Subgroups — C₅×#35324 #11958044

Order 1280.

1566 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2864	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#2862	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2855	C₂	1	2	yes	maximal
4	C₅×#2645	C₂	1	2	yes	maximal, complemented
5	C₅×#2628	C₂	1	1	yes	maximal, characteristic
6	C₅×#2621	C₂	1	1	yes	maximal, characteristic
7	C₅×#2588	C₂	1	4	yes	maximal, complemented
8	C₅×#2575	C₂	1	4	yes	maximal
9	C₅×#2528	C₂	1	4	yes	maximal, complemented
10	C₅×#2527	C₂	1	4	yes	maximal
11	C₅×#2331	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2327	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#2323	C₂	1	2	yes	maximal
14	C₅×#2295	C₂	1	2	yes	maximal, complemented
15	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic
16	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
20	C₂×C₅×#117	C₂²	1	1	yes	characteristic
21	C₂×C₅×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₅×#401	C₂²	1	4	yes	—
24	C₅×#400	C₂²	1	4	yes	—
25	C₅×#400	C₂²	1	2	yes	—
26	C₅×#400	C₂²	1	4	yes	—
27	C₅×#400	C₂²	1	4	yes	—
28	C₅×#399	C₂²	1	2	yes	—
29	C₅×#398	C₂²	1	2	yes	—
30	C₅×#398	C₂²	1	2	yes	—
31	C₅×#397	C₂²	1	2	yes	—
32	C₅×#397	C₂²	1	2	yes	—
33	C₅×#395	C₂²	1	2	yes	—
34	C₅×#393	C₂²	1	2	yes	—
35	C₅×#391	C₂²	1	4	yes	—
36	C₅×#391	C₂²	1	4	yes	—
37	C₅×#391	C₂²	1	2	yes	—
38	C₅×#391	C₂²	1	2	yes	—
39	C₅×#391	C₂²	1	2	yes	—
40	C₅×#391	C₂²	1	2	yes	—
41	C₅×#389	C₂²	1	4	yes	—
42	C₅×#389	C₂²	1	2	yes	—
43	C₅×#389	C₂²	1	2	yes	—
44	C₅×#389	C₂²	1	2	yes	—
45	C₅×#389	C₂²	1	2	yes	—
46	C₅×#388	C₂²	1	4	yes	—
47	C₅×#388	C₂²	1	4	yes	—
48	C₅×#387	C₂²	1	4	yes	—
49	C₅×#387	C₂²	1	4	yes	—
50	C₅×#387	C₂²	1	4	yes	—
51	C₅×#387	C₂²	1	4	yes	—
52	C₅×#387	C₂²	1	4	yes	—
53	C₅×#387	C₂²	1	4	yes	—
54	C₅×#387	C₂²	1	4	yes	—
55	C₅×#387	C₂²	1	4	yes	—
56	C₅×#387	C₂²	1	4	yes	—
57	C₅×#387	C₂²	1	4	yes	—
58	C₅×#385	C₂²	1	4	yes	—
59	C₅×#382	C₂²	1	4	yes	—
60	C₅×#382	C₂²	1	1	yes	characteristic
61	C₅×#382	C₂²	1	1	yes	characteristic
62	C₅×#381	C₂²	1	4	yes	—
63	C₅×#380	C₂²	1	2	yes	—
64	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
65	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
66	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
67	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
68	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
69	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
70	C₅×#376	C₂²	1	1	yes	characteristic
71	C₅×#376	C₂²	1	1	yes	characteristic
72	C₅×#376	C₂²	1	4	yes	—
73	C₄³×C₅	C₂²	1	1	yes	characteristic
74	C₄³×C₅	C₂²	1	1	yes	characteristic
75	#35324	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂²×C₅×Q₈	C₂³	1	2	yes	—
77	C₂²×C₅×Q₈	C₂³	1	2	yes	—
78	C₂³×C₄×C₅	C₂³	1	2	yes	—
79	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₅×C₄⋊Q₈	—	2	4	no	—
