Subgroups — C₅×#35283 #11958003

Order 1280.

1738 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2868	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#2862	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2857	C₂	1	2	yes	maximal
4	C₅×#2647	C₂	1	2	yes	maximal, complemented
5	C₅×#2628	C₂	1	2	yes	maximal
6	C₅×#2511	C₂	1	4	yes	maximal, complemented
7	C₅×#2492	C₂	1	4	yes	maximal
8	C₅×#2451	C₂	1	4	yes	maximal, complemented
9	C₅×#2423	C₂	1	4	yes	maximal
10	C₅×#2331	C₂	1	2	yes	maximal, complemented
11	C₅×#2314	C₂	1	2	yes	maximal
12	C₄×C₅×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
13	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic
14	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₅×C₄⋊Q₈	C₂²	1	4	yes	—
17	C₂×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
18	C₂×C₄×C₅×Q₈	C₂²	1	4	yes	—
19	C₂×C₅×#117	C₂²	1	1	yes	characteristic
20	C₂×C₅×#117	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₅×#400	C₂²	1	8	yes	—
23	C₅×#400	C₂²	1	4	yes	—
24	C₅×#399	C₂²	1	4	yes	—
25	C₅×#398	C₂²	1	8	yes	—
26	C₅×#395	C₂²	1	4	yes	—
27	C₅×#393	C₂²	1	4	yes	—
28	C₅×#391	C₂²	1	4	yes	—
29	C₅×#391	C₂²	1	8	yes	—
30	C₅×#391	C₂²	1	4	yes	—
31	C₅×#391	C₂²	1	4	yes	—
32	C₅×#391	C₂²	1	4	yes	—
33	C₅×#389	C₂²	1	4	yes	—
34	C₅×#389	C₂²	1	4	yes	—
35	C₅×#389	C₂²	1	4	yes	—
36	C₅×#389	C₂²	1	4	yes	—
37	C₅×#388	C₂²	1	8	yes	—
38	C₅×#387	C₂²	1	8	yes	—
39	C₅×#387	C₂²	1	8	yes	—
40	C₅×#384	C₂²	1	4	yes	—
41	C₅×#384	C₂²	1	2	yes	—
42	C₅×#384	C₂²	1	2	yes	—
43	C₅×#382	C₂²	1	2	yes	—
44	C₅×#382	C₂²	1	2	yes	—
45	C₅×#380	C₂²	1	4	yes	—
46	C₅×#380	C₂²	1	4	yes	—
47	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
48	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
49	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
50	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
51	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
52	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
53	C₅×#376	C₂²	1	1	yes	characteristic
54	C₅×#376	C₂²	1	1	yes	characteristic
55	C₄³×C₅	C₂²	1	1	yes	characteristic
56	C₄³×C₅	C₂²	1	1	yes	characteristic
57	#35283	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂²×C₅×Q₈	C₂³	1	4	yes	—
59	C₂²×C₅×Q₈	C₂³	1	4	yes	—
60	C₂³×C₄×C₅	C₂³	1	2	yes	—
61	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₅×C₄⋊Q₈	—	2	8	no	—
63	C₅×C₄⋊Q₈	—	2	8	no	—
64	C₅×C₄⋊Q₈	—	4	8	no	—
65	C₅×C₂²⋊Q₈	—	4	8	no	—
66	C₄×C₅×Q₈	—	4	8	no	—
67	C₅×#117	—	2	4	no	—
68	C₅×#117	Q₈	1	8	yes	complemented
69	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
72	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
73	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
74	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
75	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
76	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
77	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
78	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
