Subgroups — C₅×#26093 #11948813

Order 1280.

638 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2571	C₂	1	1	yes	maximal, characteristic
2	C₅×#2355	C₂	1	1	yes	maximal, characteristic
3	C₅×#2097	C₂	1	2	yes	maximal
4	C₅×#2068	C₂	1	2	yes	maximal
5	C₅×#1949	C₂	1	2	yes	maximal
6	C₅×#1948	C₂	1	1	yes	maximal, characteristic
7	C₅×#1939	C₂	1	1	yes	maximal, characteristic
8	C₅×#1918	C₂	1	2	yes	maximal
9	C₅×#1845	C₂	1	1	yes	maximal, characteristic
10	C₅×#1803	C₂	1	1	yes	maximal, characteristic
11	C₄×C₅×#103	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×#107	C₂²	1	2	yes	—
14	C₂×C₅×#107	C₂²	1	2	yes	—
15	C₂×C₅×#106	C₂²	1	2	yes	—
16	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₅×#103	C₂²	1	1	yes	characteristic
19	C₂×C₅×#103	C₂²	1	1	yes	characteristic
20	C₂×C₅×#103	C₂²	1	2	yes	—
21	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
22	C₅×#400	—	2	2	no	—
23	C₅×#391	C₂²	1	2	yes	—
24	C₅×#389	—	2	1	no	—
25	C₅×#389	C₂²	1	2	yes	—
26	C₅×#387	—	2	2	no	—
27	C₅×#384	C₂²	1	1	yes	characteristic
28	C₅×#384	C₂²	1	1	yes	characteristic
29	C₅×#382	—	2	1	no	—
30	C₅×#382	—	2	1	no	—
31	C₅×#382	C₂²	1	2	yes	—
32	C₄×C₅×C₄⋊C₄	—	2	1	no	—
33	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
35	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₅×#340	C₂²	1	1	yes	characteristic
37	C₅×#340	C₂²	1	1	yes	characteristic
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	—
41	#26093	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
43	C₂²×C₅×C₈	C₂³	1	2	yes	—
44	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
46	C₄×C₅×Q₈	—	2	2	no	—
47	C₄×C₅×Q₈	Q₈	1	4	yes	—
48	C₂×C₅×C₄⋊C₄	—	2	1	no	—
49	C₂×C₅×C₄⋊C₄	—	2	1	no	—
50	C₂×C₅×C₄⋊C₄	—	2	1	no	—
51	C₂×C₅×C₄⋊C₄	—	2	1	no	—
52	C₂×C₅×C₄⋊C₄	—	2	1	no	—
53	C₂×C₅×C₄⋊C₄	—	2	2	no	—
54	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
55	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
56	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
57	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
58	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
59	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
60	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₅	—	2	1	no	—
62	C₂×C₄²×C₅	—	2	1	no	—
63	C₂×C₄²×C₅	—	2	2	no	—
64	C₂×C₄²×C₅	C₂³	1	2	yes	—
65	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₅×#107	—	2	4	no	—
67	C₅×#107	—	4	2	no	—
68	C₅×#106	—	4	2	no	—
69	C₅×C₄⋊C₈	—	2	4	no	—
70	C₅×C₄⋊C₈	—	2	2	no	—
71	C₅×#103	—	2	2	no	—
72	C₅×#103	—	2	2	no	—
73	C₅×#103	—	4	2	no	—
74	C₄×C₅×C₈	—	2	2	no	—
75	C₅×#95	—	2	2	no	—
76	C₅×#95	—	2	2	no	—
77	C₅×#95	—	2	1	no	—
78	C₅×#95	—	2	2	no	—
79	C₅×#95	—	2	2	no	—
80	C₅×#95	—	2	2	no	—
81	C₅×#95	—	2	2	no	—
82	C₅×#95	D₄	1	2	yes	—
83	#2571	C₂×C₅	1	1	yes	characteristic
84	#2355	C₂×C₅	1	1	yes	characteristic
85	#2097	C₂×C₅	1	2	yes	—