81	C₅×C₄⋊Q₈	—	2	4	no	—
82	C₅×C₂²⋊Q₈	—	2	8	no	—
83	C₄×C₅×Q₈	—	2	8	no	—
84	C₅×#117	—	2	4	no	—
85	C₅×#117	—	2	4	no	—
86	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
87	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
92	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
93	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
94	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
97	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
98	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
100	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
101	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
102	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
105	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
106	C₂×C₄²×C₅	—	2	4	no	—
107	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₅	C₂³	1	2	yes	—
109	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₅	C₂³	1	2	yes	—
112	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₅	C₂³	1	4	yes	—
114	C₂×C₄²×C₅	C₂³	1	2	yes	—
115	C₂×C₄²×C₅	C₂³	1	2	yes	—
116	C₂×C₄²×C₅	C₂³	1	2	yes	—
117	C₂×C₄²×C₅	C₂³	1	4	yes	—
118	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
120	C₅×#95	C₂³	1	2	yes	—
121	C₅×#95	C₂³	1	2	yes	—
122	C₅×#95	C₂³	1	2	yes	—
123	C₅×#95	C₂³	1	2	yes	—
124	C₅×#95	C₂³	1	4	yes	—
125	C₅×#95	C₂³	1	4	yes	—
126	C₅×#95	C₂³	1	4	yes	—
127	C₅×#95	C₂³	1	4	yes	—
128	C₅×#95	C₂³	1	4	yes	—
129	C₅×#95	C₂³	1	4	yes	—
130	C₅×#95	C₂³	1	4	yes	—
131	C₅×#95	C₂³	1	4	yes	—
132	C₅×#95	C₂³	1	4	yes	—
133	C₅×#95	C₂³	1	4	yes	—
134	C₅×#95	C₂³	1	2	yes	—
135	C₅×#95	C₂³	1	2	yes	—
136	C₅×#95	C₂³	1	2	yes	—
137	C₅×#95	C₂³	1	2	yes	—
138	C₅×#95	C₂³	1	4	yes	—
139	C₅×#95	C₂³	1	4	yes	—
140	C₅×#95	C₂³	1	4	yes	—
141	C₅×#95	C₂³	1	4	yes	—
142	#2864	C₂×C₅	1	1	yes	characteristic, complemented
143	#2862	C₂×C₅	1	1	yes	characteristic, complemented
144	#2855	C₂×C₅	1	2	yes	—
145	#2645	C₂×C₅	1	2	yes	complemented
146	#2628	C₂×C₅	1	1	yes	characteristic
147	#2621	C₂×C₅	1	1	yes	characteristic
148	#2588	C₂×C₅	1	4	yes	complemented
149	#2575	C₂×C₅	1	4	yes	—
150	#2528	C₂×C₅	1	4	yes	complemented
151	#2527	C₂×C₅	1	4	yes	—
152	#2331	C₂×C₅	1	1	yes	characteristic, complemented
153	#2327	C₂×C₅	1	1	yes	characteristic, complemented
154	#2323	C₂×C₅	1	2	yes	—
155	#2295	C₂×C₅	1	2	yes	complemented
156	C₄×#117	C₂×C₅	1	1	yes	characteristic
157	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
158	C₂×C₅×Q₈	—	2	4	no	—
159	C₂×C₅×Q₈	—	2	4	no	—
160	C₂×C₅×Q₈	—	2	4	no	—
161	C₂×C₅×Q₈	—	2	4	no	—
162	C₂×C₅×Q₈	—	4	4	no	—
163	C₂²×C₄×C₅	—	2	2	no	—
164	C₂²×C₄×C₅	—	2	2	no	—
165	C₂²×C₄×C₅	—	2	4	no	—
166	C₂²×C₄×C₅	—	2	4	no	—
167	C₂²×C₄×C₅	—	4	2	no	—
168	C₂²×C₄×C₅	#41	1	4	yes	—
