Subgroups — D₅×#4097 #13106554

Order 1600.

576 conjugacy classes of subgroups.

The subgroup lattice has 425 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×D₅×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	#11717271	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4097	C₂	1	1	yes	maximal, characteristic, complemented
5	#11717061	C₂	1	2	yes	maximal, complemented
6	D₅×#689	C₂	1	2	yes	maximal, complemented
7	#11717047	C₂	1	2	yes	maximal, complemented
8	D₅×#687	C₂	1	2	yes	maximal, complemented
9	#11716949	C₂	1	1	yes	maximal, characteristic, complemented
10	#11716945	C₂	1	1	yes	maximal, characteristic, complemented
11	D₅×#681	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅²×#41	C₂²	1	1	yes	characteristic
13	C₂×#6045	C₂²	1	1	yes	characteristic, complemented
14	C₅×#713	C₂²	1	1	yes	characteristic
15	C₅×Q₈×D₅	C₂²	1	1	yes	characteristic
16	C₅×#711	—	2	1	no	—
17	C₅×#711	C₂²	1	1	yes	characteristic
18	C₅×D₄×D₅	—	2	1	no	—
19	C₅×D₄×D₅	C₂²	1	1	yes	characteristic
20	C₅×#709	—	2	1	no	—
21	C₅×#709	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×D₅	—	2	1	no	—
23	C₂×C₄×C₅×D₅	C₂²	1	1	yes	characteristic
24	C₂×C₅×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
25	C₂×#6039	—	2	1	no	—
26	C₂×D₅×Dic₅	—	2	1	no	—
27	D₅×Dic₁₀	—	2	1	no	—
28	D₅×Dic₁₀	—	2	1	no	—
29	D₅×Dic₁₀	C₂²	1	2	yes	—
30	D₅×Dic₁₀	C₂²	1	2	yes	complemented
31	#87812	C₂²	1	2	yes	complemented
32	#87810	C₂²	1	2	yes	complemented
33	#87804	C₂²	1	1	yes	characteristic, complemented
34	C₅×#689	C₂²	1	2	yes	complemented
35	C₅×#687	C₂²	1	2	yes	complemented
36	C₅×#681	C₂²	1	1	yes	characteristic, complemented
37	#87776	C₂²	1	2	yes	complemented
38	#87775	C₂²	1	2	yes	complemented
39	#87773	C₂²	1	2	yes	complemented
40	#87772	C₂²	1	2	yes	complemented
41	#87768	C₂²	1	2	yes	complemented
42	D₅×#168	C₂²	1	2	yes	—
43	C₂×#4097	—	5	1	no	maximal
44	D₅×#137	—	5	1	no	maximal
45	C₂²×C₅×D₅	—	2	1	no	—
46	C₂²×C₅×D₅	D₄	1	1	yes	characteristic
47	C₅²×Q₈	C₂³	1	1	yes	characteristic
48	C₅²×D₄	—	2	1	no	—
49	C₅²×D₄	C₂³	1	1	yes	characteristic
50	C₂×C₄×C₅²	—	2	1	no	—
51	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
52	C₂×#1039	—	2	1	no	—
53	#6045	—	2	1	no	—
54	#6045	C₂³	1	2	yes	—
