristic
101	C₃×#387	C₂²	1	2	yes	—
102	C₃×#387	C₂²	1	2	yes	—
103	C₃×#387	C₂²	1	1	yes	characteristic
104	C₃×#387	C₂²	1	2	yes	—
105	C₃×#387	C₂²	1	1	yes	characteristic
106	C₃×#387	C₂²	1	2	yes	—
107	C₃×#386	C₂²	1	2	yes	—
108	C₃×#386	C₂²	1	1	yes	characteristic
109	C₃×#386	C₂²	1	2	yes	—
110	C₃×#386	C₂²	1	1	yes	characteristic
111	C₃×#386	C₂²	1	2	yes	—
112	C₃×#385	C₂²	1	2	yes	—
113	C₃×#385	C₂²	1	1	yes	characteristic
114	C₃×#385	C₂²	1	1	yes	characteristic
115	C₃×#384	C₂²	1	2	yes	—
116	C₃×#382	C₂²	1	1	yes	characteristic
117	C₃×#380	C₂²	1	2	yes	—
118	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
119	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
120	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
121	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
122	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
123	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
124	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
125	C₃×#376	C₂²	1	1	yes	characteristic
126	C₂×#542	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂×#533	C₂×C₃	1	1	yes	characteristic, complemented
128	#2850	C₂×C₃	1	1	yes	characteristic, complemented
129	#2732	C₂×C₃	1	2	yes	complemented
130	#2730	C₂×C₃	1	2	yes	complemented
131	#2721	C₂×C₃	1	2	yes	complemented
132	#2694	C₂×C₃	1	2	yes	complemented
133	#2658	C₂×C₃	1	1	yes	characteristic, complemented
134	#2621	C₂×C₃	1	1	yes	characteristic, complemented
135	#2542	C₂×C₃	1	1	yes	characteristic, complemented
136	#2540	C₂×C₃	1	1	yes	characteristic
137	#2479	C₂×C₃	1	2	yes	complemented
138	#2471	C₂×C₃	1	2	yes	complemented
139	#2448	C₂×C₃	1	2	yes	complemented
140	#2429	C₂×C₃	1	1	yes	characteristic, complemented
141	#2429	C₂×C₃	1	1	yes	characteristic, complemented
142	#2427	C₂×C₃	1	1	yes	characteristic, complemented
143	#2426	C₂×C₃	1	1	yes	characteristic, complemented
144	#2423	C₂×C₃	1	2	yes	complemented
145	#2367	C₂×C₃	1	1	yes	characteristic, complemented
146	#2365	C₂×C₃	1	1	yes	characteristic, complemented
147	#2331	C₂×C₃	1	1	yes	characteristic, complemented
148	#2290	C₂×C₃	1	1	yes	characteristic, complemented
149	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
150	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
151	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
152	C₂²×C₃×Q₈	C₂³	1	2	yes	—
153	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
154	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
155	C₂²×C₃×D₄	C₂³	1	2	yes	—
156	C₂²×C₃×D₄	C₂³	1	2	yes	—
157	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
158	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
159	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
160	C₂³×C₃×C₄	C₂³	1	2	yes	—
161	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
162	C₃×C₄⋊Q₈	—	2	4	no	—
163	C₃×C₄⋊Q₈	—	2	4	no	—
164	C₃×C₄⋊Q₈	—	4	2	no	—
165	C₃×C₄⋊Q₈	D₄	1	8	yes	complemented
166	C₃×#126	—	2	8	no	—
167	C₃×#125	—	2	8	no	—
168	C₃×#124	—	2	8	no	—
169	C₃×#124	—	2	4	no	—
170	C₃×#124	—	2	4	no	—
171	C₃×#124	—	4	2	no	—
172	C₃×#123	—	2	8	no	—
173	C₃×C₂²⋊Q₈	—	2	8	no	—
174	C₃×C₂²⋊Q₈	—	2	8	no	—
175	C₃×C₂²⋊Q₈	—	2	4	no	—
176	C₃×C₂²⋊Q₈	—	2	4	no	—
177	C₃×C₂²⋊Q₈	—	2	4	no	—
178	C₃×C₂²⋊Q₈	—	4	2	no	—
179	C₃×C₂²⋊Q₈	—	4	2	no	—
180	C₃×C₂²⋊Q₈	—	4	2	no	—
181	C₃×#121	—	2	4	no	—
182	C₃×#121	—	4	2	no	—
183	C₃×C₄×Q₈	—	2	8	no	—
184	C₃×C₄×Q₈	—	2	4	no	—
185	C₃×C₄×Q₈	—	2	4	no	—
186	C₃×C₄×Q₈	—	2	4	no	—
187	C₃×C₄×D₄	—	2	4	no	—
188	C₃×C₄×D₄	—	2	4	no	—
189	C₃×#117	—	2	8	no	—
190	C₃×#117	—	2	4	no	—
191	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
