Subgroups — C₅×#34919 #11957639

Order 1280.

2392 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2560	C₂	1	2	yes	maximal, complemented
4	C₅×#2558	C₂	1	2	yes	maximal, complemented
5	C₅×#2550	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2545	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2540	C₂	1	1	yes	maximal, characteristic
8	C₅×#2536	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2519	C₂	1	2	yes	maximal, complemented
10	C₅×#2491	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2489	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2461	C₂	1	2	yes	maximal, complemented
13	C₅×#2429	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#2426	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#2396	C₂	1	2	yes	maximal, complemented
16	C₅×#2392	C₂	1	2	yes	maximal, complemented
17	C₄×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₅×#124	C₂	1	2	yes	maximal, complemented
19	C₄×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅×#2293	C₂	1	2	yes	maximal, complemented
22	C₄²×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅×#533	—	2	8	no	—
25	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₅×#529	—	2	8	no	—
28	C₂×C₅×#126	C₂²	1	2	yes	—
29	C₂×C₅×#125	C₂²	1	1	yes	characteristic
30	C₂×C₅×#125	C₂²	1	2	yes	—
31	C₂×C₅×#124	C₂²	1	2	yes	—
32	C₂×C₅×#124	C₂²	1	1	yes	characteristic
33	C₂×C₅×#124	C₂²	1	1	yes	characteristic
34	C₂×C₅×#123	C₂²	1	2	yes	—
35	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
40	C₂×C₅×#121	C₂²	1	1	yes	characteristic
41	C₂×C₅×#121	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
46	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
51	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
52	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
53	C₂×C₅×#117	C₂²	1	2	yes	—
54	C₂×C₅×#117	C₂²	1	2	yes	—
55	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
56	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
57	C₅×#400	C₂²	1	2	yes	—
58	C₅×#399	C₂²	1	2	yes	—
59	C₅×#398	C₂²	1	2	yes	—
60	C₅×#398	C₂²	1	2	yes	—
61	C₅×#398	C₂²	1	2	yes	—
62	C₅×#397	C₂²	1	2	yes	—
63	C₅×#396	C₂²	1	2	yes	—
64	C₅×#396	C₂²	1	2	yes	—
65	C₅×#396	C₂²	1	2	yes	—
66	C₅×#396	C₂²	1	2	yes	—
67	C₅×#395	C₂²	1	2	yes	—
68	C₅×#394	C₂²	1	2	yes	—
69	C₅×#394	C₂²	1	2	yes	—
70	C₅×#394	C₂²	1	2	yes	—
71	C₅×#393	C₂²	1	2	yes	—
72	C₅×#392	C₂²	1	2	yes	—
73	C₅×#391	C₂²	1	1	yes	characteristic
74	C₅×#391	C₂²	1	1	yes	characteristic
75	C₅×#391	C₂²	1	2	yes	—
76	C₅×#390	C₂²	1	1	yes	characteristic
77	C₅×#390	C₂²	1	1	yes	characteristic
78	C₅×#390	C₂²	1	2	yes	—
79	C₅×#390	C₂²	1	2	yes	—
80	C₅×#390	C₂²	1	2	yes	—
81	C₅×#389	C₂²	1	2	yes	—
82	C₅×#389	C₂²	1	2	yes	—
83	C₅×#389	C₂²	1	1	yes	characteristic
84	C₅×#389	C₂²	1	1	yes	characteristic
85	C₅×#388	C₂²	1	2	yes	—
86	C₅×#388	C₂²	1	2	yes	—
87	C₅×#388	C₂²	1	2	yes	—
88	C₅×#388	C₂²	1	2	yes	—
89	C₅×#388	C₂²	1	2	yes	—
90	C₅×#388	C₂²	1	2	yes	—
91	C₅×#388	C₂²	1	2	yes	—
92	C₅×#388	C₂²	1	2	yes	—
93	C₅×#388	C₂²	1	2	yes	—
94	C₅×#388	C₂²	1	2	yes	—
95	C₅×#388	C₂²	1	2	yes	—
96	C₅×#387	C₂²	1	2	yes	—
97	C₅×#386	C₂²	1	2	yes	—
98	C₅×#385	C₂²	1	2	yes	—
99	C₅×#382	C₂²	1	2	yes	—
100	C₅×#382	C₂²	1	1	yes	characteristic
101	C₅×#380	C₂²	1	1	yes	characteristic
102	C₅×#380	C₂²	1	1	yes	characteristic
103	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
106	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
111	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
112	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
113	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
114	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
117	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
118	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
119	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
123	C₄³×C₅	C₂²	1	1	yes	characteristic
