Subgroups — C₅×#5592 #11755977

Order 960.

668 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	C₂²×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#237	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#953	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#940	C₂	1	2	yes	maximal, complemented
6	C₅×#939	C₂	1	2	yes	maximal, complemented
7	C₅×#937	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#885	C₂	1	2	yes	maximal, complemented
9	C₅×#884	C₂	1	2	yes	maximal, complemented
10	C₅×#882	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#535	—	3	1	no	maximal, Hall
13	C₂⁴×C₃×C₅	C₂²	1	1	yes	characteristic
14	C₂³×C₅×D₃	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×D₄	C₂²	1	2	yes	complemented
17	C₂×C₅×#67	—	2	4	no	—
18	C₂×C₅×#67	C₂²	1	1	yes	characteristic
19	C₂×C₅×#67	C₂²	1	2	yes	—
20	C₂×C₅×#67	C₂²	1	2	yes	—
21	C₂×C₅×#67	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₅×#67	C₂²	1	2	yes	complemented
23	C₂×C₅×#67	C₂²	1	2	yes	complemented
24	C₂²×C₅×Dic₃	C₂²	1	1	yes	characteristic
25	C₂²×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
26	C₅×#237	—	2	4	no	—
27	C₂×C₅×D₁₂	C₂²	1	2	yes	complemented
28	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
32	C₅×#217	C₂²	1	1	yes	characteristic
33	C₅×#217	C₂²	1	2	yes	complemented
34	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
35	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
36	C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
37	C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
38	#5592	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₂×C₅×#41	—	3	1	no	—
40	C₂²×C₅×D₄	—	3	1	no	—
41	C₅×#127	—	3	2	no	—
42	C₅×#124	—	3	2	no	—
43	C₅×#121	—	3	2	no	—
44	C₅×#121	—	3	2	no	—
45	C₅×#120	—	3	1	no	—
46	C₅×#120	—	3	1	no	—
47	C₅×#120	—	3	1	no	—
48	C₅×#120	D₃	1	1	yes	characteristic, complemented
49	C₅×#117	—	3	1	no	—
50	C₂³×C₃×C₅	—	2	2	no	—
51	C₂³×C₃×C₅	—	4	2	no	—
52	C₂³×C₃×C₅	C₂³	1	2	yes	—
53	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
54	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₅×D₃	—	2	2	no	—
56	C₂²×C₅×D₃	—	4	2	no	—
57	C₂²×C₅×D₃	C₂³	1	2	yes	—
58	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
59	C₃×C₅×D₄	—	2	2	no	—
60	C₃×C₅×D₄	—	4	2	no	—
61	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
62	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₅×#67	—	2	2	no	—
64	C₅×#67	—	2	2	no	—
65	C₅×#67	—	2	4	no	—
66	C₅×#67	—	2	4	no	—
67	C₅×#67	—	4	2	no	—
68	C₅×#67	—	4	2	no	—
69	C₂×C₅×Dic₃	—	2	2	no	—
