Subgroups — D₅×#4088 #13106455

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	C₂×C₅×Q₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×#709	C₂	1	1	yes	maximal, characteristic
3	#11717262	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4088	C₂	1	1	yes	maximal, characteristic, complemented
5	#11717066	C₂	1	2	yes	maximal, complemented
6	#11717064	C₂	1	2	yes	maximal, complemented
7	D₅×#689	C₂	1	2	yes	maximal, complemented
8	D₅×#688	C₂	1	2	yes	maximal, complemented
9	#11716951	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	C₂×C₅²×Q₈	C₂²	1	1	yes	characteristic, complemented
13	#87900	C₂²	1	1	yes	characteristic
14	C₅×Q₈×D₅	—	2	1	no	—
15	C₅×Q₈×D₅	—	2	1	no	—
16	C₅×Q₈×D₅	C₂²	1	2	yes	—
17	C₅×Q₈×D₅	C₂²	1	2	yes	complemented
18	C₅×#709	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×D₅	—	2	1	no	—
20	C₂×C₄×C₅×D₅	C₂²	1	1	yes	characteristic
21	C₂×C₅×Dic₁₀	—	2	1	no	—
22	C₂×C₅×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
23	D₅×C₂²⋊D₅	—	2	1	no	—
24	#87879	—	2	1	no	—
25	D₅×D₂₀	C₂²	1	1	yes	characteristic
26	C₄×D₅²	—	2	1	no	—
27	#87874	C₂²	1	1	yes	characteristic
28	#87873	—	2	1	no	—
29	#87870	C₂²	1	1	yes	characteristic
30	D₅×Dic₁₀	C₂²	1	1	yes	characteristic
31	#87812	C₂²	1	2	yes	complemented
32	#87811	C₂²	1	2	yes	complemented
33	#87804	C₂²	1	1	yes	characteristic, complemented
34	C₅×#689	C₂²	1	2	yes	complemented
35	C₅×#688	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	#87774	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×#4088	—	5	1	no	maximal
44	D₅×#137	—	5	1	no	maximal
45	C₂²×C₅×D₅	D₄	1	1	yes	characteristic
46	C₂×D₅²	—	2	1	no	—
47	C₅²×Q₈	—	2	1	no	—
48	C₅²×Q₈	C₂³	1	2	yes	—
49	C₂×C₄×C₅²	—	2	1	no	—
50	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
51	C₂²⋊(C₅⋊D₅)	—	2	1	no	—
52	C₄⋊(C₅⋊D₅)	C₂³	1	1	yes	characteristic
53	C₄×C₅⋊D₅	—	2	1	no	—
54	#6045	C₂³	1	1	yes	characteristic
55	C₅×C₂²⋊D₅	—	2	1	no	—
56	C₂×C₅×Dic₅	—	2	1	no	—
57	C₂×C₅×Dic₅	D₄	1	1	yes	characteristic
58	C₅×D₂₀	C₂³	1	1	yes	characteristic
59	C₄×C₅×D₅	—	2	2	no	—
60	C₄×C₅×D₅	—	2	2	no	—
61	C₄×C₅×D₅	—	2	1	no	—
62	C₄×C₅×D₅	D₄	1	1	yes	characteristic
63	C₄×C₅×D₅	D₄	1	1	yes	characteristic
64	C₄×C₅×D₅	C₂³	1	1	yes	characteristic
65	C₄×C₅×D₅	C₂³	1	1	yes	characteristic
66	C₅×Dic₁₀	—	2	1	no	—
67	C₅×Dic₁₀	—	2	2	no	—
68	C₅×Dic₁₀	—	2	2	no	—
69	C₅×Dic₁₀	C₂³	1	1	yes	characteristic
70	C₅×Dic₁₀	C₂³	1	2	yes	—
71	#6039	—	2	1	no	—
72	#6038	—	2	1	no	—
73	#6038	—	2	1	no	—
74	#6037	—	2	1	no	—
75	#6036	—	2	1	no	—
76	D₅×Dic₅	—	2	1	no	—
77	D₅×Dic₅	—	2	1	no	—
78	#6029	C₂³	1	2	yes	—
79	C₅×#168	C₂³	1	2	yes	—
80	C₂²×C₅×Q₈	—	5	1	no	—
81	D₅×#41	—	5	1	no	—
82	C₂×Q₈×D₅	D₅	1	1	yes	characteristic, complemented
83	C₂×#709	—	5	1	no	—
84	C₅×#137	—	5	1	no	—
85	#4097	—	5	1	no	—
