Subgroups — C₅×#66156 #13106979

Order 1600.

688 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#709	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4097	C₂	1	2	yes	maximal, complemented
4	C₅×#4096	C₂	1	4	yes	maximal, complemented
5	C₅×#4095	C₂	1	2	yes	maximal, complemented
6	C₅×#4088	C₂	1	2	yes	maximal, complemented
7	C₅×#4078	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#681	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅²×#41	—	2	1	no	—
10	C₅²×#41	—	2	1	no	—
11	C₅²×#41	C₂²	1	2	yes	—
12	C₅²×#41	C₂²	1	2	yes	complemented
13	C₂×C₅²×Q₈	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₅²×D₄	—	2	1	no	—
15	C₂×C₅²×D₄	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₄×C₅²	—	2	1	no	—
17	C₂²×C₄×C₅²	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₂²⋊D₅	—	2	1	no	—
19	C₅×#709	—	2	1	no	—
20	C₅×#709	—	2	1	no	—
21	C₅×#709	C₂²	1	2	yes	—
22	C₅×#709	C₂²	1	2	yes	complemented
23	C₂×C₅×D₂₀	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₄×C₅×D₅	—	2	1	no	—
25	C₂×C₅×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
26	C₅×#689	C₂²	1	4	yes	complemented
27	C₅×#688	C₂²	1	4	yes	complemented
28	C₅×#687	C₂²	1	4	yes	complemented
29	C₅×#686	C₂²	1	4	yes	complemented
30	C₅×#681	C₂²	1	2	yes	complemented
31	C₅×#681	C₂²	1	2	yes	complemented
32	C₂×C₅×#168	C₂²	1	2	yes	complemented
33	C₅×#575	—	5	1	no	maximal
34	#66156	C₅	1	1	yes	maximal, characteristic, direct product factor
35	C₂³×C₅²	—	2	1	no	—
36	C₂³×C₅²	D₄	1	1	yes	characteristic
37	C₂²×C₅×D₅	—	2	1	no	—
38	C₅²×Q₈	—	2	1	no	—
39	C₅²×Q₈	C₂³	1	2	yes	—
40	C₅²×D₄	—	2	2	no	—
41	C₅²×D₄	—	2	2	no	—
42	C₅²×D₄	—	2	1	no	—
43	C₅²×D₄	C₂³	1	2	yes	—
44	C₂×C₄×C₅²	—	2	1	no	—
45	C₂×C₄×C₅²	—	2	2	no	—
46	C₂×C₄×C₅²	—	2	2	no	—
47	C₂×C₄×C₅²	D₄	1	1	yes	characteristic
48	C₂×C₄×C₅²	D₄	1	1	yes	characteristic
49	C₂×C₄×C₅²	D₄	1	1	yes	characteristic
50	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
51	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
52	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
53	C₅×C₂²⋊D₅	—	2	2	no	—
54	C₅×C₂²⋊D₅	—	2	2	no	—
55	C₂×C₅×Dic₅	—	2	1	no	—
56	C₅×D₂₀	—	2	1	no	—
57	C₅×D₂₀	C₂³	1	2	yes	—
58	C₄×C₅×D₅	—	2	2	no	—
59	C₄×C₅×D₅	—	2	2	no	—
60	C₅×Dic₁₀	—	2	1	no	—
61	C₅×Dic₁₀	C₂³	1	2	yes	—
62	C₅×#168	C₂³	1	4	yes	—
63	C₂×C₅×#41	—	2	2	no	—
64	C₂×C₅×#41	—	5	1	no	—
65	C₂×C₅×#41	D₅	1	1	yes	characteristic, complemented
66	C₂×C₅×#41	C₂×C₅	1	1	yes	characteristic, complemented
67	C₂×#709	C₂×C₅	1	1	yes	characteristic, complemented
68	C₅×#137	—	5	2	no	—
69	C₅×#137	—	5	2	no	—
70	C₅×AGL(1,ℤ/8)	—	5	2	no	—
71	C₅×AGL(1,ℤ/8)	—	5	2	no	—
72	C₅×#135	—	5	4	no	—