70	C₂×C₅×Dic₃	D₄	1	4	yes	complemented
71	C₂×C₅×Dic₃	C₂³	1	2	yes	—
72	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
73	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
74	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
75	C₅×D₁₂	—	4	2	no	—
76	C₄×C₅×D₃	—	2	2	no	—
77	C₅×Dic₆	—	2	2	no	—
78	C₂²×#67	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂×#237	C₂×C₅	1	1	yes	characteristic, complemented
80	C₃×#120	C₂×C₅	1	1	yes	characteristic, complemented
81	#953	C₂×C₅	1	1	yes	characteristic, complemented
82	#940	C₂×C₅	1	2	yes	complemented
83	#939	C₂×C₅	1	2	yes	complemented
84	#937	C₂×C₅	1	1	yes	characteristic, complemented
85	#885	C₂×C₅	1	2	yes	complemented
86	#884	C₂×C₅	1	2	yes	complemented
87	#882	C₂×C₅	1	1	yes	characteristic, complemented
88	#877	C₂×C₅	1	1	yes	characteristic, complemented
89	C₂⁴×C₅	—	3	1	no	—
90	C₂⁴×C₅	C₂×D₃	1	1	yes	characteristic
91	C₅×#41	—	6	4	no	—
92	C₂×C₅×Q₈	—	3	1	no	—
93	C₂×C₅×D₄	—	3	1	no	—
94	C₂×C₅×D₄	—	3	2	no	—
95	C₂×C₅×D₄	—	3	2	no	—
96	C₂×C₅×D₄	—	3	1	no	—
97	C₂×C₅×D₄	—	3	2	no	—
98	C₂×C₅×D₄	—	3	2	no	—
99	C₂×C₅×D₄	—	3	2	no	—
100	C₂×C₅×D₄	—	6	4	no	—
101	C₂×C₅×D₄	C₂×D₃	1	1	yes	characteristic
102	C₂×C₅×D₄	C₂×D₃	1	2	yes	complemented
103	C₂²×C₄×C₅	—	3	1	no	—
104	C₂²×C₄×C₅	—	3	1	no	—
105	C₂²×C₄×C₅	—	3	1	no	—
106	C₅×C₄⋊C₄	—	3	2	no	—
107	C₅×C₂²⋊C₄	—	3	1	no	—
108	C₅×C₂²⋊C₄	—	3	2	no	—
109	C₅×C₂²⋊C₄	—	3	2	no	—
110	C₅×C₂²⋊C₄	—	3	2	no	—
111	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
112	C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
113	C₄²×C₅	—	3	2	no	—
114	#535	—	3	1	no	Sylow
115	C₂²×C₃×C₅	—	2	2	no	—
116	C₂²×C₃×C₅	—	2	1	no	—
117	C₂²×C₃×C₅	—	2	2	no	—
118	C₂²×C₃×C₅	—	2	2	no	—
119	C₂²×C₃×C₅	—	2	2	no	—
120	C₂²×C₃×C₅	—	2	2	no	—
121	C₂²×C₃×C₅	—	4	4	no	—
122	C₂²×C₃×C₅	C₂×D₄	1	2	yes	—
123	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
124	C₂×C₅×D₃	—	2	1	no	—
125	C₂×C₅×D₃	—	2	2	no	—
126	C₂×C₅×D₃	—	2	2	no	—
127	C₂×C₅×D₃	—	2	2	no	—
128	C₂×C₅×D₃	—	2	2	no	—
129	C₂×C₅×D₃	—	4	4	no	—
130	C₃×C₄×C₅	—	2	1	no	—
131	C₃×C₄×C₅	—	2	2	no	—
132	C₅×Dic₃	—	2	1	no	—
133	C₅×Dic₃	—	2	2	no	—
134	C₅×Dic₃	C₂×D₄	1	2	yes	—
135	C₅×Dic₃	C₂×D₄	1	2	yes	—
136	C₂⁴×C₃	C₂²×C₅	1	1	yes	characteristic
137	C₂³×D₃	C₂²×C₅	1	1	yes	characteristic
138	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
139	C₂×C₃×D₄	C₂²×C₅	1	2	yes	complemented
140	C₂×#67	—	2	4	no	—
141	C₂×#67	C₂²×C₅	1	1	yes	characteristic
142	C₂×#67	C₂²×C₅	1	2	yes	—
143	C₂×#67	C₂²×C₅	1	2	yes	—
144	C₂×#67	C₂²×C₅	1	1	yes	characteristic, complemented
145	C₂×#67	C₂²×C₅	1	2	yes	complemented