124	C₄³×C₅	C₂²	1	2	yes	—
125	#34919	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
127	C₂²×C₅×Q₈	C₂³	1	2	yes	—
128	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
129	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
130	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
131	C₂²×C₅×D₄	C₂³	1	2	yes	—
132	C₂²×C₅×D₄	C₂³	1	2	yes	—
133	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₅	C₂³	1	2	yes	—
137	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
140	C₅×C₄⋊Q₈	—	2	4	no	—
141	C₅×C₄⋊Q₈	—	2	4	no	—
142	C₅×#126	—	2	8	no	—
143	C₅×#125	—	2	4	no	—
144	C₅×#125	—	2	8	no	—
145	C₅×#124	—	2	4	no	—
146	C₅×#124	—	2	8	no	—
147	C₅×#124	—	2	4	no	—
148	C₅×#123	—	2	8	no	—
149	C₅×C₂²⋊Q₈	—	2	4	no	—
150	C₅×C₂²⋊Q₈	—	2	4	no	—
151	C₅×C₂²⋊Q₈	—	2	4	no	—
152	C₅×C₂²⋊Q₈	—	2	8	no	—
153	C₅×C₂²⋊Q₈	—	2	4	no	—
154	C₅×#121	—	2	4	no	—
155	C₅×#121	—	2	4	no	—
156	C₄×C₅×Q₈	—	2	4	no	—
157	C₄×C₅×Q₈	—	2	8	no	—
158	C₄×C₅×Q₈	—	2	4	no	—
159	C₄×C₅×Q₈	—	2	4	no	—
160	C₄×C₅×Q₈	D₄	1	8	yes	complemented
161	C₄×C₅×D₄	—	2	4	no	—
162	C₄×C₅×D₄	—	2	8	no	—
163	C₄×C₅×D₄	—	2	4	no	—
164	C₄×C₅×D₄	—	2	4	no	—
165	C₄×C₅×D₄	—	2	8	no	—
166	C₄×C₅×D₄	—	2	4	no	—
167	C₅×#117	—	2	8	no	—
168	C₅×#117	—	2	8	no	—
169	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
185	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
188	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₅	—	2	4	no	—
216	C₂×C₄²×C₅	—	2	4	no	—
217	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₅	C₂³	1	2	yes	—
220	C₂×C₄²×C₅	C₂³	1	2	yes	—
221	C₂×C₄²×C₅	C₂³	1	2	yes	—
222	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₅	C₂³	1	2	yes	—
229	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₅	C₂³	1	2	yes	—
231	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₅	C₂³	1	2	yes	—
234	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₅	C₂³	1	2	yes	—
236	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
237	C₅×#95	C₂³	1	1	yes	characteristic
238	C₅×#95	C₂³	1	1	yes	characteristic
239	C₅×#95	C₂³	1	1	yes	characteristic
240	C₅×#95	C₂³	1	1	yes	characteristic
241	C₅×#95	C₂³	1	1	yes	characteristic
242	C₅×#95	C₂³	1	1	yes	characteristic
243	C₅×#95	C₂³	1	2	yes	—
244	C₅×#95	C₂³	1	2	yes	—
245	C₅×#95	C₂³	1	2	yes	—
246	C₅×#95	C₂³	1	2	yes	—
247	C₅×#95	C₂³	1	2	yes	—
248	C₅×#95	C₂³	1	2	yes	—
249	C₅×#95	C₂³	1	2	yes	—
250	C₅×#95	C₂³	1	2	yes	—
251	C₅×#95	C₂³	1	2	yes	—
252	C₅×#95	C₂³	1	2	yes	—
253	C₅×#95	C₂³	1	2	yes	—
254	C₅×#95	C₂³	1	2	yes	—
255	C₅×#95	C₂³	1	2	yes	—
256	C₂×#533	C₂×C₅	1	1	yes	characteristic, complemented
257	C₂×#529	C₂×C₅	1	1	yes	characteristic, complemented
258	#2560	C₂×C₅	1	2	yes	complemented
259	#2558	C₂×C₅	1	2	yes	complemented
260	#2550	C₂×C₅	1	1	yes	characteristic, complemented
261	#2545	C₂×C₅	1	1	yes	characteristic, complemented
262	#2540	C₂×C₅	1	1	yes	characteristic
263	#2536	C₂×C₅	1	1	yes	characteristic, complemented
264	#2519	C₂×C₅	1	2	yes	complemented
265	#2491	C₂×C₅	1	1	yes	characteristic, complemented
266	#2489	C₂×C₅	1	1	yes	characteristic, complemented
267	#2461	C₂×C₅	1	2	yes	complemented
268	#2429	C₂×C₅	1	1	yes	characteristic, complemented
269	#2426	C₂×C₅	1	1	yes	characteristic, complemented
270	#2396	C₂×C₅	1	2	yes	complemented
271	#2392	C₂×C₅	1	2	yes	complemented
272	C₄×#124	C₂×C₅	1	2	yes	complemented
273	C₄×#124	C₂×C₅	1	1	yes	characteristic, complemented
274	C₄×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
275	C₄×#121	C₂×C₅	1	1	yes	characteristic, complemented
276	#2293	C₂×C₅	1	2	yes	complemented
277	C₄²×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
278	C₄²×D₄	C₂×C₅	1	1	yes	characteristic, complemented
279	C₂⁴×C₅	C₂⁴	1	2	yes	—
280	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
281	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
282	C₂×C₅×Q₈	—	2	4	no	—
283	C₂×C₅×Q₈	—	2	2	no	—
284	C₂×C₅×Q₈	—	2	2	no	—