73	C₂×C₅×M₁₆	—	5	1	no	—
74	#4097	C₂×C₅	1	2	yes	complemented
75	#4096	C₂×C₅	1	4	yes	complemented
76	#4095	C₂×C₅	1	2	yes	complemented
77	#4088	C₂×C₅	1	2	yes	complemented
78	#4078	C₂×C₅	1	2	yes	complemented
79	C₂×#681	C₂×C₅	1	1	yes	characteristic, complemented
80	C₂²×C₅²	—	2	2	no	—
81	C₂²×C₅²	—	4	1	no	—
82	C₂²×C₅²	—	4	2	no	—
83	C₂²×C₅²	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₅²	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₅²	C₂×D₄	1	1	yes	characteristic
86	C₂×C₅×D₅	—	2	2	no	—
87	C₂×C₅×D₅	—	4	2	no	—
88	C₄×C₅²	—	2	2	no	—
89	C₄×C₅²	C₂×D₄	1	1	yes	characteristic
90	C₄×C₅²	C₂×D₄	1	1	yes	characteristic
91	C₄×C₅²	C₂×D₄	1	1	yes	characteristic
92	C₄×C₅²	C₂⁴	1	1	yes	characteristic
93	C₅×Dic₅	—	2	2	no	—
94	C₅×#41	—	2	4	no	—
95	C₅×#41	—	2	4	no	—
96	C₅×#41	—	2	1	no	—
97	C₅×#41	—	2	1	no	—
98	C₅×#41	—	2	1	no	—
99	C₅×#41	—	2	1	no	—
100	C₅×#41	—	2	4	no	—
101	C₅×#41	—	2	4	no	—
102	C₅×#41	—	5	2	no	—
103	C₅×#41	—	5	2	no	—
104	C₅×#41	—	10	1	no	—
105	C₅×#41	—	10	1	no	—
106	C₅×#41	C₂×D₅	1	2	yes	—
107	C₅×#41	C₂×D₅	1	2	yes	complemented
108	C₅×#41	C₂²×C₅	1	2	yes	—
109	C₅×#41	C₂²×C₅	1	2	yes	complemented
110	C₂×C₅×Q₈	—	2	2	no	—
111	C₂×C₅×Q₈	—	5	1	no	—
112	C₂×C₅×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
113	C₂×C₅×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
114	C₂×C₅×D₄	—	2	4	no	—
115	C₂×C₅×D₄	—	2	1	no	—
116	C₂×C₅×D₄	—	2	1	no	—
117	C₂×C₅×D₄	—	2	2	no	—
118	C₂×C₅×D₄	—	5	1	no	—
119	C₂×C₅×D₄	—	10	1	no	—
120	C₂×C₅×D₄	C₂×D₅	1	1	yes	characteristic, complemented
121	C₂×C₅×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
122	C₂²×C₄×C₅	—	2	4	no	—
123	C₂²×C₄×C₅	—	2	1	no	—
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	10	1	no	—
127	C₂²×C₄×C₅	C₂×D₅	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₂²⋊D₅	—	2	1	no	—
130	#709	—	2	1	no	—
131	#709	—	2	1	no	—
132	#709	C₂²×C₅	1	2	yes	—
133	#709	C₂²×C₅	1	2	yes	complemented
134	C₂×D₂₀	C₂²×C₅	1	1	yes	characteristic, complemented
135	C₂×C₄×D₅	—	2	1	no	—
136	C₂×Dic₁₀	C₂²×C₅	1	1	yes	characteristic, complemented
137	C₅×Q₁₆	—	5	4	no	—
138	C₅×SD₁₆	—	5	4	no	—
139	C₅×SD₁₆	—	5	4	no	—
140	C₅×D₈	—	5	4	no	—
141	C₅×M₁₆	—	5	2	no	—
142	C₅×M₁₆	—	5	2	no	—
143	C₂×C₅×C₈	—	5	2	no	—
144	#689	C₂²×C₅	1	4	yes	complemented
145	#688	C₂²×C₅	1	4	yes	complemented
146	#687	C₂²×C₅	1	4	yes	complemented
147	#686	C₂²×C₅	1	4	yes	complemented
148	#681	C₂²×C₅	1	2	yes	complemented
149	#681	C₂²×C₅	1	2	yes	complemented
150	C₂×#168	C₂²×C₅	1	2	yes	complemented
151	#575	—	5	1	no	Sylow
152	C₂×C₅²	—	2	1	no	—
153	C₂×C₅²	—	2	1	no	—
154	C₂×C₅²	—	2	1	no	—
155	C₂×C₅²	—	4	2	no	—
156	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