146	C₂×#67	C₂²×C₅	1	2	yes	complemented
147	C₂²×Dic₃	C₂²×C₅	1	1	yes	characteristic
148	C₂²×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
149	#237	—	2	4	no	—
150	C₂×D₁₂	C₂²×C₅	1	2	yes	complemented
151	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
152	C₂×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
153	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
154	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
155	#217	C₂²×C₅	1	1	yes	characteristic
156	#217	C₂²×C₅	1	2	yes	complemented
157	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
158	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
159	Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
160	C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
161	C₂³×C₅	—	2	2	no	—
162	C₂³×C₅	—	3	2	no	—
163	C₂³×C₅	—	3	1	no	—
164	C₂³×C₅	—	4	2	no	—
165	C₂³×C₅	—	6	2	no	—
166	C₂³×C₅	—	12	2	no	—
167	C₂³×C₅	C₂²×D₃	1	2	yes	—
168	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
169	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
170	C₅×Q₈	—	6	2	no	—
171	C₅×D₄	—	2	2	no	—
172	C₅×D₄	—	4	2	no	—
173	C₅×D₄	—	6	4	no	—
174	C₅×D₄	—	6	4	no	—
175	C₅×D₄	—	6	2	no	—
176	C₅×D₄	—	6	2	no	—
177	C₅×D₄	—	12	2	no	—
178	C₅×D₄	—	12	2	no	—
179	C₅×D₄	—	12	2	no	—
180	C₂×C₄×C₅	—	3	4	no	—
181	C₂×C₄×C₅	—	3	1	no	—
182	C₂×C₄×C₅	—	3	1	no	—
183	C₂×C₄×C₅	—	3	2	no	—
184	C₂×C₄×C₅	—	3	1	no	—
185	C₂×C₄×C₅	—	6	2	no	—
186	C₂×C₄×C₅	—	6	2	no	—
187	C₂×C₄×C₅	C₂²×D₃	1	2	yes	—
188	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
189	C₂×#41	—	3	1	no	—
190	C₂²×D₄	—	3	1	no	—
191	#127	—	3	2	no	—
192	#124	—	3	2	no	—
193	#121	—	3	2	no	—
194	#121	—	3	2	no	—
195	#120	—	3	1	no	—
196	#120	—	3	1	no	—
197	#120	—	3	1	no	—
198	#120	C₅×D₃	1	1	yes	characteristic, complemented
199	#117	—	3	1	no	—
200	C₂×C₃×C₅	—	2	2	no	—
201	C₂×C₃×C₅	—	4	1	no	—
202	C₂×C₃×C₅	—	4	2	no	—
203	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
205	C₅×D₃	—	4	1	no	—
206	C₅×D₃	—	4	2	no	—
207	C₂³×C₃	—	2	2	no	—
208	C₂³×C₃	—	4	2	no	—
209	C₂³×C₃	C₂³×C₅	1	2	yes	—
210	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
211	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
212	C₂²×D₃	—	2	2	no	—
213	C₂²×D₃	—	4	2	no	—
214	C₂²×D₃	C₂³×C₅	1	2	yes	—
215	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
216	C₃×D₄	—	2	2	no	—
217	C₃×D₄	—	4	2	no	—
218	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
219	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
220	#67	—	2	2	no	—
221	#67	—	2	2	no	—
222	#67	—	2	4	no	—
