Subgroups — C₅×#5775 #11756160

Order 960.

516 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#1010	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#1004	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#950	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#214	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#915	C₂	1	2	yes	maximal, complemented
7	C₅×D₃×SD₁₆	C₂	1	2	yes	maximal, complemented
8	C₅×#912	C₂	1	2	yes	maximal, complemented
9	C₅×#911	C₂	1	2	yes	maximal, complemented
10	C₅×#909	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#907	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#577	—	3	1	no	maximal, Hall
13	C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₅×#67	—	2	2	no	—
16	C₅×D₃×Q₈	C₂²	1	2	yes	complemented
17	C₅×#237	—	2	2	no	—
18	C₅×#237	—	2	1	no	—
19	C₅×#237	C₂²	1	2	yes	—
20	C₅×#237	C₂²	1	2	yes	complemented
21	C₅×D₃×D₄	—	2	1	no	—
22	C₅×D₃×D₄	C₂²	1	2	yes	—
23	C₅×#235	—	2	1	no	—
24	C₅×#235	C₂²	1	1	yes	characteristic
25	C₅×#235	C₂²	1	1	yes	characteristic
26	C₂×C₅×Dic₆	—	2	1	no	—
27	C₂×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
29	C₃×C₅×D₈	C₂²	1	2	yes	complemented
30	C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₅×#216	C₂²	1	1	yes	characteristic, complemented
32	C₅×#215	C₂²	1	1	yes	characteristic, complemented
33	C₅×#214	C₂²	1	2	yes	complemented
34	C₅×#214	C₂²	1	1	yes	characteristic, complemented
35	C₅×#214	C₂²	1	2	yes	complemented
36	C₅×#213	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	C₅×Dic₁₂	C₂²	1	2	yes	complemented
39	C₅×#204	C₂²	1	2	yes	complemented
40	C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
41	C₅×D₃×C₈	C₂²	1	2	yes	complemented
42	#5775	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×2₋¹⁺⁴	—	3	1	no	—
44	C₅×H(5,𝔽₂)	—	3	1	no	—
45	C₅×#137	—	3	2	no	—
46	C₅×#137	—	3	1	no	—
47	C₅×AGL(1,ℤ/8)	—	3	2	no	—
48	C₅×AGL(1,ℤ/8)	D₃	1	1	yes	characteristic, complemented
49	C₅×#135	—	3	1	no	—
50	C₅×#135	—	3	2	no	—
51	C₂×C₅×SD₁₆	—	3	1	no	—
52	C₂×C₅×SD₁₆	—	3	2	no	—
53	C₅×#131	—	3	1	no	—
54	C₂³×C₃×C₅	—	2	1	no	—
55	C₂²×C₅×D₃	—	2	2	no	—
56	C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
57	C₃×C₅×D₄	—	2	1	no	—
58	C₃×C₅×D₄	—	2	1	no	—
59	C₃×C₅×D₄	C₂³	1	1	yes	characteristic
60	C₃×C₅×D₄	C₂³	1	2	yes	—
61	C₂×C₃×C₄×C₅	—	2	1	no	—
62	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₅×#67	—	2	1	no	—
