Subgroups — C₅×#60639 #11983359

Order 1280.

3314 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#575	C₂	1	4	yes	maximal, complemented
2	C₂×C₅×#532	C₂	1	2	yes	maximal, complemented
3	C₅×#3153	C₂	1	8	yes	maximal, complemented
4	C₅×#3152	C₂	1	4	yes	maximal, complemented
5	C₅×#3151	C₂	1	4	yes	maximal, complemented
6	C₅×#3150	C₂	1	4	yes	maximal, complemented
7	C₅×#3147	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₅×#41	C₂²	1	4	yes	—
10	C₅×#575	—	2	32	no	—
11	C₂×C₅×#137	C₂²	1	16	yes	complemented
12	C₂×C₅×AGL(1,ℤ/8)	C₂²	1	16	yes	complemented
13	C₂×C₅×#135	C₂²	1	16	yes	complemented
14	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
15	C₅×#532	—	2	4	no	—
16	C₅×#532	—	2	4	no	—
17	C₅×#532	C₂²	1	4	yes	—
18	C₅×#532	C₂²	1	4	yes	—
19	C₅×#532	C₂²	1	4	yes	complemented
20	C₅×#532	C₂²	1	4	yes	complemented
21	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
22	C₂×C₅×#127	C₂²	1	2	yes	complemented
23	C₂×C₅×#124	C₂²	1	4	yes	complemented
24	C₂×C₅×#121	—	2	4	no	—
25	C₂×C₄×C₅×D₄	—	2	4	no	—
26	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
27	C₅×#497	C₂²	1	16	yes	complemented
28	C₅×#496	C₂²	1	16	yes	complemented
29	C₅×#495	C₂²	1	16	yes	complemented
30	C₅×#494	C₂²	1	4	yes	complemented
31	C₅×#493	C₂²	1	4	yes	complemented
32	C₅×#492	C₂²	1	8	yes	complemented
33	C₄×C₅×M₁₆	C₂²	1	4	yes	complemented
34	C₄×C₅×M₁₆	C₂²	1	4	yes	complemented
35	C₂×C₅×#97	C₂²	1	2	yes	complemented
36	C₂×C₄×C₅×C₈	C₂²	1	2	yes	complemented
37	#60639	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂×C₅×#41	—	2	4	no	—
39	C₂×C₅×#41	—	2	4	no	—
40	C₂×C₅×#41	—	2	32	no	—
41	C₂×C₅×#41	C₂³	1	8	yes	—
42	C₂×C₅×#41	C₂³	1	8	yes	—
43	C₂²×C₅×Q₈	C₂³	1	4	yes	—
44	C₂²×C₅×D₄	—	2	4	no	—
45	C₂²×C₅×D₄	—	2	4	no	—
46	C₂²×C₅×D₄	C₂³	1	4	yes	—
47	C₂³×C₄×C₅	—	2	4	no	—
48	C₂³×C₄×C₅	D₄	1	2	yes	—
49	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₅×#137	—	2	64	no	—
51	C₅×AGL(1,ℤ/8)	—	2	64	no	—
52	C₅×#135	—	2	64	no	—
53	C₂×C₅×Q₁₆	C₂³	1	16	yes	—
54	C₂×C₅×SD₁₆	C₂³	1	32	yes	—
55	C₂×C₅×D₈	C₂³	1	16	yes	—
56	C₂×C₅×M₁₆	D₄	1	16	yes	complemented
57	C₂×C₅×M₁₆	C₂³	1	8	yes	—
58	C₂²×C₅×C₈	C₂³	1	4	yes	—
59	C₅×C₄⋊Q₈	—	2	4	no	—
60	C₅×C₄⋊Q₈	C₂³	1	4	yes	—
61	C₅×C₄⋊Q₈	C₂³	1	4	yes	—
62	C₅×#127	—	2	4	no	—
63	C₅×#127	C₂³	1	4	yes	—
64	C₅×#127	C₂³	1	4	yes	—
65	C₅×#124	—	2	8	no	—
66	C₅×#124	C₂³	1	8	yes	—
67	C₅×#124	C₂³	1	8	yes	—
68	C₅×#121	—	2	8	no	—
69	C₅×#121	—	2	8	no	—
70	C₅×#121	—	2	8	no	—
71	C₅×#121	—	2	8	no	—
72	C₄×C₅×D₄	—	2	8	no	—
73	C₄×C₅×D₄	—	2	8	no	—
74	C₄×C₅×D₄	—	2	8	no	—
75	C₄×C₅×D₄	—	2	8	no	—
76	C₂×C₅×C₄⋊C₄	—	2	4	no	—
77	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
78	C₂×C₄²×C₅	D₄	1	4	yes	—
79	C₂×C₄²×C₅	D₄	1	2	yes	—
80	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₅	C₂³	1	2	yes	—