86	#2068	C₂×C₅	1	2	yes	—
87	#1949	C₂×C₅	1	2	yes	—
88	#1948	C₂×C₅	1	1	yes	characteristic
89	#1939	C₂×C₅	1	1	yes	characteristic
90	#1918	C₂×C₅	1	2	yes	—
91	#1845	C₂×C₅	1	1	yes	characteristic
92	#1803	C₂×C₅	1	1	yes	characteristic
93	C₄×#103	C₂×C₅	1	1	yes	characteristic
94	C₂×C₅×Q₈	—	2	1	no	—
95	C₂×C₅×Q₈	—	2	1	no	—
96	C₂×C₅×Q₈	—	2	1	no	—
97	C₂×C₅×Q₈	—	2	1	no	—
98	C₂×C₅×Q₈	—	2	1	no	—
99	C₂×C₅×Q₈	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₅	—	2	1	no	—
101	C₂²×C₄×C₅	—	2	1	no	—
102	C₂²×C₄×C₅	—	2	1	no	—
103	C₂²×C₄×C₅	—	2	2	no	—
104	C₂²×C₄×C₅	—	2	1	no	—
105	C₂²×C₄×C₅	—	2	2	no	—
106	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
111	C₂×C₅×C₈	—	2	1	no	—
112	C₂×C₅×C₈	—	2	1	no	—
113	C₂×C₅×C₈	—	2	1	no	—
114	C₂×C₅×C₈	—	2	1	no	—
115	C₂×C₅×C₈	—	2	2	no	—
116	C₂×C₅×C₈	—	2	2	no	—
117	C₂×C₅×C₈	—	2	2	no	—
118	C₂×C₅×C₈	#41	1	2	yes	—
119	C₂×C₅×C₈	#41	1	2	yes	—
120	C₅×C₄⋊C₄	—	2	4	no	—
121	C₅×C₄⋊C₄	—	2	2	no	—
122	C₅×C₄⋊C₄	—	2	2	no	—
123	C₅×C₄⋊C₄	—	2	1	no	—
124	C₅×C₄⋊C₄	—	2	1	no	—
125	C₅×C₄⋊C₄	—	2	1	no	—
126	C₅×C₄⋊C₄	—	2	2	no	—
127	C₅×C₄⋊C₄	—	2	2	no	—
128	C₅×C₄⋊C₄	—	2	2	no	—
129	C₅×C₄⋊C₄	—	2	1	no	—
130	C₅×C₄⋊C₄	—	2	2	no	—
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₄⋊C₄	—	4	2	no	—
133	C₅×C₄⋊C₄	—	4	2	no	—
134	C₅×C₄⋊C₄	—	8	1	no	—
135	C₅×C₄⋊C₄	—	8	1	no	—
136	C₅×C₄⋊C₄	—	8	2	no	—
137	C₅×C₄⋊C₄	C₂×Q₈	1	2	yes	—
138	C₄²×C₅	—	2	4	no	—
139	C₄²×C₅	—	2	2	no	—
140	C₄²×C₅	—	2	2	no	—
141	C₄²×C₅	—	4	2	no	—
142	C₄²×C₅	—	8	2	no	—
143	C₄²×C₅	C₂×Q₈	1	2	yes	—
144	C₄²×C₅	#41	1	2	yes	—
145	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
146	C₂×#107	C₂²×C₅	1	2	yes	—
147	C₂×#107	C₂²×C₅	1	2	yes	—
148	C₂×#106	C₂²×C₅	1	2	yes	—
149	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
150	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
151	C₂×#103	C₂²×C₅	1	1	yes	characteristic
152	C₂×#103	C₂²×C₅	1	1	yes	characteristic
153	C₂×#103	C₂²×C₅	1	2	yes	—
154	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
155	#400	—	2	2	no	—
156	#391	C₂²×C₅	1	2	yes	—
157	#389	—	2	1	no	—
158	#389	C₂²×C₅	1	2	yes	—
159	#387	—	2	2	no	—
160	#384	C₂²×C₅	1	1	yes	characteristic
161	#384	C₂²×C₅	1	1	yes	characteristic
162	#382	—	2	1	no	—
163	#382	—	2	1	no	—
164	#382	C₂²×C₅	1	2	yes	—
165	C₄×C₄⋊C₄	—	2	1	no	—
166	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
167	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
168	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
169	#340	C₂²×C₅	1	2	yes	—
170	#340	C₂²×C₅	1	2	yes	—
171	#340	C₂²×C₅	1	1	yes	characteristic
172	#340	C₂²×C₅	1	1	yes	characteristic
173	#336	C₂²×C₅	1	2	yes	—
174	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
175	C₅×Q₈	—	2	2	no	—
176	C₅×Q₈	—	2	2	no	—
177	C₅×Q₈	—	4	1	no	—
178	C₅×Q₈	—	4	1	no	—
179	C₂×C₄×C₅	—	2	1	no	—
180	C₂×C₄×C₅	—	2	1	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	—	2	2	no	—