223	#67	—	2	4	no	—
224	#67	—	4	2	no	—
225	#67	—	4	2	no	—
226	C₂×Dic₃	—	2	2	no	—
227	C₂×Dic₃	C₅×D₄	1	4	yes	complemented
228	C₂×Dic₃	C₂³×C₅	1	2	yes	—
229	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
230	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
231	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
232	D₁₂	—	4	2	no	—
233	C₄×D₃	—	2	2	no	—
234	Dic₆	—	2	2	no	—
235	C₂²×C₅	—	2	2	no	—
236	C₂²×C₅	—	2	1	no	—
237	C₂²×C₅	—	2	2	no	—
238	C₂²×C₅	—	2	2	no	—
239	C₂²×C₅	—	2	2	no	—
240	C₂²×C₅	—	2	2	no	—
241	C₂²×C₅	—	4	4	no	—
242	C₂²×C₅	—	6	1	no	—
243	C₂²×C₅	—	6	2	no	—
244	C₂²×C₅	—	6	2	no	—
245	C₂²×C₅	—	6	2	no	—
246	C₂²×C₅	—	6	2	no	—
247	C₂²×C₅	—	12	4	no	—
248	C₂²×C₅	D₃×D₄	1	2	yes	—
249	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
250	C₄×C₅	—	2	1	no	—
251	C₄×C₅	—	2	2	no	—
252	C₄×C₅	—	3	2	no	—
253	C₄×C₅	—	3	2	no	—
254	C₄×C₅	—	6	1	no	—
255	C₄×C₅	—	6	2	no	—
256	C₂⁴	—	3	1	no	—
257	C₂⁴	C₂×C₅×D₃	1	1	yes	characteristic
258	#41	—	6	4	no	—
259	C₂×Q₈	—	3	1	no	—
260	C₂×D₄	—	3	1	no	—
261	C₂×D₄	—	3	2	no	—
262	C₂×D₄	—	3	2	no	—
263	C₂×D₄	—	3	1	no	—
264	C₂×D₄	—	3	2	no	—
265	C₂×D₄	—	3	2	no	—
266	C₂×D₄	—	3	2	no	—
267	C₂×D₄	—	6	4	no	—
268	C₂×D₄	C₂×C₅×D₃	1	1	yes	characteristic
269	C₂×D₄	C₂×C₅×D₃	1	2	yes	complemented
270	C₂²×C₄	—	3	1	no	—
271	C₂²×C₄	—	3	1	no	—
272	C₂²×C₄	—	3	1	no	—
273	C₄⋊C₄	—	3	2	no	—
274	C₂²⋊C₄	—	3	1	no	—
275	C₂²⋊C₄	—	3	2	no	—
276	C₂²⋊C₄	—	3	2	no	—
277	C₂²⋊C₄	—	3	2	no	—
278	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
279	C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
280	C₄²	—	3	2	no	—
281	C₃×C₅	#535	1	1	yes	characteristic, complemented, Hall
282	C₂²×C₃	—	2	2	no	—
283	C₂²×C₃	—	2	1	no	—
284	C₂²×C₃	—	2	2	no	—
285	C₂²×C₃	—	2	2	no	—
286	C₂²×C₃	—	2	2	no	—
287	C₂²×C₃	—	2	2	no	—
288	C₂²×C₃	—	4	4	no	—
289	C₂²×C₃	C₂×C₅×D₄	1	2	yes	—
290	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
291	C₂×D₃	—	2	1	no	—
292	C₂×D₃	—	2	2	no	—
293	C₂×D₃	—	2	2	no	—
294	C₂×D₃	—	2	2	no	—
295	C₂×D₃	—	2	2	no	—
296	C₂×D₃	—	4	4	no	—
297	C₃×C₄	—	2	1	no	—
298	C₃×C₄	—	2	2	no	—
299	Dic₃	—	2	1	no	—
300	Dic₃	—	2	2	no	—
301	Dic₃	C₂×C₅×D₄	1	2	yes	—
302	Dic₃	C₂×C₅×D₄	1	2	yes	—
303	C₂×C₅	—	2	2	no	—
304	C₂×C₅	—	4	2	no	—
305	C₂×C₅	—	4	1	no	—
306	C₂×C₅	—	12	2	no	—
307	C₂×C₅	—	12	1	no	—
308	C₂×C₅	C₂×D₃×D₄	1	1	yes	characteristic
309	C₂×C₅	#1004	1	2	yes	—
310	C₂³	—	2	2	no	—
311	C₂³	—	3	2	no	—
312	C₂³	—	3	1	no	—
313	C₂³	—	4	2	no	—
314	C₂³	—	6	2	no	—
315	C₂³	—	12	2	no	—
316	C₂³	C₂²×C₅×D₃	1	2	yes	—
317	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
