Subgroups — C₅×#5774 #11756159

Order 960.

536 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#1009	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×#213	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#916	C₂	1	2	yes	maximal, complemented
7	C₅×#914	C₂	1	2	yes	maximal, complemented
8	C₅×#911	C₂	1	2	yes	maximal, complemented
9	C₅×D₃×D₈	C₂	1	2	yes	maximal, complemented
10	C₅×#908	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#907	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#576	—	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, complemented
15	C₂×C₅×#67	—	2	2	no	—
16	C₅×#239	C₂²	1	2	yes	complemented
17	C₅×#237	—	2	1	no	—
18	C₅×#237	C₂²	1	2	yes	complemented
19	C₅×D₃×D₄	—	2	2	no	—
20	C₅×D₃×D₄	—	2	1	no	—
21	C₅×D₃×D₄	C₂²	1	2	yes	complemented
22	C₅×D₃×D₄	C₂²	1	2	yes	complemented
23	C₅×#235	—	2	1	no	—
24	C₅×#235	C₂²	1	1	yes	characteristic
25	C₅×#235	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×D₁₂	—	2	1	no	—
27	C₂×C₅×D₁₂	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	1	yes	characteristic, complemented
34	C₅×#213	C₂²	1	1	yes	characteristic, complemented
35	C₅×#213	C₂²	1	2	yes	complemented
36	C₅×#213	C₂²	1	2	yes	complemented
37	C₂×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	C₅×D₂₄	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	#5774	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×H(5,𝔽₂)	—	3	1	no	—
44	C₅×H(5,𝔽₂)	—	3	1	no	—
45	C₅×AGL(1,ℤ/8)	—	3	2	no	—
46	C₅×AGL(1,ℤ/8)	—	3	2	no	—
47	C₅×AGL(1,ℤ/8)	—	3	1	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×D₈	—	3	1	no	—
52	C₂×C₅×D₈	—	3	2	no	—
53	C₅×#131	—	3	1	no	—
54	C₂³×C₃×C₅	—	2	1	no	—
55	C₂²×C₅×D₃	—	2	1	no	—
56	C₂²×C₅×D₃	—	2	2	no	—
57	C₂²×C₅×D₃	—	2	2	no	—
58	C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₃×C₅×D₄	—	2	1	no	—
60	C₃×C₅×D₄	—	2	1	no	—
61	C₃×C₅×D₄	C₂³	1	2	yes	—
62	C₃×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×C₅	—	2	1	no	—
64	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₅×#67	—	2	1	no	—
66	C₅×#67	—	2	2	no	—
67	C₅×#67	—	2	2	no	—
68	C₅×#67	—	2	2	no	—
69	C₅×#67	D₄	1	2	yes	—
70	C₂×C₅×Dic₃	—	2	2	no	—
71	C₅×D₁₂	—	2	2	no	—
72	C₅×D₁₂	—	2	1	no	—
73	C₅×D₁₂	D₄	1	1	yes	characteristic
74	C₅×D₁₂	C₂³	1	2	yes	—
75	C₅×D₁₂	C₂³	1	1	yes	characteristic
76	C₄×C₅×D₃	—	2	1	no	—
77	C₄×C₅×D₃	—	2	2	no	—
78	C₄×C₅×D₃	C₂³	1	2	yes	—
79	C₅×Dic₆	D₄	1	1	yes	characteristic
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	#1009	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×#213	C₂×C₅	1	1	yes	characteristic, complemented
89	#916	C₂×C₅	1	2	yes	complemented
90	#914	C₂×C₅	1	2	yes	complemented
91	#911	C₂×C₅	1	2	yes	complemented
