Subgroups — C₅×#35288 #11958008

Order 1280.

1978 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2859	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#2858	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2856	C₂	1	1	yes	maximal, characteristic
5	C₅×#2644	C₂	1	2	yes	maximal, complemented
6	C₅×#2624	C₂	1	2	yes	maximal, complemented
7	C₅×#2513	C₂	1	2	yes	maximal, complemented
8	C₅×#2490	C₂	1	2	yes	maximal, complemented
9	C₅×#2454	C₂	1	2	yes	maximal, complemented
10	C₅×#2448	C₂	1	2	yes	maximal, complemented
11	C₅×#2447	C₂	1	2	yes	maximal, complemented
12	C₅×#2427	C₂	1	2	yes	maximal, complemented
13	C₅×#2426	C₂	1	2	yes	maximal, complemented
14	C₅×#2420	C₂	1	2	yes	maximal, complemented
15	C₅×#2324	C₂	1	2	yes	maximal, complemented
16	C₅×#2319	C₂	1	2	yes	maximal, complemented
17	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×#127	C₂²	1	1	yes	characteristic
22	C₂×C₅×#125	C₂²	1	2	yes	—
23	C₂×C₅×#124	C₂²	1	2	yes	—
24	C₂×C₅×#124	C₂²	1	2	yes	—
25	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₅×#121	C₂²	1	2	yes	—
27	C₂×C₅×#121	C₂²	1	2	yes	—
28	C₂×C₅×#121	C₂²	1	2	yes	—
29	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
30	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
31	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
32	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
33	C₂×C₅×#117	C₂²	1	1	yes	characteristic
34	C₂×C₅×#117	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
36	C₅×#399	C₂²	1	4	yes	—
37	C₅×#397	C₂²	1	4	yes	—
38	C₅×#397	C₂²	1	4	yes	—
39	C₅×#397	C₂²	1	4	yes	—
40	C₅×#397	C₂²	1	4	yes	—
41	C₅×#396	C₂²	1	4	yes	—
42	C₅×#394	C₂²	1	4	yes	—
43	C₅×#394	C₂²	1	4	yes	—
44	C₅×#391	C₂²	1	2	yes	—
45	C₅×#391	C₂²	1	2	yes	—
46	C₅×#390	C₂²	1	2	yes	—
47	C₅×#390	C₂²	1	4	yes	—
48	C₅×#390	C₂²	1	2	yes	—
49	C₅×#390	C₂²	1	2	yes	—
50	C₅×#390	C₂²	1	2	yes	—
51	C₅×#390	C₂²	1	2	yes	—
52	C₅×#390	C₂²	1	2	yes	—
53	C₅×#390	C₂²	1	2	yes	—
54	C₅×#390	C₂²	1	2	yes	—
55	C₅×#390	C₂²	1	2	yes	—
56	C₅×#390	C₂²	1	2	yes	—
57	C₅×#389	C₂²	1	2	yes	—
58	C₅×#389	C₂²	1	2	yes	—
59	C₅×#389	C₂²	1	2	yes	—
60	C₅×#389	C₂²	1	2	yes	—
61	C₅×#389	C₂²	1	2	yes	—
62	C₅×#389	C₂²	1	2	yes	—
63	C₅×#389	C₂²	1	2	yes	—
64	C₅×#389	C₂²	1	2	yes	—
65	C₅×#388	C₂²	1	4	yes	—
66	C₅×#388	C₂²	1	4	yes	—
67	C₅×#388	C₂²	1	4	yes	—
68	C₅×#386	C₂²	1	4	yes	—
69	C₅×#385	C₂²	1	4	yes	—
70	C₅×#384	C₂²	1	1	yes	characteristic
71	C₅×#384	C₂²	1	1	yes	characteristic
72	C₅×#382	C₂²	1	2	yes	—
73	C₅×#381	C₂²	1	4	yes	—
74	C₅×#380	C₂²	1	2	yes	—
75	C₅×#380	C₂²	1	4	yes	—
76	C₅×#380	C₂²	1	2	yes	—
77	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
78	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
79	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
80	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