55	C₅×C₂²⋊D₅	—	2	1	no	—
56	C₅×C₂²⋊D₅	—	2	1	no	—
57	C₅×C₂²⋊D₅	—	2	1	no	—
58	C₂×C₅×Dic₅	—	2	1	no	—
59	C₂×C₅×Dic₅	—	2	1	no	—
60	C₂×C₅×Dic₅	D₄	1	1	yes	characteristic
61	C₅×D₂₀	—	2	1	no	—
62	C₅×D₂₀	C₂³	1	1	yes	characteristic
63	C₄×C₅×D₅	—	2	1	no	—
64	C₄×C₅×D₅	—	2	1	no	—
65	C₄×C₅×D₅	—	2	1	no	—
66	C₄×C₅×D₅	D₄	1	1	yes	characteristic
67	C₄×C₅×D₅	D₄	1	1	yes	characteristic
68	C₄×C₅×D₅	C₂³	1	1	yes	characteristic
69	C₄×C₅×D₅	C₂³	1	1	yes	characteristic
70	C₅×Dic₁₀	—	2	1	no	—
71	C₅×Dic₁₀	—	2	1	no	—
72	C₅×Dic₁₀	C₂³	1	2	yes	—
73	C₅×Dic₁₀	C₂³	1	1	yes	characteristic
74	#6039	—	2	2	no	—
75	#6039	—	2	2	no	—
76	D₅×Dic₅	—	2	2	no	—
77	D₅×Dic₅	—	2	2	no	—
78	#6029	C₂³	1	2	yes	—
79	C₅×#168	C₂³	1	2	yes	—
80	C₂×C₅×#41	—	5	1	no	—
81	D₅×#41	D₅	1	1	yes	characteristic
82	C₂×Q₈×D₅	—	5	1	no	—
83	C₂²×Dic₁₀	—	5	1	no	—
84	C₅×#137	—	5	1	no	—
85	#4097	—	5	1	no	—
86	#4097	—	5	1	no	—
87	#4097	—	5	1	no	—
88	#4097	—	5	2	no	—
89	#4097	—	5	2	no	—
90	#4097	—	5	1	no	—
91	#4097	—	10	2	no	—
92	#4097	D₅	1	1	yes	characteristic, direct product factor
93	C₂×#689	—	5	2	no	—
94	#4088	—	5	1	no	—
95	C₂×#687	—	5	2	no	—
96	C₂×#681	—	5	1	no	—
97	#4064	—	5	2	no	—
98	D₅×Q₁₆	—	5	2	no	—
99	#4061	—	5	2	no	—
100	D₅×SD₁₆	—	5	2	no	—
101	#4055	—	5	1	no	—
102	D₅×M₁₆	—	5	1	no	—
103	C₂²×C₅²	—	2	1	no	—
104	C₂²×C₅²	C₂×D₄	1	1	yes	characteristic
105	C₂×C₅×D₅	—	2	2	no	—
106	C₂×C₅×D₅	—	2	1	no	—
107	C₂×C₅×D₅	—	4	2	no	—
108	C₂×C₅×D₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₅×D₅	C₂×D₄	1	1	yes	characteristic
110	C₄×C₅²	—	2	1	no	—
111	C₄×C₅²	C₂×D₄	1	1	yes	characteristic
112	C₄×C₅²	C₂⁴	1	1	yes	characteristic
113	#1039	—	2	2	no	—
114	C₅×Dic₅	—	2	2	no	—
115	C₅×Dic₅	—	2	1	no	—
116	C₅×Dic₅	C₂×D₄	1	1	yes	characteristic
117	C₅×Dic₅	C₂×D₄	1	1	yes	characteristic
118	C₅×#41	—	2	2	no	—
119	C₅×#41	—	5	1	no	—
120	C₅×#41	—	5	1	no	—
121	C₅×#41	—	5	1	no	—
122	C₅×#41	—	10	1	no	—
123	C₅×#41	—	10	1	no	—
124	C₅×#41	C₂×D₅	1	1	yes	characteristic
125	C₅×#41	C₂×D₅	1	1	yes	characteristic
126	C₂×C₅×Q₈	—	5	1	no	—
127	C₂×C₅×Q₈	—	5	1	no	—
128	C₂×C₅×D₄	—	5	1	no	—
129	C₂×C₅×D₄	—	10	1	no	—
130	C₂²×C₄×C₅	—	5	1	no	—
131	C₂²×C₄×C₅	—	10	1	no	—
132	C₂²×Dic₅	—	10	1	no	—
133	#713	C₂×D₅	1	1	yes	characteristic
134	Q₈×D₅	—	5	2	no	—
135	Q₈×D₅	—	5	2	no	—