200	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
207	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
209	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
210	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
211	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
212	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
213	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
214	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
215	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
218	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
219	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
221	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
225	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
226	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
230	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
231	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
233	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
234	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
235	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
236	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
237	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
238	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
239	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
240	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
241	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
242	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
243	C₂×C₃×C₄²	—	2	4	no	—
244	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
245	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
246	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
247	C₂×C₃×C₄²	C₂³	1	2	yes	—
248	C₂×C₃×C₄²	C₂³	1	2	yes	—
249	C₂×C₃×C₄²	C₂³	1	2	yes	—
250	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
251	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
252	C₂×C₃×C₄²	C₂³	1	2	yes	—
253	C₂×C₃×C₄²	C₂³	1	2	yes	—
254	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
255	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
256	C₃×#95	C₂³	1	1	yes	characteristic
257	C₃×#95	C₂³	1	1	yes	characteristic
258	C₃×#95	C₂³	1	1	yes	characteristic
259	C₃×#95	C₂³	1	1	yes	characteristic
260	C₃×#95	C₂³	1	1	yes	characteristic
261	C₃×#95	C₂³	1	1	yes	characteristic
262	C₃×#95	C₂³	1	1	yes	characteristic
263	C₃×#95	C₂³	1	1	yes	characteristic
264	C₃×#95	C₂³	1	2	yes	—
265	C₃×#95	C₂³	1	1	yes	characteristic
266	C₃×#95	C₂³	1	2	yes	—
267	C₃×#95	C₂³	1	1	yes	characteristic
268	C₃×#95	C₂³	1	2	yes	—
269	C₃×#95	C₂³	1	2	yes	—
270	C₃×#95	C₂³	1	2	yes	—
271	C₃×#95	C₂³	1	2	yes	—
272	C₃×#95	C₂³	1	2	yes	—
273	C₃×#95	C₂³	1	2	yes	—
274	C₃×#95	C₂³	1	2	yes	—
275	C₃×#95	C₂³	1	2	yes	—
276	C₃×#95	C₂³	1	2	yes	—
277	C₃×#95	C₂³	1	2	yes	—
278	#542	—	2	8	no	—
279	#533	—	2	8	no	—
280	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
281	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
282	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
283	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
284	C₂×#126	C₂²×C₃	1	2	yes	—
285	C₂×#125	C₂²×C₃	1	2	yes	—
286	C₂×#124	C₂²×C₃	1	1	yes	characteristic
287	C₂×#124	C₂²×C₃	1	1	yes	characteristic
288	C₂×#124	C₂²×C₃	1	2	yes	—
289	C₂×#124	C₂²×C₃	1	1	yes	characteristic
290	C₂×#123	C₂²×C₃	1	2	yes	—
291	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
292	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
293	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
294	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