157	C₅×D₅	—	4	2	no	—
158	C₂³×C₅	—	2	4	no	—
159	C₂³×C₅	—	2	1	no	—
160	C₂³×C₅	—	2	1	no	—
161	C₂³×C₅	—	2	2	no	—
162	C₂³×C₅	—	10	1	no	—
163	C₂³×C₅	C₂²⋊D₅	1	1	yes	characteristic
164	C₂³×C₅	C₅×D₄	1	1	yes	characteristic
165	C₂²×D₅	—	2	1	no	—
166	C₅×Q₈	—	2	4	no	—
167	C₅×Q₈	—	2	1	no	—
168	C₅×Q₈	—	2	1	no	—
169	C₅×Q₈	—	2	4	no	—
170	C₅×Q₈	—	5	2	no	—
171	C₅×Q₈	—	10	1	no	—
172	C₅×Q₈	C₂²×D₅	1	2	yes	—
173	C₅×Q₈	C₂³×C₅	1	2	yes	—
174	C₅×D₄	—	2	8	no	—
175	C₅×D₄	—	2	8	no	—
176	C₅×D₄	—	2	4	no	—
177	C₅×D₄	—	2	2	no	—
178	C₅×D₄	—	2	2	no	—
179	C₅×D₄	—	2	2	no	—
180	C₅×D₄	—	2	2	no	—
181	C₅×D₄	—	2	1	no	—
182	C₅×D₄	—	2	1	no	—
183	C₅×D₄	—	2	4	no	—
184	C₅×D₄	—	5	2	no	—
185	C₅×D₄	—	10	2	no	—
186	C₅×D₄	—	10	2	no	—
187	C₅×D₄	—	10	1	no	—
188	C₅×D₄	C₂²×D₅	1	2	yes	—
189	C₅×D₄	C₂³×C₅	1	2	yes	—
190	C₂×C₄×C₅	—	2	4	no	—
191	C₂×C₄×C₅	—	2	8	no	—
192	C₂×C₄×C₅	—	2	8	no	—
193	C₂×C₄×C₅	—	2	1	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	10	1	no	—
206	C₂×C₄×C₅	—	10	2	no	—
207	C₂×C₄×C₅	—	10	2	no	—
208	C₂×C₄×C₅	C₂²⋊D₅	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂²⋊D₅	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂²⋊D₅	1	1	yes	characteristic
211	C₂×C₄×C₅	C₅×D₄	1	1	yes	characteristic
212	C₂×C₄×C₅	C₅×D₄	1	1	yes	characteristic
213	C₂×C₄×C₅	C₅×D₄	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
220	C₂²⋊D₅	—	2	2	no	—
221	C₂²⋊D₅	—	2	2	no	—
222	C₂×Dic₅	—	2	1	no	—
223	D₂₀	—	2	1	no	—
224	D₂₀	C₂³×C₅	1	2	yes	—
225	C₄×D₅	—	2	2	no	—
226	C₄×D₅	—	2	2	no	—
227	Dic₁₀	—	2	1	no	—
228	Dic₁₀	C₂³×C₅	1	2	yes	—
229	C₅×C₈	—	5	4	no	—
230	#168	C₂³×C₅	1	4	yes	—
231	C₂×#41	—	5	1	no	—
232	C₂×#41	C₅×D₅	1	1	yes	characteristic, complemented
233	#137	—	5	2	no	—
234	#137	—	5	2	no	—
235	AGL(1,ℤ/8)	—	5	2	no	—
236	AGL(1,ℤ/8)	—	5	2	no	—
237	#135	—	5	4	no	—
238	C₂×M₁₆	—	5	1	no	—
239	C₅²	#575	1	1	yes	characteristic, complemented, Sylow
240	C₂²×C₅	—	2	8	no	—
241	C₂²×C₅	—	2	2	no	—
242	C₂²×C₅	—	2	2	no	—
243	C₂²×C₅	—	2	2	no	—
244	C₂²×C₅	—	2	2	no	—
245	C₂²×C₅	—	2	2	no	—
246	C₂²×C₅	—	4	1	no	—
247	C₂²×C₅	—	4	1	no	—
248	C₂²×C₅	—	4	4	no	—
249	C₂²×C₅	—	4	8	no	—
250	C₂²×C₅	—	4	2	no	—
251	C₂²×C₅	—	4	2	no	—
252	C₂²×C₅	—	10	2	no	—
253	C₂²×C₅	—	20	2	no	—
254	C₂²×C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
255	C₂²×C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
256	C₂²×C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
257	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
258	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
259	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
260	C₂×D₅	—	2	2	no	—
261	C₂×D₅	—	4	2	no	—
262	C₄×C₅	—	2	8	no	—