64	C₅×#67	—	2	2	no	—
65	C₅×#67	—	2	2	no	—
66	C₅×#67	—	2	2	no	—
67	C₅×#67	D₄	1	2	yes	—
68	C₂×C₅×Dic₃	—	2	1	no	—
69	C₂×C₅×Dic₃	—	2	2	no	—
70	C₂×C₅×Dic₃	—	2	2	no	—
71	C₅×D₁₂	D₄	1	1	yes	characteristic
72	C₅×D₁₂	C₂³	1	1	yes	characteristic
73	C₄×C₅×D₃	—	2	2	no	—
74	C₄×C₅×D₃	—	2	1	no	—
75	C₄×C₅×D₃	C₂³	1	2	yes	—
76	C₅×Dic₆	—	2	1	no	—
77	C₅×Dic₆	—	2	2	no	—
78	C₅×Dic₆	D₄	1	1	yes	characteristic
79	C₅×Dic₆	C₂³	1	2	yes	—
80	C₅×Dic₆	C₂³	1	1	yes	characteristic
81	C₃×C₅×C₈	C₂³	1	2	yes	—
82	C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
83	C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
84	#1010	C₂×C₅	1	1	yes	characteristic, complemented
85	#1004	C₂×C₅	1	1	yes	characteristic, complemented
86	C₃×AGL(1,ℤ/8)	C₂×C₅	1	1	yes	characteristic, complemented
87	#950	C₂×C₅	1	1	yes	characteristic, complemented
88	C₂×#214	C₂×C₅	1	1	yes	characteristic, complemented
89	#915	C₂×C₅	1	2	yes	complemented
90	D₃×SD₁₆	C₂×C₅	1	2	yes	complemented
91	#912	C₂×C₅	1	2	yes	complemented
92	#911	C₂×C₅	1	2	yes	complemented
93	#909	C₂×C₅	1	1	yes	characteristic, complemented
94	#907	C₂×C₅	1	1	yes	characteristic, complemented
95	C₅×#41	—	3	1	no	—
96	C₅×#41	—	3	2	no	—
97	C₅×#41	—	3	2	no	—
98	C₅×#41	—	3	1	no	—
99	C₅×#41	—	6	1	no	—
100	C₅×#41	—	6	2	no	—
101	C₅×#41	—	6	1	no	—
102	C₅×#41	C₂×D₃	1	1	yes	characteristic, complemented
103	C₂×C₅×Q₈	—	3	2	no	—
104	C₂×C₅×Q₈	—	3	1	no	—
105	C₂×C₅×Q₈	—	6	1	no	—
106	C₂×C₅×D₄	—	3	2	no	—
107	C₂×C₅×D₄	—	6	1	no	—
108	C₂×C₅×D₄	—	6	2	no	—
109	C₂×C₅×D₄	C₂×D₃	1	1	yes	characteristic
110	C₅×Q₁₆	—	3	1	no	—
111	C₅×Q₁₆	—	3	2	no	—
112	C₅×SD₁₆	—	3	1	no	—
113	C₅×SD₁₆	—	3	2	no	—
114	C₅×SD₁₆	—	3	2	no	—
115	C₅×SD₁₆	—	3	1	no	—
116	C₅×SD₁₆	—	3	2	no	—
117	C₅×SD₁₆	C₂×D₃	1	2	yes	complemented
118	C₅×D₈	—	3	1	no	—
119	C₅×D₈	C₂×D₃	1	2	yes	complemented
120	C₅×M₁₆	—	3	2	no	—
121	C₅×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
122	C₂×C₅×C₈	—	3	1	no	—
123	C₂×C₅×C₈	—	3	2	no	—
124	#577	—	3	1	no	Sylow
125	C₂²×C₃×C₅	—	2	1	no	—
126	C₂²×C₃×C₅	—	2	2	no	—
127	C₂²×C₃×C₅	—	8	1	no	—
128	C₂²×C₃×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂×C₅×D₃	—	2	1	no	—
130	C₂×C₅×D₃	—	8	2	no	—
131	C₂×C₅×D₃	C₂×D₄	1	2	yes	—
132	C₃×C₄×C₅	—	2	1	no	—
133	C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
135	C₅×Dic₃	—	2	2	no	—
136	C₅×Dic₃	—	2	1	no	—
