Subgroups — C₅×#5777 #11756162

Order 960.

524 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#239	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#949	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#942	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#919	C₂	1	2	yes	maximal, complemented
7	C₅×#918	C₂	1	2	yes	maximal, complemented
8	C₅×#916	C₂	1	2	yes	maximal, complemented
9	C₅×#914	C₂	1	2	yes	maximal, complemented
10	C₅×#908	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#575	—	3	1	no	maximal, Hall
13	C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
15	C₅×#239	—	2	1	no	—
16	C₅×#239	—	2	1	no	—
17	C₅×#239	C₂²	1	2	yes	—
18	C₅×#239	C₂²	1	2	yes	complemented
19	C₅×#239	C₂²	1	1	yes	characteristic, complemented
20	C₅×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₅×#237	—	2	1	no	—
22	C₅×#237	C₂²	1	1	yes	characteristic, complemented
23	C₅×D₃×D₄	—	2	1	no	—
24	C₅×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
25	C₅×#235	—	2	1	no	—
26	C₅×#235	C₂²	1	1	yes	characteristic
27	C₂×C₅×D₁₂	—	2	1	no	—
28	C₂×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×C₅×D₃	—	2	1	no	—
30	C₂×C₄×C₅×D₃	—	2	1	no	—
31	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
32	C₃×C₅×Q₁₆	C₂²	1	2	yes	complemented
33	C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
34	C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
35	C₅×#216	C₂²	1	2	yes	complemented
36	C₅×#215	C₂²	1	2	yes	complemented
37	C₅×#215	C₂²	1	2	yes	complemented
38	C₅×#213	C₂²	1	2	yes	complemented
39	C₅×#208	C₂²	1	1	yes	characteristic, complemented
40	C₅×D₂₄	C₂²	1	2	yes	complemented
41	C₅×#204	C₂²	1	2	yes	complemented
42	C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
43	C₅×D₃×C₈	C₂²	1	2	yes	complemented
44	#5777	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₂×C₅×#41	—	3	1	no	—
46	C₂×C₅×#41	—	3	1	no	—
47	C₅×#137	—	3	1	no	—
48	C₅×#137	—	3	2	no	—
49	C₅×#137	D₃	1	1	yes	characteristic, complemented
50	C₅×AGL(1,ℤ/8)	—	3	1	no	—
51	C₅×AGL(1,ℤ/8)	—	3	2	no	—
52	C₅×AGL(1,ℤ/8)	—	3	1	no	—
53	C₅×#135	—	3	2	no	—
54	C₅×#135	—	3	2	no	—
55	C₂×C₅×M₁₆	—	3	1	no	—
56	C₂²×C₅×D₃	—	2	1	no	—
57	C₂²×C₅×D₃	—	2	1	no	—
58	C₂²×C₅×D₃	D₄	1	1	yes	characteristic
59	C₃×C₅×Q₈	—	2	1	no	—
60	C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
61	C₃×C₅×Q₈	C₂³	1	2	yes	—
62	C₃×C₅×D₄	—	2	1	no	—
63	C₃×C₅×D₄	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₄×C₅	—	2	1	no	—
65	C₂×C₃×C₄×C₅	—	2	1	no	—
66	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₅×#67	—	2	1	no	—