263	C₄×C₅	—	2	2	no	—
264	C₄×C₅	—	2	2	no	—
265	C₄×C₅	—	2	2	no	—
266	C₄×C₅	—	2	2	no	—
267	C₄×C₅	—	2	2	no	—
268	C₄×C₅	—	2	2	no	—
269	C₄×C₅	—	10	2	no	—
270	C₄×C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
271	C₄×C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
272	C₄×C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
273	C₄×C₅	C₂×C₅×D₄	1	1	yes	characteristic
274	C₄×C₅	C₂×C₅×D₄	1	1	yes	characteristic
275	C₄×C₅	C₂×C₅×D₄	1	1	yes	characteristic
276	C₄×C₅	C₂³×D₅	1	1	yes	characteristic
277	C₄×C₅	C₂⁴×C₅	1	1	yes	characteristic
278	Dic₅	—	2	2	no	—
279	#41	—	2	1	no	—
280	#41	—	2	1	no	—
281	#41	—	5	2	no	—
282	#41	—	5	2	no	—
283	#41	—	10	1	no	—
284	#41	—	10	1	no	—
285	#41	C₂×C₅×D₅	1	2	yes	—
286	#41	C₂×C₅×D₅	1	2	yes	complemented
287	C₂×Q₈	—	5	1	no	—
288	C₂×Q₈	C₂×C₅×D₅	1	1	yes	characteristic, complemented
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	5	1	no	—
291	C₂×D₄	—	10	1	no	—
292	C₂×D₄	C₂×C₅×D₅	1	1	yes	characteristic, complemented
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	10	1	no	—
295	C₂²×C₄	C₂×C₅×D₅	1	1	yes	characteristic
296	Q₁₆	—	5	4	no	—
297	SD₁₆	—	5	4	no	—
298	SD₁₆	—	5	4	no	—
299	D₈	—	5	4	no	—
300	M₁₆	—	5	2	no	—
301	M₁₆	—	5	2	no	—
302	C₂×C₈	—	5	2	no	—
303	C₂×C₅	—	2	4	no	—
304	C₂×C₅	—	2	1	no	—
305	C₂×C₅	—	2	1	no	—
306	C₂×C₅	—	2	1	no	—
307	C₂×C₅	—	2	1	no	—
308	C₂×C₅	—	2	1	no	—
309	C₂×C₅	—	2	1	no	—
310	C₂×C₅	—	2	2	no	—
311	C₂×C₅	—	4	2	no	—
312	C₂×C₅	—	4	2	no	—
313	C₂×C₅	—	4	8	no	—
314	C₂×C₅	—	4	2	no	—
315	C₂×C₅	—	4	2	no	—
316	C₂×C₅	—	20	2	no	—
317	C₂×C₅	C₂²×C₂²⋊D₅	1	1	yes	characteristic
318	C₂×C₅	C₂²×C₅×D₄	1	1	yes	characteristic
319	D₅	—	4	2	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	10	1	no	—
322	C₂³	C₅×C₂²⋊D₅	1	1	yes	characteristic
323	Q₈	—	2	1	no	—
324	Q₈	—	5	2	no	—
325	Q₈	—	10	1	no	—
326	Q₈	C₂²×C₅×D₅	1	2	yes	—
327	D₄	—	2	2	no	—
328	D₄	—	2	2	no	—
329	D₄	—	2	1	no	—
330	D₄	—	5	2	no	—
331	D₄	—	10	2	no	—
332	D₄	—	10	2	no	—
333	D₄	—	10	1	no	—
334	D₄	C₂²×C₅×D₅	1	2	yes	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	10	1	no	—
339	C₂×C₄	—	10	2	no	—
340	C₂×C₄	—	10	2	no	—
341	C₂×C₄	C₅×C₂²⋊D₅	1	1	yes	characteristic
342	C₂×C₄	C₅×C₂²⋊D₅	1	1	yes	characteristic
343	C₂×C₄	C₅×C₂²⋊D₅	1	1	yes	characteristic
344	C₂×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
345	C₂×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
346	C₂×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
347	C₈	—	5	4	no	—
348	C₅	—	2	2	no	—
349	C₅	#66156	1	1	yes	characteristic, direct product factor
350	C₅	C₅×#575	1	1	yes	characteristic, complemented
351	C₂²	—	2	2	no	—