81	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
82	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
83	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
84	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
85	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
86	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
87	C₅×#376	C₂²	1	1	yes	characteristic
88	C₅×#376	C₂²	1	1	yes	characteristic
89	C₄³×C₅	C₂²	1	1	yes	characteristic
90	C₄³×C₅	C₂²	1	1	yes	characteristic
91	#35288	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂²×C₅×Q₈	C₂³	1	2	yes	—
93	C₂²×C₅×D₄	C₂³	1	2	yes	—
94	C₂²×C₅×D₄	C₂³	1	2	yes	—
95	C₂²×C₅×D₄	C₂³	1	2	yes	—
96	C₂²×C₅×D₄	C₂³	1	4	yes	—
97	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₅	C₂³	1	4	yes	—
101	C₅×C₄⋊Q₈	—	2	4	no	—
102	C₅×#127	—	2	4	no	—
103	C₅×#125	—	4	4	no	—
104	C₅×#124	—	4	4	no	—
105	C₅×#124	—	4	4	no	—
106	C₅×C₂²⋊Q₈	—	4	4	no	—
107	C₅×#121	—	2	8	no	—
108	C₅×#121	—	4	4	no	—
109	C₅×#121	—	4	4	no	—
110	C₄×C₅×Q₈	—	4	4	no	—
111	C₄×C₅×D₄	—	2	8	no	—
112	C₄×C₅×D₄	—	4	4	no	—
113	C₄×C₅×D₄	—	4	4	no	—
114	C₅×#117	—	2	4	no	—
115	C₅×#117	—	2	4	no	—
116	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
122	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
123	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
125	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
126	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
129	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
130	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
131	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
132	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
133	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
134	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
135	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
136	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
142	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
144	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
145	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₂×C₄²×C₅	—	2	4	no	—
148	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₅	C₂³	1	4	yes	—
163	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
165	C₅×#95	C₂³	1	1	yes	characteristic
166	C₅×#95	C₂³	1	1	yes	characteristic
167	C₅×#95	C₂³	1	1	yes	characteristic
168	C₅×#95	C₂³	1	1	yes	characteristic
169	C₅×#95	C₂³	1	1	yes	characteristic
170	C₅×#95	C₂³	1	1	yes	characteristic
171	C₅×#95	C₂³	1	1	yes	characteristic
172	C₅×#95	C₂³	1	1	yes	characteristic
173	C₅×#95	C₂³	1	4	yes	—
174	C₅×#95	C₂³	1	4	yes	—
175	C₅×#95	C₂³	1	4	yes	—
176	C₅×#95	C₂³	1	4	yes	—
177	C₅×#95	C₂³	1	4	yes	—
178	C₅×#95	C₂³	1	4	yes	—
179	#2859	C₂×C₅	1	1	yes	characteristic, complemented
180	#2858	C₂×C₅	1	1	yes	characteristic, complemented