86	C₂×#689	—	5	2	no	—
87	#4088	—	5	1	no	—
88	#4088	—	5	1	no	—
89	#4088	—	5	1	no	—
90	#4088	—	5	2	no	—
91	#4088	—	5	2	no	—
92	#4088	—	5	1	no	—
93	#4088	—	10	2	no	—
94	#4088	D₅	1	1	yes	characteristic, direct product factor
95	C₂×#688	—	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	C₂×D₄	1	1	yes	characteristic
104	C₂×C₅⋊D₅	—	2	1	no	—
105	C₂×C₅×D₅	—	2	2	no	—
106	C₂×C₅×D₅	—	2	1	no	—
107	C₂×C₅×D₅	C₂×D₄	1	1	yes	characteristic
108	C₂×C₅×D₅	C₂×D₄	1	1	yes	characteristic
109	D₅²	—	4	2	no	—
110	C₄×C₅²	—	2	2	no	—
111	C₄×C₅²	C₂×D₄	1	1	yes	characteristic
112	C₄×C₅²	C₂⁴	1	1	yes	characteristic
113	#1039	—	2	1	no	—
114	C₅×Dic₅	—	2	1	no	—
115	C₅×Dic₅	—	2	2	no	—
116	C₅×Dic₅	C₂×D₄	1	1	yes	characteristic
117	C₅×Dic₅	C₂×D₄	1	1	yes	characteristic
118	C₅×#41	—	5	1	no	—
119	C₂×C₅×Q₈	—	2	2	no	—
120	C₂×C₅×Q₈	—	5	2	no	—
121	C₂×C₅×Q₈	—	5	2	no	—
122	C₂×C₅×Q₈	—	5	1	no	—
123	C₂×C₅×Q₈	—	10	1	no	—
124	C₂×C₅×Q₈	—	10	1	no	—
125	C₂×C₅×Q₈	—	10	1	no	—
126	C₂×C₅×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
127	C₂×C₅×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
128	C₂²×C₄×C₅	—	5	1	no	—
129	C₂²×C₄×C₅	—	10	1	no	—
130	C₂×C₂²⋊D₅	—	10	1	no	—
131	#713	—	5	1	no	—
132	Q₈×D₅	—	2	1	no	—
133	Q₈×D₅	—	2	1	no	—
134	Q₈×D₅	—	5	1	no	—
135	Q₈×D₅	C₂×D₅	1	2	yes	—
136	Q₈×D₅	C₂×D₅	1	2	yes	complemented
137	#711	—	5	1	no	—
138	#711	—	10	1	no	—
139	D₄×D₅	—	5	1	no	—
140	D₄×D₅	—	10	1	no	—
141	#709	—	5	1	no	—
142	#709	—	5	1	no	—
143	#709	—	5	1	no	—
144	#709	—	5	1	no	—
145	#709	—	10	2	no	—
146	#709	—	10	1	no	—
147	#709	—	10	1	no	—
148	#709	—	10	1	no	—
149	#709	C₂×D₅	1	1	yes	characteristic
150	C₂×D₂₀	—	5	1	no	—
151	C₂×C₄×D₅	—	2	1	no	—
152	C₂×C₄×D₅	—	10	1	no	—
153	C₂×C₄×D₅	—	10	1	no	—
154	C₂×C₄×D₅	C₂×D₅	1	1	yes	characteristic
155	C₂×Dic₁₀	—	2	1	no	—
156	C₂×Dic₁₀	—	5	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	#688	—	5	2	no	—
170	#688	—	5	2	no	—
171	#688	—	5	2	no	—
172	#688	—	10	4	no	—
173	#688	C₂×D₅	1	2	yes	complemented
174	#687	—	5	2	no	—
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	C₂²×D₄	1	1	yes	characteristic
188	C₅⋊D₅	—	4	1	no	—
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	C₂²×D₅	—	10	1	no	—
194	C₂²×D₅	—	10	1	no	—
195	C₂²×D₅	C₂²⋊D₅	1	1	yes	characteristic
196	C₅×Q₈	—	2	1	no	—
197	C₅×Q₈	—	2	1	no	—
198	C₅×Q₈	—	2	4	no	—
199	C₅×Q₈	—	4	2	no	—
200	C₅×Q₈	—	5	2	no	—
201	C₅×Q₈	—	5	1	no	—
202	C₅×Q₈	—	10	2	no	—
203	C₅×Q₈	—	10	2	no	—
204	C₅×Q₈	—	10	1	no	—
205	C₅×Q₈	C₂²×D₅	1	2	yes	—
206	C₅×Q₈	C₂²×D₅	1	2	yes	—
207	C₅×D₄	—	5	1	no	—
208	C₅×D₄	—	10	1	no	—
209	C₂×C₄×C₅	—	2	1	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	4	2	no	—
213	C₂×C₄×C₅	—	5	1	no	—
214	C₂×C₄×C₅	—	5	1	no	—
215	C₂×C₄×C₅	—	5	1	no	—
216	C₂×C₄×C₅	—	5	1	no	—
217	C₂×C₄×C₅	—	5	1	no	—