295	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
296	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
297	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
298	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
299	C₂×#121	C₂²×C₃	1	1	yes	characteristic
300	C₂×#121	C₂²×C₃	1	1	yes	characteristic
301	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
302	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
303	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
304	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
305	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
306	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
307	C₂×#117	C₂²×C₃	1	1	yes	characteristic
308	C₂×#117	C₂²×C₃	1	2	yes	—
309	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
310	#399	C₂²×C₃	1	2	yes	—
311	#399	C₂²×C₃	1	2	yes	—
312	#399	C₂²×C₃	1	2	yes	—
313	#399	C₂²×C₃	1	2	yes	—
314	#399	C₂²×C₃	1	2	yes	—
315	#399	C₂²×C₃	1	2	yes	—
316	#399	C₂²×C₃	1	2	yes	—
317	#398	C₂²×C₃	1	2	yes	—
318	#398	C₂²×C₃	1	2	yes	—
319	#398	C₂²×C₃	1	2	yes	—
320	#398	C₂²×C₃	1	2	yes	—
321	#397	C₂²×C₃	1	2	yes	—
322	#397	C₂²×C₃	1	2	yes	—
323	#397	C₂²×C₃	1	2	yes	—
324	#396	C₂²×C₃	1	2	yes	—
325	#396	C₂²×C₃	1	2	yes	—
326	#396	C₂²×C₃	1	2	yes	—
327	#394	C₂²×C₃	1	2	yes	—
328	#394	C₂²×C₃	1	2	yes	—
329	#392	C₂²×C₃	1	2	yes	—
330	#391	C₂²×C₃	1	2	yes	—
331	#391	C₂²×C₃	1	2	yes	—
332	#391	C₂²×C₃	1	1	yes	characteristic
333	#391	C₂²×C₃	1	1	yes	characteristic
334	#391	C₂²×C₃	1	1	yes	characteristic
335	#390	C₂²×C₃	1	1	yes	characteristic
336	#390	C₂²×C₃	1	2	yes	—
337	#390	C₂²×C₃	1	2	yes	—
338	#390	C₂²×C₃	1	2	yes	—
339	#390	C₂²×C₃	1	2	yes	—
340	#389	C₂²×C₃	1	1	yes	characteristic
341	#389	C₂²×C₃	1	1	yes	characteristic
342	#389	C₂²×C₃	1	2	yes	—
343	#389	C₂²×C₃	1	2	yes	—
344	#389	C₂²×C₃	1	2	yes	—
345	#388	C₂²×C₃	1	2	yes	—
346	#388	C₂²×C₃	1	2	yes	—
347	#388	C₂²×C₃	1	2	yes	—
348	#388	C₂²×C₃	1	2	yes	—
349	#388	C₂²×C₃	1	2	yes	—
350	#388	C₂²×C₃	1	2	yes	—
351	#388	C₂²×C₃	1	2	yes	—
352	#388	C₂²×C₃	1	1	yes	characteristic
353	#388	C₂²×C₃	1	1	yes	characteristic
354	#387	C₂²×C₃	1	2	yes	—
355	#387	C₂²×C₃	1	2	yes	—
356	#387	C₂²×C₃	1	2	yes	—
357	#387	C₂²×C₃	1	2	yes	—
358	#387	C₂²×C₃	1	1	yes	characteristic
359	#387	C₂²×C₃	1	1	yes	characteristic
360	#386	C₂²×C₃	1	2	yes	—
361	#386	C₂²×C₃	1	2	yes	—
362	#386	C₂²×C₃	1	2	yes	—
363	#386	C₂²×C₃	1	1	yes	characteristic
364	#386	C₂²×C₃	1	1	yes	characteristic
365	#385	C₂²×C₃	1	2	yes	—
366	#385	C₂²×C₃	1	1	yes	characteristic
367	#385	C₂²×C₃	1	1	yes	characteristic
368	#384	C₂²×C₃	1	2	yes	—
369	#382	C₂²×C₃	1	1	yes	characteristic
370	#380	C₂²×C₃	1	2	yes	—
371	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
372	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
373	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
374	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
375	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
376	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
377	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
378	#376	C₂²×C₃	1	1	yes	characteristic
379	C₂⁴×C₃	C₂⁴	1	2	yes	—
380	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
381	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
382	C₂×C₃×Q₈	—	2	2	no	—
383	C₂×C₃×Q₈	—	2	2	no	—
384	C₂×C₃×Q₈	—	2	2	no	—
385	C₂×C₃×Q₈	—	2	2	no	—
386	C₂×C₃×Q₈	—	2	2	no	—
387	C₂×C₃×Q₈	—	2	2	no	—
388	C₂×C₃×Q₈	—	2	2	no	—
389	C₂×C₃×Q₈	—	2	2	no	—
390	C₂×C₃×Q₈	—	2	2	no	—
391	C₂×C₃×Q₈	—	4	2	no	—
392	C₂×C₃×Q₈	—	4	2	no	—
393	C₂×C₃×Q₈	C₂×D₄	1	8	yes	—
394	C₂×C₃×D₄	—	2	2	no	—
