Subgroups — C₃×#35253 #10653860

Order 768.

2470 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#117	C₂	1	1	yes	maximal, characteristic
3	C₃×#2857	C₂	1	2	yes	maximal, complemented
4	C₃×#2851	C₂	1	2	yes	maximal, complemented
5	C₃×#2629	C₂	1	2	yes	maximal, complemented
6	C₃×#2628	C₂	1	2	yes	maximal, complemented
7	C₃×#2442	C₂	1	2	yes	maximal, complemented
8	C₃×#2441	C₂	1	2	yes	maximal, complemented
9	C₃×#2440	C₂	1	2	yes	maximal, complemented
10	C₃×#2439	C₂	1	2	yes	maximal, complemented
11	C₃×#2438	C₂	1	4	yes	maximal, complemented
12	C₃×#2437	C₂	1	4	yes	maximal
13	C₃×#2317	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2317	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2316	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2280	C₂	1	1	yes	maximal, characteristic
17	C₂×C₃×#380	C₂	1	1	yes	maximal, characteristic
18	#35253	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
20	C₃×#544	—	2	8	no	—
21	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
22	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
23	C₂×C₃×#125	C₂²	1	2	yes	complemented
24	C₂×C₃×#125	C₂²	1	2	yes	complemented
25	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
26	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
27	C₂×C₃×#117	—	2	8	no	—
28	C₂×C₃×#117	C₂²	1	2	yes	—
29	C₂×C₃×#117	C₂²	1	2	yes	—
30	C₂×C₃×#117	C₂²	1	1	yes	characteristic
31	C₂×C₃×#117	C₂²	1	1	yes	characteristic
32	C₂×C₃×#117	C₂²	1	1	yes	characteristic
33	C₂×C₃×#117	C₂²	1	1	yes	characteristic
34	C₂×C₃×#117	C₂²	1	1	yes	characteristic
35	C₂×C₃×#117	C₂²	1	1	yes	characteristic
36	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
41	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
42	C₂²×C₃×C₄²	C₂²	1	2	yes	—
43	C₃×#400	C₂²	1	4	yes	complemented
44	C₃×#399	C₂²	1	4	yes	—
45	C₃×#398	C₂²	1	4	yes	complemented
46	C₃×#398	C₂²	1	4	yes	complemented
47	C₃×#396	C₂²	1	4	yes	—
48	C₃×#396	C₂²	1	4	yes	—
49	C₃×#395	C₂²	1	4	yes	complemented
50	C₃×#393	C₂²	1	4	yes	—
51	C₃×#391	C₂²	1	4	yes	complemented
52	C₃×#389	C₂²	1	2	yes	complemented
53	C₃×#389	C₂²	1	2	yes	complemented
54	C₃×#389	C₂²	1	2	yes	complemented
55	C₃×#389	C₂²	1	2	yes	complemented
56	C₃×#389	C₂²	1	4	yes	complemented
57	C₃×#389	C₂²	1	2	yes	complemented
58	C₃×#389	C₂²	1	2	yes	complemented
59	C₃×#389	C₂²	1	2	yes	complemented
60	C₃×#389	C₂²	1	2	yes	complemented
61	C₃×#387	C₂²	1	4	yes	complemented
62	C₃×#387	C₂²	1	4	yes	complemented
63	C₃×#385	C₂²	1	4	yes	—
64	C₃×#385	C₂²	1	4	yes	—
65	C₃×#385	C₂²	1	4	yes	—
66	C₃×#385	C₂²	1	4	yes	—
67	C₃×#384	C₂²	1	2	yes	complemented
68	C₃×#384	C₂²	1	2	yes	complemented
69	C₃×#382	C₂²	1	2	yes	complemented
70	C₃×#382	C₂²	1	2	yes	complemented
71	C₃×#381	C₂²	1	2	yes	—
72	C₃×#380	C₂²	1	1	yes	characteristic
73	C₃×#380	C₂²	1	2	yes	—
74	C₃×#380	C₂²	1	1	yes	characteristic
75	C₃×#380	C₂²	1	4	yes	—
76	C₃×#380	C₂²	1	4	yes	—
77	C₃×#380	C₂²	1	2	yes	—
78	C₃×#380	C₂²	1	2	yes	—
79	C₃×#380	C₂²	1	2	yes	—
80	C₃×#380	C₂²	1	1	yes	characteristic
81	C₃×#380	C₂²	1	1	yes	characteristic
82	C₃×#379	C₂²	1	2	yes	—
83	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
84	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
85	C₂×C₃×#95	C₂²	1	2	yes	—
86	C₂×#544	C₂×C₃	1	1	yes	characteristic, complemented
87	C₂²×#117	C₂×C₃	1	1	yes	characteristic
88	#2857	C₂×C₃	1	2	yes	complemented
89	#2851	C₂×C₃	1	2	yes	complemented