137	C₅×Dic₃	C₂×D₄	1	2	yes	—
138	C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
139	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
140	C₂×#67	—	2	2	no	—
141	D₃×Q₈	C₂²×C₅	1	2	yes	complemented
142	#237	—	2	2	no	—
143	#237	—	2	1	no	—
144	#237	C₂²×C₅	1	2	yes	—
145	#237	C₂²×C₅	1	2	yes	complemented
146	D₃×D₄	—	2	1	no	—
147	D₃×D₄	C₂²×C₅	1	2	yes	—
148	#235	—	2	1	no	—
149	#235	C₂²×C₅	1	1	yes	characteristic
150	#235	C₂²×C₅	1	1	yes	characteristic
151	C₂×Dic₆	—	2	1	no	—
152	C₂×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
153	C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
154	C₃×D₈	C₂²×C₅	1	2	yes	complemented
155	C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
156	#216	C₂²×C₅	1	1	yes	characteristic, complemented
157	#215	C₂²×C₅	1	1	yes	characteristic, complemented
158	#214	C₂²×C₅	1	2	yes	complemented
159	#214	C₂²×C₅	1	1	yes	characteristic, complemented
160	#214	C₂²×C₅	1	2	yes	complemented
161	#213	C₂²×C₅	1	1	yes	characteristic, complemented
162	C₂×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
163	Dic₁₂	C₂²×C₅	1	2	yes	complemented
164	#204	C₂²×C₅	1	2	yes	complemented
165	ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	complemented
166	D₃×C₈	C₂²×C₅	1	2	yes	complemented
167	C₂³×C₅	—	2	1	no	—
168	C₂³×C₅	—	6	2	no	—
169	C₅×Q₈	—	3	1	no	—
170	C₅×Q₈	—	3	2	no	—
171	C₅×Q₈	—	3	1	no	—
172	C₅×Q₈	—	6	2	no	—
173	C₅×Q₈	—	6	1	no	—
174	C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
175	C₅×D₄	—	2	1	no	—
176	C₅×D₄	—	2	1	no	—
177	C₅×D₄	—	3	2	no	—
178	C₅×D₄	—	3	1	no	—
179	C₅×D₄	—	3	1	no	—
180	C₅×D₄	—	6	2	no	—
181	C₅×D₄	—	6	2	no	—
182	C₅×D₄	—	6	2	no	—
183	C₅×D₄	—	6	1	no	—
184	C₅×D₄	C₂²×D₃	1	1	yes	characteristic
185	C₅×D₄	C₂²×D₃	1	2	yes	—
186	C₂×C₄×C₅	—	2	1	no	—
187	C₂×C₄×C₅	—	3	2	no	—
188	C₂×C₄×C₅	—	6	2	no	—
189	C₂×C₄×C₅	—	6	2	no	—
190	C₂×C₄×C₅	—	6	2	no	—
191	C₂×C₄×C₅	—	6	1	no	—
192	C₂×C₄×C₅	—	6	1	no	—
193	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
194	C₅×C₈	—	3	1	no	—
195	C₅×C₈	—	3	1	no	—
196	C₅×C₈	C₂²×D₃	1	2	yes	—
197	2₋¹⁺⁴	—	3	1	no	—
198	H(5,𝔽₂)	—	3	1	no	—
199	#137	—	3	2	no	—
200	#137	—	3	1	no	—
201	AGL(1,ℤ/8)	—	3	2	no	—
202	AGL(1,ℤ/8)	C₅×D₃	1	1	yes	characteristic, complemented
203	#135	—	3	1	no	—
204	#135	—	3	2	no	—
205	C₂×SD₁₆	—	3	1	no	—
206	C₂×SD₁₆	—	3	2	no	—
207	#131	—	3	1	no	—
208	C₂×C₃×C₅	—	2	1	no	—