68	C₅×#67	—	2	1	no	—
69	C₅×#67	—	2	1	no	—
70	C₂×C₅×Dic₃	—	2	1	no	—
71	C₂×C₅×Dic₃	D₄	1	1	yes	characteristic
72	C₅×D₁₂	—	2	2	no	—
73	C₅×D₁₂	—	2	2	no	—
74	C₅×D₁₂	—	2	1	no	—
75	C₅×D₁₂	—	2	1	no	—
76	C₅×D₁₂	C₂³	1	2	yes	—
77	C₅×D₁₂	C₂³	1	1	yes	characteristic
78	C₄×C₅×D₃	—	2	1	no	—
79	C₄×C₅×D₃	—	2	1	no	—
80	C₄×C₅×D₃	—	2	1	no	—
81	C₄×C₅×D₃	—	2	2	no	—
82	C₄×C₅×D₃	—	2	2	no	—
83	C₄×C₅×D₃	D₄	1	1	yes	characteristic
84	C₄×C₅×D₃	D₄	1	1	yes	characteristic
85	C₄×C₅×D₃	C₂³	1	1	yes	characteristic
86	C₄×C₅×D₃	C₂³	1	1	yes	characteristic
87	C₅×Dic₆	—	2	1	no	—
88	C₅×Dic₆	C₂³	1	1	yes	characteristic
89	C₃×C₅×C₈	C₂³	1	2	yes	—
90	C₅×C₃⋊C₈	C₂³	1	2	yes	—
91	D₃×#41	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂×#239	C₂×C₅	1	1	yes	characteristic, complemented
93	C₃×#137	C₂×C₅	1	1	yes	characteristic, complemented
94	#949	C₂×C₅	1	1	yes	characteristic, complemented
95	#942	C₂×C₅	1	1	yes	characteristic, complemented
96	#919	C₂×C₅	1	2	yes	complemented
97	#918	C₂×C₅	1	2	yes	complemented
98	#916	C₂×C₅	1	2	yes	complemented
99	#914	C₂×C₅	1	2	yes	complemented
100	#908	C₂×C₅	1	1	yes	characteristic, complemented
101	D₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
102	C₅×#41	—	3	1	no	—
103	C₅×#41	—	3	2	no	—
104	C₅×#41	—	3	2	no	—
105	C₅×#41	—	3	1	no	—
106	C₅×#41	—	3	1	no	—
107	C₅×#41	—	6	1	no	—
108	C₅×#41	—	6	1	no	—
109	C₅×#41	—	6	1	no	—
110	C₅×#41	—	6	1	no	—
111	C₅×#41	C₂×D₃	1	1	yes	characteristic
112	C₂×C₅×Q₈	—	3	1	no	—
113	C₂×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
114	C₂×C₅×D₄	—	3	1	no	—
115	C₂×C₅×D₄	—	3	1	no	—
116	C₂×C₅×D₄	—	6	1	no	—
117	C₂×C₅×D₄	—	6	1	no	—
118	C₂²×C₄×C₅	—	3	1	no	—
119	C₂²×C₄×C₅	—	6	1	no	—
120	C₂²×C₄×C₅	—	6	1	no	—
121	C₅×Q₁₆	—	3	2	no	—
122	C₅×Q₁₆	C₂×D₃	1	2	yes	complemented
123	C₅×SD₁₆	—	3	2	no	—
124	C₅×SD₁₆	—	3	2	no	—
125	C₅×SD₁₆	—	3	2	no	—
126	C₅×SD₁₆	C₂×D₃	1	2	yes	complemented
127	C₅×D₈	—	3	2	no	—
128	C₅×D₈	—	3	2	no	—
129	C₅×M₁₆	—	3	1	no	—
130	C₅×M₁₆	—	3	2	no	—
131	C₅×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
132	C₂×C₅×C₈	—	3	2	no	—
133	#575	—	3	1	no	Sylow
134	C₂²×C₃×C₅	—	2	1	no	—
135	C₂²×C₃×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂×C₅×D₃	—	2	2	no	—
137	C₂×C₅×D₃	—	2	1	no	—
138	C₂×C₅×D₃	—	4	1	no	—
139	C₂×C₅×D₃	—	4	2	no	—
140	C₂×C₅×D₃	—	4	2	no	—
141	C₂×C₅×D₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₅×D₃	C₂×D₄	1	1	yes	characteristic
143	C₃×C₄×C₅	—	2	1	no	—
144	C₃×C₄×C₅	—	2	2	no	—
145	C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
147	C₅×Dic₃	—	2	1	no	—