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	4	1	no	—
190	C₂×C₄×C₅	—	4	1	no	—
191	C₂×C₄×C₅	—	4	1	no	—
192	C₂×C₄×C₅	—	4	1	no	—
193	C₂×C₄×C₅	—	4	1	no	—
194	C₂×C₄×C₅	—	4	2	no	—
195	C₂×C₄×C₅	—	4	2	no	—
196	C₂×C₄×C₅	—	4	1	no	—
197	C₂×C₄×C₅	—	4	2	no	—
198	C₂×C₄×C₅	—	4	2	no	—
199	C₂×C₄×C₅	—	4	1	no	—
200	C₂×C₄×C₅	—	4	1	no	—
201	C₂×C₄×C₅	—	4	2	no	—
202	C₂×C₄×C₅	—	4	1	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	—	4	1	no	—
205	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
206	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
207	C₂×C₄×C₅	#135	1	2	yes	—
208	C₂×C₄×C₅	#137	1	2	yes	—
209	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
214	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
215	C₅×C₈	—	2	2	no	—
216	C₅×C₈	—	2	2	no	—
217	C₅×C₈	—	4	2	no	—
218	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
219	C₂²×C₈	C₂³×C₅	1	2	yes	—
220	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
221	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
222	C₄×Q₈	—	2	2	no	—
223	C₄×Q₈	C₅×Q₈	1	4	yes	—
224	C₂×C₄⋊C₄	—	2	1	no	—
225	C₂×C₄⋊C₄	—	2	1	no	—
226	C₂×C₄⋊C₄	—	2	1	no	—
227	C₂×C₄⋊C₄	—	2	1	no	—
228	C₂×C₄⋊C₄	—	2	1	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
231	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
235	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
236	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
237	C₂×C₄²	—	2	1	no	—
238	C₂×C₄²	—	2	1	no	—
239	C₂×C₄²	—	2	2	no	—
240	C₂×C₄²	C₂³×C₅	1	2	yes	—
241	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
242	#107	—	2	4	no	—
243	#107	—	4	2	no	—
244	#106	—	4	2	no	—
245	C₄⋊C₈	—	2	4	no	—
246	C₄⋊C₈	—	2	2	no	—
247	#103	—	2	2	no	—
248	#103	—	2	2	no	—
249	#103	—	4	2	no	—
250	C₄×C₈	—	2	2	no	—
251	#95	—	2	2	no	—
252	#95	—	2	2	no	—
253	#95	—	2	1	no	—
254	#95	—	2	2	no	—
255	#95	—	2	2	no	—
256	#95	—	2	2	no	—
257	#95	—	2	2	no	—
258	#95	C₅×D₄	1	2	yes	—
259	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
260	C₂²×C₅	#547	1	1	yes	characteristic
261	C₂²×C₅	#550	1	1	yes	characteristic
262	C₂²×C₅	C₂×#135	1	1	yes	characteristic
263	C₂²×C₅	C₂×#137	1	1	yes	characteristic
264	C₂²×C₅	#576	1	1	yes	characteristic
265	C₂²×C₅	#578	1	1	yes	characteristic
266	C₄×C₅	—	2	2	no	—
267	C₄×C₅	—	4	2	no	—
268	C₄×C₅	—	4	2	no	—
269	C₄×C₅	—	4	2	no	—
270	C₄×C₅	—	4	2	no	—
271	C₄×C₅	—	8	1	no	—
272	C₄×C₅	—	8	2	no	—
273	C₄×C₅	—	8	2	no	—
274	C₄×C₅	—	8	1	no	—
275	C₄×C₅	#479	1	4	yes	—
276	C₄×C₅	#533	1	1	yes	characteristic
277	C₄×C₅	#544	1	1	yes	characteristic
278	C₄×C₅	#552	1	1	yes	characteristic
279	C₄×C₅	#553	1	1	yes	characteristic
280	C₂×Q₈	—	2	1	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	C₂×C₅×Q₈	1	2	yes	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