169	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
175	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
183	C₅×C₄⋊C₄	—	2	4	no	—
184	C₅×C₄⋊C₄	—	2	2	no	—
185	C₅×C₄⋊C₄	—	2	2	no	—
186	C₅×C₄⋊C₄	—	2	4	no	—
187	C₅×C₄⋊C₄	—	2	8	no	—
188	C₅×C₄⋊C₄	—	2	4	no	—
189	C₅×C₄⋊C₄	—	2	8	no	—
190	C₅×C₄⋊C₄	—	2	4	no	—
191	C₅×C₄⋊C₄	—	2	4	no	—
192	C₅×C₄⋊C₄	—	2	4	no	—
193	C₅×C₄⋊C₄	—	2	4	no	—
194	C₅×C₄⋊C₄	—	2	8	no	—
195	C₅×C₄⋊C₄	—	4	4	no	—
196	C₅×C₄⋊C₄	—	4	4	no	—
197	C₅×C₄⋊C₄	—	4	4	no	—
198	C₅×C₂²⋊C₄	—	2	8	no	—
199	C₅×C₂²⋊C₄	—	2	4	no	—
200	C₅×C₂²⋊C₄	—	2	2	no	—
201	C₅×C₂²⋊C₄	—	2	2	no	—
202	C₅×C₂²⋊C₄	—	4	4	no	—
203	C₄²×C₅	—	2	2	no	—
204	C₄²×C₅	—	2	4	no	—
205	C₄²×C₅	—	2	2	no	—
206	C₄²×C₅	—	2	2	no	—
207	C₄²×C₅	—	2	2	no	—
208	C₄²×C₅	—	2	8	no	—
209	C₄²×C₅	—	2	4	no	—
210	C₄²×C₅	—	2	4	no	—
211	C₄²×C₅	—	4	2	no	—
212	C₄²×C₅	—	4	4	no	—
213	C₄²×C₅	—	4	2	no	—
214	C₄²×C₅	#41	1	4	yes	—
215	C₄²×C₅	#41	1	4	yes	—
216	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
217	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
218	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
219	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
220	C₂×#117	C₂²×C₅	1	1	yes	characteristic
221	C₂×#117	C₂²×C₅	1	1	yes	characteristic
222	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
223	#401	C₂²×C₅	1	4	yes	—
224	#400	C₂²×C₅	1	4	yes	—
225	#400	C₂²×C₅	1	4	yes	—
226	#400	C₂²×C₅	1	2	yes	—
227	#400	C₂²×C₅	1	4	yes	—
228	#399	C₂²×C₅	1	2	yes	—
229	#398	C₂²×C₅	1	2	yes	—
230	#398	C₂²×C₅	1	2	yes	—
231	#397	C₂²×C₅	1	2	yes	—
232	#397	C₂²×C₅	1	2	yes	—
233	#395	C₂²×C₅	1	2	yes	—
234	#393	C₂²×C₅	1	2	yes	—
235	#391	C₂²×C₅	1	2	yes	—
236	#391	C₂²×C₅	1	2	yes	—
237	#391	C₂²×C₅	1	4	yes	—
238	#391	C₂²×C₅	1	4	yes	—
239	#391	C₂²×C₅	1	2	yes	—
240	#391	C₂²×C₅	1	2	yes	—
241	#389	C₂²×C₅	1	4	yes	—
242	#389	C₂²×C₅	1	2	yes	—
243	#389	C₂²×C₅	1	2	yes	—
244	#389	C₂²×C₅	1	2	yes	—
245	#389	C₂²×C₅	1	2	yes	—
246	#388	C₂²×C₅	1	4	yes	—
247	#388	C₂²×C₅	1	4	yes	—
248	#387	C₂²×C₅	1	4	yes	—
249	#387	C₂²×C₅	1	4	yes	—
250	#387	C₂²×C₅	1	4	yes	—
251	#387	C₂²×C₅	1	4	yes	—
252	#387	C₂²×C₅	1	4	yes	—
253	#387	C₂²×C₅	1	4	yes	—
254	#387	C₂²×C₅	1	4	yes	—
255	#387	C₂²×C₅	1	4	yes	—
256	#387	C₂²×C₅	1	4	yes	—
257	#387	C₂²×C₅	1	4	yes	—
258	#385	C₂²×C₅	1	4	yes	—
259	#382	C₂²×C₅	1	4	yes	—
260	#382	C₂²×C₅	1	1	yes	characteristic
261	#382	C₂²×C₅	1	1	yes	characteristic
262	#381	C₂²×C₅	1	4	yes	—
263	#380	C₂²×C₅	1	2	yes	—
264	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
265	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
266	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
267	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
268	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
269	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
