Subgroups — C₅×#5770 #11756155

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×#1009	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#951	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#949	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#918	C₂	1	2	yes	maximal, complemented
7	C₅×#916	C₂	1	2	yes	maximal, complemented
8	C₅×D₃×SD₁₆	C₂	1	2	yes	maximal, complemented
9	C₅×#911	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#204	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#901	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#577	—	3	1	no	maximal, Hall
13	C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
15	C₅×#239	C₂²	1	2	yes	—
16	C₅×D₃×Q₈	C₂²	1	2	yes	complemented
17	C₅×#237	—	2	2	no	—
18	C₅×#237	C₂²	1	2	yes	complemented
19	C₅×D₃×D₄	—	2	2	no	—
20	C₅×D₃×D₄	C₂²	1	2	yes	—
21	C₅×#235	—	2	1	no	—
22	C₅×#235	—	2	1	no	—
23	C₅×#235	C₂²	1	1	yes	characteristic
24	C₂×C₅×D₁₂	—	2	1	no	—
25	C₂×C₅×D₁₂	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×Q₁₆	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
33	C₅×#216	C₂²	1	2	yes	complemented
34	C₅×#215	C₂²	1	2	yes	complemented
35	C₅×#214	C₂²	1	2	yes	complemented
36	C₅×#213	C₂²	1	2	yes	complemented
37	C₅×#208	C₂²	1	1	yes	characteristic, complemented
38	C₅×#204	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	#5770	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	1	no	—
46	C₅×#137	—	3	2	no	—
47	C₅×AGL(1,ℤ/8)	—	3	1	no	—
48	C₅×AGL(1,ℤ/8)	—	3	2	no	—
49	C₅×#135	—	3	2	no	—
50	C₅×#135	D₃	1	1	yes	characteristic, complemented
51	C₂×C₅×SD₁₆	—	3	2	no	—
52	C₂×C₅×SD₁₆	—	3	1	no	—
53	C₅×#131	—	3	1	no	—
54	C₂²×C₅×D₃	—	2	1	no	—
55	C₂²×C₅×D₃	—	2	2	no	—
56	C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
57	C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
58	C₃×C₅×D₄	—	2	1	no	—
59	C₃×C₅×D₄	—	2	1	no	—
60	C₃×C₅×D₄	C₂³	1	1	yes	characteristic
61	C₃×C₅×D₄	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₄×C₅	—	2	1	no	—
63	C₂×C₃×C₄×C₅	—	2	1	no	—
64	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
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	C₅×D₁₂	—	2	2	no	—
71	C₅×D₁₂	—	2	1	no	—
72	C₅×D₁₂	D₄	1	1	yes	characteristic
73	C₅×D₁₂	C₂³	1	2	yes	—
74	C₄×C₅×D₃	—	2	2	no	—
75	C₄×C₅×D₃	—	2	2	no	—
76	C₄×C₅×D₃	C₂³	1	2	yes	—
77	C₅×Dic₆	—	2	1	no	—
78	C₅×Dic₆	—	2	2	no	—
79	C₅×Dic₆	D₄	1	1	yes	characteristic
80	C₅×Dic₆	C₂³	1	2	yes	—
81	C₃×C₅×C₈	C₂³	1	1	yes	characteristic
82	C₃×C₅×C₈	C₂³	1	1	yes	characteristic
83	C₅×C₃⋊C₈	C₂³	1	2	yes	—
84	#1010	C₂×C₅	1	1	yes	characteristic, complemented
85	#1009	C₂×C₅	1	1	yes	characteristic, complemented
86	C₃×#135	C₂×C₅	1	1	yes	characteristic, complemented
87	#951	C₂×C₅	1	1	yes	characteristic, complemented
88	#949	C₂×C₅	1	1	yes	characteristic, complemented
89	#918	C₂×C₅	1	2	yes	complemented
90	#916	C₂×C₅	1	2	yes	complemented
91	D₃×SD₁₆	C₂×C₅	1	2	yes	complemented
92	#911	C₂×C₅	1	2	yes	complemented
93	C₂×#204	C₂×C₅	1	1	yes	characteristic, complemented
94	#901	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	—	6	1	no	—
99	C₅×#41	—	6	1	no	—
100	C₅×#41	—	6	2	no	—
101	C₅×#41	C₂×D₃	1	1	yes	characteristic