395	C₂×C₃×D₄	—	2	4	no	—
396	C₂×C₃×D₄	—	2	2	no	—
397	C₂×C₃×D₄	—	2	4	no	—
398	C₂×C₃×D₄	—	2	2	no	—
399	C₂×C₃×D₄	—	2	2	no	—
400	C₂×C₃×D₄	—	2	2	no	—
401	C₂×C₃×D₄	—	4	1	no	—
402	C₂×C₃×D₄	—	4	2	no	—
403	C₂×C₃×D₄	—	4	2	no	—
404	C₂×C₃×D₄	—	4	2	no	—
405	C₂×C₃×D₄	—	4	2	no	—
406	C₂²×C₃×C₄	—	2	2	no	—
407	C₂²×C₃×C₄	—	2	2	no	—
408	C₂²×C₃×C₄	—	2	2	no	—
409	C₂²×C₃×C₄	—	2	2	no	—
410	C₂²×C₃×C₄	—	2	2	no	—
411	C₂²×C₃×C₄	—	2	2	no	—
412	C₂²×C₃×C₄	—	2	2	no	—
413	C₂²×C₃×C₄	—	2	2	no	—
414	C₂²×C₃×C₄	—	2	2	no	—
415	C₂²×C₃×C₄	—	2	2	no	—
416	C₂²×C₃×C₄	—	2	4	no	—
417	C₂²×C₃×C₄	—	4	1	no	—
418	C₂²×C₃×C₄	—	4	1	no	—
419	C₂²×C₃×C₄	—	4	2	no	—
420	C₂²×C₃×C₄	—	4	2	no	—
421	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
422	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
423	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
424	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
425	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
426	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
427	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
428	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
429	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
430	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
431	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
432	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
433	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
434	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
435	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
436	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
437	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
438	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
439	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
440	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
441	C₃×C₄⋊C₄	—	2	2	no	—
442	C₃×C₄⋊C₄	—	2	4	no	—
443	C₃×C₄⋊C₄	—	2	2	no	—
444	C₃×C₄⋊C₄	—	2	4	no	—
445	C₃×C₄⋊C₄	—	2	4	no	—
446	C₃×C₄⋊C₄	—	2	4	no	—
447	C₃×C₄⋊C₄	—	2	4	no	—
448	C₃×C₄⋊C₄	—	2	4	no	—
449	C₃×C₄⋊C₄	—	2	4	no	—
450	C₃×C₄⋊C₄	—	2	4	no	—
451	C₃×C₄⋊C₄	—	2	2	no	—
452	C₃×C₄⋊C₄	—	2	4	no	—
453	C₃×C₄⋊C₄	—	2	4	no	—
454	C₃×C₄⋊C₄	—	2	2	no	—
455	C₃×C₄⋊C₄	—	2	2	no	—
456	C₃×C₄⋊C₄	—	2	2	no	—
457	C₃×C₄⋊C₄	—	4	1	no	—
458	C₃×C₄⋊C₄	—	4	2	no	—
459	C₃×C₄⋊C₄	—	4	2	no	—
460	C₃×C₄⋊C₄	—	4	2	no	—
461	C₃×C₄⋊C₄	—	4	2	no	—
462	C₃×C₄⋊C₄	—	4	2	no	—
463	C₃×C₄⋊C₄	—	4	2	no	—
464	C₃×C₄⋊C₄	—	4	2	no	—
465	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
466	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
467	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
468	C₃×C₂²⋊C₄	—	2	2	no	—
469	C₃×C₂²⋊C₄	—	2	4	no	—
470	C₃×C₂²⋊C₄	—	2	4	no	—
471	C₃×C₂²⋊C₄	—	2	2	no	—
472	C₃×C₂²⋊C₄	—	2	2	no	—
473	C₃×C₂²⋊C₄	—	2	4	no	—
474	C₃×C₂²⋊C₄	—	2	4	no	—
475	C₃×C₂²⋊C₄	—	2	4	no	—
476	C₃×C₂²⋊C₄	—	2	4	no	—
477	C₃×C₂²⋊C₄	—	2	4	no	—
478	C₃×C₂²⋊C₄	—	2	2	no	—
479	C₃×C₂²⋊C₄	—	2	2	no	—
480	C₃×C₂²⋊C₄	—	2	4	no	—
481	C₃×C₂²⋊C₄	—	2	4	no	—
482	C₃×C₂²⋊C₄	—	2	4	no	—
483	C₃×C₂²⋊C₄	—	2	2	no	—
484	C₃×C₂²⋊C₄	—	4	2	no	—
485	C₃×C₂²⋊C₄	—	4	1	no	—
486	C₃×C₂²⋊C₄	—	4	1	no	—
487	C₃×C₂²⋊C₄	—	4	2	no	—
488	C₃×C₂²⋊C₄	—	4	2	no	—
489	C₃×C₂²⋊C₄	—	4	2	no	—
490	C₃×C₂²⋊C₄	—	4	2	no	—
491	C₃×C₂²⋊C₄	—	4	2	no	—
492	C₃×C₂²⋊C₄	—	4	2	no	—
493	C₃×C₄²	—	2	2	no	—
494	C₃×C₄²	—	2	2	no	—
495	C₃×C₄²	—	2	2	no	—
496	C₃×C₄²	—	2	2	no	—
497	C₃×C₄²	—	2	4	no	—
498	C₃×C₄²	—	2	4	no	—
499	C₃×C₄²	—	2	4	no	—
500	C₃×C₄²	—	2	2	no	—
501	C₃×C₄²	—	4	2	no	—
502	C₃×C₄²	—	4	2	no	—
503	C₃×C₄²	C₂×D₄	1	4	yes	—
504	C₃×C₄²	#41	1	4	yes	—
505	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