83	C₂×C₄²×C₅	C₂³	1	2	yes	—
84	C₅×#97	C₂³	1	8	yes	—
85	C₄×C₅×C₈	C₂³	1	4	yes	—
86	C₄×C₅×C₈	C₂³	1	4	yes	—
87	C₂×#575	C₂×C₅	1	4	yes	complemented
88	C₂×#532	C₂×C₅	1	2	yes	complemented
89	#3153	C₂×C₅	1	8	yes	complemented
90	#3152	C₂×C₅	1	4	yes	complemented
91	#3151	C₂×C₅	1	4	yes	complemented
92	#3150	C₂×C₅	1	4	yes	complemented
93	#3147	C₂×C₅	1	4	yes	complemented
94	C₂×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂⁴×C₅	—	2	4	no	—
96	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
97	C₅×#41	—	2	32	no	—
98	C₅×#41	—	2	32	no	—
99	C₅×#41	—	4	16	no	—
100	C₅×#41	—	4	16	no	—
101	C₂×C₅×Q₈	—	2	4	no	—
102	C₂×C₅×Q₈	—	2	16	no	—
103	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
104	C₂×C₅×D₄	—	2	8	no	—
105	C₂×C₅×D₄	—	2	8	no	—
106	C₂×C₅×D₄	—	2	16	no	—
107	C₂×C₅×D₄	—	2	8	no	—
108	C₂×C₅×D₄	—	2	8	no	—
109	C₂×C₅×D₄	—	2	4	no	—
110	C₂×C₅×D₄	—	4	16	no	—
111	C₂×C₅×D₄	—	4	16	no	—
112	C₂×C₅×D₄	C₂⁴	1	8	yes	—
113	C₂²×C₄×C₅	—	2	4	no	—
114	C₂²×C₄×C₅	—	2	8	no	—
115	C₂²×C₄×C₅	—	2	8	no	—
116	C₂²×C₄×C₅	—	4	4	no	—
117	C₂²×C₄×C₅	—	4	16	no	—
118	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
121	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₅	C₂×D₄	1	8	yes	—
125	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
126	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
127	C₅×Q₁₆	—	2	32	no	—
128	C₅×SD₁₆	—	2	64	no	—
129	C₅×D₈	—	2	32	no	—
130	C₅×M₁₆	C₂×D₄	1	32	yes	complemented
131	C₂×C₅×C₈	C₂×D₄	1	16	yes	complemented
132	C₂×C₅×C₈	C₂⁴	1	8	yes	—
133	C₅×C₄⋊C₄	—	2	8	no	—
134	C₅×C₄⋊C₄	—	2	8	no	—
135	C₅×C₂²⋊C₄	—	2	16	no	—
136	C₅×C₂²⋊C₄	—	2	16	no	—
137	C₄²×C₅	C₂×D₄	1	4	yes	—
138	C₄²×C₅	C₂×D₄	1	4	yes	—
139	C₄²×C₅	C₂×D₄	1	2	yes	—
140	C₄²×C₅	C₂×D₄	1	2	yes	—
141	C₄²×C₅	C₂⁴	1	1	yes	characteristic
142	C₄²×C₅	C₂⁴	1	2	yes	—
143	C₄²×C₅	C₂⁴	1	1	yes	characteristic
144	C₂²×#41	C₂²×C₅	1	4	yes	—
145	#575	—	2	32	no	—
146	C₂×#137	C₂²×C₅	1	16	yes	complemented
147	C₂×AGL(1,ℤ/8)	C₂²×C₅	1	16	yes	complemented
148	C₂×#135	C₂²×C₅	1	16	yes	complemented
149	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
150	#532	—	2	4	no	—
151	#532	—	2	4	no	—
152	#532	C₂²×C₅	1	4	yes	—
153	#532	C₂²×C₅	1	4	yes	—
154	#532	C₂²×C₅	1	4	yes	complemented
155	#532	C₂²×C₅	1	4	yes	complemented
156	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
157	C₂×#127	C₂²×C₅	1	2	yes	complemented
158	C₂×#124	C₂²×C₅	1	4	yes	complemented
159	C₂×#121	—	2	4	no	—
160	C₂×C₄×D₄	—	2	4	no	—
161	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
162	#497	C₂²×C₅	1	16	yes	complemented
163	#496	C₂²×C₅	1	16	yes	complemented
164	#495	C₂²×C₅	1	16	yes	complemented
165	#494	C₂²×C₅	1	4	yes	complemented
166	#493	C₂²×C₅	1	4	yes	complemented
167	#492	C₂²×C₅	1	8	yes	complemented
168	C₄×M₁₆	C₂²×C₅	1	4	yes	complemented
169	C₄×M₁₆	C₂²×C₅	1	4	yes	complemented
