Subgroups — #13106456

Order 1600.

584 conjugacy classes of subgroups.

The subgroup lattice has 433 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#713	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×#709	C₂	1	1	yes	maximal, characteristic, complemented
3	#11717262	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4088	C₂	1	1	yes	maximal, characteristic, complemented
5	#11717067	C₂	1	2	yes	maximal, complemented
6	#11717065	C₂	1	2	yes	maximal, complemented
7	#11717061	C₂	1	2	yes	maximal, complemented
8	#11717057	C₂	1	2	yes	maximal, complemented
9	#11716948	C₂	1	1	yes	maximal, characteristic, complemented
10	#11716941	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×#713	—	2	1	no	—
15	C₅×#713	—	2	1	no	—
16	C₅×#713	C₂²	1	2	yes	—
17	C₅×#713	C₂²	1	2	yes	complemented
18	C₅×#709	C₂²	1	1	yes	characteristic
19	C₂×C₅×D₂₀	—	2	1	no	—
20	C₂×C₅×D₂₀	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₄×C₅×D₅	—	2	1	no	—
22	C₂×C₄×C₅×D₅	C₂²	1	1	yes	characteristic
23	D₅×C₂²⋊D₅	—	2	1	no	—
24	#87879	—	2	1	no	—
25	D₅×D₂₀	C₂²	1	1	yes	characteristic, complemented
26	C₄×D₅²	—	2	1	no	—
27	#87874	C₂²	1	1	yes	characteristic, complemented
28	#87873	—	2	1	no	—
29	#87870	C₂²	1	1	yes	characteristic, complemented
30	D₅×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
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	#87773	C₂²	1	2	yes	complemented
38	#87772	C₂²	1	2	yes	complemented
39	#87771	C₂²	1	2	yes	complemented
40	#87770	C₂²	1	2	yes	complemented
41	#87768	C₂²	1	2	yes	complemented
42	D₅×#168	C₂²	1	2	yes	complemented
43	#66156	—	5	1	no	maximal
44	#66111	—	5	1	no	maximal
45	C₂²×C₅×D₅	—	2	1	no	—
46	C₂²×C₅×D₅	D₄	1	1	yes	characteristic
47	C₂×D₅²	—	2	1	no	—
48	C₅²×Q₈	—	2	1	no	—
49	C₅²×Q₈	C₂³	1	2	yes	—
50	C₂×C₄×C₅²	—	2	1	no	—
51	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
52	C₂²⋊(C₅⋊D₅)	—	2	1	no	—
53	C₄⋊(C₅⋊D₅)	C₂³	1	1	yes	characteristic
54	C₄×C₅⋊D₅	—	2	1	no	—
55	#6045	C₂³	1	1	yes	characteristic
56	C₅×C₂²⋊D₅	—	2	1	no	—
57	C₂×C₅×Dic₅	D₄	1	1	yes	characteristic
58	C₅×D₂₀	—	2	2	no	—
59	C₅×D₂₀	—	2	2	no	—
60	C₅×D₂₀	—	2	1	no	—
61	C₅×D₂₀	C₂³	1	1	yes	characteristic
62	C₅×D₂₀	C₂³	1	2	yes	—
63	C₄×C₅×D₅	—	2	1	no	—
64	C₄×C₅×D₅	—	2	2	no	—
65	C₄×C₅×D₅	—	2	2	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	C₂³	1	1	yes	characteristic
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	C₂×C₅×#41	—	5	1	no	—
81	D₅×#41	—	5	1	no	—
82	C₂×#713	D₅	1	1	yes	characteristic, complemented