506	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
507	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
508	C₂²×Q₈	C₂³×C₃	1	2	yes	—
509	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
510	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
511	C₂²×D₄	C₂³×C₃	1	2	yes	—
512	C₂²×D₄	C₂³×C₃	1	2	yes	—
513	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
514	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
516	C₂³×C₄	C₂³×C₃	1	2	yes	—
517	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
518	C₄⋊Q₈	—	2	4	no	—
519	C₄⋊Q₈	—	2	4	no	—
520	C₄⋊Q₈	—	4	2	no	—
521	C₄⋊Q₈	C₃×D₄	1	8	yes	complemented
522	#126	—	2	8	no	—
523	#125	—	2	8	no	—
524	#124	—	2	8	no	—
525	#124	—	2	4	no	—
526	#124	—	2	4	no	—
527	#124	—	4	2	no	—
528	#123	—	2	8	no	—
529	C₂²⋊Q₈	—	2	8	no	—
530	C₂²⋊Q₈	—	2	8	no	—
531	C₂²⋊Q₈	—	2	4	no	—
532	C₂²⋊Q₈	—	2	4	no	—
533	C₂²⋊Q₈	—	2	4	no	—
534	C₂²⋊Q₈	—	4	2	no	—
535	C₂²⋊Q₈	—	4	2	no	—
536	C₂²⋊Q₈	—	4	2	no	—
537	#121	—	2	4	no	—
538	#121	—	4	2	no	—
539	C₄×Q₈	—	2	8	no	—
540	C₄×Q₈	—	2	4	no	—
541	C₄×Q₈	—	2	4	no	—
542	C₄×Q₈	—	2	4	no	—
543	C₄×D₄	—	2	4	no	—
544	C₄×D₄	—	2	4	no	—
545	#117	—	2	8	no	—
546	#117	—	2	4	no	—
547	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
551	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
574	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
577	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
578	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
580	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
581	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
588	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
590	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
598	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
599	C₂×C₄²	—	2	4	no	—
600	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₃	1	2	yes	—
602	C₂×C₄²	C₂³×C₃	1	2	yes	—
603	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₃	1	2	yes	—
606	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₃	1	2	yes	—
609	C₂×C₄²	C₂³×C₃	1	2	yes	—
610	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
611	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
612	#95	C₂³×C₃	1	1	yes	characteristic
613	#95	C₂³×C₃	1	1	yes	characteristic
614	#95	C₂³×C₃	1	1	yes	characteristic
615	#95	C₂³×C₃	1	1	yes	characteristic
616	#95	C₂³×C₃	1	1	yes	characteristic
617	#95	C₂³×C₃	1	1	yes	characteristic
618	#95	C₂³×C₃	1	1	yes	characteristic
619	#95	C₂³×C₃	1	1	yes	characteristic
620	#95	C₂³×C₃	1	2	yes	—
621	#95	C₂³×C₃	1	1	yes	characteristic
622	#95	C₂³×C₃	1	2	yes	—
623	#95	C₂³×C₃	1	1	yes	characteristic
624	#95	C₂³×C₃	1	2	yes	—
625	#95	C₂³×C₃	1	2	yes	—
626	#95	C₂³×C₃	1	2	yes	—
627	#95	C₂³×C₃	1	2	yes	—
628	#95	C₂³×C₃	1	2	yes	—
629	#95	C₂³×C₃	1	2	yes	—
630	#95	C₂³×C₃	1	2	yes	—
631	#95	C₂³×C₃	1	2	yes	—
632	#95	C₂³×C₃	1	2	yes	—
633	#95	C₂³×C₃	1	2	yes	—
634	C₂³×C₃	—	2	1	no	—
635	C₂³×C₃	—	2	1	no	—
636	C₂³×C₃	—	2	1	no	—
637	C₂³×C₃	—	2	1	no	—
638	C₂³×C₃	—	2	1	no	—
639	C₂³×C₃	—	2	1	no	—
640	C₂³×C₃	—	2	1	no	—
641	C₂³×C₃	—	2	2	no	—
642	C₂³×C₃	—	2	2	no	—
643	C₂³×C₃	—	2	1	no	—
644	C₂³×C₃	—	2	1	no	—
645	C₂³×C₃	—	2	2	no	—
646	C₂³×C₃	—	2	2	no	—
647	C₂³×C₃	—	2	1	no	—
648	C₂³×C₃	—	2	1	no	—
649	C₂³×C₃	—	2	2	no	—
650	C₂³×C₃	—	2	2	no	—
651	C₂³×C₃	—	2	1	no	—
652	C₂³×C₃	—	2	2	no	—
653	C₂³×C₃	—	2	1	no	—
654	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
655	C₂³×C₃	C₂⁵	1	1	yes	characteristic
656	C₃×Q₈	—	4	8	no	—
657	C₃×Q₈	—	4	4	no	—
658	C₃×Q₈	—	4	4	no	—
659	C₃×Q₈	—	4	4	no	—
660	C₃×D₄	—	4	4	no	—
661	C₃×D₄	—	4	4	no	—