90	#2629	C₂×C₃	1	2	yes	complemented
91	#2628	C₂×C₃	1	2	yes	complemented
92	#2442	C₂×C₃	1	2	yes	complemented
93	#2441	C₂×C₃	1	2	yes	complemented
94	#2440	C₂×C₃	1	2	yes	complemented
95	#2439	C₂×C₃	1	2	yes	complemented
96	#2438	C₂×C₃	1	4	yes	complemented
97	#2437	C₂×C₃	1	4	yes	—
98	#2317	C₂×C₃	1	1	yes	characteristic, complemented
99	#2317	C₂×C₃	1	1	yes	characteristic, complemented
100	#2316	C₂×C₃	1	1	yes	characteristic, complemented
101	#2280	C₂×C₃	1	1	yes	characteristic
102	C₂×#380	C₂×C₃	1	1	yes	characteristic
103	C₂⁵×C₃	C₂³	1	1	yes	characteristic
104	C₂²×C₃×Q₈	C₂³	1	4	yes	—
105	C₂³×C₃×C₄	—	2	4	no	—
106	C₂³×C₃×C₄	—	2	4	no	—
107	C₂³×C₃×C₄	Q₈	1	8	yes	complemented
108	C₂³×C₃×C₄	C₂³	1	2	yes	—
109	C₂³×C₃×C₄	C₂³	1	2	yes	—
110	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
111	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
112	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
113	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
114	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
115	C₂³×C₃×C₄	C₂³	1	2	yes	—
116	C₂³×C₃×C₄	C₂³	1	2	yes	—
117	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
118	C₃×C₄⋊Q₈	—	2	8	no	—
119	C₃×C₄⋊Q₈	—	2	8	no	—
120	C₃×#125	—	2	8	no	—
121	C₃×#125	—	2	8	no	—
122	C₃×C₂²⋊Q₈	—	2	16	no	—
123	C₃×C₂²⋊Q₈	—	4	8	no	—
124	C₃×#117	—	2	4	no	—
125	C₃×#117	—	2	4	no	—
126	C₃×#117	—	2	4	no	—
127	C₃×#117	—	2	4	no	—
128	C₃×#117	—	2	4	no	—
129	C₃×#117	—	2	8	no	—
130	C₃×#117	—	2	8	no	—
131	C₃×#117	D₄	1	8	yes	—
132	C₂×C₃×C₄⋊C₄	—	2	4	no	—
133	C₂×C₃×C₄⋊C₄	—	2	4	no	—
134	C₂×C₃×C₄⋊C₄	—	2	4	no	—
135	C₂×C₃×C₄⋊C₄	—	2	4	no	—
136	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
137	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
140	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
145	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
148	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
149	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
152	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
153	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
154	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
155	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
156	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
157	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
160	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
161	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
166	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
172	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₃×C₄²	—	2	8	no	—
174	C₂×C₃×C₄²	C₂³	1	2	yes	—
175	C₂×C₃×C₄²	C₂³	1	2	yes	—
176	C₂×C₃×C₄²	C₂³	1	2	yes	—
177	C₂×C₃×C₄²	C₂³	1	2	yes	—
178	C₂×C₃×C₄²	C₂³	1	2	yes	—
179	C₂×C₃×C₄²	C₂³	1	2	yes	—
180	C₃×#95	C₂³	1	4	yes	—
181	C₃×#95	C₂³	1	4	yes	—
182	C₃×#95	C₂³	1	2	yes	—
183	C₃×#95	C₂³	1	2	yes	—
184	C₃×#95	C₂³	1	2	yes	—
185	C₃×#95	C₂³	1	2	yes	—
186	C₃×#95	C₂³	1	4	yes	—
187	C₃×#95	C₂³	1	4	yes	—
188	C₃×#95	C₂³	1	4	yes	—
189	C₃×#95	C₂³	1	4	yes	—
190	C₃×#95	C₂³	1	4	yes	—
191	C₃×#95	C₂³	1	4	yes	—
192	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
193	#544	—	2	8	no	—
194	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
195	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
196	C₂×#125	C₂²×C₃	1	2	yes	complemented
197	C₂×#125	C₂²×C₃	1	2	yes	complemented
198	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