209	C₂×C₃×C₅	—	4	2	no	—
210	C₂×C₃×C₅	—	4	1	no	—
211	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
212	C₅×D₃	—	2	2	no	—
213	C₅×D₃	—	4	1	no	—
214	C₂³×C₃	—	2	1	no	—
215	C₂²×D₃	—	2	2	no	—
216	C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
217	C₃×D₄	—	2	1	no	—
218	C₃×D₄	—	2	1	no	—
219	C₃×D₄	C₂³×C₅	1	1	yes	characteristic
220	C₃×D₄	C₂³×C₅	1	2	yes	—
221	C₂×C₃×C₄	—	2	1	no	—
222	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
223	#67	—	2	1	no	—
224	#67	—	2	2	no	—
225	#67	—	2	2	no	—
226	#67	—	2	2	no	—
227	#67	C₅×D₄	1	2	yes	—
228	C₂×Dic₃	—	2	1	no	—
229	C₂×Dic₃	—	2	2	no	—
230	C₂×Dic₃	—	2	2	no	—
231	D₁₂	C₅×D₄	1	1	yes	characteristic
232	D₁₂	C₂³×C₅	1	1	yes	characteristic
233	C₄×D₃	—	2	2	no	—
234	C₄×D₃	—	2	1	no	—
235	C₄×D₃	C₂³×C₅	1	2	yes	—
236	Dic₆	—	2	1	no	—
237	Dic₆	—	2	2	no	—
238	Dic₆	C₅×D₄	1	1	yes	characteristic
239	Dic₆	C₂³×C₅	1	2	yes	—
240	Dic₆	C₂³×C₅	1	1	yes	characteristic
241	C₃×C₈	C₂³×C₅	1	2	yes	—
242	C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
243	C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
244	C₂²×C₅	—	2	1	no	—
245	C₂²×C₅	—	2	2	no	—
246	C₂²×C₅	—	3	2	no	—
247	C₂²×C₅	—	6	1	no	—
248	C₂²×C₅	—	8	1	no	—
249	C₂²×C₅	—	24	2	no	—
250	C₂²×C₅	D₃×D₄	1	1	yes	characteristic
251	C₄×C₅	—	2	1	no	—
252	C₄×C₅	—	3	2	no	—
253	C₄×C₅	—	6	1	no	—
254	C₄×C₅	—	6	2	no	—
255	C₄×C₅	D₃×D₄	1	1	yes	characteristic
256	C₄×C₅	C₂³×D₃	1	1	yes	characteristic
257	#41	—	3	1	no	—
258	#41	—	3	2	no	—
259	#41	—	3	2	no	—
260	#41	—	3	1	no	—
261	#41	—	6	1	no	—
262	#41	—	6	2	no	—
263	#41	—	6	1	no	—
264	#41	C₂×C₅×D₃	1	1	yes	characteristic, complemented
265	C₂×Q₈	—	3	2	no	—
266	C₂×Q₈	—	3	1	no	—
267	C₂×Q₈	—	6	1	no	—
268	C₂×D₄	—	3	2	no	—
269	C₂×D₄	—	6	1	no	—
270	C₂×D₄	—	6	2	no	—
271	C₂×D₄	C₂×C₅×D₃	1	1	yes	characteristic
272	Q₁₆	—	3	1	no	—
273	Q₁₆	—	3	2	no	—
274	SD₁₆	—	3	1	no	—
275	SD₁₆	—	3	2	no	—
276	SD₁₆	—	3	2	no	—
277	SD₁₆	—	3	1	no	—
278	SD₁₆	—	3	2	no	—
279	SD₁₆	C₂×C₅×D₃	1	2	yes	complemented
280	D₈	—	3	1	no	—
281	D₈	C₂×C₅×D₃	1	2	yes	complemented
282	M₁₆	—	3	2	no	—
283	M₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
284	C₂×C₈	—	3	1	no	—
285	C₂×C₈	—	3	2	no	—
286	C₃×C₅	#577	1	1	yes	characteristic, complemented, Hall
287	C₂²×C₃	—	2	1	no	—
288	C₂²×C₃	—	2	2	no	—
289	C₂²×C₃	—	8	1	no	—
290	C₂²×C₃	C₂×C₅×D₄	1	1	yes	characteristic
291	C₂×D₃	—	2	1	no	—