170	C₂×#97	C₂²×C₅	1	2	yes	complemented
171	C₂×C₄×C₈	C₂²×C₅	1	2	yes	complemented
172	C₂³×C₅	—	2	8	no	—
173	C₂³×C₅	—	4	2	no	—
174	C₂³×C₅	—	4	16	no	—
175	C₂³×C₅	—	4	8	no	—
176	C₂³×C₅	#127	1	4	yes	—
177	C₂³×C₅	C₂²×D₄	1	2	yes	—
178	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
179	C₅×Q₈	—	2	16	no	—
180	C₅×Q₈	—	4	8	no	—
181	C₅×D₄	—	2	16	no	—
182	C₅×D₄	—	4	16	no	—
183	C₅×D₄	—	4	16	no	—
184	C₅×D₄	—	4	16	no	—
185	C₅×D₄	—	4	8	no	—
186	C₅×D₄	—	4	16	no	—
187	C₂×C₄×C₅	—	2	4	no	—
188	C₂×C₄×C₅	—	2	8	no	—
189	C₂×C₄×C₅	—	2	8	no	—
190	C₂×C₄×C₅	—	4	4	no	—
191	C₂×C₄×C₅	—	4	2	no	—
192	C₂×C₄×C₅	—	4	8	no	—
193	C₂×C₄×C₅	—	4	16	no	—
194	C₂×C₄×C₅	—	4	16	no	—
195	C₂×C₄×C₅	#127	1	8	yes	—
196	C₂×C₄×C₅	#127	1	4	yes	—
197	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
199	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
201	C₂×C₄×C₅	C₂²×D₄	1	8	yes	—
202	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
203	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
205	C₅×C₈	C₂²×D₄	1	16	yes	—
206	C₂×#41	—	2	4	no	—
207	C₂×#41	—	2	4	no	—
208	C₂×#41	—	2	32	no	—
209	C₂×#41	C₂³×C₅	1	8	yes	—
210	C₂×#41	C₂³×C₅	1	8	yes	—
211	C₂²×Q₈	C₂³×C₅	1	4	yes	—
212	C₂²×D₄	—	2	4	no	—
213	C₂²×D₄	—	2	4	no	—
214	C₂²×D₄	C₂³×C₅	1	4	yes	—
215	C₂³×C₄	—	2	4	no	—
216	C₂³×C₄	C₅×D₄	1	2	yes	—
217	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
218	#137	—	2	64	no	—
219	AGL(1,ℤ/8)	—	2	64	no	—
220	#135	—	2	64	no	—
221	C₂×Q₁₆	C₂³×C₅	1	16	yes	—
222	C₂×SD₁₆	C₂³×C₅	1	32	yes	—
223	C₂×D₈	C₂³×C₅	1	16	yes	—
224	C₂×M₁₆	C₅×D₄	1	16	yes	complemented
225	C₂×M₁₆	C₂³×C₅	1	8	yes	—
226	C₂²×C₈	C₂³×C₅	1	4	yes	—
227	C₄⋊Q₈	—	2	4	no	—
228	C₄⋊Q₈	C₂³×C₅	1	4	yes	—
229	C₄⋊Q₈	C₂³×C₅	1	4	yes	—
230	#127	—	2	4	no	—
231	#127	C₂³×C₅	1	4	yes	—
232	#127	C₂³×C₅	1	4	yes	—
233	#124	—	2	8	no	—
234	#124	C₂³×C₅	1	8	yes	—
235	#124	C₂³×C₅	1	8	yes	—
236	#121	—	2	8	no	—
237	#121	—	2	8	no	—
238	#121	—	2	8	no	—
239	#121	—	2	8	no	—
240	C₄×D₄	—	2	8	no	—
241	C₄×D₄	—	2	8	no	—
242	C₄×D₄	—	2	8	no	—
243	C₄×D₄	—	2	8	no	—
244	C₂×C₄⋊C₄	—	2	4	no	—
245	C₂×C₂²⋊C₄	—	2	8	no	—
246	C₂×C₄²	C₅×D₄	1	4	yes	—
247	C₂×C₄²	C₅×D₄	1	2	yes	—
248	C₂×C₄²	C₂³×C₅	1	2	yes	—
249	C₂×C₄²	C₂³×C₅	1	2	yes	—
250	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
252	#97	C₂³×C₅	1	8	yes	—
253	C₄×C₈	C₂³×C₅	1	4	yes	—
254	C₄×C₈	C₂³×C₅	1	4	yes	—
255	C₂²×C₅	—	2	4	no	—
256	C₂²×C₅	—	2	2	no	—
257	C₂²×C₅	—	4	4	no	—
258	C₂²×C₅	—	4	8	no	—
259	C₂²×C₅	—	4	16	no	—
260	C₂²×C₅	—	8	16	no	—
261	C₂²×C₅	C₂×#127	1	4	yes	—
262	C₂²×C₅	C₂×#127	1	2	yes	—
263	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
264	C₄×C₅	—	2	2	no	—
265	C₄×C₅	—	2	4	no	—
266	C₄×C₅	—	4	8	no	—
267	C₄×C₅	C₂×#127	1	2	yes	—
268	C₄×C₅	C₂×#127	1	4	yes	—
269	C₄×C₅	#575	1	4	yes	complemented
270	C₄×C₅	C₂³×D₄	1	2	yes	—