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	—	3	1	no	—
108	C₂×C₅×D₄	—	6	1	no	—
109	C₂×C₅×D₄	—	6	2	no	—
110	C₅×Q₁₆	—	3	2	no	—
111	C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
112	C₅×SD₁₆	—	3	2	no	—
113	C₅×SD₁₆	—	3	2	no	—
114	C₅×SD₁₆	—	3	2	no	—
115	C₅×SD₁₆	—	3	2	no	—
116	C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic, complemented
117	C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic, complemented
118	C₅×D₈	—	3	2	no	—
119	C₅×D₈	C₂×D₃	1	1	yes	characteristic, complemented
120	C₅×M₁₆	—	3	1	no	—
121	C₅×M₁₆	—	3	2	no	—
122	C₂×C₅×C₈	—	3	2	no	—
123	C₂×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
124	#577	—	3	1	no	Sylow
125	C₂²×C₃×C₅	—	2	1	no	—
126	C₂²×C₃×C₅	—	2	1	no	—
127	C₂²×C₃×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂×C₅×D₃	—	2	2	no	—
129	C₂×C₅×D₃	—	8	2	no	—
130	C₂×C₅×D₃	—	8	1	no	—
131	C₂×C₅×D₃	C₂×D₄	1	2	yes	—
132	C₃×C₄×C₅	—	2	1	no	—
133	C₃×C₄×C₅	—	2	1	no	—
134	C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
136	C₅×Dic₃	—	2	2	no	—
137	C₅×Dic₃	C₂×D₄	1	2	yes	—
138	C₃×#41	C₂²×C₅	1	1	yes	characteristic
139	C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
140	#239	C₂²×C₅	1	2	yes	—
141	D₃×Q₈	C₂²×C₅	1	2	yes	complemented
142	#237	—	2	2	no	—
143	#237	C₂²×C₅	1	2	yes	complemented
144	D₃×D₄	—	2	2	no	—
145	D₃×D₄	C₂²×C₅	1	2	yes	—
146	#235	—	2	1	no	—
147	#235	—	2	1	no	—
148	#235	C₂²×C₅	1	1	yes	characteristic
149	C₂×D₁₂	—	2	1	no	—
150	C₂×D₁₂	C₂²×C₅	1	1	yes	characteristic
151	C₂×Dic₆	—	2	1	no	—
152	C₂×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
153	C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
154	C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
155	C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
156	C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
157	C₂×C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
158	#216	C₂²×C₅	1	2	yes	complemented
159	#215	C₂²×C₅	1	2	yes	complemented
160	#214	C₂²×C₅	1	2	yes	complemented
161	#213	C₂²×C₅	1	2	yes	complemented
162	#208	C₂²×C₅	1	1	yes	characteristic, complemented
163	#204	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	—	6	2	no	—
168	C₂³×C₅	—	6	1	no	—
169	C₅×Q₈	—	3	1	no	—
170	C₅×Q₈	—	3	2	no	—
171	C₅×Q₈	—	6	2	no	—
172	C₅×Q₈	—	6	1	no	—
173	C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
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	2	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	1	yes	characteristic
186	C₂×C₄×C₅	—	2	1	no	—
187	C₂×C₄×C₅	—	2	1	no	—
188	C₂×C₄×C₅	—	3	2	no	—
189	C₂×C₄×C₅	—	6	2	no	—
190	C₂×C₄×C₅	—	6	2	no	—
191	C₂×C₄×C₅	—	6	2	no	—
192	C₂×C₄×C₅	—	6	1	no	—
193	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
194	C₅×C₈	—	3	2	no	—
195	C₅×C₈	C₂²×D₃	1	1	yes	characteristic
196	C₅×C₈	C₂²×D₃	1	1	yes	characteristic
197	2₋¹⁺⁴	—	3	1	no	—
198	H(5,𝔽₂)	—	3	1	no	—
199	#137	—	3	1	no	—
200	#137	—	3	2	no	—
201	AGL(1,ℤ/8)	—	3	1	no	—
202	AGL(1,ℤ/8)	—	3	2	no	—
203	#135	—	3	2	no	—
204	#135	C₅×D₃	1	1	yes	characteristic, complemented
205	C₂×SD₁₆	—	3	2	no	—
206	C₂×SD₁₆	—	3	1	no	—
207	#131	—	3	1	no	—
208	C₂×C₃×C₅	—	2	1	no	—
209	C₂×C₃×C₅	—	4	1	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	2	no	—