270	#376	C₂²×C₅	1	1	yes	characteristic
271	#376	C₂²×C₅	1	1	yes	characteristic
272	#376	C₂²×C₅	1	4	yes	—
273	C₄³	C₂²×C₅	1	1	yes	characteristic
274	C₄³	C₂²×C₅	1	1	yes	characteristic
275	C₂³×C₅	—	2	1	no	—
276	C₂³×C₅	—	2	1	no	—
277	C₂³×C₅	—	2	2	no	—
278	C₂³×C₅	—	2	2	no	—
279	C₂³×C₅	C₂×#41	1	2	yes	—
280	C₂³×C₅	C₂⁵	1	1	yes	characteristic
281	C₅×Q₈	—	4	8	no	—
282	C₅×Q₈	—	8	4	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	2	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	2	8	no	—
292	C₂×C₄×C₅	—	2	2	no	—
293	C₂×C₄×C₅	—	2	2	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	2	4	no	—
297	C₂×C₄×C₅	—	2	4	no	—
298	C₂×C₄×C₅	—	2	4	no	—
299	C₂×C₄×C₅	—	2	4	no	—
300	C₂×C₄×C₅	—	2	4	no	—
301	C₂×C₄×C₅	—	2	4	no	—
302	C₂×C₄×C₅	—	2	2	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	4	no	—
305	C₂×C₄×C₅	—	2	4	no	—
306	C₂×C₄×C₅	—	2	2	no	—
307	C₂×C₄×C₅	—	2	4	no	—
308	C₂×C₄×C₅	—	2	2	no	—
309	C₂×C₄×C₅	—	2	4	no	—
310	C₂×C₄×C₅	—	2	2	no	—
311	C₂×C₄×C₅	—	2	4	no	—
312	C₂×C₄×C₅	—	2	2	no	—
313	C₂×C₄×C₅	—	2	4	no	—
314	C₂×C₄×C₅	—	4	8	no	—
315	C₂×C₄×C₅	C₂×#41	1	4	yes	—
316	C₂×C₄×C₅	C₂×#41	1	2	yes	—
317	C₂×C₄×C₅	C₂×#41	1	2	yes	—
318	C₂×C₄×C₅	C₂×#41	1	2	yes	—
319	C₂×C₄×C₅	C₂×#41	1	2	yes	—
320	C₂×C₄×C₅	C₂×#41	1	2	yes	—
321	C₂×C₄×C₅	C₂×#41	1	2	yes	—
322	C₂×C₄×C₅	2₋¹⁺⁴	1	4	yes	—
323	C₂²×Q₈	C₂³×C₅	1	2	yes	—
324	C₂²×Q₈	C₂³×C₅	1	2	yes	—
325	C₂³×C₄	C₂³×C₅	1	2	yes	—
326	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
327	C₄⋊Q₈	—	2	4	no	—
328	C₄⋊Q₈	—	2	4	no	—
329	C₂²⋊Q₈	—	2	8	no	—
330	C₄×Q₈	—	2	8	no	—
331	#117	—	2	4	no	—
332	#117	—	2	4	no	—
333	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
337	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
338	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
339	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
340	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
341	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
343	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
344	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
345	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
346	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
347	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
350	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
351	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
353	C₂×C₄²	—	2	4	no	—
354	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
355	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
356	C₂×C₄²	C₂³×C₅	1	4	yes	—
357	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₅	1	2	yes	—
359	C₂×C₄²	C₂³×C₅	1	2	yes	—
360	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
361	C₂×C₄²	C₂³×C₅	1	2	yes	—
362	C₂×C₄²	C₂³×C₅	1	2	yes	—