83	C₂×#709	—	5	1	no	—
84	C₅×#137	—	5	1	no	—
85	#4097	—	5	2	no	—
86	#4096	—	5	2	no	—
87	#4096	—	5	2	no	—
88	#4095	—	5	1	no	—
89	#4095	—	5	2	no	—
90	#4088	—	5	1	no	—
91	#4088	—	5	1	no	—
92	#4088	—	10	2	no	—
93	#4088	D₅	1	1	yes	characteristic, complemented
94	#4078	—	5	1	no	—
95	#4078	—	5	1	no	—
96	C₂×#681	—	5	1	no	—
97	#4065	—	5	2	no	—
98	#4064	—	5	2	no	—
99	#4062	—	5	2	no	—
100	#4060	—	5	2	no	—
101	#4054	—	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	1	no	—
106	C₂×C₅×D₅	—	2	2	no	—
107	C₂×C₅×D₅	—	4	1	no	—
108	C₂×C₅×D₅	—	4	2	no	—
109	C₂×C₅×D₅	C₂×D₄	1	1	yes	characteristic
110	C₂×C₅×D₅	C₂×D₄	1	1	yes	characteristic
111	D₅²	—	4	2	no	—
112	C₄×C₅²	—	2	2	no	—
113	C₄×C₅²	C₂×D₄	1	1	yes	characteristic
114	C₄×C₅²	C₂⁴	1	1	yes	characteristic
115	#1039	—	2	1	no	—
116	C₅×Dic₅	—	2	1	no	—
117	C₅×Dic₅	C₂×D₄	1	1	yes	characteristic
118	C₅×Dic₅	C₂×D₄	1	1	yes	characteristic
119	C₅×#41	—	5	2	no	—
120	C₅×#41	—	5	2	no	—
121	C₅×#41	—	5	1	no	—
122	C₅×#41	—	10	1	no	—
123	C₅×#41	—	10	1	no	—
124	C₂×C₅×Q₈	—	2	2	no	—
125	C₂×C₅×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
126	C₂×C₅×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
127	C₂×C₅×D₄	—	5	1	no	—
128	C₂×C₅×D₄	—	10	1	no	—
129	C₂²×C₄×C₅	—	5	1	no	—
130	C₂²×C₄×C₅	—	10	1	no	—
131	C₂×C₂²⋊D₅	—	10	1	no	—
132	#713	—	2	1	no	—
133	#713	—	2	1	no	—
134	#713	—	5	1	no	—
135	#713	C₂×D₅	1	2	yes	—
136	#713	C₂×D₅	1	2	yes	complemented
137	Q₈×D₅	—	5	1	no	—
138	#711	—	5	1	no	—
139	#711	—	10	1	no	—
140	D₄×D₅	—	5	1	no	—
141	D₄×D₅	—	10	1	no	—
142	#709	—	5	1	no	—
143	#709	—	5	1	no	—
144	#709	—	5	1	no	—
145	#709	—	5	1	no	—
146	#709	—	10	2	no	—
147	#709	—	10	1	no	—
148	#709	—	10	1	no	—
149	#709	—	10	1	no	—
150	#709	C₂×D₅	1	1	yes	characteristic
151	C₂×D₂₀	—	2	1	no	—
152	C₂×D₂₀	—	5	1	no	—
153	C₂×D₂₀	C₂×D₅	1	1	yes	characteristic, complemented
154	C₂×C₄×D₅	—	2	1	no	—
155	C₂×C₄×D₅	—	10	1	no	—
156	C₂×C₄×D₅	—	10	1	no	—
157	C₂×C₄×D₅	C₂×D₅	1	1	yes	characteristic
158	C₂×Dic₁₀	—	5	1	no	—
159	C₅×Q₁₆	—	5	2	no	—
160	C₅×SD₁₆	—	5	2	no	—
161	C₅×M₁₆	—	5	1	no	—
162	#689	—	5	2	no	—
163	#689	—	5	2	no	—
164	#689	—	10	4	no	—
165	#689	C₂×D₅	1	2	yes	complemented
166	#688	—	5	2	no	—
167	#688	—	5	2	no	—
168	#688	—	5	2	no	—
169	#688	—	10	4	no	—
170	#688	C₂×D₅	1	2	yes	complemented
171	#687	—	5	2	no	—
172	#687	—	5	2	no	—
173	#686	—	5	2	no	—
174	#686	—	5	2	no	—
175	#686	—	5	2	no	—
176	#681	—	5	1	no	—
177	#681	—	5	1	no	—
178	#681	—	5	2	no	—
179	#681	—	10	2	no	—
180	#681	C₂×D₅	1	1	yes	characteristic, complemented