148	C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
149	C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
150	C₃×#41	C₂²×C₅	1	1	yes	characteristic
151	C₂×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
152	#239	—	2	1	no	—
153	#239	—	2	1	no	—
154	#239	C₂²×C₅	1	2	yes	—
155	#239	C₂²×C₅	1	2	yes	complemented
156	#239	C₂²×C₅	1	1	yes	characteristic, complemented
157	D₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
158	#237	—	2	1	no	—
159	#237	C₂²×C₅	1	1	yes	characteristic, complemented
160	D₃×D₄	—	2	1	no	—
161	D₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
162	#235	—	2	1	no	—
163	#235	C₂²×C₅	1	1	yes	characteristic
164	C₂×D₁₂	—	2	1	no	—
165	C₂×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
166	C₂×C₄×D₃	—	2	1	no	—
167	C₂×C₄×D₃	—	2	1	no	—
168	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
169	C₃×Q₁₆	C₂²×C₅	1	2	yes	complemented
170	C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
171	C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
172	#216	C₂²×C₅	1	2	yes	complemented
173	#215	C₂²×C₅	1	2	yes	complemented
174	#215	C₂²×C₅	1	2	yes	complemented
175	#213	C₂²×C₅	1	2	yes	complemented
176	#208	C₂²×C₅	1	1	yes	characteristic, complemented
177	D₂₄	C₂²×C₅	1	2	yes	complemented
178	#204	C₂²×C₅	1	2	yes	complemented
179	ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	complemented
180	D₃×C₈	C₂²×C₅	1	2	yes	complemented
181	C₂³×C₅	—	3	1	no	—
182	C₂³×C₅	—	6	1	no	—
183	C₂³×C₅	—	6	1	no	—
184	C₅×Q₈	—	2	1	no	—
185	C₅×Q₈	—	3	1	no	—
186	C₅×Q₈	—	6	1	no	—
187	C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
188	C₅×Q₈	C₂²×D₃	1	2	yes	—
189	C₅×D₄	—	2	1	no	—
190	C₅×D₄	—	3	2	no	—
191	C₅×D₄	—	3	1	no	—
192	C₅×D₄	—	6	1	no	—
193	C₅×D₄	—	6	2	no	—
194	C₅×D₄	—	6	2	no	—
195	C₅×D₄	—	6	1	no	—
196	C₅×D₄	—	6	1	no	—
197	C₅×D₄	—	6	1	no	—
198	C₅×D₄	—	6	1	no	—
199	C₅×D₄	C₂²×D₃	1	1	yes	characteristic
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	—	3	1	no	—
203	C₂×C₄×C₅	—	3	1	no	—
204	C₂×C₄×C₅	—	3	1	no	—
205	C₂×C₄×C₅	—	3	1	no	—
206	C₂×C₄×C₅	—	3	1	no	—
207	C₂×C₄×C₅	—	6	1	no	—
208	C₂×C₄×C₅	—	6	2	no	—
209	C₂×C₄×C₅	—	6	2	no	—
210	C₂×C₄×C₅	—	6	1	no	—
211	C₂×C₄×C₅	—	6	1	no	—
212	C₂×C₄×C₅	—	6	1	no	—
213	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
214	C₅×C₈	—	3	2	no	—
215	C₅×C₈	C₂²×D₃	1	2	yes	—
216	C₂×#41	—	3	1	no	—
217	C₂×#41	—	3	1	no	—
218	#137	—	3	1	no	—
219	#137	—	3	2	no	—
220	#137	C₅×D₃	1	1	yes	characteristic, complemented
221	AGL(1,ℤ/8)	—	3	1	no	—
222	AGL(1,ℤ/8)	—	3	2	no	—
223	AGL(1,ℤ/8)	—	3	1	no	—