271	C₂⁴	—	2	4	no	—
272	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
273	#41	—	2	32	no	—
274	#41	—	2	32	no	—
275	#41	—	4	16	no	—
276	#41	—	4	16	no	—
277	C₂×Q₈	—	2	4	no	—
278	C₂×Q₈	—	2	16	no	—
279	C₂×Q₈	C₂⁴×C₅	1	8	yes	—
280	C₂×D₄	—	2	8	no	—
281	C₂×D₄	—	2	8	no	—
282	C₂×D₄	—	2	16	no	—
283	C₂×D₄	—	2	8	no	—
284	C₂×D₄	—	2	8	no	—
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	—	4	16	no	—
287	C₂×D₄	—	4	16	no	—
288	C₂×D₄	C₂⁴×C₅	1	8	yes	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	—	2	8	no	—
292	C₂²×C₄	—	4	4	no	—
293	C₂²×C₄	—	4	16	no	—
294	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
295	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
296	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
297	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
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	8	yes	—
301	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
302	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
303	Q₁₆	—	2	32	no	—
304	SD₁₆	—	2	64	no	—
305	D₈	—	2	32	no	—
306	M₁₆	C₂×C₅×D₄	1	32	yes	complemented
307	C₂×C₈	C₂×C₅×D₄	1	16	yes	complemented
308	C₂×C₈	C₂⁴×C₅	1	8	yes	—
309	C₄⋊C₄	—	2	8	no	—
310	C₄⋊C₄	—	2	8	no	—
311	C₂²⋊C₄	—	2	16	no	—
312	C₂²⋊C₄	—	2	16	no	—
313	C₄²	C₂×C₅×D₄	1	2	yes	—
314	C₄²	C₂×C₅×D₄	1	2	yes	—
315	C₄²	C₂×C₅×D₄	1	4	yes	—
316	C₄²	C₂×C₅×D₄	1	4	yes	—
317	C₄²	C₂⁴×C₅	1	1	yes	characteristic
318	C₄²	C₂⁴×C₅	1	1	yes	characteristic
319	C₄²	C₂⁴×C₅	1	2	yes	—
320	C₂×C₅	—	2	4	no	—
321	C₂×C₅	—	2	2	no	—
322	C₂×C₅	—	8	8	no	—
323	C₂×C₅	C₂²×#127	1	1	yes	characteristic
324	C₂×C₅	C₂×#575	1	2	yes	—
325	C₂³	—	2	8	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	16	no	—
328	C₂³	—	4	8	no	—
329	C₂³	C₅×#127	1	4	yes	—
330	C₂³	C₂²×C₅×D₄	1	2	yes	—
331	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
332	Q₈	—	2	16	no	—
333	Q₈	—	4	8	no	—
334	D₄	—	2	16	no	—
335	D₄	—	4	16	no	—
336	D₄	—	4	16	no	—
337	D₄	—	4	16	no	—
338	D₄	—	4	8	no	—
339	D₄	—	4	16	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	8	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	8	no	—
346	C₂×C₄	—	4	16	no	—
347	C₂×C₄	—	4	16	no	—
348	C₂×C₄	C₅×#127	1	8	yes	—
349	C₂×C₄	C₅×#127	1	4	yes	—
350	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
351	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
352	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
353	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
354	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
355	C₂×C₄	C₂²×C₅×D₄	1	8	yes	—
356	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
357	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
358	C₈	C₂²×C₅×D₄	1	16	yes	—
359	C₅	#60639	1	1	yes	characteristic, direct product factor, Sylow