662	C₃×D₄	—	8	4	no	—
663	C₃×D₄	—	8	4	no	—
664	C₂×C₃×C₄	—	2	8	no	—
665	C₂×C₃×C₄	—	2	1	no	—
666	C₂×C₃×C₄	—	2	1	no	—
667	C₂×C₃×C₄	—	2	1	no	—
668	C₂×C₃×C₄	—	2	1	no	—
669	C₂×C₃×C₄	—	2	1	no	—
670	C₂×C₃×C₄	—	2	1	no	—
671	C₂×C₃×C₄	—	2	1	no	—
672	C₂×C₃×C₄	—	2	1	no	—
673	C₂×C₃×C₄	—	2	2	no	—
674	C₂×C₃×C₄	—	2	2	no	—
675	C₂×C₃×C₄	—	2	2	no	—
676	C₂×C₃×C₄	—	2	2	no	—
677	C₂×C₃×C₄	—	2	1	no	—
678	C₂×C₃×C₄	—	2	1	no	—
679	C₂×C₃×C₄	—	2	1	no	—
680	C₂×C₃×C₄	—	2	1	no	—
681	C₂×C₃×C₄	—	2	1	no	—
682	C₂×C₃×C₄	—	2	2	no	—
683	C₂×C₃×C₄	—	2	2	no	—
684	C₂×C₃×C₄	—	2	2	no	—
685	C₂×C₃×C₄	—	2	1	no	—
686	C₂×C₃×C₄	—	2	1	no	—
687	C₂×C₃×C₄	—	2	2	no	—
688	C₂×C₃×C₄	—	2	1	no	—
689	C₂×C₃×C₄	—	2	1	no	—
690	C₂×C₃×C₄	—	2	2	no	—
691	C₂×C₃×C₄	—	2	2	no	—
692	C₂×C₃×C₄	—	2	1	no	—
693	C₂×C₃×C₄	—	2	1	no	—
694	C₂×C₃×C₄	—	2	2	no	—
695	C₂×C₃×C₄	—	2	2	no	—
696	C₂×C₃×C₄	—	2	2	no	—
697	C₂×C₃×C₄	—	2	1	no	—
698	C₂×C₃×C₄	—	2	2	no	—
699	C₂×C₃×C₄	—	2	2	no	—
700	C₂×C₃×C₄	—	2	1	no	—
701	C₂×C₃×C₄	—	2	1	no	—
702	C₂×C₃×C₄	—	2	1	no	—
703	C₂×C₃×C₄	—	2	2	no	—
704	C₂×C₃×C₄	—	2	1	no	—
705	C₂×C₃×C₄	—	2	1	no	—
706	C₂×C₃×C₄	—	2	2	no	—
707	C₂×C₃×C₄	—	2	2	no	—
708	C₂×C₃×C₄	—	2	2	no	—
709	C₂×C₃×C₄	—	2	1	no	—
710	C₂×C₃×C₄	—	2	1	no	—
711	C₂×C₃×C₄	—	2	1	no	—
712	C₂×C₃×C₄	—	2	1	no	—
713	C₂×C₃×C₄	—	2	1	no	—
714	C₂×C₃×C₄	—	2	1	no	—
715	C₂×C₃×C₄	—	4	4	no	—
716	C₂×C₃×C₄	—	4	4	no	—
717	C₂×C₃×C₄	—	4	4	no	—
718	C₂×C₃×C₄	—	8	4	no	—
719	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
720	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
721	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
722	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
723	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
724	C₂×C₃×C₄	C₂×#41	1	2	yes	—
725	C₂×C₃×C₄	C₂×#41	1	2	yes	—
726	C₂×C₃×C₄	C₂×#41	1	2	yes	—
727	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
728	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
729	C₂⁴	C₂⁴×C₃	1	2	yes	—
730	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
731	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
732	C₂×Q₈	—	2	2	no	—
733	C₂×Q₈	—	2	2	no	—
734	C₂×Q₈	—	2	2	no	—
735	C₂×Q₈	—	2	2	no	—
736	C₂×Q₈	—	2	2	no	—
737	C₂×Q₈	—	2	2	no	—
738	C₂×Q₈	—	2	2	no	—
739	C₂×Q₈	—	2	2	no	—
740	C₂×Q₈	—	2	2	no	—
741	C₂×Q₈	—	4	2	no	—
742	C₂×Q₈	—	4	2	no	—
743	C₂×Q₈	C₂×C₃×D₄	1	8	yes	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	4	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	4	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	4	1	no	—
752	C₂×D₄	—	4	2	no	—
753	C₂×D₄	—	4	2	no	—
754	C₂×D₄	—	4	2	no	—
755	C₂×D₄	—	4	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	2	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	4	no	—
767	C₂²×C₄	—	4	1	no	—
768	C₂²×C₄	—	4	1	no	—
769	C₂²×C₄	—	4	2	no	—
770	C₂²×C₄	—	4	2	no	—
771	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
782	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
786	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	4	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	4	no	—
795	C₄⋊C₄	—	2	4	no	—
796	C₄⋊C₄	—	2	4	no	—
797	C₄⋊C₄	—	2	4	no	—
798	C₄⋊C₄	—	2	4	no	—
799	C₄⋊C₄	—	2	4	no	—
800	C₄⋊C₄	—	2	4	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	4	no	—
803	C₄⋊C₄	—	2	4	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	4	2	no	—
808	C₄⋊C₄	—	4	2	no	—
809	C₄⋊C₄	—	4	2	no	—
810	C₄⋊C₄	—	4	2	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	1	no	—
813	C₄⋊C₄	—	4	2	no	—
814	C₄⋊C₄	—	4	2	no	—
815	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
816	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