79	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
80	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
84	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
85	C₂×C₄²×C₅	—	2	4	no	—
86	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₅	C₂³	1	2	yes	—
88	C₂×C₄²×C₅	C₂³	1	2	yes	—
89	C₂×C₄²×C₅	C₂³	1	2	yes	—
90	C₂×C₄²×C₅	C₂³	1	2	yes	—
91	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₅	C₂³	1	2	yes	—
93	C₂×C₄²×C₅	C₂³	1	8	yes	—
94	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
98	C₅×#95	C₂³	1	2	yes	—
99	C₅×#95	C₂³	1	2	yes	—
100	C₅×#95	C₂³	1	2	yes	—
101	C₅×#95	C₂³	1	2	yes	—
102	C₅×#95	C₂³	1	8	yes	—
103	C₅×#95	C₂³	1	8	yes	—
104	C₅×#95	C₂³	1	8	yes	—
105	C₅×#95	C₂³	1	8	yes	—
106	C₅×#95	C₂³	1	4	yes	—
107	C₅×#95	C₂³	1	8	yes	—
108	C₅×#95	C₂³	1	4	yes	—
109	#2868	C₂×C₅	1	1	yes	characteristic, complemented
110	#2862	C₂×C₅	1	1	yes	characteristic, complemented
111	#2857	C₂×C₅	1	2	yes	—
112	#2647	C₂×C₅	1	2	yes	complemented
113	#2628	C₂×C₅	1	2	yes	—
114	#2511	C₂×C₅	1	4	yes	complemented
115	#2492	C₂×C₅	1	4	yes	—
116	#2451	C₂×C₅	1	4	yes	complemented
117	#2423	C₂×C₅	1	4	yes	—
118	#2331	C₂×C₅	1	2	yes	complemented
119	#2314	C₂×C₅	1	2	yes	—
120	C₄×C₄⋊Q₈	C₂×C₅	1	2	yes	complemented
121	C₄×#117	C₂×C₅	1	1	yes	characteristic
122	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
123	C₂×C₅×Q₈	—	2	8	no	—
124	C₂×C₅×Q₈	—	2	8	no	—
125	C₂×C₅×Q₈	—	2	8	no	—
126	C₂×C₅×Q₈	—	2	8	no	—
127	C₂×C₅×Q₈	—	4	8	no	—
128	C₂²×C₄×C₅	—	2	2	no	—
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	—	2	4	no	—
131	C₂²×C₄×C₅	—	2	4	no	—
132	C₂²×C₄×C₅	—	2	4	no	—
133	C₂²×C₄×C₅	C₂×Q₈	1	4	yes	—
134	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
138	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
139	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
141	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	2	8	no	—
149	C₅×C₄⋊C₄	—	2	8	no	—
150	C₅×C₄⋊C₄	—	2	8	no	—
151	C₅×C₄⋊C₄	—	2	8	no	—
152	C₅×C₄⋊C₄	—	2	8	no	—
153	C₅×C₄⋊C₄	—	2	8	no	—
154	C₅×C₄⋊C₄	—	4	8	no	—
155	C₅×C₄⋊C₄	—	4	8	no	—
156	C₅×C₄⋊C₄	—	4	8	no	—
157	C₅×C₄⋊C₄	C₂×Q₈	1	8	yes	—
158	C₅×C₂²⋊C₄	—	2	2	no	—
159	C₅×C₂²⋊C₄	—	2	2	no	—
160	C₅×C₂²⋊C₄	—	4	8	no	—
161	C₅×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
162	C₄²×C₅	—	2	4	no	—
163	C₄²×C₅	—	2	2	no	—
164	C₄²×C₅	—	2	2	no	—
165	C₄²×C₅	—	2	4	no	—
166	C₄²×C₅	—	2	4	no	—
167	C₄²×C₅	—	2	4	no	—
168	C₄²×C₅	—	2	4	no	—
169	C₄²×C₅	—	4	8	no	—
170	C₄²×C₅	C₂×Q₈	1	4	yes	—
171	C₄²×C₅	C₂×Q₈	1	4	yes	—
172	C₄²×C₅	#41	1	4	yes	—
173	C₄²×C₅	#41	1	4	yes	—
174	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
175	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
176	C₂×C₄⋊Q₈	C₂²×C₅	1	4	yes	—
177	C₂×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
178	C₂×C₄×Q₈	C₂²×C₅	1	4	yes	—
179	C₂×#117	C₂²×C₅	1	1	yes	characteristic
180	C₂×#117	C₂²×C₅	1	1	yes	characteristic
181	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
182	#400	C₂²×C₅	1	4	yes	—
183	#400	C₂²×C₅	1	8	yes	—