181	#2857	C₂×C₅	1	1	yes	characteristic, complemented
182	#2856	C₂×C₅	1	1	yes	characteristic
183	#2644	C₂×C₅	1	2	yes	complemented
184	#2624	C₂×C₅	1	2	yes	complemented
185	#2513	C₂×C₅	1	2	yes	complemented
186	#2490	C₂×C₅	1	2	yes	complemented
187	#2454	C₂×C₅	1	2	yes	complemented
188	#2448	C₂×C₅	1	2	yes	complemented
189	#2447	C₂×C₅	1	2	yes	complemented
190	#2427	C₂×C₅	1	2	yes	complemented
191	#2426	C₂×C₅	1	2	yes	complemented
192	#2420	C₂×C₅	1	2	yes	complemented
193	#2324	C₂×C₅	1	2	yes	complemented
194	#2319	C₂×C₅	1	2	yes	complemented
195	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
196	C₄×#127	C₂×C₅	1	1	yes	characteristic, complemented
197	C₄×#117	C₂×C₅	1	1	yes	characteristic, complemented
198	C₂⁴×C₅	C₂⁴	1	4	yes	—
199	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
200	C₂×C₅×Q₈	—	2	4	no	—
201	C₂×C₅×Q₈	—	2	4	no	—
202	C₂×C₅×Q₈	—	2	4	no	—
203	C₂×C₅×D₄	—	2	8	no	—
204	C₂×C₅×D₄	—	2	4	no	—
205	C₂×C₅×D₄	—	2	4	no	—
206	C₂×C₅×D₄	—	2	4	no	—
207	C₂×C₅×D₄	—	2	4	no	—
208	C₂×C₅×D₄	—	2	4	no	—
209	C₂×C₅×D₄	—	2	4	no	—
210	C₂×C₅×D₄	—	2	4	no	—
211	C₂×C₅×D₄	—	2	4	no	—
212	C₂×C₅×D₄	—	2	4	no	—
213	C₂×C₅×D₄	—	4	4	no	—
214	C₂×C₅×D₄	—	4	4	no	—
215	C₂²×C₄×C₅	—	2	2	no	—
216	C₂²×C₄×C₅	—	2	2	no	—
217	C₂²×C₄×C₅	—	2	2	no	—
218	C₂²×C₄×C₅	—	2	2	no	—
219	C₂²×C₄×C₅	—	2	2	no	—
220	C₂²×C₄×C₅	—	2	2	no	—
221	C₂²×C₄×C₅	—	2	2	no	—
222	C₂²×C₄×C₅	—	2	2	no	—
223	C₂²×C₄×C₅	—	2	8	no	—
224	C₂²×C₄×C₅	—	4	4	no	—
225	C₂²×C₄×C₅	—	4	4	no	—
226	C₂²×C₄×C₅	#41	1	4	yes	—
227	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
236	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
237	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
238	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
244	C₅×C₄⋊C₄	—	2	2	no	—
245	C₅×C₄⋊C₄	—	2	2	no	—
246	C₅×C₄⋊C₄	—	2	2	no	—
247	C₅×C₄⋊C₄	—	2	2	no	—
248	C₅×C₄⋊C₄	—	2	4	no	—
249	C₅×C₄⋊C₄	—	2	4	no	—
250	C₅×C₄⋊C₄	—	2	4	no	—
251	C₅×C₄⋊C₄	—	2	4	no	—
252	C₅×C₄⋊C₄	—	2	4	no	—
253	C₅×C₄⋊C₄	—	2	4	no	—
254	C₅×C₄⋊C₄	—	2	4	no	—
255	C₅×C₄⋊C₄	—	2	4	no	—
256	C₅×C₄⋊C₄	—	4	4	no	—
257	C₅×C₄⋊C₄	—	4	4	no	—
258	C₅×C₄⋊C₄	—	4	4	no	—
259	C₅×C₄⋊C₄	—	4	4	no	—
260	C₅×C₂²⋊C₄	—	2	2	no	—
261	C₅×C₂²⋊C₄	—	2	2	no	—
262	C₅×C₂²⋊C₄	—	2	2	no	—
263	C₅×C₂²⋊C₄	—	2	2	no	—
264	C₅×C₂²⋊C₄	—	2	8	no	—
265	C₅×C₂²⋊C₄	—	2	8	no	—
266	C₅×C₂²⋊C₄	—	4	4	no	—
267	C₅×C₂²⋊C₄	—	4	4	no	—
268	C₅×C₂²⋊C₄	—	4	4	no	—
269	C₅×C₂²⋊C₄	—	4	4	no	—
270	C₅×C₂²⋊C₄	—	4	4	no	—
271	C₅×C₂²⋊C₄	—	4	4	no	—
272	C₅×C₂²⋊C₄	—	4	4	no	—
273	C₅×C₂²⋊C₄	—	4	4	no	—
274	C₅×C₂²⋊C₄	—	4	4	no	—
275	C₄²×C₅	—	2	2	no	—
276	C₄²×C₅	—	2	2	no	—
277	C₄²×C₅	—	2	2	no	—
278	C₄²×C₅	—	2	2	no	—
279	C₄²×C₅	—	2	2	no	—
280	C₄²×C₅	—	2	2	no	—
281	C₄²×C₅	—	2	2	no	—
282	C₄²×C₅	—	2	2	no	—
283	C₄²×C₅	—	2	2	no	—
284	C₄²×C₅	—	2	2	no	—
285	C₄²×C₅	—	2	2	no	—
286	C₄²×C₅	—	2	2	no	—
287	C₄²×C₅	—	2	2	no	—
288	C₄²×C₅	—	2	2	no	—
