Subgroups — C₅×#26108 #11948828

Order 1280.

702 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2552	C₂	1	1	yes	maximal, characteristic
2	C₅×Q₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₅×#2099	C₂	1	2	yes	maximal
4	C₅×#2088	C₂	1	2	yes	maximal
5	C₅×#1948	C₂	1	1	yes	maximal, characteristic
6	C₅×#1939	C₂	1	1	yes	maximal, characteristic
7	C₅×#1865	C₂	1	2	yes	maximal
8	C₅×#1834	C₂	1	1	yes	maximal, characteristic
9	C₅×#1803	C₂	1	1	yes	maximal, characteristic
10	C₅×#1803	C₂	1	2	yes	maximal
11	C₄×C₅×#103	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×#125	—	2	1	no	—
13	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
14	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
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×#398	—	2	2	no	—
23	C₅×#389	—	2	2	no	—
24	C₅×#389	—	2	1	no	—
25	C₅×#389	C₂²	1	2	yes	—
26	C₅×#389	C₂²	1	2	yes	—
27	C₅×#384	—	2	1	no	—
28	C₅×#384	C₂²	1	1	yes	characteristic
29	C₅×#384	C₂²	1	2	yes	—
30	C₅×#384	C₂²	1	1	yes	characteristic
31	C₄×C₅×C₄⋊C₄	—	2	1	no	—
32	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₅×#340	C₂²	1	1	yes	characteristic
35	C₅×#340	C₂²	1	1	yes	characteristic
36	C₅×#340	C₂²	1	2	yes	—
37	C₅×#340	C₂²	1	2	yes	—
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	—
41	#26108	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	1	yes	characteristic
44	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₅×C₈	C₂³	1	2	yes	—
46	C₅×#125	—	4	4	no	—
47	C₄×C₅×Q₈	—	2	2	no	—
48	C₄×C₅×Q₈	—	2	4	no	—
49	C₄×C₅×Q₈	—	4	2	no	—
50	C₄×C₅×Q₈	Q₈	1	4	yes	—
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	—	2	1	no	—
55	C₂×C₅×C₄⋊C₄	—	2	2	no	—
56	C₂×C₅×C₄⋊C₄	—	2	2	no	—
57	C₂×C₅×C₄⋊C₄	—	2	2	no	—
58	C₂×C₅×C₄⋊C₄	—	2	1	no	—
59	C₂×C₅×C₄⋊C₄	—	2	2	no	—
60	C₂×C₅×C₄⋊C₄	—	2	1	no	—
61	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
62	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
63	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₅	—	2	1	no	—
69	C₂×C₄²×C₅	—	2	2	no	—
70	C₂×C₄²×C₅	—	2	1	no	—
71	C₂×C₄²×C₅	C₂³	1	2	yes	—
72	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₅×#106	—	4	2	no	—
74	C₅×C₄⋊C₈	—	2	2	no	—
75	C₅×C₄⋊C₈	—	4	2	no	—
76	C₅×#103	—	2	2	no	—
77	C₅×#103	—	2	2	no	—
78	C₅×#103	—	2	4	no	—
79	C₄×C₅×C₈	—	2	2	no	—
80	C₅×#95	—	2	2	no	—
81	C₅×#95	—	2	1	no	—
82	C₅×#95	—	2	2	no	—
83	C₅×#95	D₄	1	2	yes	—
84	#2552	C₂×C₅	1	1	yes	characteristic
85	Q₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
86	#2099	C₂×C₅	1	2	yes	—
87	#2088	C₂×C₅	1	2	yes	—
88	#1948	C₂×C₅	1	1	yes	characteristic
89	#1939	C₂×C₅	1	1	yes	characteristic
90	#1865	C₂×C₅	1	2	yes	—
91	#1834	C₂×C₅	1	1	yes	characteristic
92	#1803	C₂×C₅	1	2	yes	—
93	#1803	C₂×C₅	1	1	yes	characteristic
94	C₄×#103	C₂×C₅	1	1	yes	characteristic
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	C₂×Q₈	1	2	yes	—
99	C₂×C₅×Q₈	#41	1	2	yes	—
100	C₂×C₅×Q₈	#41	1	2	yes	—
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	1	no	—
106	C₂²×C₄×C₅	—	2	2	no	—
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	2	yes	—
110	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	1	no	—
116	C₂×C₅×C₈	—	2	2	no	—
117	C₂×C₅×C₈	—	2	2	no	—
118	C₂×C₅×C₈	—	2	1	no	—
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	—	2	1	no	—
121	C₅×C₄⋊C₄	—	2	4	no	—
122	C₅×C₄⋊C₄	—	2	2	no	—
123	C₅×C₄⋊C₄	—	2	1	no	—
124	C₅×C₄⋊C₄	—	2	2	no	—
125	C₅×C₄⋊C₄	—	2	1	no	—
126	C₅×C₄⋊C₄	—	2	1	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	1	no	—
131	C₅×C₄⋊C₄	—	2	2	no	—
132	C₅×C₄⋊C₄	—	4	4	no	—
133	C₅×C₄⋊C₄	—	4	4	no	—
134	C₅×C₄⋊C₄	—	4	4	no	—
135	C₅×C₄⋊C₄	—	4	2	no	—
136	C₅×C₄⋊C₄	—	4	2	no	—
137	C₅×C₄⋊C₄	—	8	1	no	—
138	C₅×C₄⋊C₄	—	8	1	no	—
139	C₅×C₄⋊C₄	—	8	2	no	—