136	Q₈×D₅	—	10	1	no	—
137	Q₈×D₅	—	10	1	no	—
138	Q₈×D₅	C₂×D₅	1	1	yes	characteristic
139	#711	—	2	1	no	—
140	#711	C₂×D₅	1	1	yes	characteristic
141	D₄×D₅	—	2	1	no	—
142	D₄×D₅	C₂×D₅	1	1	yes	characteristic
143	#709	—	2	1	no	—
144	#709	C₂×D₅	1	1	yes	characteristic
145	C₂×C₄×D₅	—	2	1	no	—
146	C₂×C₄×D₅	—	10	1	no	—
147	C₂×C₄×D₅	C₂×D₅	1	1	yes	characteristic
148	C₂×Dic₁₀	—	5	1	no	—
149	C₂×Dic₁₀	—	5	1	no	—
150	C₂×Dic₁₀	—	5	2	no	—
151	C₂×Dic₁₀	—	5	2	no	—
152	C₂×Dic₁₀	—	10	2	no	—
153	C₂×Dic₁₀	—	10	1	no	—
154	C₂×Dic₁₀	—	10	1	no	—
155	C₂×Dic₁₀	—	10	1	no	—
156	C₂×Dic₁₀	—	10	1	no	—
157	C₂×Dic₁₀	C₂×D₅	1	1	yes	characteristic, complemented
158	C₅×Q₁₆	—	5	2	no	—
159	C₅×SD₁₆	—	5	2	no	—
160	C₅×M₁₆	—	5	1	no	—
161	#689	—	5	2	no	—
162	#689	—	5	2	no	—
163	#689	—	5	2	no	—
164	#689	—	5	2	no	—
165	#689	—	5	2	no	—
166	#689	—	10	4	no	—
167	#689	C₂×D₅	1	2	yes	complemented
168	#688	—	5	2	no	—
169	#687	—	5	2	no	—
170	#687	—	5	2	no	—
171	#687	—	5	2	no	—
172	#687	—	5	2	no	—
173	#687	—	10	4	no	—
174	#687	C₂×D₅	1	2	yes	complemented
175	#681	—	5	1	no	—
176	#681	—	5	1	no	—
177	#681	—	5	2	no	—
178	#681	—	10	2	no	—
179	#681	C₂×D₅	1	1	yes	characteristic, complemented
180	C₂×#168	—	5	2	no	—
181	Dic₂₀	—	5	2	no	—
182	#677	—	5	2	no	—
183	#676	—	5	2	no	—
184	C₈×D₅	—	5	2	no	—
185	C₂×#137	—	25	1	no	Sylow
186	C₂×C₅²	—	2	1	no	—
187	C₂×C₅²	—	4	1	no	—
188	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
189	C₅×D₅	—	2	1	no	—
190	C₅×D₅	—	4	1	no	—
191	C₅×D₅	#137	1	2	yes	complemented
192	C₂³×C₅	—	5	1	no	—
193	C₂³×C₅	—	10	1	no	—
194	C₂²×D₅	—	2	1	no	—
195	C₂²×D₅	C₂²⋊D₅	1	1	yes	characteristic
196	C₅×Q₈	—	2	2	no	—
197	C₅×Q₈	—	5	2	no	—
198	C₅×Q₈	—	5	1	no	—
199	C₅×Q₈	—	10	1	no	—
200	C₅×Q₈	—	10	1	no	—
201	C₅×Q₈	C₂²×D₅	1	1	yes	characteristic
202	C₅×Q₈	C₂²×D₅	1	1	yes	characteristic
203	C₅×D₄	—	2	1	no	—
204	C₅×D₄	—	2	1	no	—
205	C₅×D₄	—	2	2	no	—
206	C₅×D₄	—	4	2	no	—
207	C₅×D₄	—	5	1	no	—
208	C₅×D₄	—	10	1	no	—
209	C₅×D₄	—	10	1	no	—
210	C₅×D₄	—	10	1	no	—
211	C₅×D₄	—	10	1	no	—
212	C₅×D₄	C₂²×D₅	1	1	yes	characteristic
213	C₅×D₄	C₂²×D₅	1	1	yes	characteristic
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	—	5	1	no	—
219	C₂×C₄×C₅	—	5	1	no	—
220	C₂×C₄×C₅	—	5	1	no	—
221	C₂×C₄×C₅	—	5	1	no	—