199	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
200	C₂×#117	—	2	8	no	—
201	C₂×#117	C₂²×C₃	1	1	yes	characteristic
202	C₂×#117	C₂²×C₃	1	1	yes	characteristic
203	C₂×#117	C₂²×C₃	1	1	yes	characteristic
204	C₂×#117	C₂²×C₃	1	2	yes	—
205	C₂×#117	C₂²×C₃	1	2	yes	—
206	C₂×#117	C₂²×C₃	1	1	yes	characteristic
207	C₂×#117	C₂²×C₃	1	1	yes	characteristic
208	C₂×#117	C₂²×C₃	1	1	yes	characteristic
209	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
210	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
211	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
212	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
213	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
214	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
215	C₂²×C₄²	C₂²×C₃	1	2	yes	—
216	#400	C₂²×C₃	1	4	yes	complemented
217	#399	C₂²×C₃	1	4	yes	—
218	#398	C₂²×C₃	1	4	yes	complemented
219	#398	C₂²×C₃	1	4	yes	complemented
220	#396	C₂²×C₃	1	4	yes	—
221	#396	C₂²×C₃	1	4	yes	—
222	#395	C₂²×C₃	1	4	yes	complemented
223	#393	C₂²×C₃	1	4	yes	—
224	#391	C₂²×C₃	1	4	yes	complemented
225	#389	C₂²×C₃	1	2	yes	complemented
226	#389	C₂²×C₃	1	2	yes	complemented
227	#389	C₂²×C₃	1	2	yes	complemented
228	#389	C₂²×C₃	1	2	yes	complemented
229	#389	C₂²×C₃	1	2	yes	complemented
230	#389	C₂²×C₃	1	2	yes	complemented
231	#389	C₂²×C₃	1	2	yes	complemented
232	#389	C₂²×C₃	1	2	yes	complemented
233	#389	C₂²×C₃	1	4	yes	complemented
234	#387	C₂²×C₃	1	4	yes	complemented
235	#387	C₂²×C₃	1	4	yes	complemented
236	#385	C₂²×C₃	1	4	yes	—
237	#385	C₂²×C₃	1	4	yes	—
238	#385	C₂²×C₃	1	4	yes	—
239	#385	C₂²×C₃	1	4	yes	—
240	#384	C₂²×C₃	1	2	yes	complemented
241	#384	C₂²×C₃	1	2	yes	complemented
242	#382	C₂²×C₃	1	2	yes	complemented
243	#382	C₂²×C₃	1	2	yes	complemented
244	#381	C₂²×C₃	1	2	yes	—
245	#380	C₂²×C₃	1	4	yes	—
246	#380	C₂²×C₃	1	1	yes	characteristic
247	#380	C₂²×C₃	1	2	yes	—
248	#380	C₂²×C₃	1	1	yes	characteristic
249	#380	C₂²×C₃	1	4	yes	—
250	#380	C₂²×C₃	1	1	yes	characteristic
251	#380	C₂²×C₃	1	2	yes	—
252	#380	C₂²×C₃	1	1	yes	characteristic
253	#380	C₂²×C₃	1	2	yes	—
254	#380	C₂²×C₃	1	2	yes	—
255	#379	C₂²×C₃	1	2	yes	—
256	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
257	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
258	C₂×#95	C₂²×C₃	1	2	yes	—
259	C₂⁴×C₃	—	2	2	no	—
260	C₂⁴×C₃	—	2	2	no	—
261	C₂⁴×C₃	—	2	2	no	—
262	C₂⁴×C₃	—	2	2	no	—
263	C₂⁴×C₃	—	4	1	no	—
264	C₂⁴×C₃	—	4	1	no	—
265	C₂⁴×C₃	C₂×Q₈	1	4	yes	—
266	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
267	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
268	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
269	C₂×C₃×Q₈	—	2	8	no	—
270	C₂×C₃×Q₈	—	4	4	no	—
271	C₂×C₃×Q₈	—	4	4	no	—
272	C₂²×C₃×C₄	—	2	2	no	—
273	C₂²×C₃×C₄	—	2	2	no	—
274	C₂²×C₃×C₄	—	2	32	no	—
275	C₂²×C₃×C₄	—	2	2	no	—
276	C₂²×C₃×C₄	—	2	2	no	—
277	C₂²×C₃×C₄	—	2	2	no	—
278	C₂²×C₃×C₄	—	2	2	no	—
279	C₂²×C₃×C₄	—	2	2	no	—
280	C₂²×C₃×C₄	—	2	2	no	—
281	C₂²×C₃×C₄	—	2	2	no	—
282	C₂²×C₃×C₄	—	2	2	no	—
283	C₂²×C₃×C₄	—	2	4	no	—
284	C₂²×C₃×C₄	—	2	4	no	—
285	C₂²×C₃×C₄	—	2	4	no	—
286	C₂²×C₃×C₄	—	2	4	no	—
287	C₂²×C₃×C₄	—	2	4	no	—
288	C₂²×C₃×C₄	—	2	4	no	—
289	C₂²×C₃×C₄	—	4	2	no	—
290	C₂²×C₃×C₄	—	4	2	no	—
291	C₂²×C₃×C₄	—	4	2	no	—
292	C₂²×C₃×C₄	—	4	2	no	—
293	C₂²×C₃×C₄	—	4	2	no	—
294	C₂²×C₃×C₄	—	4	2	no	—
295	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
296	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