289	C₄²×C₅	—	4	4	no	—
290	C₄²×C₅	#41	1	4	yes	—
291	C₄²×C₅	#41	1	4	yes	—
292	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
293	C₂×#127	C₂²×C₅	1	1	yes	characteristic
294	C₂×#125	C₂²×C₅	1	2	yes	—
295	C₂×#124	C₂²×C₅	1	2	yes	—
296	C₂×#124	C₂²×C₅	1	2	yes	—
297	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
298	C₂×#121	C₂²×C₅	1	2	yes	—
299	C₂×#121	C₂²×C₅	1	2	yes	—
300	C₂×#121	C₂²×C₅	1	2	yes	—
301	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
302	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
303	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
304	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
305	C₂×#117	C₂²×C₅	1	1	yes	characteristic
306	C₂×#117	C₂²×C₅	1	1	yes	characteristic
307	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
308	#399	C₂²×C₅	1	4	yes	—
309	#397	C₂²×C₅	1	4	yes	—
310	#397	C₂²×C₅	1	4	yes	—
311	#397	C₂²×C₅	1	4	yes	—
312	#397	C₂²×C₅	1	4	yes	—
313	#396	C₂²×C₅	1	4	yes	—
314	#394	C₂²×C₅	1	4	yes	—
315	#394	C₂²×C₅	1	4	yes	—
316	#391	C₂²×C₅	1	2	yes	—
317	#391	C₂²×C₅	1	2	yes	—
318	#390	C₂²×C₅	1	2	yes	—
319	#390	C₂²×C₅	1	2	yes	—
320	#390	C₂²×C₅	1	2	yes	—
321	#390	C₂²×C₅	1	2	yes	—
322	#390	C₂²×C₅	1	2	yes	—
323	#390	C₂²×C₅	1	2	yes	—
324	#390	C₂²×C₅	1	4	yes	—
325	#390	C₂²×C₅	1	2	yes	—
326	#390	C₂²×C₅	1	2	yes	—
327	#390	C₂²×C₅	1	2	yes	—
328	#390	C₂²×C₅	1	2	yes	—
329	#389	C₂²×C₅	1	2	yes	—
330	#389	C₂²×C₅	1	2	yes	—
331	#389	C₂²×C₅	1	2	yes	—
332	#389	C₂²×C₅	1	2	yes	—
333	#389	C₂²×C₅	1	2	yes	—
334	#389	C₂²×C₅	1	2	yes	—
335	#389	C₂²×C₅	1	2	yes	—
336	#389	C₂²×C₅	1	2	yes	—
337	#388	C₂²×C₅	1	4	yes	—
338	#388	C₂²×C₅	1	4	yes	—
339	#388	C₂²×C₅	1	4	yes	—
340	#386	C₂²×C₅	1	4	yes	—
341	#385	C₂²×C₅	1	4	yes	—
342	#384	C₂²×C₅	1	1	yes	characteristic
343	#384	C₂²×C₅	1	1	yes	characteristic
344	#382	C₂²×C₅	1	2	yes	—
345	#381	C₂²×C₅	1	4	yes	—
346	#380	C₂²×C₅	1	4	yes	—
347	#380	C₂²×C₅	1	2	yes	—
348	#380	C₂²×C₅	1	2	yes	—
349	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
350	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
351	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
352	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
353	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
354	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
355	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
356	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
357	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
358	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
359	#376	C₂²×C₅	1	1	yes	characteristic
360	#376	C₂²×C₅	1	1	yes	characteristic
361	C₄³	C₂²×C₅	1	1	yes	characteristic
362	C₄³	C₂²×C₅	1	1	yes	characteristic
363	C₂³×C₅	—	2	1	no	—
364	C₂³×C₅	—	2	1	no	—
365	C₂³×C₅	—	2	1	no	—
366	C₂³×C₅	—	2	1	no	—
367	C₂³×C₅	—	2	1	no	—
368	C₂³×C₅	—	2	1	no	—