363	C₂×C₄²	C₂³×C₅	1	2	yes	—
364	C₂×C₄²	C₂³×C₅	1	4	yes	—
365	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
367	#95	C₂³×C₅	1	2	yes	—
368	#95	C₂³×C₅	1	2	yes	—
369	#95	C₂³×C₅	1	2	yes	—
370	#95	C₂³×C₅	1	2	yes	—
371	#95	C₂³×C₅	1	4	yes	—
372	#95	C₂³×C₅	1	4	yes	—
373	#95	C₂³×C₅	1	4	yes	—
374	#95	C₂³×C₅	1	4	yes	—
375	#95	C₂³×C₅	1	4	yes	—
376	#95	C₂³×C₅	1	4	yes	—
377	#95	C₂³×C₅	1	4	yes	—
378	#95	C₂³×C₅	1	4	yes	—
379	#95	C₂³×C₅	1	4	yes	—
380	#95	C₂³×C₅	1	4	yes	—
381	#95	C₂³×C₅	1	2	yes	—
382	#95	C₂³×C₅	1	2	yes	—
383	#95	C₂³×C₅	1	2	yes	—
384	#95	C₂³×C₅	1	2	yes	—
385	#95	C₂³×C₅	1	4	yes	—
386	#95	C₂³×C₅	1	4	yes	—
387	#95	C₂³×C₅	1	4	yes	—
388	#95	C₂³×C₅	1	4	yes	—
389	C₂²×C₅	—	2	2	no	—
390	C₂²×C₅	—	2	4	no	—
391	C₂²×C₅	—	4	2	no	—
392	C₂²×C₅	—	4	1	no	—
393	C₂²×C₅	—	4	1	no	—
394	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
395	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
396	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
397	C₂²×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
398	C₂²×C₅	#585	1	2	yes	—
399	C₄×C₅	—	2	2	no	—
400	C₄×C₅	—	2	4	no	—
401	C₄×C₅	—	2	4	no	—
402	C₄×C₅	—	2	2	no	—
403	C₄×C₅	—	2	2	no	—
404	C₄×C₅	—	4	4	no	—
405	C₄×C₅	—	4	2	no	—
406	C₄×C₅	—	4	4	no	—
407	C₄×C₅	—	4	4	no	—
408	C₄×C₅	—	4	2	no	—
409	C₄×C₅	—	4	1	no	—
410	C₄×C₅	—	4	1	no	—
411	C₄×C₅	—	4	4	no	—
412	C₄×C₅	#529	1	4	yes	—
413	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
414	C₂×Q₈	—	2	4	no	—
415	C₂×Q₈	—	2	4	no	—
416	C₂×Q₈	—	2	4	no	—
417	C₂×Q₈	—	2	4	no	—
418	C₂×Q₈	—	4	4	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	C₅×#41	1	4	yes	—
425	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
426	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
427	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
428	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
429	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
430	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
431	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
432	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
433	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
434	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
435	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
436	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
437	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
438	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	8	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	2	8	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	8	no	—
451	C₄⋊C₄	—	4	4	no	—
452	C₄⋊C₄	—	4	4	no	—
453	C₄⋊C₄	—	4	4	no	—
454	C₂²⋊C₄	—	2	8	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	4	4	no	—
459	C₄²	—	2	2	no	—
460	C₄²	—	2	4	no	—
461	C₄²	—	2	2	no	—