224	#135	—	3	2	no	—
225	#135	—	3	2	no	—
226	C₂×M₁₆	—	3	1	no	—
227	C₂×C₃×C₅	—	2	1	no	—
228	C₂×C₃×C₅	—	4	1	no	—
229	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
230	C₅×D₃	—	2	1	no	—
231	C₅×D₃	—	2	1	no	—
232	C₅×D₃	—	4	2	no	—
233	C₅×D₃	—	4	1	no	—
234	C₂²×D₃	—	2	1	no	—
235	C₂²×D₃	—	2	1	no	—
236	C₂²×D₃	C₅×D₄	1	1	yes	characteristic
237	C₃×Q₈	—	2	1	no	—
238	C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
239	C₃×Q₈	C₂³×C₅	1	2	yes	—
240	C₃×D₄	—	2	1	no	—
241	C₃×D₄	C₂³×C₅	1	1	yes	characteristic
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
245	#67	—	2	1	no	—
246	#67	—	2	1	no	—
247	#67	—	2	1	no	—
248	C₂×Dic₃	—	2	1	no	—
249	C₂×Dic₃	C₅×D₄	1	1	yes	characteristic
250	D₁₂	—	2	2	no	—
251	D₁₂	—	2	2	no	—
252	D₁₂	—	2	1	no	—
253	D₁₂	—	2	1	no	—
254	D₁₂	C₂³×C₅	1	2	yes	—
255	D₁₂	C₂³×C₅	1	1	yes	characteristic
256	C₄×D₃	—	2	1	no	—
257	C₄×D₃	—	2	1	no	—
258	C₄×D₃	—	2	1	no	—
259	C₄×D₃	—	2	2	no	—
260	C₄×D₃	—	2	2	no	—
261	C₄×D₃	C₅×D₄	1	1	yes	characteristic
262	C₄×D₃	C₅×D₄	1	1	yes	characteristic
263	C₄×D₃	C₂³×C₅	1	1	yes	characteristic
264	C₄×D₃	C₂³×C₅	1	1	yes	characteristic
265	Dic₆	—	2	1	no	—
266	Dic₆	C₂³×C₅	1	1	yes	characteristic
267	C₃×C₈	C₂³×C₅	1	2	yes	—
268	C₃⋊C₈	C₂³×C₅	1	2	yes	—
269	C₂²×C₅	—	2	1	no	—
270	C₂²×C₅	—	3	1	no	—
271	C₂²×C₅	—	3	1	no	—
272	C₂²×C₅	—	6	2	no	—
273	C₂²×C₅	—	6	1	no	—
274	C₂²×C₅	—	12	1	no	—
275	C₂²×C₅	—	12	2	no	—
276	C₂²×C₅	—	12	2	no	—
277	C₂²×C₅	D₃×D₄	1	1	yes	characteristic
278	C₄×C₅	—	2	1	no	—
279	C₄×C₅	—	2	2	no	—
280	C₄×C₅	—	3	1	no	—
281	C₄×C₅	—	3	1	no	—
282	C₄×C₅	—	6	1	no	—
283	C₄×C₅	D₃×D₄	1	1	yes	characteristic
284	C₄×C₅	C₂³×D₃	1	1	yes	characteristic
285	#41	—	3	1	no	—
286	#41	—	3	2	no	—
287	#41	—	3	2	no	—
288	#41	—	3	1	no	—
289	#41	—	3	1	no	—
290	#41	—	6	1	no	—
291	#41	—	6	1	no	—
292	#41	—	6	1	no	—
293	#41	—	6	1	no	—
294	#41	C₂×C₅×D₃	1	1	yes	characteristic
295	C₂×Q₈	—	3	1	no	—
296	C₂×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
297	C₂×D₄	—	3	1	no	—
298	C₂×D₄	—	3	1	no	—
299	C₂×D₄	—	6	1	no	—
300	C₂×D₄	—	6	1	no	—
301	C₂²×C₄	—	3	1	no	—
302	C₂²×C₄	—	6	1	no	—
303	C₂²×C₄	—	6	1	no	—
304	Q₁₆	—	3	2	no	—
305	Q₁₆	C₂×C₅×D₃	1	2	yes	complemented
306	SD₁₆	—	3	2	no	—
307	SD₁₆	—	3	2	no	—
308	SD₁₆	—	3	2	no	—
309	SD₁₆	C₂×C₅×D₃	1	2	yes	complemented
310	D₈	—	3	2	no	—
311	D₈	—	3	2	no	—
312	M₁₆	—	3	1	no	—
313	M₁₆	—	3	2	no	—
314	M₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
315	C₂×C₈	—	3	2	no	—
316	C₃×C₅	#575	1	1	yes	characteristic, complemented, Hall
317	C₂²×C₃	—	2	1	no	—
318	C₂²×C₃	C₂×C₅×D₄	1	1	yes	characteristic