140	C₅×C₄⋊C₄	—	8	2	no	—
141	C₅×C₄⋊C₄	SD₁₆	1	4	yes	—
142	C₅×C₄⋊C₄	C₂×Q₈	1	2	yes	—
143	C₄²×C₅	—	2	4	no	—
144	C₄²×C₅	—	2	2	no	—
145	C₄²×C₅	—	2	2	no	—
146	C₄²×C₅	—	4	4	no	—
147	C₄²×C₅	—	4	2	no	—
148	C₄²×C₅	C₂×Q₈	1	2	yes	—
149	C₄²×C₅	#41	1	2	yes	—
150	C₂×#125	—	2	1	no	—
151	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
152	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
153	C₂×#106	C₂²×C₅	1	2	yes	—
154	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
155	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
156	C₂×#103	C₂²×C₅	1	2	yes	—
157	C₂×#103	C₂²×C₅	1	1	yes	characteristic
158	C₂×#103	C₂²×C₅	1	1	yes	characteristic
159	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
160	#398	—	2	2	no	—
161	#389	—	2	1	no	—
162	#389	—	2	2	no	—
163	#389	C₂²×C₅	1	2	yes	—
164	#389	C₂²×C₅	1	2	yes	—
165	#384	—	2	1	no	—
166	#384	C₂²×C₅	1	1	yes	characteristic
167	#384	C₂²×C₅	1	2	yes	—
168	#384	C₂²×C₅	1	1	yes	characteristic
169	C₄×C₄⋊C₄	—	2	1	no	—
170	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
171	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
172	#340	C₂²×C₅	1	2	yes	—
173	#340	C₂²×C₅	1	2	yes	—
174	#340	C₂²×C₅	1	2	yes	—
175	#340	C₂²×C₅	1	1	yes	characteristic
176	#340	C₂²×C₅	1	2	yes	—
177	#340	C₂²×C₅	1	1	yes	characteristic
178	#336	C₂²×C₅	1	2	yes	—
179	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
180	C₅×Q₈	—	2	2	no	—
181	C₅×Q₈	—	2	2	no	—
182	C₅×Q₈	—	2	2	no	—
183	C₅×Q₈	#125	1	4	yes	complemented
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	1	no	—
189	C₂×C₄×C₅	—	2	1	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	4	1	no	—
196	C₂×C₄×C₅	—	4	1	no	—
197	C₂×C₄×C₅	—	4	2	no	—
198	C₂×C₄×C₅	—	4	1	no	—
199	C₂×C₄×C₅	—	4	1	no	—
200	C₂×C₄×C₅	—	4	2	no	—
201	C₂×C₄×C₅	—	4	1	no	—
202	C₂×C₄×C₅	—	4	1	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	—	4	1	no	—
207	C₂×C₄×C₅	—	4	2	no	—
208	C₂×C₄×C₅	—	4	1	no	—
209	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
210	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
211	C₂×C₄×C₅	C₂×SD₁₆	1	4	yes	—
212	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
213	C₂×C₄×C₅	#137	1	2	yes	—
214	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
219	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
220	C₅×C₈	—	4	1	no	—
221	C₅×C₈	—	4	1	no	—
222	C₅×C₈	—	4	2	no	—
223	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
224	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
225	C₂²×C₈	C₂³×C₅	1	2	yes	—
226	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
227	#125	—	4	4	no	—
228	C₄×Q₈	—	2	2	no	—
229	C₄×Q₈	—	2	4	no	—
230	C₄×Q₈	—	4	2	no	—
231	C₄×Q₈	C₅×Q₈	1	4	yes	—
232	C₂×C₄⋊C₄	—	2	1	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
245	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
247	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
249	C₂×C₄²	—	2	1	no	—
250	C₂×C₄²	—	2	2	no	—
251	C₂×C₄²	—	2	1	no	—
252	C₂×C₄²	C₂³×C₅	1	2	yes	—
253	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
254	#106	—	4	2	no	—
255	C₄⋊C₈	—	2	2	no	—
256	C₄⋊C₈	—	4	2	no	—
257	#103	—	2	4	no	—
258	#103	—	2	2	no	—
259	#103	—	2	2	no	—
260	C₄×C₈	—	2	2	no	—
261	#95	—	2	2	no	—
262	#95	—	2	1	no	—
263	#95	—	2	2	no	—
264	#95	C₅×D₄	1	2	yes	—
265	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
266	C₂²×C₅	#546	1	1	yes	characteristic
267	C₂²×C₅	#548	1	1	yes	characteristic
268	C₂²×C₅	C₂²×SD₁₆	1	1	yes	characteristic
269	C₂²×C₅	C₂×#137	1	1	yes	characteristic
270	C₂²×C₅	#576	1	1	yes	characteristic
271	C₂²×C₅	#578	1	1	yes	characteristic
272	C₄×C₅	—	2	2	no	—
273	C₄×C₅	—	2	4	no	—
274	C₄×C₅	—	2	4	no	—
275	C₄×C₅	—	4	2	no	—
276	C₄×C₅	—	4	2	no	—
277	C₄×C₅	—	8	2	no	—