222	C₂×C₄×C₅	—	5	1	no	—
223	C₂×C₄×C₅	—	10	1	no	—
224	C₂×C₄×C₅	—	10	1	no	—
225	C₂×C₄×C₅	—	10	1	no	—
226	C₂×C₄×C₅	—	10	1	no	—
227	C₂×C₄×C₅	—	10	1	no	—
228	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
230	C₂²⋊D₅	—	2	1	no	—
231	C₂²⋊D₅	—	2	1	no	—
232	C₂²⋊D₅	—	2	1	no	—
233	C₂×Dic₅	—	2	1	no	—
234	C₂×Dic₅	—	2	1	no	—
235	C₂×Dic₅	—	10	2	no	—
236	C₂×Dic₅	—	10	2	no	—
237	C₂×Dic₅	—	10	1	no	—
238	C₂×Dic₅	—	10	1	no	—
239	C₂×Dic₅	—	20	2	no	—
240	C₂×Dic₅	C₂²⋊D₅	1	1	yes	characteristic
241	D₂₀	—	2	1	no	—
242	D₂₀	C₂²×D₅	1	1	yes	characteristic
243	C₄×D₅	—	2	1	no	—
244	C₄×D₅	—	2	1	no	—
245	C₄×D₅	—	2	1	no	—
246	C₄×D₅	—	10	2	no	—
247	C₄×D₅	—	10	2	no	—
248	C₄×D₅	C₂²⋊D₅	1	1	yes	characteristic
249	C₄×D₅	C₂²⋊D₅	1	1	yes	characteristic
250	C₄×D₅	C₂²×D₅	1	1	yes	characteristic
251	C₄×D₅	C₂²×D₅	1	1	yes	characteristic
252	Dic₁₀	—	2	1	no	—
253	Dic₁₀	—	2	1	no	—
254	Dic₁₀	—	5	2	no	—
255	Dic₁₀	—	5	2	no	—
256	Dic₁₀	—	10	4	no	—
257	Dic₁₀	—	10	2	no	—
258	Dic₁₀	—	10	2	no	—
259	Dic₁₀	—	10	1	no	—
260	Dic₁₀	—	10	1	no	—
261	Dic₁₀	—	10	2	no	—
262	Dic₁₀	—	10	2	no	—
263	Dic₁₀	—	20	2	no	—
264	Dic₁₀	C₂²×D₅	1	1	yes	characteristic
265	Dic₁₀	C₂²×D₅	1	2	yes	—
266	C₅×C₈	—	5	2	no	—
267	#168	—	5	2	no	—
268	#168	—	5	2	no	—
269	#168	—	10	4	no	—
270	#168	C₂²×D₅	1	2	yes	—
271	C₂×#41	—	5	1	no	—
272	C₂²×Q₈	—	25	1	no	—
273	#137	—	5	1	no	—
274	#137	—	25	1	no	—
275	#137	—	25	2	no	—
276	#137	—	25	2	no	—
277	#137	—	25	1	no	—
278	#137	—	25	1	no	—
279	C₂×Q₁₆	—	25	2	no	—
280	C₂×SD₁₆	—	25	2	no	—
281	C₂×M₁₆	—	25	1	no	—
282	C₅²	C₂×#137	1	1	yes	characteristic, complemented, Sylow
283	C₂²×C₅	—	2	1	no	—
284	C₂²×C₅	—	2	1	no	—
285	C₂²×C₅	—	2	2	no	—
286	C₂²×C₅	—	4	2	no	—
287	C₂²×C₅	—	5	1	no	—
288	C₂²×C₅	—	5	1	no	—
289	C₂²×C₅	—	10	2	no	—
290	C₂²×C₅	—	10	1	no	—
291	C₂²×C₅	—	20	2	no	—
292	C₂²×C₅	D₄×D₅	1	1	yes	characteristic
293	C₂²×C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
294	C₂×D₅	—	2	2	no	—
295	C₂×D₅	—	2	1	no	—
296	C₂×D₅	—	4	2	no	—
297	C₂×D₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
298	C₂×D₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
299	C₄×C₅	—	2	1	no	—
300	C₄×C₅	—	2	1	no	—
301	C₄×C₅	—	2	2	no	—
302	C₄×C₅	—	2	2	no	—
303	C₄×C₅	—	4	2	no	—
304	C₄×C₅	—	5	1	no	—
305	C₄×C₅	—	5	1	no	—