218	C₂×C₄×C₅	—	10	2	no	—
219	C₂×C₄×C₅	—	10	2	no	—
220	C₂×C₄×C₅	—	10	1	no	—
221	C₂×C₄×C₅	—	10	1	no	—
222	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
224	C₂²⋊D₅	—	2	1	no	—
225	C₂²⋊D₅	—	10	1	no	—
226	C₂²⋊D₅	—	10	1	no	—
227	C₂²⋊D₅	—	10	1	no	—
228	C₂²⋊D₅	—	10	1	no	—
229	C₂²⋊D₅	—	10	1	no	—
230	C₂²⋊D₅	—	10	1	no	—
231	C₂²⋊D₅	—	20	2	no	—
232	C₂×Dic₅	—	2	1	no	—
233	C₂×Dic₅	—	10	1	no	—
234	C₂×Dic₅	—	10	1	no	—
235	C₂×Dic₅	C₂²⋊D₅	1	1	yes	characteristic
236	D₂₀	—	5	1	no	—
237	D₂₀	—	5	1	no	—
238	D₂₀	—	10	2	no	—
239	D₂₀	—	10	1	no	—
240	D₂₀	—	10	1	no	—
241	D₂₀	C₂²×D₅	1	1	yes	characteristic
242	C₄×D₅	—	2	2	no	—
243	C₄×D₅	—	2	2	no	—
244	C₄×D₅	—	2	1	no	—
245	C₄×D₅	—	10	1	no	—
246	C₄×D₅	—	10	1	no	—
247	C₄×D₅	—	10	1	no	—
248	C₄×D₅	—	10	1	no	—
249	C₄×D₅	—	10	1	no	—
250	C₄×D₅	—	10	1	no	—
251	C₄×D₅	—	20	2	no	—
252	C₄×D₅	C₂²⋊D₅	1	1	yes	characteristic
253	C₄×D₅	C₂²⋊D₅	1	1	yes	characteristic
254	C₄×D₅	C₂²×D₅	1	1	yes	characteristic
255	C₄×D₅	C₂²×D₅	1	1	yes	characteristic
256	Dic₁₀	—	2	1	no	—
257	Dic₁₀	—	2	2	no	—
258	Dic₁₀	—	2	2	no	—
259	Dic₁₀	—	5	1	no	—
260	Dic₁₀	—	5	1	no	—
261	Dic₁₀	—	10	2	no	—
262	Dic₁₀	—	10	1	no	—
263	Dic₁₀	—	10	1	no	—
264	Dic₁₀	C₂²×D₅	1	2	yes	—
265	Dic₁₀	C₂²×D₅	1	1	yes	characteristic
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	—	25	1	no	—
272	C₂²×Q₈	—	5	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	2	no	—
284	C₂²×C₅	—	5	1	no	—
285	C₂²×C₅	—	5	1	no	—
286	C₂²×C₅	—	10	2	no	—
287	C₂²×C₅	—	10	1	no	—
288	C₂²×C₅	D₄×D₅	1	1	yes	characteristic
289	C₂²×C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
290	C₂×D₅	—	2	2	no	—
291	C₂×D₅	—	2	1	no	—
292	C₂×D₅	—	10	1	no	—
293	C₂×D₅	—	10	1	no	—
294	C₂×D₅	—	20	2	no	—
295	C₂×D₅	—	20	2	no	—
296	C₂×D₅	—	20	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	2	no	—
300	C₄×C₅	—	2	2	no	—
301	C₄×C₅	—	2	2	no	—
302	C₄×C₅	—	2	2	no	—
303	C₄×C₅	—	4	4	no	—
304	C₄×C₅	—	5	1	no	—
305	C₄×C₅	—	5	1	no	—
306	C₄×C₅	—	10	2	no	—
307	C₄×C₅	—	10	1	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	1	no	—
313	Dic₅	—	2	2	no	—
314	Dic₅	—	10	1	no	—
315	Dic₅	—	10	1	no	—
316	Dic₅	—	20	2	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	—	25	1	no	—
321	#41	—	25	1	no	—
322	#41	—	25	1	no	—
323	#41	—	50	1	no	—
324	#41	—	50	1	no	—
325	C₂×Q₈	—	5	2	no	—
326	C₂×Q₈	—	5	2	no	—
327	C₂×Q₈	—	5	1	no	—
328	C₂×Q₈	—	10	1	no	—
329	C₂×Q₈	—	10	1	no	—
330	C₂×Q₈	—	10	1	no	—
331	C₂×Q₈	—	25	1	no	—
332	C₂×Q₈	D₅²	1	1	yes	characteristic, complemented
333	C₂×D₄	—	25	1	no	—
334	C₂×D₄	—	50	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	—	5	2	no	—
355	C₂×C₅	—	10	1	no	—
356	C₂×C₅	—	20	1	no	—
357	C₂×C₅	C₂×D₄×D₅	1	1	yes	characteristic
358	C₂×C₅	C₂²×C₂²⋊D₅	1	1	yes	characteristic
359	D₅	—	2	1	no	—
360	D₅	—	4	1	no	—