285	C₂×C₅×Q₈	—	2	2	no	—
286	C₂×C₅×Q₈	—	2	2	no	—
287	C₂×C₅×Q₈	—	2	4	no	—
288	C₂×C₅×Q₈	—	2	2	no	—
289	C₂×C₅×Q₈	—	4	2	no	—
290	C₂×C₅×Q₈	C₂×D₄	1	4	yes	—
291	C₂×C₅×D₄	—	2	2	no	—
292	C₂×C₅×D₄	—	2	2	no	—
293	C₂×C₅×D₄	—	2	4	no	—
294	C₂×C₅×D₄	—	2	4	no	—
295	C₂×C₅×D₄	—	2	4	no	—
296	C₂×C₅×D₄	—	2	2	no	—
297	C₂×C₅×D₄	—	2	2	no	—
298	C₂×C₅×D₄	—	2	4	no	—
299	C₂×C₅×D₄	—	2	2	no	—
300	C₂×C₅×D₄	—	2	2	no	—
301	C₂×C₅×D₄	—	4	2	no	—
302	C₂×C₅×D₄	—	4	2	no	—
303	C₂²×C₄×C₅	—	2	2	no	—
304	C₂²×C₄×C₅	—	2	2	no	—
305	C₂²×C₄×C₅	—	2	2	no	—
306	C₂²×C₄×C₅	—	2	2	no	—
307	C₂²×C₄×C₅	—	2	2	no	—
308	C₂²×C₄×C₅	—	2	2	no	—
309	C₂²×C₄×C₅	—	2	2	no	—
310	C₂²×C₄×C₅	—	2	2	no	—
311	C₂²×C₄×C₅	—	2	4	no	—
312	C₂²×C₄×C₅	—	2	2	no	—
313	C₂²×C₄×C₅	—	2	2	no	—
314	C₂²×C₄×C₅	—	2	2	no	—
315	C₂²×C₄×C₅	—	2	2	no	—
316	C₂²×C₄×C₅	—	2	4	no	—
317	C₂²×C₄×C₅	—	2	2	no	—
318	C₂²×C₄×C₅	—	2	2	no	—
319	C₂²×C₄×C₅	—	2	2	no	—
320	C₂²×C₄×C₅	—	2	4	no	—
321	C₂²×C₄×C₅	—	4	1	no	—
322	C₂²×C₄×C₅	—	4	1	no	—
323	C₂²×C₄×C₅	#41	1	4	yes	—
324	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
344	C₅×C₄⋊C₄	—	2	4	no	—
345	C₅×C₄⋊C₄	—	2	4	no	—
346	C₅×C₄⋊C₄	—	2	4	no	—
347	C₅×C₄⋊C₄	—	2	4	no	—
348	C₅×C₄⋊C₄	—	2	2	no	—
349	C₅×C₄⋊C₄	—	2	4	no	—
350	C₅×C₄⋊C₄	—	2	4	no	—
351	C₅×C₄⋊C₄	—	2	4	no	—
352	C₅×C₄⋊C₄	—	2	4	no	—
353	C₅×C₄⋊C₄	—	2	4	no	—
354	C₅×C₄⋊C₄	—	2	2	no	—
355	C₅×C₄⋊C₄	—	2	2	no	—
356	C₅×C₄⋊C₄	—	2	4	no	—
357	C₅×C₄⋊C₄	—	2	2	no	—
358	C₅×C₄⋊C₄	—	2	2	no	—
359	C₅×C₄⋊C₄	—	2	4	no	—
360	C₅×C₄⋊C₄	—	2	4	no	—
361	C₅×C₄⋊C₄	—	2	2	no	—
362	C₅×C₄⋊C₄	—	2	4	no	—
363	C₅×C₄⋊C₄	—	4	2	no	—
364	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
365	C₅×C₄⋊C₄	C₂×D₄	1	8	yes	—
366	C₅×C₄⋊C₄	#41	1	4	yes	—
367	C₅×C₂²⋊C₄	—	2	2	no	—
368	C₅×C₂²⋊C₄	—	2	4	no	—
369	C₅×C₂²⋊C₄	—	2	4	no	—
370	C₅×C₂²⋊C₄	—	2	4	no	—
371	C₅×C₂²⋊C₄	—	2	4	no	—
372	C₅×C₂²⋊C₄	—	2	4	no	—
373	C₅×C₂²⋊C₄	—	2	4	no	—
374	C₅×C₂²⋊C₄	—	2	4	no	—
375	C₅×C₂²⋊C₄	—	2	4	no	—
376	C₅×C₂²⋊C₄	—	2	4	no	—
377	C₅×C₂²⋊C₄	—	2	2	no	—
378	C₅×C₂²⋊C₄	—	2	4	no	—
379	C₅×C₂²⋊C₄	—	2	2	no	—
380	C₅×C₂²⋊C₄	—	2	2	no	—
381	C₅×C₂²⋊C₄	—	2	2	no	—
382	C₅×C₂²⋊C₄	—	2	4	no	—
383	C₅×C₂²⋊C₄	—	2	4	no	—
384	C₅×C₂²⋊C₄	—	2	4	no	—
385	C₅×C₂²⋊C₄	—	2	4	no	—
386	C₅×C₂²⋊C₄	—	2	4	no	—
387	C₅×C₂²⋊C₄	—	2	4	no	—
388	C₅×C₂²⋊C₄	—	4	2	no	—
389	C₅×C₂²⋊C₄	#41	1	4	yes	—
390	C₄²×C₅	—	2	2	no	—
391	C₄²×C₅	—	2	2	no	—
392	C₄²×C₅	—	2	2	no	—
393	C₄²×C₅	—	2	2	no	—
394	C₄²×C₅	—	2	2	no	—
395	C₄²×C₅	—	2	2	no	—
396	C₄²×C₅	—	2	4	no	—
397	C₄²×C₅	—	2	2	no	—
398	C₄²×C₅	—	2	2	no	—
399	C₄²×C₅	—	2	4	no	—
400	C₄²×C₅	—	2	4	no	—
401	C₄²×C₅	—	2	2	no	—
402	C₄²×C₅	—	2	4	no	—
403	C₄²×C₅	—	2	4	no	—
404	C₄²×C₅	—	2	2	no	—
405	C₄²×C₅	—	4	2	no	—
406	C₄²×C₅	—	4	1	no	—
407	C₄²×C₅	C₂×D₄	1	4	yes	—
408	C₄²×C₅	C₂×D₄	1	8	yes	—
409	C₄²×C₅	#41	1	4	yes	—
410	#533	—	2	8	no	—
411	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
412	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
413	#529	—	2	8	no	—
414	C₂×#126	C₂²×C₅	1	2	yes	—
415	C₂×#125	C₂²×C₅	1	1	yes	characteristic
416	C₂×#125	C₂²×C₅	1	2	yes	—
417	C₂×#124	C₂²×C₅	1	1	yes	characteristic
418	C₂×#124	C₂²×C₅	1	2	yes	—
419	C₂×#124	C₂²×C₅	1	1	yes	characteristic
420	C₂×#123	C₂²×C₅	1	2	yes	—
421	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
422	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
423	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
424	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
425	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
426	C₂×#121	C₂²×C₅	1	1	yes	characteristic
427	C₂×#121	C₂²×C₅	1	1	yes	characteristic
428	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
429	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
430	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
431	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
432	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