369	C₂³×C₅	—	2	4	no	—
370	C₂³×C₅	—	2	4	no	—
371	C₂³×C₅	—	2	4	no	—
372	C₂³×C₅	—	2	4	no	—
373	C₂³×C₅	—	2	4	no	—
374	C₂³×C₅	—	2	4	no	—
375	C₂³×C₅	—	2	4	no	—
376	C₂³×C₅	C₂×#41	1	2	yes	—
377	C₂³×C₅	C₂⁵	1	1	yes	characteristic
378	C₅×Q₈	—	4	8	no	—
379	C₅×D₄	—	4	8	no	—
380	C₅×D₄	—	4	8	no	—
381	C₅×D₄	—	4	8	no	—
382	C₅×D₄	—	8	8	no	—
383	C₂×C₄×C₅	—	2	1	no	—
384	C₂×C₄×C₅	—	2	1	no	—
385	C₂×C₄×C₅	—	2	1	no	—
386	C₂×C₄×C₅	—	2	1	no	—
387	C₂×C₄×C₅	—	2	1	no	—
388	C₂×C₄×C₅	—	2	1	no	—
389	C₂×C₄×C₅	—	2	8	no	—
390	C₂×C₄×C₅	—	2	1	no	—
391	C₂×C₄×C₅	—	2	1	no	—
392	C₂×C₄×C₅	—	2	1	no	—
393	C₂×C₄×C₅	—	2	1	no	—
394	C₂×C₄×C₅	—	2	1	no	—
395	C₂×C₄×C₅	—	2	1	no	—
396	C₂×C₄×C₅	—	2	1	no	—
397	C₂×C₄×C₅	—	2	1	no	—
398	C₂×C₄×C₅	—	2	4	no	—
399	C₂×C₄×C₅	—	2	4	no	—
400	C₂×C₄×C₅	—	2	4	no	—
401	C₂×C₄×C₅	—	2	1	no	—
402	C₂×C₄×C₅	—	2	1	no	—
403	C₂×C₄×C₅	—	2	1	no	—
404	C₂×C₄×C₅	—	2	1	no	—
405	C₂×C₄×C₅	—	2	1	no	—
406	C₂×C₄×C₅	—	2	1	no	—
407	C₂×C₄×C₅	—	2	1	no	—
408	C₂×C₄×C₅	—	2	1	no	—
409	C₂×C₄×C₅	—	2	1	no	—
410	C₂×C₄×C₅	—	2	4	no	—
411	C₂×C₄×C₅	—	2	4	no	—
412	C₂×C₄×C₅	—	2	1	no	—
413	C₂×C₄×C₅	—	2	1	no	—
414	C₂×C₄×C₅	—	2	4	no	—
415	C₂×C₄×C₅	—	2	4	no	—
416	C₂×C₄×C₅	—	2	4	no	—
417	C₂×C₄×C₅	—	2	4	no	—
418	C₂×C₄×C₅	—	2	1	no	—
419	C₂×C₄×C₅	—	2	1	no	—
420	C₂×C₄×C₅	—	2	1	no	—
421	C₂×C₄×C₅	—	2	1	no	—
422	C₂×C₄×C₅	—	2	1	no	—
423	C₂×C₄×C₅	—	4	4	no	—
424	C₂×C₄×C₅	—	4	4	no	—
425	C₂×C₄×C₅	—	8	8	no	—
426	C₂×C₄×C₅	C₂×#41	1	2	yes	—
427	C₂×C₄×C₅	C₂×#41	1	2	yes	—
428	C₂×C₄×C₅	C₂×#41	1	2	yes	—
429	C₂×C₄×C₅	C₂×#41	1	2	yes	—
430	C₂×C₄×C₅	C₂×#41	1	2	yes	—
431	C₂×C₄×C₅	C₂×#41	1	2	yes	—
432	C₂×C₄×C₅	C₂×#41	1	2	yes	—
433	C₂×C₄×C₅	C₂×#41	1	2	yes	—
434	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
435	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
436	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
437	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
438	C₂²×Q₈	C₂³×C₅	1	2	yes	—
439	C₂²×D₄	C₂³×C₅	1	2	yes	—
440	C₂²×D₄	C₂³×C₅	1	2	yes	—
441	C₂²×D₄	C₂³×C₅	1	2	yes	—
442	C₂²×D₄	C₂³×C₅	1	4	yes	—
443	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
444	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
445	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
446	C₂³×C₄	C₂³×C₅	1	4	yes	—
447	C₄⋊Q₈	—	2	4	no	—
448	#127	—	2	4	no	—
449	#125	—	4	4	no	—
450	#124	—	4	4	no	—
451	#124	—	4	4	no	—
452	C₂²⋊Q₈	—	4	4	no	—
453	#121	—	2	8	no	—
454	#121	—	4	4	no	—
455	#121	—	4	4	no	—
456	C₄×Q₈	—	4	4	no	—
457	C₄×D₄	—	2	8	no	—
458	C₄×D₄	—	4	4	no	—
459	C₄×D₄	—	4	4	no	—
460	#117	—	2	4	no	—
461	#117	—	2	4	no	—
462	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
475	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
476	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
477	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