184	#399	C₂²×C₅	1	4	yes	—
185	#398	C₂²×C₅	1	8	yes	—
186	#395	C₂²×C₅	1	4	yes	—
187	#393	C₂²×C₅	1	4	yes	—
188	#391	C₂²×C₅	1	4	yes	—
189	#391	C₂²×C₅	1	8	yes	—
190	#391	C₂²×C₅	1	4	yes	—
191	#391	C₂²×C₅	1	4	yes	—
192	#391	C₂²×C₅	1	4	yes	—
193	#389	C₂²×C₅	1	4	yes	—
194	#389	C₂²×C₅	1	4	yes	—
195	#389	C₂²×C₅	1	4	yes	—
196	#389	C₂²×C₅	1	4	yes	—
197	#388	C₂²×C₅	1	8	yes	—
198	#387	C₂²×C₅	1	8	yes	—
199	#387	C₂²×C₅	1	8	yes	—
200	#384	C₂²×C₅	1	2	yes	—
201	#384	C₂²×C₅	1	2	yes	—
202	#384	C₂²×C₅	1	4	yes	—
203	#382	C₂²×C₅	1	2	yes	—
204	#382	C₂²×C₅	1	2	yes	—
205	#380	C₂²×C₅	1	4	yes	—
206	#380	C₂²×C₅	1	4	yes	—
207	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
208	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
209	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
210	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
211	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
212	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
213	#376	C₂²×C₅	1	1	yes	characteristic
214	#376	C₂²×C₅	1	1	yes	characteristic
215	C₄³	C₂²×C₅	1	1	yes	characteristic
216	C₄³	C₂²×C₅	1	1	yes	characteristic
217	C₂³×C₅	—	2	1	no	—
218	C₂³×C₅	—	2	1	no	—
219	C₂³×C₅	—	2	2	no	—
220	C₂³×C₅	—	2	2	no	—
221	C₂³×C₅	C₂²×Q₈	1	2	yes	—
222	C₂³×C₅	C₂⁵	1	1	yes	characteristic
223	C₅×Q₈	—	4	16	no	—
224	C₅×Q₈	—	8	8	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	8	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	2	1	no	—
237	C₂×C₄×C₅	—	2	8	no	—
238	C₂×C₄×C₅	—	2	8	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	8	no	—
241	C₂×C₄×C₅	—	2	8	no	—
242	C₂×C₄×C₅	—	2	8	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	8	no	—
247	C₂×C₄×C₅	—	4	8	no	—
248	C₂×C₄×C₅	C₂²×Q₈	1	4	yes	—
249	C₂×C₄×C₅	C₂²×Q₈	1	4	yes	—
250	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
251	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
252	C₂×C₄×C₅	C₂×#41	1	2	yes	—
253	C₂×C₄×C₅	C₂×#41	1	2	yes	—
254	C₂×C₄×C₅	C₂×#41	1	2	yes	—
255	C₂×C₄×C₅	C₂×#41	1	2	yes	—
256	C₂×C₄×C₅	C₂×#41	1	4	yes	—
257	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
258	C₂×C₄×C₅	2₋¹⁺⁴	1	4	yes	—
259	C₂²×Q₈	C₂³×C₅	1	4	yes	—
260	C₂²×Q₈	C₂³×C₅	1	4	yes	—
261	C₂³×C₄	C₂³×C₅	1	2	yes	—
262	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
263	C₄⋊Q₈	—	2	8	no	—
264	C₄⋊Q₈	—	2	8	no	—
265	C₄⋊Q₈	—	4	8	no	—
266	C₂²⋊Q₈	—	4	8	no	—
267	C₄×Q₈	—	4	8	no	—
268	#117	—	2	4	no	—
269	#117	C₅×Q₈	1	8	yes	complemented
270	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
273	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
274	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
275	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
276	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
277	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
278	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
279	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
280	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