319	C₂×D₃	—	2	2	no	—
320	C₂×D₃	—	2	1	no	—
321	C₂×D₃	—	4	1	no	—
322	C₂×D₃	—	4	2	no	—
323	C₂×D₃	—	4	2	no	—
324	C₂×D₃	C₂×C₅×D₄	1	1	yes	characteristic
325	C₂×D₃	C₂×C₅×D₄	1	1	yes	characteristic
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	—	2	2	no	—
328	C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
329	C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
330	Dic₃	—	2	1	no	—
331	Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
332	Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
333	C₂×C₅	—	2	1	no	—
334	C₂×C₅	—	4	1	no	—
335	C₂×C₅	—	6	1	no	—
336	C₂×C₅	—	6	1	no	—
337	C₂×C₅	—	12	2	no	—
338	C₂×C₅	—	12	1	no	—
339	C₂×C₅	C₂×D₃×D₄	1	1	yes	characteristic
340	C₂³	—	3	1	no	—
341	C₂³	—	6	1	no	—
342	C₂³	—	6	1	no	—
343	Q₈	—	2	1	no	—
344	Q₈	—	3	1	no	—
345	Q₈	—	6	1	no	—
346	Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
347	Q₈	C₂²×C₅×D₃	1	2	yes	—
348	D₄	—	2	1	no	—
349	D₄	—	3	2	no	—
350	D₄	—	3	1	no	—
351	D₄	—	6	1	no	—
352	D₄	—	6	2	no	—
353	D₄	—	6	2	no	—
354	D₄	—	6	1	no	—
355	D₄	—	6	1	no	—
356	D₄	—	6	1	no	—
357	D₄	—	6	1	no	—
358	D₄	C₂²×C₅×D₃	1	1	yes	characteristic
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	3	1	no	—
362	C₂×C₄	—	3	1	no	—
363	C₂×C₄	—	3	1	no	—
364	C₂×C₄	—	3	1	no	—
365	C₂×C₄	—	3	1	no	—
366	C₂×C₄	—	6	1	no	—
367	C₂×C₄	—	6	2	no	—
368	C₂×C₄	—	6	2	no	—
369	C₂×C₄	—	6	1	no	—
370	C₂×C₄	—	6	1	no	—
371	C₂×C₄	—	6	1	no	—
372	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
373	C₈	—	3	2	no	—
374	C₈	C₂²×C₅×D₃	1	2	yes	—
375	C₂×C₃	—	2	1	no	—
376	C₂×C₃	—	4	1	no	—
377	C₂×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
378	D₃	—	2	1	no	—
379	D₃	—	2	1	no	—
380	D₃	—	4	2	no	—
381	D₃	—	4	1	no	—
382	C₅	#5777	1	1	yes	characteristic, direct product factor, Sylow
383	C₂²	—	2	1	no	—
384	C₂²	—	3	1	no	—
385	C₂²	—	3	1	no	—
386	C₂²	—	6	2	no	—
387	C₂²	—	6	1	no	—
388	C₂²	—	12	1	no	—
389	C₂²	—	12	2	no	—
390	C₂²	—	12	2	no	—
391	C₂²	C₅×D₃×D₄	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	2	no	—
394	C₄	—	3	1	no	—
395	C₄	—	3	1	no	—
396	C₄	—	6	1	no	—
397	C₄	C₅×D₃×D₄	1	1	yes	characteristic
398	C₄	C₂³×C₅×D₃	1	1	yes	characteristic
399	C₃	C₅×#575	1	1	yes	characteristic, complemented, Sylow
400	C₂	—	2	1	no	—
401	C₂	—	4	1	no	—
402	C₂	—	6	1	no	—
403	C₂	—	6	1	no	—
404	C₂	—	12	2	no	—
405	C₂	—	12	1	no	—
406	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×#137	C₂
socle	C₂×C₃×C₅	C₂²×D₄
hypercenter	C₅×#137	D₃
hypocenter	C₃	C₅×#575
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#137

Complements