433	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
434	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
435	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
436	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
437	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
438	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
439	C₂×#117	C₂²×C₅	1	2	yes	—
440	C₂×#117	C₂²×C₅	1	2	yes	—
441	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
442	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
443	#400	C₂²×C₅	1	2	yes	—
444	#399	C₂²×C₅	1	2	yes	—
445	#398	C₂²×C₅	1	2	yes	—
446	#398	C₂²×C₅	1	2	yes	—
447	#398	C₂²×C₅	1	2	yes	—
448	#397	C₂²×C₅	1	2	yes	—
449	#396	C₂²×C₅	1	2	yes	—
450	#396	C₂²×C₅	1	2	yes	—
451	#396	C₂²×C₅	1	2	yes	—
452	#396	C₂²×C₅	1	2	yes	—
453	#395	C₂²×C₅	1	2	yes	—
454	#394	C₂²×C₅	1	2	yes	—
455	#394	C₂²×C₅	1	2	yes	—
456	#394	C₂²×C₅	1	2	yes	—
457	#393	C₂²×C₅	1	2	yes	—
458	#392	C₂²×C₅	1	2	yes	—
459	#391	C₂²×C₅	1	2	yes	—
460	#391	C₂²×C₅	1	1	yes	characteristic
461	#391	C₂²×C₅	1	1	yes	characteristic
462	#390	C₂²×C₅	1	2	yes	—
463	#390	C₂²×C₅	1	2	yes	—
464	#390	C₂²×C₅	1	1	yes	characteristic
465	#390	C₂²×C₅	1	1	yes	characteristic
466	#390	C₂²×C₅	1	2	yes	—
467	#389	C₂²×C₅	1	1	yes	characteristic
468	#389	C₂²×C₅	1	2	yes	—
469	#389	C₂²×C₅	1	1	yes	characteristic
470	#389	C₂²×C₅	1	2	yes	—
471	#388	C₂²×C₅	1	2	yes	—
472	#388	C₂²×C₅	1	2	yes	—
473	#388	C₂²×C₅	1	2	yes	—
474	#388	C₂²×C₅	1	2	yes	—
475	#388	C₂²×C₅	1	2	yes	—
476	#388	C₂²×C₅	1	2	yes	—
477	#388	C₂²×C₅	1	2	yes	—
478	#388	C₂²×C₅	1	2	yes	—
479	#388	C₂²×C₅	1	2	yes	—
480	#388	C₂²×C₅	1	2	yes	—
481	#388	C₂²×C₅	1	2	yes	—
482	#387	C₂²×C₅	1	2	yes	—
483	#386	C₂²×C₅	1	2	yes	—
484	#385	C₂²×C₅	1	2	yes	—
485	#382	C₂²×C₅	1	2	yes	—
486	#382	C₂²×C₅	1	1	yes	characteristic
487	#380	C₂²×C₅	1	1	yes	characteristic
488	#380	C₂²×C₅	1	1	yes	characteristic
489	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
490	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
491	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
492	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
493	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
494	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
495	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
496	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
497	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
498	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
499	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
500	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
501	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
502	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
503	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
504	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
505	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
506	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
507	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
508	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
509	C₄³	C₂²×C₅	1	1	yes	characteristic
510	C₄³	C₂²×C₅	1	2	yes	—
511	C₂³×C₅	—	2	1	no	—
512	C₂³×C₅	—	2	1	no	—
513	C₂³×C₅	—	2	1	no	—
514	C₂³×C₅	—	2	1	no	—
515	C₂³×C₅	—	2	1	no	—
516	C₂³×C₅	—	2	1	no	—
517	C₂³×C₅	—	2	1	no	—
518	C₂³×C₅	—	2	1	no	—
519	C₂³×C₅	—	2	1	no	—
520	C₂³×C₅	—	2	1	no	—
521	C₂³×C₅	—	2	1	no	—
522	C₂³×C₅	—	2	1	no	—
523	C₂³×C₅	—	2	2	no	—
524	C₂³×C₅	—	2	2	no	—
525	C₂³×C₅	—	2	2	no	—
526	C₂³×C₅	—	2	2	no	—
527	C₂³×C₅	—	2	2	no	—
528	C₂³×C₅	—	2	2	no	—
529	C₂³×C₅	—	2	2	no	—
530	C₂³×C₅	C₂×#41	1	2	yes	—
531	C₂³×C₅	C₂×#41	1	2	yes	—
532	C₂³×C₅	C₂⁵	1	1	yes	characteristic
533	C₅×Q₈	—	2	8	no	—
534	C₅×Q₈	—	4	8	no	—
535	C₅×Q₈	—	4	4	no	—
536	C₅×D₄	—	2	8	no	—
537	C₅×D₄	—	4	8	no	—
538	C₅×D₄	—	4	8	no	—
539	C₅×D₄	—	4	4	no	—
540	C₂×C₄×C₅	—	2	1	no	—
541	C₂×C₄×C₅	—	2	1	no	—