92	D₃×D₈	C₂×C₅	1	2	yes	complemented
93	#908	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	1	no	—
101	C₅×#41	C₂×D₃	1	1	yes	characteristic, complemented
102	C₂×C₅×D₄	—	3	2	no	—
103	C₂×C₅×D₄	—	3	2	no	—
104	C₂×C₅×D₄	—	3	1	no	—
105	C₂×C₅×D₄	—	6	1	no	—
106	C₂×C₅×D₄	—	6	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, complemented
110	C₅×Q₁₆	—	3	1	no	—
111	C₅×SD₁₆	—	3	1	no	—
112	C₅×SD₁₆	—	3	1	no	—
113	C₅×SD₁₆	—	3	2	no	—
114	C₅×SD₁₆	C₂×D₃	1	2	yes	complemented
115	C₅×D₈	—	3	2	no	—
116	C₅×D₈	—	3	1	no	—
117	C₅×D₈	—	3	2	no	—
118	C₅×D₈	—	3	2	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	#576	—	3	1	no	Sylow
125	C₂²×C₃×C₅	—	2	2	no	—
126	C₂²×C₃×C₅	—	2	1	no	—
127	C₂²×C₃×C₅	—	8	1	no	—
128	C₂²×C₃×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂×C₅×D₃	—	2	2	no	—
130	C₂×C₅×D₃	—	2	1	no	—
131	C₂×C₅×D₃	—	8	2	no	—
132	C₂×C₅×D₃	—	8	2	no	—
133	C₂×C₅×D₃	—	8	1	no	—
134	C₂×C₅×D₃	C₂×D₄	1	2	yes	—
135	C₃×C₄×C₅	—	2	1	no	—
136	C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
138	C₅×Dic₃	—	2	1	no	—
139	C₅×Dic₃	C₂×D₄	1	2	yes	—
140	C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
141	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
142	C₂×#67	—	2	2	no	—
143	#239	C₂²×C₅	1	2	yes	complemented
144	#237	—	2	1	no	—
145	#237	C₂²×C₅	1	2	yes	complemented
146	D₃×D₄	—	2	2	no	—
147	D₃×D₄	—	2	1	no	—
148	D₃×D₄	C₂²×C₅	1	2	yes	complemented
149	D₃×D₄	C₂²×C₅	1	2	yes	complemented
150	#235	—	2	1	no	—
151	#235	C₂²×C₅	1	1	yes	characteristic
152	#235	C₂²×C₅	1	1	yes	characteristic, complemented
153	C₂×D₁₂	—	2	1	no	—
154	C₂×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
155	C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
156	C₃×D₈	C₂²×C₅	1	2	yes	complemented
157	C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
158	#216	C₂²×C₅	1	1	yes	characteristic, complemented
159	#215	C₂²×C₅	1	1	yes	characteristic, complemented
160	#214	C₂²×C₅	1	1	yes	characteristic, complemented
161	#213	C₂²×C₅	1	1	yes	characteristic, complemented
162	#213	C₂²×C₅	1	2	yes	complemented
163	#213	C₂²×C₅	1	2	yes	complemented
164	C₂×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
165	D₂₄	C₂²×C₅	1	2	yes	complemented
166	#204	C₂²×C₅	1	2	yes	complemented
167	ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	complemented
168	D₃×C₈	C₂²×C₅	1	2	yes	complemented
169	C₂³×C₅	—	2	1	no	—
170	C₂³×C₅	—	6	2	no	—
171	C₂³×C₅	—	6	2	no	—
172	C₂³×C₅	—	6	1	no	—
173	C₅×Q₈	—	3	1	no	—
174	C₅×Q₈	—	3	1	no	—
175	C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
176	C₅×D₄	—	2	1	no	—
177	C₅×D₄	—	2	1	no	—
178	C₅×D₄	—	3	2	no	—
179	C₅×D₄	—	3	1	no	—
180	C₅×D₄	—	3	2	no	—
181	C₅×D₄	—	3	1	no	—