181	C₂×#168	—	5	2	no	—
182	D₄₀	—	5	2	no	—
183	#677	—	5	2	no	—
184	#676	—	5	2	no	—
185	C₈×D₅	—	5	2	no	—
186	#575	—	25	1	no	Sylow
187	C₂×C₅²	—	2	1	no	—
188	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
189	C₅⋊D₅	—	4	1	no	—
190	C₅×D₅	—	2	1	no	—
191	C₅×D₅	—	2	1	no	—
192	C₅×D₅	—	4	1	no	—
193	C₅×D₅	—	4	2	no	—
194	C₂³×C₅	—	5	1	no	—
195	C₂³×C₅	—	10	1	no	—
196	C₂²×D₅	—	2	1	no	—
197	C₂²×D₅	—	10	1	no	—
198	C₂²×D₅	—	10	1	no	—
199	C₂²×D₅	C₂²⋊D₅	1	1	yes	characteristic
200	C₅×Q₈	—	2	1	no	—
201	C₅×Q₈	—	2	1	no	—
202	C₅×Q₈	—	2	4	no	—
203	C₅×Q₈	—	4	2	no	—
204	C₅×Q₈	—	5	1	no	—
205	C₅×Q₈	C₂²×D₅	1	2	yes	—
206	C₅×Q₈	C₂²×D₅	1	2	yes	—
207	C₅×D₄	—	5	2	no	—
208	C₅×D₄	—	5	1	no	—
209	C₅×D₄	—	10	2	no	—
210	C₅×D₄	—	10	2	no	—
211	C₅×D₄	—	10	1	no	—
212	C₅×D₄	—	10	1	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	4	2	no	—
217	C₂×C₄×C₅	—	5	1	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	—	10	2	no	—
223	C₂×C₄×C₅	—	10	2	no	—
224	C₂×C₄×C₅	—	10	1	no	—
225	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
227	C₂²⋊D₅	—	2	1	no	—
228	C₂²⋊D₅	—	10	1	no	—
229	C₂²⋊D₅	—	10	1	no	—
230	C₂²⋊D₅	—	10	1	no	—
231	C₂²⋊D₅	—	10	1	no	—
232	C₂²⋊D₅	—	10	1	no	—
233	C₂²⋊D₅	—	10	1	no	—
234	C₂²⋊D₅	—	20	2	no	—
235	C₂×Dic₅	—	10	1	no	—
236	C₂×Dic₅	—	10	1	no	—
237	C₂×Dic₅	C₂²⋊D₅	1	1	yes	characteristic
238	D₂₀	—	2	2	no	—
239	D₂₀	—	2	2	no	—
240	D₂₀	—	2	1	no	—
241	D₂₀	—	5	1	no	—
242	D₂₀	—	5	1	no	—
243	D₂₀	—	10	2	no	—
244	D₂₀	—	10	1	no	—
245	D₂₀	—	10	1	no	—
246	D₂₀	C₂²×D₅	1	2	yes	—
247	D₂₀	C₂²×D₅	1	1	yes	characteristic
248	C₄×D₅	—	2	1	no	—
249	C₄×D₅	—	2	2	no	—
250	C₄×D₅	—	2	2	no	—
251	C₄×D₅	—	10	1	no	—
252	C₄×D₅	—	10	1	no	—
253	C₄×D₅	—	10	1	no	—
254	C₄×D₅	—	10	1	no	—
255	C₄×D₅	—	10	1	no	—
256	C₄×D₅	—	10	1	no	—
257	C₄×D₅	—	20	2	no	—
258	C₄×D₅	C₂²⋊D₅	1	1	yes	characteristic
259	C₄×D₅	C₂²⋊D₅	1	1	yes	characteristic
260	C₄×D₅	C₂²×D₅	1	1	yes	characteristic
261	C₄×D₅	C₂²×D₅	1	1	yes	characteristic
262	Dic₁₀	—	5	1	no	—
263	Dic₁₀	—	5	1	no	—
264	Dic₁₀	—	10	2	no	—
265	Dic₁₀	—	10	1	no	—
266	Dic₁₀	—	10	1	no	—
267	Dic₁₀	C₂²×D₅	1	1	yes	characteristic
268	C₅×C₈	—	5	2	no	—
269	#168	—	5	2	no	—
270	#168	—	5	2	no	—
271	#168	—	10	4	no	—
272	#168	C₂²×D₅	1	2	yes	—
273	C₂×#41	—	5	1	no	—
274	C₂×#41	—	25	1	no	—
275	#137	—	5	1	no	—
276	#137	—	25	2	no	—
277	#137	—	25	1	no	—
278	AGL(1,ℤ/8)	—	25	1	no	—
279	AGL(1,ℤ/8)	—	25	2	no	—
280	AGL(1,ℤ/8)	—	25	1	no	—
281	#135	—	25	2	no	—
282	#135	—	25	2	no	—
283	C₂×M₁₆	—	25	1	no	—