542	C₂×C₄×C₅	—	2	1	no	—
543	C₂×C₄×C₅	—	2	1	no	—
544	C₂×C₄×C₅	—	2	1	no	—
545	C₂×C₄×C₅	—	2	2	no	—
546	C₂×C₄×C₅	—	2	2	no	—
547	C₂×C₄×C₅	—	2	2	no	—
548	C₂×C₄×C₅	—	2	1	no	—
549	C₂×C₄×C₅	—	2	2	no	—
550	C₂×C₄×C₅	—	2	1	no	—
551	C₂×C₄×C₅	—	2	1	no	—
552	C₂×C₄×C₅	—	2	1	no	—
553	C₂×C₄×C₅	—	2	1	no	—
554	C₂×C₄×C₅	—	2	2	no	—
555	C₂×C₄×C₅	—	2	1	no	—
556	C₂×C₄×C₅	—	2	2	no	—
557	C₂×C₄×C₅	—	2	1	no	—
558	C₂×C₄×C₅	—	2	8	no	—
559	C₂×C₄×C₅	—	2	1	no	—
560	C₂×C₄×C₅	—	2	1	no	—
561	C₂×C₄×C₅	—	2	1	no	—
562	C₂×C₄×C₅	—	2	1	no	—
563	C₂×C₄×C₅	—	2	2	no	—
564	C₂×C₄×C₅	—	2	2	no	—
565	C₂×C₄×C₅	—	2	2	no	—
566	C₂×C₄×C₅	—	2	2	no	—
567	C₂×C₄×C₅	—	2	2	no	—
568	C₂×C₄×C₅	—	2	1	no	—
569	C₂×C₄×C₅	—	2	2	no	—
570	C₂×C₄×C₅	—	2	1	no	—
571	C₂×C₄×C₅	—	2	1	no	—
572	C₂×C₄×C₅	—	2	2	no	—
573	C₂×C₄×C₅	—	2	2	no	—
574	C₂×C₄×C₅	—	2	1	no	—
575	C₂×C₄×C₅	—	2	1	no	—
576	C₂×C₄×C₅	—	2	1	no	—
577	C₂×C₄×C₅	—	2	2	no	—
578	C₂×C₄×C₅	—	2	1	no	—
579	C₂×C₄×C₅	—	2	2	no	—
580	C₂×C₄×C₅	—	2	1	no	—
581	C₂×C₄×C₅	—	2	1	no	—
582	C₂×C₄×C₅	—	2	2	no	—
583	C₂×C₄×C₅	—	2	1	no	—
584	C₂×C₄×C₅	—	2	2	no	—
585	C₂×C₄×C₅	—	2	1	no	—
586	C₂×C₄×C₅	—	4	4	no	—
587	C₂×C₄×C₅	—	4	4	no	—
588	C₂×C₄×C₅	—	4	4	no	—
589	C₂×C₄×C₅	—	4	4	no	—
590	C₂×C₄×C₅	—	4	4	no	—
591	C₂×C₄×C₅	—	4	8	no	—
592	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
593	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
594	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
595	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
596	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
597	C₂×C₄×C₅	C₂×#41	1	2	yes	—
598	C₂×C₄×C₅	C₂×#41	1	2	yes	—
599	C₂×C₄×C₅	C₂×#41	1	4	yes	—
600	C₂×C₄×C₅	C₂×#41	1	2	yes	—
601	C₂×C₄×C₅	C₂×#41	1	2	yes	—
602	C₂×C₄×C₅	C₂×#41	1	2	yes	—
603	C₂×C₄×C₅	C₂×#41	1	2	yes	—
604	C₂×C₄×C₅	C₂×#41	1	2	yes	—
605	C₂×C₄×C₅	C₂×#41	1	2	yes	—
606	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
607	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
608	C₂²×Q₈	C₂³×C₅	1	2	yes	—
609	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
610	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
611	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
612	C₂²×D₄	C₂³×C₅	1	2	yes	—
613	C₂²×D₄	C₂³×C₅	1	2	yes	—
614	C₂³×C₄	C₂³×C₅	1	2	yes	—
615	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
616	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
617	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
618	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
619	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
620	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
621	C₄⋊Q₈	—	2	4	no	—
622	C₄⋊Q₈	—	2	4	no	—
623	#126	—	2	8	no	—
624	#125	—	2	4	no	—
625	#125	—	2	8	no	—
626	#124	—	2	4	no	—
627	#124	—	2	8	no	—
628	#124	—	2	4	no	—
629	#123	—	2	8	no	—
630	C₂²⋊Q₈	—	2	4	no	—
631	C₂²⋊Q₈	—	2	4	no	—
632	C₂²⋊Q₈	—	2	4	no	—
633	C₂²⋊Q₈	—	2	8	no	—
634	C₂²⋊Q₈	—	2	4	no	—
635	#121	—	2	4	no	—
636	#121	—	2	4	no	—
637	C₄×Q₈	—	2	4	no	—
638	C₄×Q₈	—	2	8	no	—
639	C₄×Q₈	—	2	4	no	—
640	C₄×Q₈	—	2	4	no	—
641	C₄×Q₈	C₅×D₄	1	8	yes	complemented
642	C₄×D₄	—	2	4	no	—
643	C₄×D₄	—	2	8	no	—
644	C₄×D₄	—	2	4	no	—
645	C₄×D₄	—	2	4	no	—
646	C₄×D₄	—	2	8	no	—
647	C₄×D₄	—	2	4	no	—
648	#117	—	2	8	no	—
649	#117	—	2	8	no	—
650	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
669	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
673	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
681	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
682	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
684	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
685	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
696	C₂×C₄²	—	2	4	no	—
697	C₂×C₄²	—	2	4	no	—
698	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
699	C₂×C₄²	C₂³×C₅	1	2	yes	—
700	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₅	1	2	yes	—