297	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
298	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
299	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
300	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
301	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
302	C₂²×C₃×C₄	#41	1	4	yes	—
303	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
304	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
305	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
306	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
307	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
308	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
309	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
310	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
311	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
312	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
313	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
314	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
315	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
316	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
317	C₃×C₄⋊C₄	—	2	4	no	—
318	C₃×C₄⋊C₄	—	2	4	no	—
319	C₃×C₄⋊C₄	—	2	2	no	—
320	C₃×C₄⋊C₄	—	2	2	no	—
321	C₃×C₄⋊C₄	—	2	4	no	—
322	C₃×C₄⋊C₄	—	2	4	no	—
323	C₃×C₄⋊C₄	—	2	2	no	—
324	C₃×C₄⋊C₄	—	2	2	no	—
325	C₃×C₄⋊C₄	—	2	8	no	—
326	C₃×C₄⋊C₄	—	2	8	no	—
327	C₃×C₄⋊C₄	—	2	8	no	—
328	C₃×C₄⋊C₄	—	2	4	no	—
329	C₃×C₄⋊C₄	—	2	4	no	—
330	C₃×C₄⋊C₄	—	2	2	no	—
331	C₃×C₄⋊C₄	—	2	2	no	—
332	C₃×C₄⋊C₄	—	4	4	no	—
333	C₃×C₄⋊C₄	—	4	4	no	—
334	C₃×C₄⋊C₄	—	4	4	no	—
335	C₃×C₄⋊C₄	—	4	4	no	—
336	C₃×C₄⋊C₄	—	4	4	no	—
337	C₃×C₄⋊C₄	—	4	4	no	—
338	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
339	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
340	C₃×C₂²⋊C₄	—	2	4	no	—
341	C₃×C₂²⋊C₄	—	2	4	no	—
342	C₃×C₂²⋊C₄	—	2	4	no	—
343	C₃×C₂²⋊C₄	—	2	8	no	—
344	C₃×C₂²⋊C₄	—	2	4	no	—
345	C₃×C₂²⋊C₄	—	2	4	no	—
346	C₃×C₂²⋊C₄	—	2	4	no	—
347	C₃×C₂²⋊C₄	—	2	4	no	—
348	C₃×C₂²⋊C₄	—	4	4	no	—
349	C₃×C₂²⋊C₄	—	4	2	no	—
350	C₃×C₂²⋊C₄	—	4	2	no	—
351	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
352	C₃×C₄²	—	2	4	no	—
353	C₃×C₄²	—	2	4	no	—
354	C₃×C₄²	—	2	4	no	—
355	C₃×C₄²	—	2	4	no	—
356	C₃×C₄²	—	2	4	no	—
357	C₃×C₄²	C₂×D₄	1	8	yes	—
358	C₂⁵	C₂³×C₃	1	1	yes	characteristic
359	C₂²×Q₈	C₂³×C₃	1	4	yes	—
360	C₂³×C₄	—	2	4	no	—
361	C₂³×C₄	—	2	4	no	—
362	C₂³×C₄	C₃×Q₈	1	8	yes	complemented
363	C₂³×C₄	C₂³×C₃	1	2	yes	—
364	C₂³×C₄	C₂³×C₃	1	2	yes	—
365	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
366	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
367	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
368	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
369	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
370	C₂³×C₄	C₂³×C₃	1	2	yes	—
371	C₂³×C₄	C₂³×C₃	1	2	yes	—
372	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
373	C₄⋊Q₈	—	2	8	no	—
374	C₄⋊Q₈	—	2	8	no	—
375	#125	—	2	8	no	—
376	#125	—	2	8	no	—
377	C₂²⋊Q₈	—	2	16	no	—
378	C₂²⋊Q₈	—	4	8	no	—
379	#117	—	2	4	no	—
380	#117	—	2	4	no	—
381	#117	—	2	4	no	—
382	#117	—	2	4	no	—
383	#117	—	2	4	no	—
384	#117	—	2	8	no	—
385	#117	—	2	8	no	—
386	#117	C₃×D₄	1	8	yes	—
387	C₂×C₄⋊C₄	—	2	4	no	—
388	C₂×C₄⋊C₄	—	2	4	no	—
389	C₂×C₄⋊C₄	—	2	4	no	—
390	C₂×C₄⋊C₄	—	2	4	no	—
391	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