284	C₅²	#575	1	1	yes	characteristic, complemented, Sylow
285	C₂²×C₅	—	2	2	no	—
286	C₂²×C₅	—	5	1	no	—
287	C₂²×C₅	—	5	1	no	—
288	C₂²×C₅	—	10	2	no	—
289	C₂²×C₅	—	10	1	no	—
290	C₂²×C₅	—	20	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	1	no	—
295	C₂×D₅	—	2	2	no	—
296	C₂×D₅	—	4	1	no	—
297	C₂×D₅	—	4	2	no	—
298	C₂×D₅	—	10	1	no	—
299	C₂×D₅	—	10	1	no	—
300	C₂×D₅	—	20	2	no	—
301	C₂×D₅	—	20	2	no	—
302	C₂×D₅	—	20	2	no	—
303	C₂×D₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
304	C₂×D₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
305	C₄×C₅	—	2	2	no	—
306	C₄×C₅	—	2	2	no	—
307	C₄×C₅	—	2	2	no	—
308	C₄×C₅	—	2	2	no	—
309	C₄×C₅	—	4	4	no	—
310	C₄×C₅	—	5	1	no	—
311	C₄×C₅	—	5	1	no	—
312	C₄×C₅	—	10	1	no	—
313	C₄×C₅	D₄×D₅	1	1	yes	characteristic
314	C₄×C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
315	C₄×C₅	C₂³×D₅	1	1	yes	characteristic
316	C₄×C₅	C₂³×D₅	1	1	yes	characteristic
317	Dic₅	—	2	1	no	—
318	Dic₅	—	10	1	no	—
319	Dic₅	—	10	1	no	—
320	Dic₅	—	20	2	no	—
321	Dic₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
322	Dic₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
323	#41	—	5	2	no	—
324	#41	—	5	2	no	—
325	#41	—	5	1	no	—
326	#41	—	10	1	no	—
327	#41	—	10	1	no	—
328	#41	—	25	1	no	—
329	#41	—	25	1	no	—
330	#41	—	25	1	no	—
331	#41	—	50	1	no	—
332	#41	—	50	1	no	—
333	C₂×Q₈	—	25	1	no	—
334	C₂×Q₈	D₅²	1	1	yes	characteristic, complemented
335	C₂×D₄	—	5	1	no	—
336	C₂×D₄	—	10	1	no	—
337	C₂×D₄	—	25	1	no	—
338	C₂×D₄	—	50	1	no	—
339	C₂²×C₄	—	5	1	no	—
340	C₂²×C₄	—	10	1	no	—
341	C₂²×C₄	—	50	1	no	—
342	Q₁₆	—	5	2	no	—
343	Q₁₆	—	25	2	no	—
344	SD₁₆	—	5	2	no	—
345	SD₁₆	—	25	2	no	—
346	SD₁₆	—	25	2	no	—
347	SD₁₆	—	25	2	no	—
348	D₈	—	25	2	no	—
349	D₈	—	25	2	no	—
350	M₁₆	—	5	1	no	—
351	M₁₆	—	25	2	no	—
352	M₁₆	—	25	1	no	—
353	C₂×C₈	—	25	2	no	—
354	C₂×C₅	—	2	1	no	—
355	C₂×C₅	—	2	1	no	—
356	C₂×C₅	—	2	2	no	—
357	C₂×C₅	—	4	2	no	—
358	C₂×C₅	—	10	1	no	—
359	C₂×C₅	—	10	1	no	—
360	C₂×C₅	—	20	2	no	—
361	C₂×C₅	—	20	1	no	—
362	C₂×C₅	C₂×D₄×D₅	1	1	yes	characteristic
363	C₂×C₅	C₂²×C₂²⋊D₅	1	1	yes	characteristic
364	D₅	—	2	1	no	—
365	D₅	—	2	1	no	—
366	D₅	—	4	1	no	—
367	D₅	—	4	2	no	—
368	D₅	—	20	1	no	—
369	D₅	—	20	1	no	—
370	D₅	—	40	2	no	—
371	C₂³	—	5	1	no	—
372	C₂³	—	10	1	no	—
373	C₂³	—	50	1	no	—
374	Q₈	—	2	1	no	—
375	Q₈	—	5	1	no	—
376	Q₈	—	25	1	no	—
377	Q₈	—	50	1	no	—
378	Q₈	C₂×D₅²	1	2	yes	—
379	D₄	—	5	1	no	—
380	D₄	—	5	2	no	—
381	D₄	—	10	2	no	—
382	D₄	—	10	2	no	—
383	D₄	—	10	1	no	—
384	D₄	—	10	1	no	—