182	C₅×D₄	—	6	2	no	—
183	C₅×D₄	—	6	2	no	—
184	C₅×D₄	—	6	2	no	—
185	C₅×D₄	—	6	2	no	—
186	C₅×D₄	—	6	1	no	—
187	C₅×D₄	—	6	1	no	—
188	C₅×D₄	C₂²×D₃	1	2	yes	—
189	C₅×D₄	C₂²×D₃	1	1	yes	characteristic
190	C₂×C₄×C₅	—	2	1	no	—
191	C₂×C₄×C₅	—	3	2	no	—
192	C₂×C₄×C₅	—	6	2	no	—
193	C₂×C₄×C₅	—	6	2	no	—
194	C₂×C₄×C₅	—	6	1	no	—
195	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
196	C₅×C₈	—	3	1	no	—
197	C₅×C₈	—	3	1	no	—
198	C₅×C₈	C₂²×D₃	1	2	yes	—
199	H(5,𝔽₂)	—	3	1	no	—
200	H(5,𝔽₂)	—	3	1	no	—
201	AGL(1,ℤ/8)	—	3	2	no	—
202	AGL(1,ℤ/8)	—	3	2	no	—
203	AGL(1,ℤ/8)	—	3	1	no	—
204	AGL(1,ℤ/8)	C₅×D₃	1	1	yes	characteristic, complemented
205	#135	—	3	1	no	—
206	#135	—	3	2	no	—
207	C₂×D₈	—	3	1	no	—
208	C₂×D₈	—	3	2	no	—
209	#131	—	3	1	no	—
210	C₂×C₃×C₅	—	2	1	no	—
211	C₂×C₃×C₅	—	4	1	no	—
212	C₂×C₃×C₅	—	4	2	no	—
213	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₅×D₃	—	2	2	no	—
215	C₅×D₃	—	4	2	no	—
216	C₅×D₃	—	4	1	no	—
217	C₂³×C₃	—	2	1	no	—
218	C₂²×D₃	—	2	1	no	—
219	C₂²×D₃	—	2	2	no	—
220	C₂²×D₃	—	2	2	no	—
221	C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
222	C₃×D₄	—	2	1	no	—
223	C₃×D₄	—	2	1	no	—
224	C₃×D₄	C₂³×C₅	1	2	yes	—
225	C₃×D₄	C₂³×C₅	1	1	yes	characteristic
226	C₂×C₃×C₄	—	2	1	no	—
227	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
228	#67	—	2	1	no	—
229	#67	—	2	2	no	—
230	#67	—	2	2	no	—
231	#67	—	2	2	no	—
232	#67	C₅×D₄	1	2	yes	—
233	C₂×Dic₃	—	2	2	no	—
234	D₁₂	—	2	2	no	—
235	D₁₂	—	2	1	no	—
236	D₁₂	C₅×D₄	1	1	yes	characteristic
237	D₁₂	C₂³×C₅	1	2	yes	—
238	D₁₂	C₂³×C₅	1	1	yes	characteristic
239	C₄×D₃	—	2	1	no	—
240	C₄×D₃	—	2	2	no	—
241	C₄×D₃	C₂³×C₅	1	2	yes	—
242	Dic₆	C₅×D₄	1	1	yes	characteristic
243	Dic₆	C₂³×C₅	1	1	yes	characteristic
244	C₃×C₈	C₂³×C₅	1	2	yes	—
245	C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
246	C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
247	C₂²×C₅	—	2	1	no	—
248	C₂²×C₅	—	2	2	no	—
249	C₂²×C₅	—	3	2	no	—
250	C₂²×C₅	—	6	2	no	—
251	C₂²×C₅	—	6	1	no	—
252	C₂²×C₅	—	8	1	no	—
253	C₂²×C₅	—	24	1	no	—
254	C₂²×C₅	—	24	2	no	—
255	C₂²×C₅	—	24	2	no	—
256	C₂²×C₅	D₃×D₄	1	1	yes	characteristic
257	C₄×C₅	—	2	1	no	—
258	C₄×C₅	—	3	2	no	—
259	C₄×C₅	—	6	1	no	—
260	C₄×C₅	D₃×D₄	1	1	yes	characteristic
261	C₄×C₅	C₂³×D₃	1	1	yes	characteristic
262	#41	—	3	1	no	—
263	#41	—	3	2	no	—
264	#41	—	3	2	no	—
265	#41	—	3	1	no	—
266	#41	—	6	1	no	—
267	#41	—	6	1	no	—
268	#41	C₂×C₅×D₃	1	1	yes	characteristic, complemented
269	C₂×D₄	—	3	2	no	—
270	C₂×D₄	—	3	2	no	—
271	C₂×D₄	—	3	1	no	—
272	C₂×D₄	—	6	1	no	—
273	C₂×D₄	—	6	2	no	—
274	C₂×D₄	—	6	1	no	—
275	C₂×D₄	—	6	2	no	—
276	C₂×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
277	Q₁₆	—	3	1	no	—