702	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
703	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
704	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
705	C₂×C₄²	C₂³×C₅	1	2	yes	—
706	C₂×C₄²	C₂³×C₅	1	2	yes	—
707	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
708	C₂×C₄²	C₂³×C₅	1	2	yes	—
709	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
710	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
711	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
712	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
713	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
714	C₂×C₄²	C₂³×C₅	1	2	yes	—
715	C₂×C₄²	C₂³×C₅	1	2	yes	—
716	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
717	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
718	#95	C₂³×C₅	1	1	yes	characteristic
719	#95	C₂³×C₅	1	1	yes	characteristic
720	#95	C₂³×C₅	1	1	yes	characteristic
721	#95	C₂³×C₅	1	1	yes	characteristic
722	#95	C₂³×C₅	1	1	yes	characteristic
723	#95	C₂³×C₅	1	1	yes	characteristic
724	#95	C₂³×C₅	1	2	yes	—
725	#95	C₂³×C₅	1	2	yes	—
726	#95	C₂³×C₅	1	2	yes	—
727	#95	C₂³×C₅	1	2	yes	—
728	#95	C₂³×C₅	1	2	yes	—
729	#95	C₂³×C₅	1	2	yes	—
730	#95	C₂³×C₅	1	2	yes	—
731	#95	C₂³×C₅	1	2	yes	—
732	#95	C₂³×C₅	1	2	yes	—
733	#95	C₂³×C₅	1	2	yes	—
734	#95	C₂³×C₅	1	2	yes	—
735	#95	C₂³×C₅	1	2	yes	—
736	#95	C₂³×C₅	1	2	yes	—
737	C₂²×C₅	—	2	2	no	—
738	C₂²×C₅	—	2	2	no	—
739	C₂²×C₅	—	2	2	no	—
740	C₂²×C₅	—	2	2	no	—
741	C₂²×C₅	—	2	2	no	—
742	C₂²×C₅	—	2	2	no	—
743	C₂²×C₅	—	4	1	no	—
744	C₂²×C₅	—	4	1	no	—
745	C₂²×C₅	—	4	1	no	—
746	C₂²×C₅	—	4	1	no	—
747	C₂²×C₅	—	4	1	no	—
748	C₂²×C₅	—	4	1	no	—
749	C₂²×C₅	—	4	1	no	—
750	C₂²×C₅	—	4	1	no	—
751	C₂²×C₅	—	4	2	no	—
752	C₂²×C₅	—	4	2	no	—
753	C₂²×C₅	—	4	2	no	—
754	C₂²×C₅	—	4	2	no	—
755	C₂²×C₅	—	4	2	no	—
756	C₂²×C₅	—	4	2	no	—
757	C₂²×C₅	—	4	2	no	—
758	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
759	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
760	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
761	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
762	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
763	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
764	C₂²×C₅	#585	1	1	yes	characteristic
765	C₄×C₅	—	2	4	no	—
766	C₄×C₅	—	2	2	no	—
767	C₄×C₅	—	2	2	no	—
768	C₄×C₅	—	2	2	no	—
769	C₄×C₅	—	2	2	no	—
770	C₄×C₅	—	2	2	no	—
771	C₄×C₅	—	2	4	no	—
772	C₄×C₅	—	2	4	no	—
773	C₄×C₅	—	2	2	no	—
774	C₄×C₅	—	4	1	no	—
775	C₄×C₅	—	4	1	no	—
776	C₄×C₅	—	4	2	no	—
777	C₄×C₅	—	4	2	no	—
778	C₄×C₅	—	4	1	no	—
779	C₄×C₅	—	4	2	no	—
780	C₄×C₅	—	4	1	no	—
781	C₄×C₅	—	4	2	no	—
782	C₄×C₅	—	4	1	no	—
783	C₄×C₅	#532	1	4	yes	—
784	C₄×C₅	#548	1	4	yes	—
785	C₂⁴	C₂⁴×C₅	1	2	yes	—
786	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
787	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
788	C₂×Q₈	—	2	4	no	—
789	C₂×Q₈	—	2	2	no	—
790	C₂×Q₈	—	2	2	no	—
791	C₂×Q₈	—	2	2	no	—
792	C₂×Q₈	—	2	2	no	—
793	C₂×Q₈	—	2	4	no	—
794	C₂×Q₈	—	2	2	no	—
795	C₂×Q₈	—	4	2	no	—
796	C₂×Q₈	C₂×C₅×D₄	1	4	yes	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	—	2	2	no	—
799	C₂×D₄	—	2	4	no	—
800	C₂×D₄	—	2	4	no	—
801	C₂×D₄	—	2	4	no	—
802	C₂×D₄	—	2	2	no	—
803	C₂×D₄	—	2	2	no	—
804	C₂×D₄	—	2	4	no	—
805	C₂×D₄	—	2	2	no	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	4	2	no	—
808	C₂×D₄	—	4	2	no	—
809	C₂²×C₄	—	2	2	no	—
810	C₂²×C₄	—	2	2	no	—
811	C₂²×C₄	—	2	2	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	4	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	2	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	4	no	—
823	C₂²×C₄	—	2	2	no	—
824	C₂²×C₄	—	2	2	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	4	no	—
827	C₂²×C₄	—	4	1	no	—
828	C₂²×C₄	—	4	1	no	—
829	C₂²×C₄	C₅×#41	1	4	yes	—
830	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
831	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