480	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
481	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
482	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
493	C₂×C₄²	—	2	4	no	—
494	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
495	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
499	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
500	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
501	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
502	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
503	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
506	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
507	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
508	C₂×C₄²	C₂³×C₅	1	4	yes	—
509	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
510	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
511	#95	C₂³×C₅	1	1	yes	characteristic
512	#95	C₂³×C₅	1	1	yes	characteristic
513	#95	C₂³×C₅	1	1	yes	characteristic
514	#95	C₂³×C₅	1	1	yes	characteristic
515	#95	C₂³×C₅	1	1	yes	characteristic
516	#95	C₂³×C₅	1	1	yes	characteristic
517	#95	C₂³×C₅	1	1	yes	characteristic
518	#95	C₂³×C₅	1	1	yes	characteristic
519	#95	C₂³×C₅	1	4	yes	—
520	#95	C₂³×C₅	1	4	yes	—
521	#95	C₂³×C₅	1	4	yes	—
522	#95	C₂³×C₅	1	4	yes	—
523	#95	C₂³×C₅	1	4	yes	—
524	#95	C₂³×C₅	1	4	yes	—
525	C₂²×C₅	—	2	2	no	—
526	C₂²×C₅	—	2	2	no	—
527	C₂²×C₅	—	2	2	no	—
528	C₂²×C₅	—	4	1	no	—
529	C₂²×C₅	—	4	1	no	—
530	C₂²×C₅	—	4	1	no	—
531	C₂²×C₅	—	4	1	no	—
532	C₂²×C₅	—	4	4	no	—
533	C₂²×C₅	—	4	4	no	—
534	C₂²×C₅	—	4	4	no	—
535	C₂²×C₅	—	4	4	no	—
536	C₂²×C₅	—	4	4	no	—
537	C₂²×C₅	—	4	4	no	—
538	C₂²×C₅	—	4	4	no	—
539	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
540	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
541	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
542	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
543	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
544	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
545	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
546	C₄×C₅	—	2	2	no	—
547	C₄×C₅	—	2	2	no	—
548	C₄×C₅	—	2	2	no	—
549	C₄×C₅	—	4	1	no	—
550	C₄×C₅	—	4	4	no	—
551	C₄×C₅	—	4	1	no	—
552	C₄×C₅	—	4	1	no	—
553	C₄×C₅	—	4	1	no	—
554	C₄×C₅	—	4	1	no	—
555	C₄×C₅	—	4	4	no	—
556	C₄×C₅	—	4	4	no	—
557	C₄×C₅	—	4	1	no	—
558	C₄×C₅	—	4	1	no	—
559	C₄×C₅	—	4	1	no	—
560	C₄×C₅	#529	1	4	yes	—
561	C₄×C₅	#540	1	4	yes	—
562	C₄×C₅	#542	1	4	yes	—
563	C₂⁴	C₂⁴×C₅	1	4	yes	—
564	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
565	C₂×Q₈	—	2	4	no	—
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	—	2	4	no	—
568	C₂×D₄	—	2	8	no	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	2	4	no	—
575	C₂×D₄	—	2	4	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	4	4	no	—