278	C₄×C₅	—	8	1	no	—
279	C₄×C₅	—	8	2	no	—
280	C₄×C₅	—	8	1	no	—
281	C₄×C₅	#475	1	4	yes	—
282	C₄×C₅	C₂×#125	1	1	yes	characteristic
283	C₄×C₅	#544	1	1	yes	characteristic
284	C₄×C₅	#552	1	1	yes	characteristic
285	C₄×C₅	#553	1	1	yes	characteristic
286	C₂×Q₈	—	2	1	no	—
287	C₂×Q₈	—	2	1	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×Q₈	C₂×C₅×Q₈	1	2	yes	—
290	C₂×Q₈	C₅×#41	1	2	yes	—
291	C₂×Q₈	C₅×#41	1	2	yes	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
299	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
301	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
302	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	1	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	4	4	no	—
324	C₄⋊C₄	—	4	4	no	—
325	C₄⋊C₄	—	4	4	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	—	4	2	no	—
328	C₄⋊C₄	—	8	1	no	—
329	C₄⋊C₄	—	8	1	no	—
330	C₄⋊C₄	—	8	2	no	—
331	C₄⋊C₄	—	8	2	no	—
332	C₄⋊C₄	C₅×SD₁₆	1	4	yes	—
333	C₄⋊C₄	C₂×C₅×Q₈	1	2	yes	—
334	C₄²	—	2	4	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	4	4	no	—
338	C₄²	—	4	2	no	—
339	C₄²	C₂×C₅×Q₈	1	2	yes	—
340	C₄²	C₅×#41	1	2	yes	—
341	C₂×C₅	#2442	1	1	yes	characteristic
342	C₂×C₅	C₂×#475	1	1	yes	characteristic
343	C₂×C₅	#3083	1	1	yes	characteristic
344	C₂×C₅	#3298	1	1	yes	characteristic
345	C₂×C₅	#3333	1	1	yes	characteristic
346	C₂×C₅	#3362	1	1	yes	characteristic
347	C₂×C₅	#3374	1	1	yes	characteristic
348	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
349	Q₈	—	2	2	no	—
350	Q₈	—	2	2	no	—
351	Q₈	—	2	2	no	—
352	Q₈	C₅×#125	1	4	yes	complemented
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
379	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
380	C₂×C₄	C₂×C₅×SD₁₆	1	4	yes	—
381	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
382	C₂×C₄	C₅×#137	1	2	yes	—
383	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
384	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
385	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
386	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
387	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
388	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
389	C₈	—	4	1	no	—
390	C₈	—	4	1	no	—
391	C₈	—	4	2	no	—
392	C₅	#26108	1	1	yes	characteristic, direct product factor, Sylow
393	C₂²	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
394	C₂²	C₅×#546	1	1	yes	characteristic
395	C₂²	C₅×#548	1	1	yes	characteristic
396	C₂²	C₂²×C₅×SD₁₆	1	1	yes	characteristic
397	C₂²	C₂×C₅×#137	1	1	yes	characteristic
398	C₂²	C₅×#576	1	1	yes	characteristic
399	C₂²	C₅×#578	1	1	yes	characteristic
400	C₄	—	2	4	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	4	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	2	no	—
405	C₄	—	8	1	no	—
406	C₄	—	8	2	no	—
407	C₄	—	8	1	no	—
408	C₄	—	8	2	no	—
409	C₄	C₅×#475	1	4	yes	—
410	C₄	C₂×C₅×#125	1	1	yes	characteristic
411	C₄	C₅×#544	1	1	yes	characteristic
412	C₄	C₅×#552	1	1	yes	characteristic
413	C₄	C₅×#553	1	1	yes	characteristic
414	C₂	C₅×#2442	1	1	yes	characteristic
415	C₂	C₂×C₅×#475	1	1	yes	characteristic
416	C₂	C₅×#3083	1	1	yes	characteristic
417	C₂	C₅×#3298	1	1	yes	characteristic
418	C₂	C₅×#3333	1	1	yes	characteristic
419	C₂	C₅×#3362	1	1	yes	characteristic
420	C₂	C₅×#3374	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. #26108	C₅	direct (N × H)
183. C₅×Q₈	#125	semidirect
352. Q₈	C₅×#125	semidirect
392. C₅	#26108	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×#2552	2
C₅×Q₈×C₄⋊C₄	2
C₅×#2099	2
C₅×#2088	2
C₅×#1948	2
C₅×#1939	2
C₅×#1865	2
C₅×#1834	2
C₅×#1803	2
C₄×C₅×#103	2
#26108	5

Subgroups — C5×#26108 #11948828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#26108 #11948828