832	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
838	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
839	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
841	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
842	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
846	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
847	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
848	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
849	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
850	C₄⋊C₄	—	2	4	no	—
851	C₄⋊C₄	—	2	4	no	—
852	C₄⋊C₄	—	2	4	no	—
853	C₄⋊C₄	—	2	4	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	4	no	—
856	C₄⋊C₄	—	2	4	no	—
857	C₄⋊C₄	—	2	4	no	—
858	C₄⋊C₄	—	2	4	no	—
859	C₄⋊C₄	—	2	4	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	4	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	4	no	—
866	C₄⋊C₄	—	2	4	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	4	no	—
869	C₄⋊C₄	—	4	2	no	—
870	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
871	C₄⋊C₄	C₂×C₅×D₄	1	8	yes	—
872	C₄⋊C₄	C₅×#41	1	4	yes	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	4	no	—
875	C₂²⋊C₄	—	2	4	no	—
876	C₂²⋊C₄	—	2	4	no	—
877	C₂²⋊C₄	—	2	4	no	—
878	C₂²⋊C₄	—	2	4	no	—
879	C₂²⋊C₄	—	2	4	no	—
880	C₂²⋊C₄	—	2	4	no	—
881	C₂²⋊C₄	—	2	4	no	—
882	C₂²⋊C₄	—	2	4	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	4	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	4	no	—
889	C₂²⋊C₄	—	2	4	no	—
890	C₂²⋊C₄	—	2	4	no	—
891	C₂²⋊C₄	—	2	4	no	—
892	C₂²⋊C₄	—	2	4	no	—
893	C₂²⋊C₄	—	2	4	no	—
894	C₂²⋊C₄	—	4	2	no	—
895	C₂²⋊C₄	C₅×#41	1	4	yes	—
896	C₄²	—	2	2	no	—
897	C₄²	—	2	2	no	—
898	C₄²	—	2	2	no	—
899	C₄²	—	2	2	no	—
900	C₄²	—	2	2	no	—
901	C₄²	—	2	2	no	—
902	C₄²	—	2	4	no	—
903	C₄²	—	2	2	no	—
904	C₄²	—	2	2	no	—
905	C₄²	—	2	4	no	—
906	C₄²	—	2	4	no	—
907	C₄²	—	2	2	no	—
908	C₄²	—	2	4	no	—
909	C₄²	—	2	4	no	—
910	C₄²	—	2	2	no	—
911	C₄²	—	4	2	no	—
912	C₄²	—	4	1	no	—
913	C₄²	C₂×C₅×D₄	1	4	yes	—
914	C₄²	C₂×C₅×D₄	1	8	yes	—
915	C₄²	C₅×#41	1	4	yes	—
916	C₂×C₅	—	4	2	no	—
917	C₂×C₅	—	4	2	no	—
918	C₂×C₅	—	8	2	no	—
919	C₂×C₅	C₂×#532	1	1	yes	characteristic
920	C₂×C₅	#3444	1	1	yes	characteristic
921	C₂×C₅	#3461	1	1	yes	characteristic
922	C₂×C₅	C₂×#548	1	1	yes	characteristic
923	C₂×C₅	D₄×#41	1	1	yes	characteristic
924	C₂×C₅	#3475	1	1	yes	characteristic
925	C₂×C₅	#3482	1	1	yes	characteristic
926	C₂³	—	2	1	no	—
927	C₂³	—	2	1	no	—
928	C₂³	—	2	1	no	—
929	C₂³	—	2	1	no	—
930	C₂³	—	2	1	no	—
931	C₂³	—	2	1	no	—
932	C₂³	—	2	1	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	2	1	no	—
935	C₂³	—	2	1	no	—
936	C₂³	—	2	1	no	—
937	C₂³	—	2	1	no	—
938	C₂³	—	2	2	no	—
939	C₂³	—	2	2	no	—
940	C₂³	—	2	2	no	—
941	C₂³	—	2	2	no	—
942	C₂³	—	2	2	no	—
943	C₂³	—	2	2	no	—
944	C₂³	—	2	2	no	—
945	C₂³	C₂×C₅×#41	1	2	yes	—
946	C₂³	C₂×C₅×#41	1	2	yes	—
947	C₂³	C₂⁵×C₅	1	1	yes	characteristic
948	Q₈	—	2	8	no	—
949	Q₈	—	4	8	no	—
950	Q₈	—	4	4	no	—
951	D₄	—	2	8	no	—
952	D₄	—	4	8	no	—
953	D₄	—	4	8	no	—
954	D₄	—	4	4	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	8	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	4	4	no	—
1002	C₂×C₄	—	4	4	no	—
1003	C₂×C₄	—	4	4	no	—
1004	C₂×C₄	—	4	4	no	—
1005	C₂×C₄	—	4	4	no	—
1006	C₂×C₄	—	4	8	no	—
1007	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
1008	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
1009	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
1010	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
1011	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
1012	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1013	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1014	C₂×C₄	C₂×C₅×#41	1	4	yes	—