385	D₄	—	25	1	no	—
386	D₄	—	50	1	no	—
387	D₄	—	50	1	no	—
388	D₄	—	50	1	no	—
389	D₄	—	50	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	5	1	no	—
392	C₂×C₄	—	5	1	no	—
393	C₂×C₄	—	5	1	no	—
394	C₂×C₄	—	5	1	no	—
395	C₂×C₄	—	5	1	no	—
396	C₂×C₄	—	10	2	no	—
397	C₂×C₄	—	10	2	no	—
398	C₂×C₄	—	10	1	no	—
399	C₂×C₄	—	50	1	no	—
400	C₂×C₄	—	50	1	no	—
401	C₂×C₄	—	50	1	no	—
402	C₂×C₄	—	50	1	no	—
403	C₂×C₄	C₂×D₅²	1	1	yes	characteristic
404	C₈	—	5	2	no	—
405	C₈	—	25	2	no	—
406	C₅	—	2	2	no	—
407	C₅	#66111	1	1	yes	characteristic, complemented
408	C₅	#66156	1	1	yes	characteristic, complemented
409	C₂²	—	5	1	no	—
410	C₂²	—	5	1	no	—
411	C₂²	—	10	2	no	—
412	C₂²	—	10	1	no	—
413	C₂²	—	20	1	no	—
414	C₂²	—	20	2	no	—
415	C₂²	—	50	1	no	—
416	C₂²	—	100	2	no	—
417	C₂²	D₅×C₂²⋊D₅	1	1	yes	characteristic
418	C₄	—	2	2	no	—
419	C₄	—	5	1	no	—
420	C₄	—	5	1	no	—
421	C₄	—	10	1	no	—
422	C₄	—	50	1	no	—
423	C₄	D₅×C₂²⋊D₅	1	1	yes	characteristic
424	C₄	C₂²×D₅²	1	1	yes	characteristic
425	C₂	—	2	1	no	—
426	C₂	—	10	1	no	—
427	C₂	—	10	1	no	—
428	C₂	—	20	2	no	—
429	C₂	—	20	1	no	—
430	C₂	—	100	1	no	—
431	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
hypercenter	C₂×Q₈	D₅²
hypocenter	C₅²	#575
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×#713	C₂	semidirect
2. D₅×#709	C₂	semidirect
3. #11717262	C₂	semidirect
4. C₅×#4088	C₂	semidirect
5. #11717067	C₂	semidirect
6. #11717065	C₂	semidirect
7. #11717061	C₂	semidirect
8. #11717057	C₂	semidirect
9. #11716948	C₂	semidirect
10. #11716941	C₂	semidirect
11. D₅×#681	C₂	semidirect
12. C₂×C₅²×Q₈	C₂²	semidirect
17. C₅×#713	C₂²	semidirect
20. C₂×C₅×D₂₀	C₂²	semidirect
25. D₅×D₂₀	C₂²	semidirect
27. #87874	C₂²	semidirect
29. #87870	C₂²	semidirect
30. D₅×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. #87773	C₂²	semidirect
38. #87772	C₂²	semidirect
39. #87771	C₂²	semidirect
40. #87770	C₂²	semidirect
41. #87768	C₂²	semidirect
42. D₅×#168	C₂²	semidirect
82. C₂×#713	D₅	semidirect
93. #4088	D₅	semidirect
125. C₂×C₅×Q₈	C₂×D₅	semidirect
126. C₂×C₅×Q₈	C₂×D₅	semidirect
136. #713	C₂×D₅	semidirect
153. C₂×D₂₀	C₂×D₅	semidirect
165. #689	C₂×D₅	semidirect
170. #688	C₂×D₅	semidirect
180. #681	C₂×D₅	semidirect
284. C₅²	#575	semidirect
334. C₂×Q₈	D₅²	semidirect
407. C₅	#66111	semidirect
408. C₅	#66156	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#713	2
D₅×#709	2
#11717262	2
C₅×#4088	2
#11717067	2
#11717065	2
#11717061	2
#11717057	2
#11716948	2
#11716941	2
D₅×#681	2
#66156	5
#66111	5