281	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
282	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
283	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
285	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
286	C₂×C₄²	—	2	4	no	—
287	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
288	C₂×C₄²	C₂³×C₅	1	2	yes	—
289	C₂×C₄²	C₂³×C₅	1	2	yes	—
290	C₂×C₄²	C₂³×C₅	1	2	yes	—
291	C₂×C₄²	C₂³×C₅	1	2	yes	—
292	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
293	C₂×C₄²	C₂³×C₅	1	2	yes	—
294	C₂×C₄²	C₂³×C₅	1	8	yes	—
295	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
296	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
297	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
299	#95	C₂³×C₅	1	2	yes	—
300	#95	C₂³×C₅	1	2	yes	—
301	#95	C₂³×C₅	1	2	yes	—
302	#95	C₂³×C₅	1	2	yes	—
303	#95	C₂³×C₅	1	8	yes	—
304	#95	C₂³×C₅	1	8	yes	—
305	#95	C₂³×C₅	1	8	yes	—
306	#95	C₂³×C₅	1	8	yes	—
307	#95	C₂³×C₅	1	4	yes	—
308	#95	C₂³×C₅	1	8	yes	—
309	#95	C₂³×C₅	1	4	yes	—
310	C₂²×C₅	—	2	2	no	—
311	C₂²×C₅	—	2	4	no	—
312	C₂²×C₅	—	4	2	no	—
313	C₂²×C₅	—	4	1	no	—
314	C₂²×C₅	—	4	1	no	—
315	C₂²×C₅	C₂³×Q₈	1	1	yes	characteristic
316	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
317	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
318	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
319	C₂²×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
320	C₄×C₅	—	2	2	no	—
321	C₄×C₅	—	2	4	no	—
322	C₄×C₅	—	2	4	no	—
323	C₄×C₅	—	2	2	no	—
324	C₄×C₅	—	2	2	no	—
325	C₄×C₅	—	4	2	no	—
326	C₄×C₅	—	4	8	no	—
327	C₄×C₅	—	4	1	no	—
328	C₄×C₅	—	4	8	no	—
329	C₄×C₅	—	4	1	no	—
330	C₄×C₅	#533	1	4	yes	—
331	C₄×C₅	#542	1	8	yes	—
332	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
333	C₂×Q₈	—	2	8	no	—
334	C₂×Q₈	—	2	8	no	—
335	C₂×Q₈	—	2	8	no	—
336	C₂×Q₈	—	2	8	no	—
337	C₂×Q₈	—	4	8	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	C₂×C₅×Q₈	1	4	yes	—
344	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
345	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
346	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
347	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
348	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
349	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
350	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
351	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
352	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
353	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
354	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
355	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	8	no	—
359	C₄⋊C₄	—	2	8	no	—
360	C₄⋊C₄	—	2	8	no	—
361	C₄⋊C₄	—	2	8	no	—
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	2	8	no	—
364	C₄⋊C₄	—	4	8	no	—
365	C₄⋊C₄	—	4	8	no	—
366	C₄⋊C₄	—	4	8	no	—
367	C₄⋊C₄	C₂×C₅×Q₈	1	8	yes	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	4	8	no	—
371	C₂²⋊C₄	C₂×C₅×Q₈	1	8	yes	—