1015	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1016	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1017	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1018	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1019	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1020	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1021	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
1022	C₅	#34919	1	1	yes	characteristic, direct product factor, Sylow
1023	C₂²	—	2	2	no	—
1024	C₂²	—	2	2	no	—
1025	C₂²	—	2	2	no	—
1026	C₂²	—	2	2	no	—
1027	C₂²	—	2	2	no	—
1028	C₂²	—	2	2	no	—
1029	C₂²	—	4	1	no	—
1030	C₂²	—	4	1	no	—
1031	C₂²	—	4	1	no	—
1032	C₂²	—	4	1	no	—
1033	C₂²	—	4	1	no	—
1034	C₂²	—	4	1	no	—
1035	C₂²	—	4	1	no	—
1036	C₂²	—	4	1	no	—
1037	C₂²	—	4	2	no	—
1038	C₂²	—	4	2	no	—
1039	C₂²	—	4	2	no	—
1040	C₂²	—	4	2	no	—
1041	C₂²	—	4	2	no	—
1042	C₂²	—	4	2	no	—
1043	C₂²	—	4	2	no	—
1044	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
1045	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
1046	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
1047	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
1048	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
1049	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
1050	C₂²	C₅×#585	1	1	yes	characteristic
1051	C₄	—	2	4	no	—
1052	C₄	—	2	2	no	—
1053	C₄	—	2	2	no	—
1054	C₄	—	2	2	no	—
1055	C₄	—	2	2	no	—
1056	C₄	—	2	2	no	—
1057	C₄	—	2	4	no	—
1058	C₄	—	2	4	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	4	1	no	—
1061	C₄	—	4	1	no	—
1062	C₄	—	4	2	no	—
1063	C₄	—	4	2	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	2	no	—
1068	C₄	—	4	1	no	—
1069	C₄	C₅×#532	1	4	yes	—
1070	C₄	C₅×#548	1	4	yes	—
1071	C₂	—	4	2	no	—
1072	C₂	—	4	2	no	—
1073	C₂	—	8	2	no	—
1074	C₂	C₂×C₅×#532	1	1	yes	characteristic
1075	C₂	C₅×#3444	1	1	yes	characteristic
1076	C₂	C₅×#3461	1	1	yes	characteristic
1077	C₂	C₂×C₅×#548	1	1	yes	characteristic
1078	C₂	C₅×D₄×#41	1	1	yes	characteristic
1079	C₂	C₅×#3475	1	1	yes	characteristic
1080	C₂	C₅×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
socle	C₂³×C₅	C₂⁵
prime radical	C₅×#2540	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#533	C₂	semidirect
2. C₂×C₅×#529	C₂	semidirect
3. C₅×#2560	C₂	semidirect
4. C₅×#2558	C₂	semidirect
5. C₅×#2550	C₂	semidirect
6. C₅×#2545	C₂	semidirect
8. C₅×#2536	C₂	semidirect
9. C₅×#2519	C₂	semidirect
10. C₅×#2491	C₂	semidirect
11. C₅×#2489	C₂	semidirect
12. C₅×#2461	C₂	semidirect
13. C₅×#2429	C₂	semidirect
14. C₅×#2426	C₂	semidirect
15. C₅×#2396	C₂	semidirect
16. C₅×#2392	C₂	semidirect
17. C₄×C₅×#124	C₂	semidirect
18. C₄×C₅×#124	C₂	semidirect
19. C₄×C₅×C₂²⋊Q₈	C₂	semidirect
20. C₄×C₅×#121	C₂	semidirect
21. C₅×#2293	C₂	semidirect
22. C₄²×C₅×Q₈	C₂	semidirect
23. C₄²×C₅×D₄	C₂	semidirect
125. #34919	C₅	direct (N × H)
160. C₄×C₅×Q₈	D₄	semidirect
256. C₂×#533	C₂×C₅	semidirect
257. C₂×#529	C₂×C₅	semidirect
258. #2560	C₂×C₅	semidirect
259. #2558	C₂×C₅	semidirect
260. #2550	C₂×C₅	semidirect
261. #2545	C₂×C₅	semidirect
263. #2536	C₂×C₅	semidirect
264. #2519	C₂×C₅	semidirect
265. #2491	C₂×C₅	semidirect
266. #2489	C₂×C₅	semidirect
267. #2461	C₂×C₅	semidirect
268. #2429	C₂×C₅	semidirect
269. #2426	C₂×C₅	semidirect
270. #2396	C₂×C₅	semidirect
271. #2392	C₂×C₅	semidirect
272. C₄×#124	C₂×C₅	semidirect
273. C₄×#124	C₂×C₅	semidirect
274. C₄×C₂²⋊Q₈	C₂×C₅	semidirect
275. C₄×#121	C₂×C₅	semidirect
276. #2293	C₂×C₅	semidirect
277. C₄²×Q₈	C₂×C₅	semidirect
278. C₄²×D₄	C₂×C₅	semidirect
641. C₄×Q₈	C₅×D₄	semidirect
1022. C₅	#34919	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×C₅×#533	2
C₂×C₅×#529	2
C₅×#2560	2
C₅×#2558	2
C₅×#2550	2
C₅×#2545	2
C₅×#2540	2
C₅×#2536	2
C₅×#2519	2
C₅×#2491	2
C₅×#2489	2
C₅×#2461	2
C₅×#2429	2
C₅×#2426	2
C₅×#2396	2
C₅×#2392	2
C₄×C₅×#124	2
C₄×C₅×C₂²⋊Q₈	2
C₄×C₅×#121	2
C₅×#2293	2
C₄²×C₅×Q₈	2
C₄²×C₅×D₄	2
#34919	5

Subgroups — C5×#34919 #11957639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34919 #11957639