579	C₂×D₄	—	4	4	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	8	no	—
589	C₂²×C₄	—	4	4	no	—
590	C₂²×C₄	—	4	4	no	—
591	C₂²×C₄	C₅×#41	1	4	yes	—
592	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
593	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
594	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
598	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
599	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
600	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	2	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	4	4	no	—
622	C₄⋊C₄	—	4	4	no	—
623	C₄⋊C₄	—	4	4	no	—
624	C₄⋊C₄	—	4	4	no	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	—	2	2	no	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	8	no	—
630	C₂²⋊C₄	—	2	8	no	—
631	C₂²⋊C₄	—	4	4	no	—
632	C₂²⋊C₄	—	4	4	no	—
633	C₂²⋊C₄	—	4	4	no	—
634	C₂²⋊C₄	—	4	4	no	—
635	C₂²⋊C₄	—	4	4	no	—
636	C₂²⋊C₄	—	4	4	no	—
637	C₂²⋊C₄	—	4	4	no	—
638	C₂²⋊C₄	—	4	4	no	—
639	C₂²⋊C₄	—	4	4	no	—
640	C₄²	—	2	2	no	—
641	C₄²	—	2	2	no	—
642	C₄²	—	2	2	no	—
643	C₄²	—	2	2	no	—
644	C₄²	—	2	2	no	—
645	C₄²	—	2	2	no	—
646	C₄²	—	2	2	no	—
647	C₄²	—	2	2	no	—
648	C₄²	—	2	2	no	—
649	C₄²	—	2	2	no	—
650	C₄²	—	2	2	no	—
651	C₄²	—	2	2	no	—
652	C₄²	—	2	2	no	—
653	C₄²	—	2	2	no	—
654	C₄²	—	4	4	no	—
655	C₄²	C₅×#41	1	4	yes	—
656	C₄²	C₅×#41	1	4	yes	—
657	C₂×C₅	—	4	2	no	—
658	C₂×C₅	—	8	4	no	—
659	C₂×C₅	C₂×#529	1	1	yes	characteristic
660	C₂×C₅	C₂×#540	1	1	yes	characteristic
661	C₂×C₅	C₂×#542	1	1	yes	characteristic
662	C₂×C₅	#3508	1	1	yes	characteristic
663	C₂×C₅	#3508	1	1	yes	characteristic
664	C₂×C₅	#3511	1	1	yes	characteristic
665	C₂×C₅	#3511	1	1	yes	characteristic
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	4	no	—
673	C₂³	—	2	4	no	—
674	C₂³	—	2	4	no	—
675	C₂³	—	2	4	no	—
676	C₂³	—	2	4	no	—
677	C₂³	—	2	4	no	—
678	C₂³	—	2	4	no	—
679	C₂³	C₂×C₅×#41	1	2	yes	—
680	C₂³	C₂⁵×C₅	1	1	yes	characteristic
681	Q₈	—	4	8	no	—
682	D₄	—	4	8	no	—
683	D₄	—	4	8	no	—
684	D₄	—	4	8	no	—
685	D₄	—	8	8	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	8	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	4	no	—
719	C₂×C₄	—	2	4	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	4	4	no	—
727	C₂×C₄	—	4	4	no	—
728	C₂×C₄	—	8	8	no	—
729	C₂×C₄	C₂×C₅×#41	1	2	yes	—
730	C₂×C₄	C₂×C₅×#41	1	2	yes	—
731	C₂×C₄	C₂×C₅×#41	1	2	yes	—
732	C₂×C₄	C₂×C₅×#41	1	2	yes	—
733	C₂×C₄	C₂×C₅×#41	1	2	yes	—
734	C₂×C₄	C₂×C₅×#41	1	2	yes	—
735	C₂×C₄	C₂×C₅×#41	1	2	yes	—
736	C₂×C₄	C₂×C₅×#41	1	2	yes	—
737	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
738	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
739	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
740	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
741	C₅	#35288	1	1	yes	characteristic, direct product factor, Sylow
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	1	no	—