306	C₄×C₅	—	10	1	no	—
307	C₄×C₅	—	10	2	no	—
308	C₄×C₅	D₄×D₅	1	1	yes	characteristic
309	C₄×C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
310	C₄×C₅	C₂³×D₅	1	1	yes	characteristic
311	C₄×C₅	C₂³×D₅	1	1	yes	characteristic
312	Dic₅	—	2	2	no	—
313	Dic₅	—	2	1	no	—
314	Dic₅	—	10	2	no	—
315	Dic₅	—	10	2	no	—
316	Dic₅	—	20	4	no	—
317	Dic₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
318	Dic₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
319	#41	—	5	1	no	—
320	#41	—	5	1	no	—
321	#41	—	5	1	no	—
322	#41	—	10	1	no	—
323	#41	—	10	1	no	—
324	#41	D₅²	1	1	yes	characteristic
325	C₂×Q₈	—	5	1	no	—
326	C₂×Q₈	—	5	1	no	—
327	C₂×Q₈	—	25	2	no	—
328	C₂×Q₈	—	25	2	no	—
329	C₂×Q₈	—	25	1	no	—
330	C₂×Q₈	—	50	1	no	—
331	C₂×Q₈	—	50	1	no	—
332	C₂×Q₈	—	50	1	no	—
333	C₂×D₄	—	5	1	no	—
334	C₂×D₄	—	10	1	no	—
335	C₂²×C₄	—	5	1	no	—
336	C₂²×C₄	—	10	1	no	—
337	C₂²×C₄	—	50	1	no	—
338	Q₁₆	—	5	2	no	—
339	Q₁₆	—	25	2	no	—
340	Q₁₆	—	25	2	no	—
341	Q₁₆	—	25	2	no	—
342	SD₁₆	—	5	2	no	—
343	SD₁₆	—	25	2	no	—
344	SD₁₆	—	25	2	no	—
345	SD₁₆	—	25	2	no	—
346	M₁₆	—	5	1	no	—
347	M₁₆	—	25	2	no	—
348	M₁₆	—	25	1	no	—
349	C₂×C₈	—	25	2	no	—
350	C₂×C₅	—	2	1	no	—
351	C₂×C₅	—	2	1	no	—
352	C₂×C₅	—	2	2	no	—
353	C₂×C₅	—	4	2	no	—
354	C₂×C₅	—	4	1	no	—
355	C₂×C₅	—	4	1	no	—
356	C₂×C₅	—	5	2	no	—
357	C₂×C₅	—	8	2	no	—
358	C₂×C₅	—	10	1	no	—
359	C₂×C₅	—	20	1	no	—
360	C₂×C₅	C₂×D₄×D₅	1	1	yes	characteristic
361	C₂×C₅	C₂²×C₂²⋊D₅	1	1	yes	characteristic
362	D₅	—	2	1	no	—
363	D₅	—	4	1	no	—
364	D₅	#4097	1	2	yes	direct product factor
365	C₂³	—	5	1	no	—
366	C₂³	—	10	1	no	—
367	Q₈	—	5	2	no	—
368	Q₈	—	5	1	no	—
369	Q₈	—	10	1	no	—
370	Q₈	—	10	1	no	—
371	Q₈	—	25	2	no	—
372	Q₈	—	50	2	no	—
373	Q₈	—	50	2	no	—
374	Q₈	—	50	1	no	—
375	Q₈	C₂×D₅²	1	1	yes	characteristic
376	D₄	—	2	1	no	—
377	D₄	—	5	1	no	—
378	D₄	—	10	1	no	—
379	D₄	—	10	1	no	—
380	D₄	—	10	1	no	—
381	D₄	—	10	1	no	—
382	D₄	C₂×D₅²	1	1	yes	characteristic
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	5	1	no	—
385	C₂×C₄	—	5	1	no	—
386	C₂×C₄	—	5	1	no	—
387	C₂×C₄	—	5	1	no	—
388	C₂×C₄	—	5	1	no	—
389	C₂×C₄	—	10	1	no	—
390	C₂×C₄	—	10	1	no	—
391	C₂×C₄	—	10	1	no	—
392	C₂×C₄	—	10	1	no	—
393	C₂×C₄	—	10	1	no	—
394	C₂×C₄	—	50	2	no	—
395	C₂×C₄	—	50	2	no	—