278	SD₁₆	—	3	1	no	—
279	SD₁₆	—	3	1	no	—
280	SD₁₆	—	3	2	no	—
281	SD₁₆	C₂×C₅×D₃	1	2	yes	complemented
282	D₈	—	3	2	no	—
283	D₈	—	3	1	no	—
284	D₈	—	3	2	no	—
285	D₈	—	3	2	no	—
286	D₈	C₂×C₅×D₃	1	2	yes	complemented
287	M₁₆	—	3	2	no	—
288	M₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
289	C₂×C₈	—	3	1	no	—
290	C₂×C₈	—	3	2	no	—
291	C₃×C₅	#576	1	1	yes	characteristic, complemented, Hall
292	C₂²×C₃	—	2	2	no	—
293	C₂²×C₃	—	2	1	no	—
294	C₂²×C₃	—	8	1	no	—
295	C₂²×C₃	C₂×C₅×D₄	1	1	yes	characteristic
296	C₂×D₃	—	2	2	no	—
297	C₂×D₃	—	2	1	no	—
298	C₂×D₃	—	8	2	no	—
299	C₂×D₃	—	8	2	no	—
300	C₂×D₃	—	8	1	no	—
301	C₂×D₃	C₂×C₅×D₄	1	2	yes	—
302	C₃×C₄	—	2	1	no	—
303	C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
304	C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
305	Dic₃	—	2	1	no	—
306	Dic₃	C₂×C₅×D₄	1	2	yes	—
307	C₂×C₅	—	2	1	no	—
308	C₂×C₅	—	4	2	no	—
309	C₂×C₅	—	4	1	no	—
310	C₂×C₅	—	6	2	no	—
311	C₂×C₅	—	12	2	no	—
312	C₂×C₅	—	12	1	no	—
313	C₂×C₅	C₂×D₃×D₄	1	1	yes	characteristic
314	C₂³	—	2	1	no	—
315	C₂³	—	6	2	no	—
316	C₂³	—	6	2	no	—
317	C₂³	—	6	1	no	—
318	Q₈	—	3	1	no	—
319	Q₈	—	3	1	no	—
320	Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
321	D₄	—	2	1	no	—
322	D₄	—	2	1	no	—
323	D₄	—	3	2	no	—
324	D₄	—	3	1	no	—
325	D₄	—	3	2	no	—
326	D₄	—	3	1	no	—
327	D₄	—	6	2	no	—
328	D₄	—	6	2	no	—
329	D₄	—	6	2	no	—
330	D₄	—	6	2	no	—
331	D₄	—	6	1	no	—
332	D₄	—	6	1	no	—
333	D₄	C₂²×C₅×D₃	1	2	yes	—
334	D₄	C₂²×C₅×D₃	1	1	yes	characteristic
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	3	2	no	—
337	C₂×C₄	—	6	2	no	—
338	C₂×C₄	—	6	2	no	—
339	C₂×C₄	—	6	1	no	—
340	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
341	C₈	—	3	1	no	—
342	C₈	—	3	1	no	—
343	C₈	C₂²×C₅×D₃	1	2	yes	—
344	C₂×C₃	—	2	1	no	—
345	C₂×C₃	—	4	1	no	—
346	C₂×C₃	—	4	2	no	—
347	C₂×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
348	D₃	—	2	2	no	—
349	D₃	—	4	2	no	—
350	D₃	—	4	1	no	—
351	C₅	#5774	1	1	yes	characteristic, direct product factor, Sylow
352	C₂²	—	2	1	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	3	2	no	—
355	C₂²	—	6	2	no	—
356	C₂²	—	6	1	no	—
357	C₂²	—	8	1	no	—
358	C₂²	—	24	1	no	—
359	C₂²	—	24	2	no	—
360	C₂²	—	24	2	no	—
361	C₂²	C₅×D₃×D₄	1	1	yes	characteristic
362	C₄	—	2	1	no	—
363	C₄	—	3	2	no	—
364	C₄	—	6	1	no	—
365	C₄	C₅×D₃×D₄	1	1	yes	characteristic
366	C₄	C₂³×C₅×D₃	1	1	yes	characteristic
367	C₃	C₅×#576	1	1	yes	characteristic, complemented, Sylow
368	C₂	—	2	1	no	—
369	C₂	—	4	2	no	—
370	C₂	—	4	1	no	—
371	C₂	—	6	2	no	—
372	C₂	—	12	2	no	—
373	C₂	—	12	1	no	—
374	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×#576
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×#1009	C₂	semidirect