361	D₅	—	20	1	no	—
362	D₅	—	20	1	no	—
363	D₅	—	40	2	no	—
364	D₅	#4088	1	2	yes	direct product factor
365	C₂³	—	5	1	no	—
366	C₂³	—	50	1	no	—
367	Q₈	—	2	1	no	—
368	Q₈	—	5	2	no	—
369	Q₈	—	5	1	no	—
370	Q₈	—	10	2	no	—
371	Q₈	—	10	2	no	—
372	Q₈	—	10	1	no	—
373	Q₈	—	25	1	no	—
374	Q₈	—	50	1	no	—
375	Q₈	C₂×D₅²	1	2	yes	—
376	D₄	—	5	1	no	—
377	D₄	—	10	1	no	—
378	D₄	—	25	1	no	—
379	D₄	—	50	1	no	—
380	D₄	—	50	1	no	—
381	D₄	—	50	1	no	—
382	D₄	—	50	1	no	—
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	2	no	—
390	C₂×C₄	—	10	2	no	—
391	C₂×C₄	—	10	1	no	—
392	C₂×C₄	—	10	1	no	—
393	C₂×C₄	—	50	1	no	—
394	C₂×C₄	—	50	1	no	—
395	C₂×C₄	—	50	1	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×#4088	1	1	yes	characteristic, complemented
403	C₂²	—	5	1	no	—
404	C₂²	—	5	1	no	—
405	C₂²	—	10	2	no	—
406	C₂²	—	10	1	no	—
407	C₂²	—	50	1	no	—
408	C₂²	—	100	2	no	—
409	C₂²	D₅×C₂²⋊D₅	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	5	1	no	—
412	C₄	—	5	1	no	—
413	C₄	—	10	2	no	—
414	C₄	—	10	1	no	—
415	C₄	—	50	1	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	—	5	2	no	—
420	C₂	—	10	1	no	—
421	C₂	—	20	1	no	—
422	C₂	—	100	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	C₂×C₅²×Q₈	C₂²
socle	C₂×C₅²	C₂²×D₄
prime radical	D₅×#709	C₂
hypercenter	C₂×Q₈	D₅²
hypocenter	C₅²	C₂×#137
LCS	G ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×Q₈×D₅	C₂	semidirect
3. #11717262	C₂	semidirect
4. C₅×#4088	C₂	semidirect
5. #11717066	C₂	semidirect
6. #11717064	C₂	semidirect
7. D₅×#689	C₂	semidirect
8. D₅×#688	C₂	semidirect
9. #11716951	C₂	semidirect
10. #11716945	C₂	semidirect
11. D₅×#681	C₂	semidirect
12. C₂×C₅²×Q₈	C₂²	semidirect
17. C₅×Q₈×D₅	C₂²	semidirect
22. C₂×C₅×Dic₁₀	C₂²	semidirect
31. #87812	C₂²	semidirect
32. #87811	C₂²	semidirect
33. #87804	C₂²	semidirect
34. C₅×#689	C₂²	semidirect
35. C₅×#688	C₂²	semidirect
36. C₅×#681	C₂²	semidirect
37. #87776	C₂²	semidirect
38. #87775	C₂²	semidirect
39. #87774	C₂²	semidirect
40. #87772	C₂²	semidirect
41. #87768	C₂²	semidirect
82. C₂×Q₈×D₅	D₅	semidirect
94. #4088	D₅	direct (N × H)
126. C₂×C₅×Q₈	C₂×D₅	semidirect
127. C₂×C₅×Q₈	C₂×D₅	semidirect
136. Q₈×D₅	C₂×D₅	semidirect
157. C₂×Dic₁₀	C₂×D₅	semidirect
167. #689	C₂×D₅	semidirect
173. #688	C₂×D₅	semidirect
179. #681	C₂×D₅	semidirect
191. C₅×D₅	#137	semidirect
282. C₅²	C₂×#137	semidirect
332. C₂×Q₈	D₅²	semidirect
364. D₅	#4088	direct (N × H)
401. C₅	D₅×#137	semidirect
402. C₅	C₂×#4088	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×Q₈×D₅	2
D₅×#709	2
#11717262	2
C₅×#4088	2
#11717066	2
#11717064	2
D₅×#689	2
D₅×#688	2
#11716951	2
#11716945	2
D₅×#681	2
C₂×#4088	5
D₅×#137	5

Subgroups — D5×#4088 #13106455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#4088 #13106455