352	C₂²	—	4	1	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	10	2	no	—
355	C₂²	—	20	2	no	—
356	C₂²	C₂×C₅×C₂²⋊D₅	1	1	yes	characteristic
357	C₂²	C₂×C₅×C₂²⋊D₅	1	1	yes	characteristic
358	C₂²	C₂×C₅×C₂²⋊D₅	1	1	yes	characteristic
359	C₄	—	2	2	no	—
360	C₄	—	10	2	no	—
361	C₄	C₂×C₅×C₂²⋊D₅	1	1	yes	characteristic
362	C₄	C₂×C₅×C₂²⋊D₅	1	1	yes	characteristic
363	C₄	C₂×C₅×C₂²⋊D₅	1	1	yes	characteristic
364	C₄	C₂³×C₅×D₅	1	1	yes	characteristic
365	C₂	—	2	1	no	—
366	C₂	—	2	1	no	—
367	C₂	—	2	1	no	—
368	C₂	—	4	2	no	—
369	C₂	—	20	2	no	—
370	C₂	C₂²×C₅×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	C₂×C₂²⋊D₅
commutator, cosocle	C₄×C₅	C₂⁴×C₅
Frattini	C₄	C₂³×C₅×D₅
Fitting	C₂×C₅²×#41	C₂
socle	C₂×C₅²	C₂²×D₄
hypercenter	C₂×C₅×#41	D₅
hypocenter	C₅	C₅×#575
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₅²×#41	C₂	semidirect
2. C₂×C₅×#709	C₂	semidirect
3. C₅×#4097	C₂	semidirect
4. C₅×#4096	C₂	semidirect
5. C₅×#4095	C₂	semidirect
6. C₅×#4088	C₂	semidirect
7. C₅×#4078	C₂	semidirect
8. C₂×C₅×#681	C₂	semidirect
12. C₅²×#41	C₂²	semidirect
13. C₂×C₅²×Q₈	C₂²	semidirect
15. C₂×C₅²×D₄	C₂²	semidirect
22. C₅×#709	C₂²	semidirect
23. C₂×C₅×D₂₀	C₂²	semidirect
25. C₂×C₅×Dic₁₀	C₂²	semidirect
26. C₅×#689	C₂²	semidirect
27. C₅×#688	C₂²	semidirect
28. C₅×#687	C₂²	semidirect
29. C₅×#686	C₂²	semidirect
30. C₅×#681	C₂²	semidirect
31. C₅×#681	C₂²	semidirect
32. C₂×C₅×#168	C₂²	semidirect
34. #66156	C₅	direct (N × H)
65. C₂×C₅×#41	D₅	semidirect
66. C₂×C₅×#41	C₂×C₅	semidirect
67. C₂×#709	C₂×C₅	semidirect
74. #4097	C₂×C₅	semidirect
75. #4096	C₂×C₅	semidirect
76. #4095	C₂×C₅	semidirect
77. #4088	C₂×C₅	semidirect
78. #4078	C₂×C₅	semidirect
79. C₂×#681	C₂×C₅	semidirect
107. C₅×#41	C₂×D₅	semidirect
109. C₅×#41	C₂²×C₅	semidirect
112. C₂×C₅×Q₈	C₂×D₅	semidirect
113. C₂×C₅×Q₈	C₂²×C₅	semidirect
120. C₂×C₅×D₄	C₂×D₅	semidirect
121. C₂×C₅×D₄	C₂²×C₅	semidirect
133. #709	C₂²×C₅	semidirect
134. C₂×D₂₀	C₂²×C₅	semidirect
136. C₂×Dic₁₀	C₂²×C₅	semidirect
144. #689	C₂²×C₅	semidirect
145. #688	C₂²×C₅	semidirect
146. #687	C₂²×C₅	semidirect
147. #686	C₂²×C₅	semidirect
148. #681	C₂²×C₅	semidirect
149. #681	C₂²×C₅	semidirect
150. C₂×#168	C₂²×C₅	semidirect
232. C₂×#41	C₅×D₅	semidirect
239. C₅²	#575	semidirect
286. #41	C₂×C₅×D₅	semidirect
288. C₂×Q₈	C₂×C₅×D₅	semidirect
292. C₂×D₄	C₂×C₅×D₅	semidirect
349. C₅	#66156	direct (N × H)
350. C₅	C₅×#575	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅²×#41	2
C₂×C₅×#709	2
C₅×#4097	2
C₅×#4096	2
C₅×#4095	2
C₅×#4088	2
C₅×#4078	2
C₂×C₅×#681	2
C₅×#575	5
#66156	5

Subgroups — C5×#66156 #13106979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#66156 #13106979