2. C₅×#1004	C₂	semidirect
3. C₃×C₅×AGL(1,ℤ/8)	C₂	semidirect
4. C₅×#950	C₂	semidirect
5. C₂×C₅×#213	C₂	semidirect
6. C₅×#916	C₂	semidirect
7. C₅×#914	C₂	semidirect
8. C₅×#911	C₂	semidirect
9. C₅×D₃×D₈	C₂	semidirect
10. C₅×#908	C₂	semidirect
11. C₅×#907	C₂	semidirect
13. C₃×C₅×#41	C₂²	semidirect
14. C₂×C₃×C₅×D₄	C₂²	semidirect
16. C₅×#239	C₂²	semidirect
18. C₅×#237	C₂²	semidirect
21. C₅×D₃×D₄	C₂²	semidirect
22. C₅×D₃×D₄	C₂²	semidirect
25. C₅×#235	C₂²	semidirect
27. C₂×C₅×D₁₂	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×#213	C₂²	semidirect
35. C₅×#213	C₂²	semidirect
36. C₅×#213	C₂²	semidirect
37. C₂×C₅×C₃⋊C₈	C₂²	semidirect
38. C₅×D₂₄	C₂²	semidirect
39. C₅×#204	C₂²	semidirect
40. C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
41. C₅×D₃×C₈	C₂²	semidirect
42. #5774	C₅	direct (N × H)
48. C₅×AGL(1,ℤ/8)	D₃	semidirect
84. #1009	C₂×C₅	semidirect
85. #1004	C₂×C₅	semidirect
86. C₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
87. #950	C₂×C₅	semidirect
88. C₂×#213	C₂×C₅	semidirect
89. #916	C₂×C₅	semidirect
90. #914	C₂×C₅	semidirect
91. #911	C₂×C₅	semidirect
92. D₃×D₈	C₂×C₅	semidirect
93. #908	C₂×C₅	semidirect
94. #907	C₂×C₅	semidirect
101. C₅×#41	C₂×D₃	semidirect
109. C₂×C₅×D₄	C₂×D₃	semidirect
114. C₅×SD₁₆	C₂×D₃	semidirect
119. C₅×D₈	C₂×D₃	semidirect
121. C₅×M₁₆	C₂×D₃	semidirect
140. C₃×#41	C₂²×C₅	semidirect
141. C₂×C₃×D₄	C₂²×C₅	semidirect
143. #239	C₂²×C₅	semidirect
145. #237	C₂²×C₅	semidirect
148. D₃×D₄	C₂²×C₅	semidirect
149. D₃×D₄	C₂²×C₅	semidirect
152. #235	C₂²×C₅	semidirect
154. C₂×D₁₂	C₂²×C₅	semidirect
155. C₃×SD₁₆	C₂²×C₅	semidirect
156. C₃×D₈	C₂²×C₅	semidirect
157. C₃×M₁₆	C₂²×C₅	semidirect
158. #216	C₂²×C₅	semidirect
159. #215	C₂²×C₅	semidirect
160. #214	C₂²×C₅	semidirect
161. #213	C₂²×C₅	semidirect
162. #213	C₂²×C₅	semidirect
163. #213	C₂²×C₅	semidirect
164. C₂×C₃⋊C₈	C₂²×C₅	semidirect
165. D₂₄	C₂²×C₅	semidirect
166. #204	C₂²×C₅	semidirect
167. ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
168. D₃×C₈	C₂²×C₅	semidirect
204. AGL(1,ℤ/8)	C₅×D₃	semidirect
268. #41	C₂×C₅×D₃	semidirect
276. C₂×D₄	C₂×C₅×D₃	semidirect
281. SD₁₆	C₂×C₅×D₃	semidirect
286. D₈	C₂×C₅×D₃	semidirect
288. M₁₆	C₂×C₅×D₃	semidirect
291. C₃×C₅	#576	semidirect
351. C₅	#5774	direct (N × H)
367. C₃	C₅×#576	semidirect

Maximal subgroups

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

subgroup	index
C₅×#1009	2
C₅×#1004	2
C₃×C₅×AGL(1,ℤ/8)	2
C₅×#950	2
C₂×C₅×#213	2
C₅×#916	2
C₅×#914	2
C₅×#911	2
C₅×D₃×D₈	2
C₅×#908	2
C₅×#907	2
C₅×#576	3
#5774	5

Subgroups — C5×#5774 #11756159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5774 #11756159