817	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	4	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	4	no	—
831	C₂²⋊C₄	—	2	4	no	—
832	C₂²⋊C₄	—	2	4	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	4	2	no	—
835	C₂²⋊C₄	—	4	2	no	—
836	C₂²⋊C₄	—	4	2	no	—
837	C₂²⋊C₄	—	4	2	no	—
838	C₂²⋊C₄	—	4	2	no	—
839	C₂²⋊C₄	—	4	2	no	—
840	C₂²⋊C₄	—	4	2	no	—
841	C₂²⋊C₄	—	4	1	no	—
842	C₂²⋊C₄	—	4	1	no	—
843	C₄²	—	2	2	no	—
844	C₄²	—	2	2	no	—
845	C₄²	—	2	2	no	—
846	C₄²	—	2	2	no	—
847	C₄²	—	2	4	no	—
848	C₄²	—	2	4	no	—
849	C₄²	—	2	4	no	—
850	C₄²	—	2	2	no	—
851	C₄²	—	4	2	no	—
852	C₄²	—	4	2	no	—
853	C₄²	C₂×C₃×D₄	1	4	yes	—
854	C₄²	C₃×#41	1	4	yes	—
855	C₂²×C₃	—	2	2	no	—
856	C₂²×C₃	—	2	2	no	—
857	C₂²×C₃	—	2	2	no	—
858	C₂²×C₃	—	4	1	no	—
859	C₂²×C₃	—	4	1	no	—
860	C₂²×C₃	—	4	1	no	—
861	C₂²×C₃	—	4	1	no	—
862	C₂²×C₃	—	4	2	no	—
863	C₂²×C₃	—	4	1	no	—
864	C₂²×C₃	—	4	1	no	—
865	C₂²×C₃	—	4	2	no	—
866	C₂²×C₃	—	4	2	no	—
867	C₂²×C₃	—	4	1	no	—
868	C₂²×C₃	—	4	1	no	—
869	C₂²×C₃	—	4	2	no	—
870	C₂²×C₃	—	4	1	no	—
871	C₂²×C₃	—	4	2	no	—
872	C₂²×C₃	—	4	1	no	—
873	C₂²×C₃	—	4	2	no	—
874	C₂²×C₃	—	4	2	no	—
875	C₂²×C₃	—	4	1	no	—
876	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
877	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
878	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
879	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
880	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
881	C₂²×C₃	#585	1	1	yes	characteristic
882	C₂²×C₃	#585	1	1	yes	characteristic
883	C₃×C₄	—	2	2	no	—
884	C₃×C₄	—	2	2	no	—
885	C₃×C₄	—	2	4	no	—
886	C₃×C₄	—	2	4	no	—
887	C₃×C₄	—	2	2	no	—
888	C₃×C₄	—	2	2	no	—
889	C₃×C₄	—	2	2	no	—
890	C₃×C₄	—	4	1	no	—
891	C₃×C₄	—	4	1	no	—
892	C₃×C₄	—	4	2	no	—
893	C₃×C₄	—	4	2	no	—
894	C₃×C₄	—	4	2	no	—
895	C₃×C₄	—	4	1	no	—
896	C₃×C₄	—	4	1	no	—
897	C₃×C₄	—	4	1	no	—
898	C₃×C₄	—	4	1	no	—
899	C₃×C₄	—	4	2	no	—
900	C₃×C₄	—	4	1	no	—
901	C₃×C₄	—	4	2	no	—
902	C₃×C₄	#550	1	4	yes	—
903	C₂³	—	2	1	no	—
904	C₂³	—	2	1	no	—
905	C₂³	—	2	1	no	—
906	C₂³	—	2	1	no	—
907	C₂³	—	2	1	no	—
908	C₂³	—	2	1	no	—
909	C₂³	—	2	1	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	2	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	1	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	2	no	—
916	C₂³	—	2	1	no	—
917	C₂³	—	2	1	no	—
918	C₂³	—	2	2	no	—
919	C₂³	—	2	2	no	—
920	C₂³	—	2	1	no	—
921	C₂³	—	2	2	no	—
922	C₂³	—	2	1	no	—
923	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
924	C₂³	C₂⁵×C₃	1	1	yes	characteristic
925	Q₈	—	4	8	no	—
926	Q₈	—	4	4	no	—
927	Q₈	—	4	4	no	—
928	Q₈	—	4	4	no	—
929	D₄	—	4	4	no	—
930	D₄	—	4	4	no	—
931	D₄	—	8	4	no	—
932	D₄	—	8	4	no	—
933	C₂×C₄	—	2	8	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	4	4	no	—
985	C₂×C₄	—	4	4	no	—
986	C₂×C₄	—	4	4	no	—
987	C₂×C₄	—	8	4	no	—
988	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
989	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
990	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
991	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
992	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
993	C₂×C₄	C₂×C₃×#41	1	2	yes	—
994	C₂×C₄	C₂×C₃×#41	1	2	yes	—
995	C₂×C₄	C₂×C₃×#41	1	2	yes	—
996	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
997	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
998	C₂×C₃	—	4	2	no	—
999	C₂×C₃	—	8	1	no	—
1000	C₂×C₃	—	8	2	no	—
1001	C₂×C₃	#3461	1	1	yes	characteristic
1002	C₂×C₃	C₂×#550	1	1	yes	characteristic
1003	C₂×C₃	#3485	1	1	yes	characteristic
1004	C₂×C₃	#3486	1	1	yes	characteristic
1005	C₂×C₃	#3495	1	1	yes	characteristic