214	C₂²×D₃	—	2	1	no	—
215	C₂²×D₃	—	2	2	no	—
216	C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
217	C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
218	C₃×D₄	—	2	1	no	—
219	C₃×D₄	—	2	1	no	—
220	C₃×D₄	C₂³×C₅	1	1	yes	characteristic
221	C₃×D₄	C₂³×C₅	1	1	yes	characteristic
222	C₂×C₃×C₄	—	2	1	no	—
223	C₂×C₃×C₄	—	2	1	no	—
224	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
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	D₁₂	—	2	2	no	—
231	D₁₂	—	2	1	no	—
232	D₁₂	C₅×D₄	1	1	yes	characteristic
233	D₁₂	C₂³×C₅	1	2	yes	—
234	C₄×D₃	—	2	2	no	—
235	C₄×D₃	—	2	2	no	—
236	C₄×D₃	C₂³×C₅	1	2	yes	—
237	Dic₆	—	2	1	no	—
238	Dic₆	—	2	2	no	—
239	Dic₆	C₅×D₄	1	1	yes	characteristic
240	Dic₆	C₂³×C₅	1	2	yes	—
241	C₃×C₈	C₂³×C₅	1	1	yes	characteristic
242	C₃×C₈	C₂³×C₅	1	1	yes	characteristic
243	C₃⋊C₈	C₂³×C₅	1	2	yes	—
244	C₂²×C₅	—	2	1	no	—
245	C₂²×C₅	—	2	1	no	—
246	C₂²×C₅	—	3	2	no	—
247	C₂²×C₅	—	6	2	no	—
248	C₂²×C₅	—	24	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	—	2	1	no	—
253	C₄×C₅	—	3	2	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	—	6	1	no	—
261	#41	—	6	1	no	—
262	#41	—	6	2	no	—
263	#41	C₂×C₅×D₃	1	1	yes	characteristic
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	—	3	1	no	—
270	C₂×D₄	—	6	1	no	—
271	C₂×D₄	—	6	2	no	—
272	Q₁₆	—	3	2	no	—
273	Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
274	SD₁₆	—	3	2	no	—
275	SD₁₆	—	3	2	no	—
276	SD₁₆	—	3	2	no	—
277	SD₁₆	—	3	2	no	—
278	SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
279	SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
280	D₈	—	3	2	no	—
281	D₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
282	M₁₆	—	3	1	no	—
283	M₁₆	—	3	2	no	—
284	C₂×C₈	—	3	2	no	—
285	C₂×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
286	C₃×C₅	#577	1	1	yes	characteristic, complemented, Hall
287	C₂²×C₃	—	2	1	no	—
288	C₂²×C₃	—	2	1	no	—
289	C₂²×C₃	C₂×C₅×D₄	1	1	yes	characteristic
290	C₂×D₃	—	2	2	no	—
291	C₂×D₃	—	8	2	no	—
292	C₂×D₃	—	8	1	no	—
293	C₂×D₃	C₂×C₅×D₄	1	2	yes	—
294	C₃×C₄	—	2	1	no	—
295	C₃×C₄	—	2	1	no	—
296	C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
297	C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
298	Dic₃	—	2	2	no	—
299	Dic₃	C₂×C₅×D₄	1	2	yes	—
300	C₂×C₅	—	2	1	no	—
301	C₂×C₅	—	4	1	no	—
302	C₂×C₅	—	4	1	no	—
303	C₂×C₅	—	6	2	no	—
304	C₂×C₅	—	12	2	no	—
305	C₂×C₅	C₂×D₃×D₄	1	1	yes	characteristic
306	C₂³	—	6	2	no	—
307	C₂³	—	6	1	no	—
308	Q₈	—	3	1	no	—
309	Q₈	—	3	2	no	—
310	Q₈	—	6	2	no	—
311	Q₈	—	6	1	no	—
312	Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
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	2	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	1	yes	characteristic
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	3	2	no	—
328	C₂×C₄	—	6	2	no	—
329	C₂×C₄	—	6	2	no	—
330	C₂×C₄	—	6	2	no	—
331	C₂×C₄	—	6	1	no	—
332	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
333	C₈	—	3	2	no	—
334	C₈	C₂²×C₅×D₃	1	1	yes	characteristic
335	C₈	C₂²×C₅×D₃	1	1	yes	characteristic
336	C₂×C₃	—	2	1	no	—
337	C₂×C₃	—	4	1	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	2	no	—