372	C₄²	—	2	4	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	4	no	—
376	C₄²	—	2	4	no	—
377	C₄²	—	2	4	no	—
378	C₄²	—	2	4	no	—
379	C₄²	—	4	8	no	—
380	C₄²	C₂×C₅×Q₈	1	4	yes	—
381	C₄²	C₂×C₅×Q₈	1	4	yes	—
382	C₄²	C₅×#41	1	4	yes	—
383	C₄²	C₅×#41	1	4	yes	—
384	C₂×C₅	—	4	2	no	—
385	C₂×C₅	C₂×#533	1	1	yes	characteristic
386	C₂×C₅	C₂×#542	1	2	yes	—
387	C₂×C₅	#3503	1	2	yes	—
388	C₂×C₅	#3508	1	1	yes	characteristic
389	C₂×C₅	#3509	1	1	yes	characteristic
390	C₂³	—	2	1	no	—
391	C₂³	—	2	1	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	C₂²×C₅×Q₈	1	2	yes	—
395	C₂³	C₂⁵×C₅	1	1	yes	characteristic
396	Q₈	—	4	16	no	—
397	Q₈	—	8	8	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	8	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	8	no	—
411	C₂×C₄	—	2	8	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	8	no	—
420	C₂×C₄	—	4	8	no	—
421	C₂×C₄	C₂²×C₅×Q₈	1	4	yes	—
422	C₂×C₄	C₂²×C₅×Q₈	1	4	yes	—
423	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
424	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
425	C₂×C₄	C₂×C₅×#41	1	2	yes	—
426	C₂×C₄	C₂×C₅×#41	1	2	yes	—
427	C₂×C₄	C₂×C₅×#41	1	2	yes	—
428	C₂×C₄	C₂×C₅×#41	1	2	yes	—
429	C₂×C₄	C₂×C₅×#41	1	4	yes	—
430	C₂×C₄	C₅×H(5,𝔽₂)	1	4	yes	—
431	C₂×C₄	C₅×2₋¹⁺⁴	1	4	yes	—
432	C₅	#35283	1	1	yes	characteristic, direct product factor, Sylow
433	C₂²	—	2	2	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	C₂³×C₅×Q₈	1	1	yes	characteristic
439	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
440	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
441	C₂²	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
442	C₂²	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
443	C₄	—	2	2	no	—
444	C₄	—	2	4	no	—
445	C₄	—	2	4	no	—
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	8	no	—
450	C₄	—	4	8	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	1	no	—
453	C₄	C₅×#533	1	4	yes	—
454	C₄	C₅×#542	1	8	yes	—
455	C₂	—	4	2	no	—
456	C₂	C₂×C₅×#533	1	1	yes	characteristic
457	C₂	C₂×C₅×#542	1	2	yes	—
458	C₂	C₅×#3503	1	2	yes	—
459	C₂	C₅×#3508	1	1	yes	characteristic
460	C₂	C₅×#3509	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×#2868	C₂	semidirect
2. C₅×#2862	C₂	semidirect
4. C₅×#2647	C₂	semidirect
6. C₅×#2511	C₂	semidirect
8. C₅×#2451	C₂	semidirect
10. C₅×#2331	C₂	semidirect
12. C₄×C₅×C₄⋊Q₈	C₂	semidirect
57. #35283	C₅	direct (N × H)
68. C₅×#117	Q₈	semidirect
109. #2868	C₂×C₅	semidirect
110. #2862	C₂×C₅	semidirect
112. #2647	C₂×C₅	semidirect
114. #2511	C₂×C₅	semidirect
116. #2451	C₂×C₅	semidirect
118. #2331	C₂×C₅	semidirect
120. C₄×C₄⋊Q₈	C₂×C₅	semidirect
269. #117	C₅×Q₈	semidirect
432. C₅	#35283	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×#2868	2
C₅×#2862	2
C₅×#2857	2
C₅×#2647	2
C₅×#2628	2
C₅×#2511	2
C₅×#2492	2
C₅×#2451	2
C₅×#2423	2
C₅×#2331	2
C₅×#2314	2
C₄×C₅×C₄⋊Q₈	2
C₄×C₅×#117	2
#35283	5

Subgroups — C5×#35283 #11958003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#35283 #11958003