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

N	H ≅ G/N	type
1. C₅×D₃×#41	C₂	semidirect
2. C₂×C₅×#239	C₂	semidirect
3. C₃×C₅×#137	C₂	semidirect
4. C₅×#949	C₂	semidirect
5. C₅×#942	C₂	semidirect
6. C₅×#919	C₂	semidirect
7. C₅×#918	C₂	semidirect
8. C₅×#916	C₂	semidirect
9. C₅×#914	C₂	semidirect
10. C₅×#908	C₂	semidirect
11. C₅×D₃×M₁₆	C₂	semidirect
14. C₂×C₃×C₅×Q₈	C₂²	semidirect
18. C₅×#239	C₂²	semidirect
19. C₅×#239	C₂²	semidirect
20. C₅×D₃×Q₈	C₂²	semidirect
22. C₅×#237	C₂²	semidirect
24. C₅×D₃×D₄	C₂²	semidirect
28. C₂×C₅×D₁₂	C₂²	semidirect
32. C₃×C₅×Q₁₆	C₂²	semidirect
33. C₃×C₅×SD₁₆	C₂²	semidirect
34. C₃×C₅×M₁₆	C₂²	semidirect
35. C₅×#216	C₂²	semidirect
36. C₅×#215	C₂²	semidirect
37. C₅×#215	C₂²	semidirect
38. C₅×#213	C₂²	semidirect
39. C₅×#208	C₂²	semidirect
40. C₅×D₂₄	C₂²	semidirect
41. C₅×#204	C₂²	semidirect
42. C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
43. C₅×D₃×C₈	C₂²	semidirect
44. #5777	C₅	direct (N × H)
49. C₅×#137	D₃	semidirect
91. D₃×#41	C₂×C₅	semidirect
92. C₂×#239	C₂×C₅	semidirect
93. C₃×#137	C₂×C₅	semidirect
94. #949	C₂×C₅	semidirect
95. #942	C₂×C₅	semidirect
96. #919	C₂×C₅	semidirect
97. #918	C₂×C₅	semidirect
98. #916	C₂×C₅	semidirect
99. #914	C₂×C₅	semidirect
100. #908	C₂×C₅	semidirect
101. D₃×M₁₆	C₂×C₅	semidirect
113. C₂×C₅×Q₈	C₂×D₃	semidirect
122. C₅×Q₁₆	C₂×D₃	semidirect
126. C₅×SD₁₆	C₂×D₃	semidirect
131. C₅×M₁₆	C₂×D₃	semidirect
151. C₂×C₃×Q₈	C₂²×C₅	semidirect
155. #239	C₂²×C₅	semidirect
156. #239	C₂²×C₅	semidirect
157. D₃×Q₈	C₂²×C₅	semidirect
159. #237	C₂²×C₅	semidirect
161. D₃×D₄	C₂²×C₅	semidirect
165. C₂×D₁₂	C₂²×C₅	semidirect
169. C₃×Q₁₆	C₂²×C₅	semidirect
170. C₃×SD₁₆	C₂²×C₅	semidirect
171. C₃×M₁₆	C₂²×C₅	semidirect
172. #216	C₂²×C₅	semidirect
173. #215	C₂²×C₅	semidirect
174. #215	C₂²×C₅	semidirect
175. #213	C₂²×C₅	semidirect
176. #208	C₂²×C₅	semidirect
177. D₂₄	C₂²×C₅	semidirect
178. #204	C₂²×C₅	semidirect
179. ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
180. D₃×C₈	C₂²×C₅	semidirect
220. #137	C₅×D₃	semidirect
296. C₂×Q₈	C₂×C₅×D₃	semidirect
305. Q₁₆	C₂×C₅×D₃	semidirect
309. SD₁₆	C₂×C₅×D₃	semidirect
314. M₁₆	C₂×C₅×D₃	semidirect
316. C₃×C₅	#575	semidirect
382. C₅	#5777	direct (N × H)
399. C₃	C₅×#575	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₃×#41	2
C₂×C₅×#239	2
C₃×C₅×#137	2
C₅×#949	2
C₅×#942	2
C₅×#919	2
C₅×#918	2
C₅×#916	2
C₅×#914	2
C₅×#908	2
C₅×D₃×M₁₆	2
C₅×#575	3
#5777	5

Subgroups — C5×#5777 #11756162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5777 #11756162