293	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
294	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
296	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	C₅×#41	1	2	yes	—
305	C₂×C₈	C₅×#41	1	2	yes	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	8	1	no	—
321	C₄⋊C₄	—	8	1	no	—
322	C₄⋊C₄	—	8	2	no	—
323	C₄⋊C₄	C₂×C₅×Q₈	1	2	yes	—
324	C₄²	—	2	4	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	4	2	no	—
328	C₄²	—	8	2	no	—
329	C₄²	C₂×C₅×Q₈	1	2	yes	—
330	C₄²	C₅×#41	1	2	yes	—
331	C₂×C₅	#2441	1	1	yes	characteristic
332	C₂×C₅	C₂×#479	1	1	yes	characteristic
333	C₂×C₅	#3083	1	1	yes	characteristic
334	C₂×C₅	#3342	1	1	yes	characteristic
335	C₂×C₅	#3357	1	1	yes	characteristic
336	C₂×C₅	#3396	1	1	yes	characteristic
337	C₂×C₅	#3398	1	1	yes	characteristic
338	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
339	Q₈	—	2	2	no	—
340	Q₈	—	2	2	no	—
341	Q₈	—	4	1	no	—
342	Q₈	—	4	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
370	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
371	C₂×C₄	C₅×#135	1	2	yes	—
372	C₂×C₄	C₅×#137	1	2	yes	—
373	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
374	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
375	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
376	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
377	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
379	C₈	—	2	2	no	—
380	C₈	—	2	2	no	—
381	C₈	—	4	2	no	—
382	C₅	#26093	1	1	yes	characteristic, direct product factor, Sylow
383	C₂²	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
384	C₂²	C₅×#547	1	1	yes	characteristic
385	C₂²	C₅×#550	1	1	yes	characteristic
386	C₂²	C₂×C₅×#135	1	1	yes	characteristic
387	C₂²	C₂×C₅×#137	1	1	yes	characteristic
388	C₂²	C₅×#576	1	1	yes	characteristic
389	C₂²	C₅×#578	1	1	yes	characteristic
390	C₄	—	2	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	2	no	—
394	C₄	—	4	2	no	—
395	C₄	—	8	1	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	2	no	—
398	C₄	—	8	1	no	—
399	C₄	C₅×#479	1	4	yes	—
400	C₄	C₅×#533	1	1	yes	characteristic
401	C₄	C₅×#544	1	1	yes	characteristic
402	C₄	C₅×#552	1	1	yes	characteristic
403	C₄	C₅×#553	1	1	yes	characteristic
404	C₂	C₅×#2441	1	1	yes	characteristic
405	C₂	C₂×C₅×#479	1	1	yes	characteristic
406	C₂	C₅×#3083	1	1	yes	characteristic
407	C₂	C₅×#3342	1	1	yes	characteristic
408	C₂	C₅×#3357	1	1	yes	characteristic
409	C₂	C₅×#3396	1	1	yes	characteristic
410	C₂	C₅×#3398	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
41. #26093	C₅	direct (N × H)
382. C₅	#26093	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×#2571	2
C₅×#2355	2
C₅×#2097	2
C₅×#2068	2
C₅×#1949	2
C₅×#1948	2
C₅×#1939	2
C₅×#1918	2
C₅×#1845	2
C₅×#1803	2
C₄×C₅×#103	2
#26093	5

Subgroups — C5×#26093 #11948813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#26093 #11948813