394	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
395	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
396	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
397	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
398	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
404	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
405	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
406	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
407	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
408	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
409	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
410	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
411	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
412	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
414	C₂×C₂²⋊C₄	—	2	8	no	—
415	C₂×C₂²⋊C₄	—	4	4	no	—
416	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
428	C₂×C₄²	—	2	8	no	—
429	C₂×C₄²	C₂³×C₃	1	2	yes	—
430	C₂×C₄²	C₂³×C₃	1	2	yes	—
431	C₂×C₄²	C₂³×C₃	1	2	yes	—
432	C₂×C₄²	C₂³×C₃	1	2	yes	—
433	C₂×C₄²	C₂³×C₃	1	2	yes	—
434	C₂×C₄²	C₂³×C₃	1	2	yes	—
435	#95	C₂³×C₃	1	4	yes	—
436	#95	C₂³×C₃	1	4	yes	—
437	#95	C₂³×C₃	1	2	yes	—
438	#95	C₂³×C₃	1	2	yes	—
439	#95	C₂³×C₃	1	2	yes	—
440	#95	C₂³×C₃	1	2	yes	—
441	#95	C₂³×C₃	1	4	yes	—
442	#95	C₂³×C₃	1	4	yes	—
443	#95	C₂³×C₃	1	4	yes	—
444	#95	C₂³×C₃	1	4	yes	—
445	#95	C₂³×C₃	1	4	yes	—
446	#95	C₂³×C₃	1	4	yes	—
447	C₂³×C₃	—	2	1	no	—
448	C₂³×C₃	—	2	1	no	—
449	C₂³×C₃	—	2	1	no	—
450	C₂³×C₃	—	2	1	no	—
451	C₂³×C₃	—	2	1	no	—
452	C₂³×C₃	—	2	1	no	—
453	C₂³×C₃	—	2	1	no	—
454	C₂³×C₃	—	2	1	no	—
455	C₂³×C₃	—	2	8	no	—
456	C₂³×C₃	—	2	8	no	—
457	C₂³×C₃	—	2	1	no	—
458	C₂³×C₃	—	2	1	no	—
459	C₂³×C₃	—	2	1	no	—
460	C₂³×C₃	—	2	1	no	—
461	C₂³×C₃	—	2	1	no	—
462	C₂³×C₃	—	2	1	no	—
463	C₂³×C₃	—	4	4	no	—
464	C₂³×C₃	—	4	4	no	—
465	C₂³×C₃	—	4	4	no	—
466	C₂³×C₃	—	4	4	no	—
467	C₂³×C₃	—	4	4	no	—
468	C₂³×C₃	C₂²×D₄	1	2	yes	—
469	C₂³×C₃	C₂²×Q₈	1	2	yes	—
470	C₂³×C₃	C₂²×Q₈	1	2	yes	—
471	C₂³×C₃	C₂²×Q₈	1	2	yes	—
472	C₂³×C₃	C₂×#41	1	2	yes	—
473	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
474	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
475	C₂³×C₃	C₂⁵	1	1	yes	characteristic
476	C₃×Q₈	—	8	8	no	—
477	C₂×C₃×C₄	—	2	8	no	—
478	C₂×C₃×C₄	—	2	1	no	—
479	C₂×C₃×C₄	—	2	1	no	—
480	C₂×C₃×C₄	—	2	1	no	—
481	C₂×C₃×C₄	—	2	1	no	—
482	C₂×C₃×C₄	—	2	2	no	—
483	C₂×C₃×C₄	—	2	2	no	—
484	C₂×C₃×C₄	—	2	2	no	—
485	C₂×C₃×C₄	—	2	2	no	—
486	C₂×C₃×C₄	—	2	8	no	—
487	C₂×C₃×C₄	—	2	8	no	—
488	C₂×C₃×C₄	—	2	8	no	—
489	C₂×C₃×C₄	—	2	8	no	—
490	C₂×C₃×C₄	—	2	2	no	—
491	C₂×C₃×C₄	—	2	2	no	—
492	C₂×C₃×C₄	—	2	2	no	—
493	C₂×C₃×C₄	—	2	2	no	—
494	C₂×C₃×C₄	—	2	4	no	—
495	C₂×C₃×C₄	—	2	2	no	—
496	C₂×C₃×C₄	—	2	2	no	—
497	C₂×C₃×C₄	—	2	4	no	—
498	C₂×C₃×C₄	—	2	4	no	—
499	C₂×C₃×C₄	—	2	4	no	—
500	C₂×C₃×C₄	—	2	2	no	—
501	C₂×C₃×C₄	—	2	2	no	—
502	C₂×C₃×C₄	—	2	2	no	—
503	C₂×C₃×C₄	—	2	2	no	—
504	C₂×C₃×C₄	—	2	2	no	—
505	C₂×C₃×C₄	—	2	2	no	—
506	C₂×C₃×C₄	—	2	2	no	—
507	C₂×C₃×C₄	—	2	2	no	—
508	C₂×C₃×C₄	—	2	2	no	—
509	C₂×C₃×C₄	—	2	2	no	—
510	C₂×C₃×C₄	—	2	2	no	—
511	C₂×C₃×C₄	—	2	2	no	—
512	C₂×C₃×C₄	—	2	4	no	—
513	C₂×C₃×C₄	—	2	4	no	—
514	C₂×C₃×C₄	—	4	8	no	—
515	C₂×C₃×C₄	—	4	8	no	—
516	C₂×C₃×C₄	—	8	4	no	—
517	C₂×C₃×C₄	—	8	4	no	—
518	C₂×C₃×C₄	C₂²⋊Q₈	1	16	yes	complemented
519	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
520	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