1006	C₂×C₃	#3554	1	1	yes	characteristic
1007	C₂×C₃	#3561	1	1	yes	characteristic
1008	C₂²	—	2	2	no	—
1009	C₂²	—	2	2	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	4	1	no	—
1012	C₂²	—	4	1	no	—
1013	C₂²	—	4	1	no	—
1014	C₂²	—	4	1	no	—
1015	C₂²	—	4	2	no	—
1016	C₂²	—	4	1	no	—
1017	C₂²	—	4	1	no	—
1018	C₂²	—	4	2	no	—
1019	C₂²	—	4	2	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	1	no	—
1022	C₂²	—	4	2	no	—
1023	C₂²	—	4	1	no	—
1024	C₂²	—	4	2	no	—
1025	C₂²	—	4	1	no	—
1026	C₂²	—	4	2	no	—
1027	C₂²	—	4	2	no	—
1028	C₂²	—	4	1	no	—
1029	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1030	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1031	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1032	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1033	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1034	C₂²	C₃×#585	1	1	yes	characteristic
1035	C₂²	C₃×#585	1	1	yes	characteristic
1036	C₄	—	2	2	no	—
1037	C₄	—	2	2	no	—
1038	C₄	—	2	4	no	—
1039	C₄	—	2	4	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	2	2	no	—
1043	C₄	—	4	1	no	—
1044	C₄	—	4	1	no	—
1045	C₄	—	4	2	no	—
1046	C₄	—	4	2	no	—
1047	C₄	—	4	2	no	—
1048	C₄	—	4	1	no	—
1049	C₄	—	4	1	no	—
1050	C₄	—	4	1	no	—
1051	C₄	—	4	1	no	—
1052	C₄	—	4	2	no	—
1053	C₄	—	4	2	no	—
1054	C₄	—	4	1	no	—
1055	C₄	C₃×#550	1	4	yes	—
1056	C₃	#37773	1	1	yes	characteristic, direct product factor, Sylow
1057	C₂	—	4	2	no	—
1058	C₂	—	8	1	no	—
1059	C₂	—	8	2	no	—
1060	C₂	C₃×#3461	1	1	yes	characteristic
1061	C₂	C₂×C₃×#550	1	1	yes	characteristic
1062	C₂	C₃×#3485	1	1	yes	characteristic
1063	C₂	C₃×#3486	1	1	yes	characteristic
1064	C₂	C₃×#3495	1	1	yes	characteristic
1065	C₂	C₃×#3554	1	1	yes	characteristic
1066	C₂	C₃×#3561	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₃×#2540	C₂
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×#542	C₂	semidirect
2. C₂×C₃×#533	C₂	semidirect
3. C₃×#2850	C₂	semidirect
4. C₃×#2732	C₂	semidirect
5. C₃×#2730	C₂	semidirect
6. C₃×#2721	C₂	semidirect
7. C₃×#2694	C₂	semidirect
8. C₃×#2658	C₂	semidirect
9. C₃×#2621	C₂	semidirect
10. C₃×#2542	C₂	semidirect
12. C₃×#2479	C₂	semidirect
13. C₃×#2471	C₂	semidirect
14. C₃×#2448	C₂	semidirect
15. C₃×#2429	C₂	semidirect
16. C₃×#2429	C₂	semidirect
17. C₃×#2427	C₂	semidirect
18. C₃×#2426	C₂	semidirect
19. C₃×#2423	C₂	semidirect
20. C₃×#2367	C₂	semidirect
21. C₃×#2365	C₂	semidirect
22. C₃×#2331	C₂	semidirect
23. C₃×#2290	C₂	semidirect
24. #37773	C₃	direct (N × H)
126. C₂×#542	C₂×C₃	semidirect
127. C₂×#533	C₂×C₃	semidirect
128. #2850	C₂×C₃	semidirect
129. #2732	C₂×C₃	semidirect
130. #2730	C₂×C₃	semidirect
131. #2721	C₂×C₃	semidirect
132. #2694	C₂×C₃	semidirect
133. #2658	C₂×C₃	semidirect
134. #2621	C₂×C₃	semidirect
135. #2542	C₂×C₃	semidirect
137. #2479	C₂×C₃	semidirect
138. #2471	C₂×C₃	semidirect
139. #2448	C₂×C₃	semidirect
140. #2429	C₂×C₃	semidirect
141. #2429	C₂×C₃	semidirect
142. #2427	C₂×C₃	semidirect
143. #2426	C₂×C₃	semidirect
144. #2423	C₂×C₃	semidirect
145. #2367	C₂×C₃	semidirect
146. #2365	C₂×C₃	semidirect
147. #2331	C₂×C₃	semidirect
148. #2290	C₂×C₃	semidirect
165. C₃×C₄⋊Q₈	D₄	semidirect
521. C₄⋊Q₈	C₃×D₄	semidirect
1056. C₃	#37773	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×#542	2
C₂×C₃×#533	2
C₃×#2850	2
C₃×#2732	2
C₃×#2730	2
C₃×#2721	2
C₃×#2694	2
C₃×#2658	2
C₃×#2621	2
C₃×#2542	2
C₃×#2540	2
C₃×#2479	2
C₃×#2471	2
C₃×#2448	2
C₃×#2429	2
C₃×#2427	2
C₃×#2426	2
C₃×#2423	2
C₃×#2367	2
C₃×#2365	2
C₃×#2331	2
C₃×#2290	2
#37773	3

Subgroups — C3×#37773 #10656380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37773 #10656380