292	C₂×D₃	—	8	2	no	—
293	C₂×D₃	C₂×C₅×D₄	1	2	yes	—
294	C₃×C₄	—	2	1	no	—
295	C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
296	C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
297	Dic₃	—	2	2	no	—
298	Dic₃	—	2	1	no	—
299	Dic₃	C₂×C₅×D₄	1	2	yes	—
300	C₂×C₅	—	2	1	no	—
301	C₂×C₅	—	4	2	no	—
302	C₂×C₅	—	4	1	no	—
303	C₂×C₅	—	6	2	no	—
304	C₂×C₅	—	12	1	no	—
305	C₂×C₅	C₂×D₃×D₄	1	1	yes	characteristic
306	C₂³	—	2	1	no	—
307	C₂³	—	6	2	no	—
308	Q₈	—	3	1	no	—
309	Q₈	—	3	2	no	—
310	Q₈	—	3	1	no	—
311	Q₈	—	6	2	no	—
312	Q₈	—	6	1	no	—
313	Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
314	D₄	—	2	1	no	—
315	D₄	—	2	1	no	—
316	D₄	—	3	2	no	—
317	D₄	—	3	1	no	—
318	D₄	—	3	1	no	—
319	D₄	—	6	2	no	—
320	D₄	—	6	2	no	—
321	D₄	—	6	2	no	—
322	D₄	—	6	1	no	—
323	D₄	C₂²×C₅×D₃	1	1	yes	characteristic
324	D₄	C₂²×C₅×D₃	1	2	yes	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	3	2	no	—
327	C₂×C₄	—	6	2	no	—
328	C₂×C₄	—	6	2	no	—
329	C₂×C₄	—	6	2	no	—
330	C₂×C₄	—	6	1	no	—
331	C₂×C₄	—	6	1	no	—
332	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
333	C₈	—	3	1	no	—
334	C₈	—	3	1	no	—
335	C₈	C₂²×C₅×D₃	1	2	yes	—
336	C₂×C₃	—	2	1	no	—
337	C₂×C₃	—	4	2	no	—
338	C₂×C₃	—	4	1	no	—
339	C₂×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
340	D₃	—	2	2	no	—
341	D₃	—	4	1	no	—
342	C₅	#5775	1	1	yes	characteristic, direct product factor, Sylow
343	C₂²	—	2	1	no	—
344	C₂²	—	2	2	no	—
345	C₂²	—	3	2	no	—
346	C₂²	—	6	1	no	—
347	C₂²	—	8	1	no	—
348	C₂²	—	24	2	no	—
349	C₂²	C₅×D₃×D₄	1	1	yes	characteristic
350	C₄	—	2	1	no	—
351	C₄	—	3	2	no	—
352	C₄	—	6	1	no	—
353	C₄	—	6	2	no	—
354	C₄	C₅×D₃×D₄	1	1	yes	characteristic
355	C₄	C₂³×C₅×D₃	1	1	yes	characteristic
356	C₃	C₅×#577	1	1	yes	characteristic, complemented, Sylow
357	C₂	—	2	1	no	—
358	C₂	—	4	2	no	—
359	C₂	—	4	1	no	—
360	C₂	—	6	2	no	—
361	C₂	—	12	1	no	—
362	C₂	C₂×C₅×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂×D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁴×C₅
Frattini	C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×AGL(1,ℤ/8)	C₂
socle	C₂×C₃×C₅	C₂²×D₄
hypercenter	C₅×AGL(1,ℤ/8)	D₃
hypocenter	C₃	C₅×#577
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₅×#1010	C₂	semidirect
2. C₅×#1004	C₂	semidirect
3. C₃×C₅×AGL(1,ℤ/8)	C₂	semidirect
4. C₅×#950	C₂	semidirect
5. C₂×C₅×#214	C₂	semidirect
6. C₅×#915	C₂	semidirect