748	C₂²	—	4	1	no	—
749	C₂²	—	4	4	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	4	4	no	—
752	C₂²	—	4	4	no	—
753	C₂²	—	4	4	no	—
754	C₂²	—	4	4	no	—
755	C₂²	—	4	4	no	—
756	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
757	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
758	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
759	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
760	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
761	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
762	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
763	C₄	—	2	2	no	—
764	C₄	—	2	2	no	—
765	C₄	—	2	2	no	—
766	C₄	—	4	1	no	—
767	C₄	—	4	4	no	—
768	C₄	—	4	1	no	—
769	C₄	—	4	4	no	—
770	C₄	—	4	4	no	—
771	C₄	—	4	1	no	—
772	C₄	—	4	1	no	—
773	C₄	—	4	1	no	—
774	C₄	—	4	1	no	—
775	C₄	—	4	1	no	—
776	C₄	—	4	1	no	—
777	C₄	C₅×#529	1	4	yes	—
778	C₄	C₅×#540	1	4	yes	—
779	C₄	C₅×#542	1	4	yes	—
780	C₂	—	4	2	no	—
781	C₂	—	8	4	no	—
782	C₂	C₂×C₅×#529	1	1	yes	characteristic
783	C₂	C₂×C₅×#540	1	1	yes	characteristic
784	C₂	C₂×C₅×#542	1	1	yes	characteristic
785	C₂	C₅×#3508	1	1	yes	characteristic
786	C₂	C₅×#3508	1	1	yes	characteristic
787	C₂	C₅×#3511	1	1	yes	characteristic
788	C₂	C₅×#3511	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₅×#2856	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#2859	C₂	semidirect
2. C₅×#2858	C₂	semidirect
3. C₅×#2857	C₂	semidirect
5. C₅×#2644	C₂	semidirect
6. C₅×#2624	C₂	semidirect
7. C₅×#2513	C₂	semidirect
8. C₅×#2490	C₂	semidirect
9. C₅×#2454	C₂	semidirect
10. C₅×#2448	C₂	semidirect
11. C₅×#2447	C₂	semidirect
12. C₅×#2427	C₂	semidirect
13. C₅×#2426	C₂	semidirect
14. C₅×#2420	C₂	semidirect
15. C₅×#2324	C₂	semidirect
16. C₅×#2319	C₂	semidirect
17. C₄×C₅×C₄⋊Q₈	C₂	semidirect
18. C₄×C₅×#127	C₂	semidirect
19. C₄×C₅×#117	C₂	semidirect
91. #35288	C₅	direct (N × H)
179. #2859	C₂×C₅	semidirect
180. #2858	C₂×C₅	semidirect
181. #2857	C₂×C₅	semidirect
183. #2644	C₂×C₅	semidirect
184. #2624	C₂×C₅	semidirect
185. #2513	C₂×C₅	semidirect
186. #2490	C₂×C₅	semidirect
187. #2454	C₂×C₅	semidirect
188. #2448	C₂×C₅	semidirect
189. #2447	C₂×C₅	semidirect
190. #2427	C₂×C₅	semidirect
191. #2426	C₂×C₅	semidirect
192. #2420	C₂×C₅	semidirect
193. #2324	C₂×C₅	semidirect
194. #2319	C₂×C₅	semidirect
195. C₄×C₄⋊Q₈	C₂×C₅	semidirect
196. C₄×#127	C₂×C₅	semidirect
197. C₄×#117	C₂×C₅	semidirect
741. C₅	#35288	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2859	2
C₅×#2858	2
C₅×#2857	2
C₅×#2856	2
C₅×#2644	2
C₅×#2624	2
C₅×#2513	2
C₅×#2490	2
C₅×#2454	2
C₅×#2448	2
C₅×#2447	2
C₅×#2427	2
C₅×#2426	2
C₅×#2420	2
C₅×#2324	2
C₅×#2319	2
C₄×C₅×C₄⋊Q₈	2
C₄×C₅×#127	2
C₄×C₅×#117	2
#35288	5

Subgroups — C5×#35288 #11958008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#35288 #11958008