396	C₂×C₄	—	50	1	no	—
397	C₂×C₄	C₂×D₅²	1	1	yes	characteristic
398	C₈	—	5	2	no	—
399	C₈	—	25	2	no	—
400	C₅	—	2	2	no	—
401	C₅	D₅×#137	1	1	yes	characteristic, complemented
402	C₅	C₂×#4097	1	1	yes	characteristic, complemented
403	C₂²	—	2	1	no	—
404	C₂²	—	5	1	no	—
405	C₂²	—	5	1	no	—
406	C₂²	—	10	2	no	—
407	C₂²	—	10	1	no	—
408	C₂²	—	20	2	no	—
409	C₂²	D₅×C₂²⋊D₅	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	5	1	no	—
412	C₄	—	5	1	no	—
413	C₄	—	10	1	no	—
414	C₄	—	10	2	no	—
415	C₄	—	50	2	no	—
416	C₄	D₅×C₂²⋊D₅	1	1	yes	characteristic
417	C₄	C₂²×D₅²	1	1	yes	characteristic
418	C₂	—	2	1	no	—
419	C₂	—	4	1	no	—
420	C₂	—	5	2	no	—
421	C₂	—	10	1	no	—
422	C₂	—	20	1	no	—
423	C₂	C₂×D₅×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₅×C₂²⋊D₅
commutator, cosocle	C₄×C₅²	C₂⁴
Frattini	C₄	C₂²×D₅²
Fitting	C₅²×#41	C₂²
socle	C₂×C₅²	C₂²×D₄
prime radical	C₅×D₅×#41	C₂
hypercenter	#41	D₅²
hypocenter	C₅²	C₂×#137
LCS	G ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
2. C₂×D₅×Dic₁₀	C₂	semidirect
3. #11717271	C₂	semidirect
4. C₅×#4097	C₂	semidirect
5. #11717061	C₂	semidirect
6. D₅×#689	C₂	semidirect
7. #11717047	C₂	semidirect
8. D₅×#687	C₂	semidirect
9. #11716949	C₂	semidirect
10. #11716945	C₂	semidirect
11. D₅×#681	C₂	semidirect
13. C₂×#6045	C₂²	semidirect
24. C₂×C₅×Dic₁₀	C₂²	semidirect
30. D₅×Dic₁₀	C₂²	semidirect
31. #87812	C₂²	semidirect
32. #87810	C₂²	semidirect
33. #87804	C₂²	semidirect
34. C₅×#689	C₂²	semidirect
35. C₅×#687	C₂²	semidirect
36. C₅×#681	C₂²	semidirect
37. #87776	C₂²	semidirect
38. #87775	C₂²	semidirect
39. #87773	C₂²	semidirect
40. #87772	C₂²	semidirect
41. #87768	C₂²	semidirect
92. #4097	D₅	direct (N × H)
157. C₂×Dic₁₀	C₂×D₅	semidirect
167. #689	C₂×D₅	semidirect
174. #687	C₂×D₅	semidirect
179. #681	C₂×D₅	semidirect
191. C₅×D₅	#137	semidirect
282. C₅²	C₂×#137	semidirect
364. D₅	#4097	direct (N × H)
401. C₅	D₅×#137	semidirect
402. C₅	C₂×#4097	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₅×#41	2
C₂×D₅×Dic₁₀	2
#11717271	2
C₅×#4097	2
#11717061	2
D₅×#689	2
#11717047	2
D₅×#687	2
#11716949	2
#11716945	2
D₅×#681	2
C₂×#4097	5
D₅×#137	5

Subgroups — D5×#4097 #13106554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#4097 #13106554