342	C₅	#5770	1	1	yes	characteristic, direct product factor, Sylow
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	3	2	no	—
346	C₂²	—	6	2	no	—
347	C₂²	—	24	1	no	—
348	C₂²	—	24	2	no	—
349	C₂²	C₅×D₃×D₄	1	1	yes	characteristic
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	3	2	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	1	no	—
359	C₂	—	4	1	no	—
360	C₂	—	6	2	no	—
361	C₂	—	12	2	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×#135	C₂
socle	C₂×C₃×C₅	C₂²×D₄
hypercenter	C₅×#135	D₃
hypocenter	C₃	C₅×#577
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#135

Complements

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

N	H ≅ G/N	type
1. C₅×#1010	C₂	semidirect
2. C₅×#1009	C₂	semidirect
3. C₃×C₅×#135	C₂	semidirect
4. C₅×#951	C₂	semidirect
5. C₅×#949	C₂	semidirect
6. C₅×#918	C₂	semidirect
7. C₅×#916	C₂	semidirect
8. C₅×D₃×SD₁₆	C₂	semidirect
9. C₅×#911	C₂	semidirect
10. C₂×C₅×#204	C₂	semidirect
11. C₅×#901	C₂	semidirect
14. C₃×C₅×#41	C₂²	semidirect
16. C₅×D₃×Q₈	C₂²	semidirect
18. C₅×#237	C₂²	semidirect
27. C₂×C₅×Dic₆	C₂²	semidirect
28. C₃×C₅×Q₁₆	C₂²	semidirect
29. C₃×C₅×SD₁₆	C₂²	semidirect
30. C₃×C₅×SD₁₆	C₂²	semidirect
31. C₃×C₅×D₈	C₂²	semidirect
32. C₂×C₃×C₅×C₈	C₂²	semidirect
33. C₅×#216	C₂²	semidirect
34. C₅×#215	C₂²	semidirect
35. C₅×#214	C₂²	semidirect
36. C₅×#213	C₂²	semidirect
37. C₅×#208	C₂²	semidirect
38. C₅×#204	C₂²	semidirect
39. C₅×#204	C₂²	semidirect
40. C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
41. C₅×D₃×C₈	C₂²	semidirect
42. #5770	C₅	direct (N × H)
50. C₅×#135	D₃	semidirect
84. #1010	C₂×C₅	semidirect
85. #1009	C₂×C₅	semidirect
86. C₃×#135	C₂×C₅	semidirect
87. #951	C₂×C₅	semidirect
88. #949	C₂×C₅	semidirect
89. #918	C₂×C₅	semidirect
90. #916	C₂×C₅	semidirect
91. D₃×SD₁₆	C₂×C₅	semidirect
92. #911	C₂×C₅	semidirect
93. C₂×#204	C₂×C₅	semidirect
94. #901	C₂×C₅	semidirect
102. C₅×#41	C₂×D₃	semidirect
111. C₅×Q₁₆	C₂×D₃	semidirect
116. C₅×SD₁₆	C₂×D₃	semidirect
117. C₅×SD₁₆	C₂×D₃	semidirect
119. C₅×D₈	C₂×D₃	semidirect
123. C₂×C₅×C₈	C₂×D₃	semidirect
139. C₃×#41	C₂²×C₅	semidirect
141. D₃×Q₈	C₂²×C₅	semidirect
143. #237	C₂²×C₅	semidirect
152. C₂×Dic₆	C₂²×C₅	semidirect
153. C₃×Q₁₆	C₂²×C₅	semidirect
154. C₃×SD₁₆	C₂²×C₅	semidirect
155. C₃×SD₁₆	C₂²×C₅	semidirect
156. C₃×D₈	C₂²×C₅	semidirect
157. C₂×C₃×C₈	C₂²×C₅	semidirect
158. #216	C₂²×C₅	semidirect
159. #215	C₂²×C₅	semidirect
160. #214	C₂²×C₅	semidirect
161. #213	C₂²×C₅	semidirect
162. #208	C₂²×C₅	semidirect
163. #204	C₂²×C₅	semidirect
164. #204	C₂²×C₅	semidirect
165. ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
166. D₃×C₈	C₂²×C₅	semidirect
204. #135	C₅×D₃	semidirect
264. #41	C₂×C₅×D₃	semidirect
273. Q₁₆	C₂×C₅×D₃	semidirect
278. SD₁₆	C₂×C₅×D₃	semidirect
279. SD₁₆	C₂×C₅×D₃	semidirect
281. D₈	C₂×C₅×D₃	semidirect
285. C₂×C₈	C₂×C₅×D₃	semidirect
286. C₃×C₅	#577	semidirect
342. C₅	#5770	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×#1009	2
C₃×C₅×#135	2
C₅×#951	2
C₅×#949	2
C₅×#918	2
C₅×#916	2
C₅×D₃×SD₁₆	2
C₅×#911	2
C₂×C₅×#204	2
C₅×#901	2
C₅×#577	3
#5770	5

Subgroups — C5×#5770 #11756155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5770 #11756155