7. C₅×D₃×SD₁₆	C₂	semidirect
8. C₅×#912	C₂	semidirect
9. C₅×#911	C₂	semidirect
10. C₅×#909	C₂	semidirect
11. C₅×#907	C₂	semidirect
13. C₃×C₅×#41	C₂²	semidirect
16. C₅×D₃×Q₈	C₂²	semidirect
20. C₅×#237	C₂²	semidirect
27. C₂×C₅×Dic₆	C₂²	semidirect
28. C₃×C₅×SD₁₆	C₂²	semidirect
29. C₃×C₅×D₈	C₂²	semidirect
30. C₃×C₅×M₁₆	C₂²	semidirect
31. C₅×#216	C₂²	semidirect
32. C₅×#215	C₂²	semidirect
33. C₅×#214	C₂²	semidirect
34. C₅×#214	C₂²	semidirect
35. C₅×#214	C₂²	semidirect
36. C₅×#213	C₂²	semidirect
37. C₂×C₅×C₃⋊C₈	C₂²	semidirect
38. C₅×Dic₁₂	C₂²	semidirect
39. C₅×#204	C₂²	semidirect
40. C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
41. C₅×D₃×C₈	C₂²	semidirect
42. #5775	C₅	direct (N × H)
48. C₅×AGL(1,ℤ/8)	D₃	semidirect
84. #1010	C₂×C₅	semidirect
85. #1004	C₂×C₅	semidirect
86. C₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
87. #950	C₂×C₅	semidirect
88. C₂×#214	C₂×C₅	semidirect
89. #915	C₂×C₅	semidirect
90. D₃×SD₁₆	C₂×C₅	semidirect
91. #912	C₂×C₅	semidirect
92. #911	C₂×C₅	semidirect
93. #909	C₂×C₅	semidirect
94. #907	C₂×C₅	semidirect
102. C₅×#41	C₂×D₃	semidirect
117. C₅×SD₁₆	C₂×D₃	semidirect
119. C₅×D₈	C₂×D₃	semidirect
121. C₅×M₁₆	C₂×D₃	semidirect
138. C₃×#41	C₂²×C₅	semidirect
141. D₃×Q₈	C₂²×C₅	semidirect
145. #237	C₂²×C₅	semidirect
152. C₂×Dic₆	C₂²×C₅	semidirect
153. C₃×SD₁₆	C₂²×C₅	semidirect
154. C₃×D₈	C₂²×C₅	semidirect
155. C₃×M₁₆	C₂²×C₅	semidirect
156. #216	C₂²×C₅	semidirect
157. #215	C₂²×C₅	semidirect
158. #214	C₂²×C₅	semidirect
159. #214	C₂²×C₅	semidirect
160. #214	C₂²×C₅	semidirect
161. #213	C₂²×C₅	semidirect
162. C₂×C₃⋊C₈	C₂²×C₅	semidirect
163. Dic₁₂	C₂²×C₅	semidirect
164. #204	C₂²×C₅	semidirect
165. ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
166. D₃×C₈	C₂²×C₅	semidirect
202. AGL(1,ℤ/8)	C₅×D₃	semidirect
264. #41	C₂×C₅×D₃	semidirect
279. SD₁₆	C₂×C₅×D₃	semidirect
281. D₈	C₂×C₅×D₃	semidirect
283. M₁₆	C₂×C₅×D₃	semidirect
286. C₃×C₅	#577	semidirect
342. C₅	#5775	direct (N × H)
356. C₃	C₅×#577	semidirect

Maximal subgroups

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

subgroup	index
C₅×#1010	2
C₅×#1004	2
C₃×C₅×AGL(1,ℤ/8)	2
C₅×#950	2
C₂×C₅×#214	2
C₅×#915	2
C₅×D₃×SD₁₆	2
C₅×#912	2
C₅×#911	2
C₅×#909	2
C₅×#907	2
C₅×#577	3
#5775	5

Subgroups — C5×#5775 #11756160

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5775 #11756160