521	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
522	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
523	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
524	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
525	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
526	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
527	C₂×C₃×C₄	C₂×#41	1	2	yes	—
528	C₂×C₃×C₄	C₂×#41	1	2	yes	—
529	C₂⁴	—	2	2	no	—
530	C₂⁴	—	2	2	no	—
531	C₂⁴	—	2	2	no	—
532	C₂⁴	—	2	2	no	—
533	C₂⁴	—	4	1	no	—
534	C₂⁴	—	4	1	no	—
535	C₂⁴	C₂×C₃×Q₈	1	4	yes	—
536	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
537	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
538	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
539	C₂×Q₈	—	2	8	no	—
540	C₂×Q₈	—	4	4	no	—
541	C₂×Q₈	—	4	4	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	32	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	4	no	—
554	C₂²×C₄	—	2	4	no	—
555	C₂²×C₄	—	2	4	no	—
556	C₂²×C₄	—	2	4	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	4	2	no	—
560	C₂²×C₄	—	4	2	no	—
561	C₂²×C₄	—	4	2	no	—
562	C₂²×C₄	—	4	2	no	—
563	C₂²×C₄	—	4	2	no	—
564	C₂²×C₄	—	4	2	no	—
565	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
566	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
567	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
568	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
569	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
570	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
571	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
572	C₂²×C₄	C₃×#41	1	4	yes	—
573	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
576	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
580	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
584	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
585	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
586	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	2	no	—
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	—	2	4	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	8	no	—
596	C₄⋊C₄	—	2	8	no	—
597	C₄⋊C₄	—	2	8	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	4	4	no	—
603	C₄⋊C₄	—	4	4	no	—
604	C₄⋊C₄	—	4	4	no	—
605	C₄⋊C₄	—	4	4	no	—
606	C₄⋊C₄	—	4	4	no	—
607	C₄⋊C₄	—	4	4	no	—
608	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
609	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	8	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	4	4	no	—
619	C₂²⋊C₄	—	4	2	no	—
620	C₂²⋊C₄	—	4	2	no	—
621	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
622	C₄²	—	2	4	no	—
623	C₄²	—	2	4	no	—
624	C₄²	—	2	4	no	—
625	C₄²	—	2	4	no	—
626	C₄²	—	2	4	no	—
627	C₄²	C₂×C₃×D₄	1	8	yes	—
628	C₂²×C₃	—	2	2	no	—
629	C₂²×C₃	—	2	2	no	—
630	C₂²×C₃	—	2	2	no	—
631	C₂²×C₃	—	2	2	no	—
632	C₂²×C₃	—	2	2	no	—
633	C₂²×C₃	—	2	2	no	—
634	C₂²×C₃	—	2	2	no	—
635	C₂²×C₃	—	2	2	no	—
636	C₂²×C₃	—	2	2	no	—
637	C₂²×C₃	—	2	2	no	—
638	C₂²×C₃	—	2	2	no	—
639	C₂²×C₃	—	2	2	no	—
640	C₂²×C₃	—	2	2	no	—
641	C₂²×C₃	—	2	2	no	—
642	C₂²×C₃	—	2	2	no	—
643	C₂²×C₃	—	4	16	no	—
644	C₂²×C₃	—	4	1	no	—
645	C₂²×C₃	—	4	1	no	—
646	C₂²×C₃	—	4	1	no	—
647	C₂²×C₃	—	4	1	no	—
648	C₂²×C₃	C₂×C₂²⋊Q₈	1	4	yes	—
649	C₂²×C₃	#544	1	4	yes	complemented
650	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
651	C₂²×C₃	C₂³×Q₈	1	1	yes	characteristic