462	C₄²	—	2	2	no	—
463	C₄²	—	2	2	no	—
464	C₄²	—	2	8	no	—
465	C₄²	—	2	4	no	—
466	C₄²	—	2	4	no	—
467	C₄²	—	4	2	no	—
468	C₄²	—	4	4	no	—
469	C₄²	—	4	2	no	—
470	C₄²	C₅×#41	1	4	yes	—
471	C₄²	C₅×#41	1	4	yes	—
472	C₂×C₅	—	4	2	no	—
473	C₂×C₅	C₂×#529	1	1	yes	characteristic
474	C₂×C₅	#3461	1	2	yes	—
475	C₂×C₅	#3495	1	2	yes	—
476	C₂×C₅	#3509	1	1	yes	characteristic
477	C₂×C₅	#3510	1	1	yes	characteristic
478	C₂³	—	2	1	no	—
479	C₂³	—	2	1	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	2	no	—
482	C₂³	C₂×C₅×#41	1	2	yes	—
483	C₂³	C₂⁵×C₅	1	1	yes	characteristic
484	Q₈	—	4	8	no	—
485	Q₈	—	8	4	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	8	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	4	8	no	—
518	C₂×C₄	C₂×C₅×#41	1	4	yes	—
519	C₂×C₄	C₂×C₅×#41	1	2	yes	—
520	C₂×C₄	C₂×C₅×#41	1	2	yes	—
521	C₂×C₄	C₂×C₅×#41	1	2	yes	—
522	C₂×C₄	C₂×C₅×#41	1	2	yes	—
523	C₂×C₄	C₂×C₅×#41	1	2	yes	—
524	C₂×C₄	C₂×C₅×#41	1	2	yes	—
525	C₂×C₄	C₅×2₋¹⁺⁴	1	4	yes	—
526	C₅	#35324	1	1	yes	characteristic, direct product factor, Sylow
527	C₂²	—	2	2	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
533	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
534	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
535	C₂²	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
536	C₂²	C₅×#585	1	2	yes	—
537	C₄	—	2	2	no	—
538	C₄	—	2	4	no	—
539	C₄	—	2	4	no	—
540	C₄	—	2	2	no	—
541	C₄	—	2	2	no	—
542	C₄	—	4	4	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	4	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	4	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	4	no	—
549	C₄	—	4	1	no	—
550	C₄	C₅×#529	1	4	yes	—
551	C₂	—	4	2	no	—
552	C₂	C₂×C₅×#529	1	1	yes	characteristic
553	C₂	C₅×#3461	1	2	yes	—
554	C₂	C₅×#3495	1	2	yes	—
555	C₂	C₅×#3509	1	1	yes	characteristic
556	C₂	C₅×#3510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂⁴×C₅	C₂⁴
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×#2864	C₂	semidirect
2. C₅×#2862	C₂	semidirect
4. C₅×#2645	C₂	semidirect
7. C₅×#2588	C₂	semidirect
9. C₅×#2528	C₂	semidirect
11. C₅×#2331	C₂	semidirect
12. C₅×#2327	C₂	semidirect
14. C₅×#2295	C₂	semidirect
75. #35324	C₅	direct (N × H)
142. #2864	C₂×C₅	semidirect
143. #2862	C₂×C₅	semidirect
145. #2645	C₂×C₅	semidirect
148. #2588	C₂×C₅	semidirect
150. #2528	C₂×C₅	semidirect
152. #2331	C₂×C₅	semidirect
153. #2327	C₂×C₅	semidirect
155. #2295	C₂×C₅	semidirect
526. C₅	#35324	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×#2864	2
C₅×#2862	2
C₅×#2855	2
C₅×#2645	2
C₅×#2628	2
C₅×#2621	2
C₅×#2588	2
C₅×#2575	2
C₅×#2528	2
C₅×#2527	2
C₅×#2331	2
C₅×#2327	2
C₅×#2323	2
C₅×#2295	2
C₄×C₅×#117	2
#35324	5

Subgroups — C5×#35324 #11958044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#35324 #11958044