360	C₂²	—	2	4	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	4	4	no	—
363	C₂²	—	4	8	no	—
364	C₂²	—	4	16	no	—
365	C₂²	—	8	16	no	—
366	C₂²	C₂×C₅×#127	1	4	yes	—
367	C₂²	C₂×C₅×#127	1	2	yes	—
368	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
369	C₄	—	2	4	no	—
370	C₄	—	2	2	no	—
371	C₄	—	4	8	no	—
372	C₄	C₂×C₅×#127	1	2	yes	—
373	C₄	C₂×C₅×#127	1	4	yes	—
374	C₄	C₅×#575	1	4	yes	complemented
375	C₄	C₂³×C₅×D₄	1	2	yes	—
376	C₂	—	2	4	no	—
377	C₂	—	2	2	no	—
378	C₂	—	8	8	no	—
379	C₂	C₂²×C₅×#127	1	1	yes	characteristic
380	C₂	C₂×C₅×#575	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
socle	C₂²×C₅	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#575	C₂	semidirect
2. C₂×C₅×#532	C₂	semidirect
3. C₅×#3153	C₂	semidirect
4. C₅×#3152	C₂	semidirect
5. C₅×#3151	C₂	semidirect
6. C₅×#3150	C₂	semidirect
7. C₅×#3147	C₂	semidirect
8. C₂×C₄×C₅×M₁₆	C₂	semidirect
11. C₂×C₅×#137	C₂²	semidirect
12. C₂×C₅×AGL(1,ℤ/8)	C₂²	semidirect
13. C₂×C₅×#135	C₂²	semidirect
19. C₅×#532	C₂²	semidirect
20. C₅×#532	C₂²	semidirect
21. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
22. C₂×C₅×#127	C₂²	semidirect
23. C₂×C₅×#124	C₂²	semidirect
27. C₅×#497	C₂²	semidirect
28. C₅×#496	C₂²	semidirect
29. C₅×#495	C₂²	semidirect
30. C₅×#494	C₂²	semidirect
31. C₅×#493	C₂²	semidirect
32. C₅×#492	C₂²	semidirect
33. C₄×C₅×M₁₆	C₂²	semidirect
34. C₄×C₅×M₁₆	C₂²	semidirect
35. C₂×C₅×#97	C₂²	semidirect
36. C₂×C₄×C₅×C₈	C₂²	semidirect
37. #60639	C₅	direct (N × H)
56. C₂×C₅×M₁₆	D₄	semidirect
87. C₂×#575	C₂×C₅	semidirect
88. C₂×#532	C₂×C₅	semidirect
89. #3153	C₂×C₅	semidirect
90. #3152	C₂×C₅	semidirect
91. #3151	C₂×C₅	semidirect
92. #3150	C₂×C₅	semidirect
93. #3147	C₂×C₅	semidirect
94. C₂×C₄×M₁₆	C₂×C₅	semidirect
130. C₅×M₁₆	C₂×D₄	semidirect
131. C₂×C₅×C₈	C₂×D₄	semidirect
146. C₂×#137	C₂²×C₅	semidirect
147. C₂×AGL(1,ℤ/8)	C₂²×C₅	semidirect
148. C₂×#135	C₂²×C₅	semidirect
154. #532	C₂²×C₅	semidirect
155. #532	C₂²×C₅	semidirect
156. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
157. C₂×#127	C₂²×C₅	semidirect
158. C₂×#124	C₂²×C₅	semidirect
162. #497	C₂²×C₅	semidirect
163. #496	C₂²×C₅	semidirect
164. #495	C₂²×C₅	semidirect
165. #494	C₂²×C₅	semidirect
166. #493	C₂²×C₅	semidirect
167. #492	C₂²×C₅	semidirect
168. C₄×M₁₆	C₂²×C₅	semidirect
169. C₄×M₁₆	C₂²×C₅	semidirect
170. C₂×#97	C₂²×C₅	semidirect
171. C₂×C₄×C₈	C₂²×C₅	semidirect
224. C₂×M₁₆	C₅×D₄	semidirect
269. C₄×C₅	#575	semidirect
306. M₁₆	C₂×C₅×D₄	semidirect
307. C₂×C₈	C₂×C₅×D₄	semidirect
359. C₅	#60639	direct (N × H)
374. C₄	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×C₅×#575	2
C₂×C₅×#532	2
C₅×#3153	2
C₅×#3152	2
C₅×#3151	2
C₅×#3150	2
C₅×#3147	2
C₂×C₄×C₅×M₁₆	2
#60639	5

Subgroups — C5×#60639 #11983359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60639 #11983359