652	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
653	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
654	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
655	C₂²×C₃	#585	1	1	yes	characteristic
656	C₂²×C₃	#585	1	1	yes	characteristic
657	C₃×C₄	—	2	2	no	—
658	C₃×C₄	—	2	2	no	—
659	C₃×C₄	—	2	4	no	—
660	C₃×C₄	—	2	4	no	—
661	C₃×C₄	—	4	2	no	—
662	C₃×C₄	—	4	4	no	—
663	C₃×C₄	—	4	2	no	—
664	C₃×C₄	—	4	2	no	—
665	C₃×C₄	—	4	2	no	—
666	C₃×C₄	—	4	2	no	—
667	C₃×C₄	—	4	4	no	—
668	C₃×C₄	—	4	2	no	—
669	C₃×C₄	C₂×C₂²⋊Q₈	1	4	yes	—
670	C₃×C₄	C₂×C₂²⋊Q₈	1	4	yes	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	1	no	—
678	C₂³	—	2	1	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	1	no	—
684	C₂³	—	2	1	no	—
685	C₂³	—	2	8	no	—
686	C₂³	—	2	8	no	—
687	C₂³	—	4	4	no	—
688	C₂³	—	4	4	no	—
689	C₂³	—	4	4	no	—
690	C₂³	—	4	4	no	—
691	C₂³	—	4	4	no	—
692	C₂³	C₂²×C₃×D₄	1	2	yes	—
693	C₂³	C₂²×C₃×Q₈	1	2	yes	—
694	C₂³	C₂²×C₃×Q₈	1	2	yes	—
695	C₂³	C₂²×C₃×Q₈	1	2	yes	—
696	C₂³	C₂×C₃×#41	1	2	yes	—
697	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
698	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
699	C₂³	C₂⁵×C₃	1	1	yes	characteristic
700	Q₈	—	8	8	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	8	no	—
710	C₂×C₄	—	2	8	no	—
711	C₂×C₄	—	2	8	no	—
712	C₂×C₄	—	2	8	no	—
713	C₂×C₄	—	2	8	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	4	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	4	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	4	no	—
737	C₂×C₄	—	2	4	no	—
738	C₂×C₄	—	4	8	no	—
739	C₂×C₄	—	4	8	no	—
740	C₂×C₄	—	8	4	no	—
741	C₂×C₄	—	8	4	no	—
742	C₂×C₄	C₃×C₂²⋊Q₈	1	16	yes	complemented
743	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
744	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
745	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
746	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
747	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
748	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
749	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
750	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
751	C₂×C₄	C₂×C₃×#41	1	2	yes	—
752	C₂×C₄	C₂×C₃×#41	1	2	yes	—
753	C₂×C₃	—	2	4	no	—
754	C₂×C₃	—	2	4	no	—
755	C₂×C₃	—	4	2	no	—
756	C₂×C₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
757	C₂×C₃	C₂×#544	1	1	yes	characteristic
758	C₂×C₃	#3458	1	1	yes	characteristic
759	C₂×C₃	#3488	1	1	yes	characteristic
760	C₂×C₃	#3489	1	1	yes	characteristic
761	C₂×C₃	#3494	1	1	yes	characteristic
762	C₂×C₃	#3495	1	1	yes	characteristic
763	C₂²	—	2	2	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	2	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	4	16	no	—
779	C₂²	—	4	1	no	—
780	C₂²	—	4	1	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	1	no	—
783	C₂²	C₂×C₃×C₂²⋊Q₈	1	4	yes	—
784	C₂²	C₃×#544	1	4	yes	complemented
785	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
786	C₂²	C₂³×C₃×Q₈	1	1	yes	characteristic
787	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
788	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
789	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
790	C₂²	C₃×#585	1	1	yes	characteristic
791	C₂²	C₃×#585	1	1	yes	characteristic
792	C₄	—	2	2	no	—
793	C₄	—	2	2	no	—
794	C₄	—	2	4	no	—
795	C₄	—	2	4	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	4	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	4	no	—
802	C₄	—	4	2	no	—
803	C₄	—	4	2	no	—
804	C₄	C₂×C₃×C₂²⋊Q₈	1	4	yes	—
805	C₄	C₂×C₃×C₂²⋊Q₈	1	4	yes	—
806	C₃	#35253	1	1	yes	characteristic, direct product factor, Sylow
807	C₂	—	2	4	no	—
808	C₂	—	2	4	no	—
809	C₂	—	4	2	no	—
810	C₂	C₂²×C₃×C₂²⋊Q₈	1	1	yes	characteristic
811	C₂	C₂×C₃×#544	1	1	yes	characteristic
812	C₂	C₃×#3458	1	1	yes	characteristic
813	C₂	C₃×#3488	1	1	yes	characteristic
814	C₂	C₃×#3489	1	1	yes	characteristic
815	C₂	C₃×#3494	1	1	yes	characteristic
816	C₂	C₃×#3495	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂⁵×C₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₃×#544	C₂	semidirect
3. C₃×#2857	C₂	semidirect
4. C₃×#2851	C₂	semidirect
5. C₃×#2629	C₂	semidirect
6. C₃×#2628	C₂	semidirect
7. C₃×#2442	C₂	semidirect
8. C₃×#2441	C₂	semidirect
9. C₃×#2440	C₂	semidirect
10. C₃×#2439	C₂	semidirect
11. C₃×#2438	C₂	semidirect
13. C₃×#2317	C₂	semidirect
14. C₃×#2317	C₂	semidirect
15. C₃×#2316	C₂	semidirect
18. #35253	C₃	direct (N × H)
21. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
22. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
23. C₂×C₃×#125	C₂²	semidirect
24. C₂×C₃×#125	C₂²	semidirect
43. C₃×#400	C₂²	semidirect
45. C₃×#398	C₂²	semidirect
46. C₃×#398	C₂²	semidirect
49. C₃×#395	C₂²	semidirect
51. C₃×#391	C₂²	semidirect
52. C₃×#389	C₂²	semidirect
53. C₃×#389	C₂²	semidirect
54. C₃×#389	C₂²	semidirect
55. C₃×#389	C₂²	semidirect
56. C₃×#389	C₂²	semidirect
57. C₃×#389	C₂²	semidirect
58. C₃×#389	C₂²	semidirect
59. C₃×#389	C₂²	semidirect
60. C₃×#389	C₂²	semidirect
61. C₃×#387	C₂²	semidirect
62. C₃×#387	C₂²	semidirect
67. C₃×#384	C₂²	semidirect
68. C₃×#384	C₂²	semidirect
69. C₃×#382	C₂²	semidirect
70. C₃×#382	C₂²	semidirect
86. C₂×#544	C₂×C₃	semidirect
88. #2857	C₂×C₃	semidirect
89. #2851	C₂×C₃	semidirect
90. #2629	C₂×C₃	semidirect
91. #2628	C₂×C₃	semidirect
92. #2442	C₂×C₃	semidirect
93. #2441	C₂×C₃	semidirect
94. #2440	C₂×C₃	semidirect
95. #2439	C₂×C₃	semidirect
96. #2438	C₂×C₃	semidirect
98. #2317	C₂×C₃	semidirect
99. #2317	C₂×C₃	semidirect
100. #2316	C₂×C₃	semidirect
107. C₂³×C₃×C₄	Q₈	semidirect
194. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
195. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
196. C₂×#125	C₂²×C₃	semidirect
197. C₂×#125	C₂²×C₃	semidirect
216. #400	C₂²×C₃	semidirect
218. #398	C₂²×C₃	semidirect
219. #398	C₂²×C₃	semidirect
222. #395	C₂²×C₃	semidirect
224. #391	C₂²×C₃	semidirect
225. #389	C₂²×C₃	semidirect
226. #389	C₂²×C₃	semidirect
227. #389	C₂²×C₃	semidirect
228. #389	C₂²×C₃	semidirect
229. #389	C₂²×C₃	semidirect
230. #389	C₂²×C₃	semidirect
231. #389	C₂²×C₃	semidirect
232. #389	C₂²×C₃	semidirect
233. #389	C₂²×C₃	semidirect
234. #387	C₂²×C₃	semidirect
235. #387	C₂²×C₃	semidirect
240. #384	C₂²×C₃	semidirect
241. #384	C₂²×C₃	semidirect
242. #382	C₂²×C₃	semidirect
243. #382	C₂²×C₃	semidirect
362. C₂³×C₄	C₃×Q₈	semidirect
518. C₂×C₃×C₄	C₂²⋊Q₈	semidirect
649. C₂²×C₃	#544	semidirect
742. C₂×C₄	C₃×C₂²⋊Q₈	semidirect
784. C₂²	C₃×#544	semidirect
806. C₃	#35253	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×#544	2
C₂²×C₃×#117	2
C₃×#2857	2
C₃×#2851	2
C₃×#2629	2
C₃×#2628	2
C₃×#2442	2
C₃×#2441	2
C₃×#2440	2
C₃×#2439	2
C₃×#2438	2
C₃×#2437	2
C₃×#2317	2
C₃×#2316	2
C₃×#2280	2
C₂×C₃×#380	2
#35253	3

Subgroups — C3×#35253 #10653860

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35253 #10653860