318	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
319	Q₈	—	6	2	no	—
320	D₄	—	2	2	no	—
321	D₄	—	4	2	no	—
322	D₄	—	6	4	no	—
323	D₄	—	6	4	no	—
324	D₄	—	6	2	no	—
325	D₄	—	6	2	no	—
326	D₄	—	12	2	no	—
327	D₄	—	12	2	no	—
328	D₄	—	12	2	no	—
329	C₂×C₄	—	3	4	no	—
330	C₂×C₄	—	3	1	no	—
331	C₂×C₄	—	3	1	no	—
332	C₂×C₄	—	3	2	no	—
333	C₂×C₄	—	3	1	no	—
334	C₂×C₄	—	6	2	no	—
335	C₂×C₄	—	6	2	no	—
336	C₂×C₄	C₂²×C₅×D₃	1	2	yes	—
337	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
338	C₂×C₃	—	2	2	no	—
339	C₂×C₃	—	4	2	no	—
340	C₂×C₃	—	4	1	no	—
341	C₂×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
342	C₂×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
343	D₃	—	4	2	no	—
344	D₃	—	4	1	no	—
345	C₅	#5592	1	1	yes	characteristic, direct product factor, Sylow
346	C₂²	—	2	2	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	4	4	no	—
353	C₂²	—	6	1	no	—
354	C₂²	—	6	2	no	—
355	C₂²	—	6	2	no	—
356	C₂²	—	6	2	no	—
357	C₂²	—	6	2	no	—
358	C₂²	—	12	4	no	—
359	C₂²	C₅×D₃×D₄	1	2	yes	—
360	C₂²	C₂³×C₅×D₃	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	2	2	no	—
363	C₄	—	3	2	no	—
364	C₄	—	3	2	no	—
365	C₄	—	6	1	no	—
366	C₄	—	6	2	no	—
367	C₃	C₅×#535	1	1	yes	characteristic, complemented, Sylow
368	C₂	—	2	2	no	—
369	C₂	—	4	2	no	—
370	C₂	—	4	1	no	—
371	C₂	—	12	2	no	—
372	C₂	—	12	1	no	—
373	C₂	C₂×C₅×D₃×D₄	1	1	yes	characteristic
374	C₂	C₅×#1004	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₅
Frattini	C₂²	C₂³×C₅×D₃
Fitting	C₃×C₅×#120	C₂
socle	C₂²×C₃×C₅	C₂⁴
hypercenter	C₅×#120	D₃
hypocenter	C₃	C₅×#535
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#120

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#67	C₂	semidirect
2. C₂×C₅×#237	C₂	semidirect
3. C₃×C₅×#120	C₂	semidirect
4. C₅×#953	C₂	semidirect
5. C₅×#940	C₂	semidirect
6. C₅×#939	C₂	semidirect
7. C₅×#937	C₂	semidirect
8. C₅×#885	C₂	semidirect
9. C₅×#884	C₂	semidirect
10. C₅×#882	C₂	semidirect
11. C₅×#877	C₂	semidirect
16. C₂×C₃×C₅×D₄	C₂²	semidirect
21. C₂×C₅×#67	C₂²	semidirect
22. C₂×C₅×#67	C₂²	semidirect
23. C₂×C₅×#67	C₂²	semidirect
25. C₂²×C₅×Dic₃	C₂²	semidirect
27. C₂×C₅×D₁₂	C₂²	semidirect
28. C₂×C₄×C₅×D₃	C₂²	semidirect
29. C₂×C₅×Dic₆	C₂²	semidirect
31. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
33. C₅×#217	C₂²	semidirect
34. C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
35. C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₅×Dic₃⋊C₄	C₂²	semidirect
37. C₄×C₅×Dic₃	C₂²	semidirect
38. #5592	C₅	direct (N × H)
48. C₅×#120	D₃	semidirect
70. C₂×C₅×Dic₃	D₄	semidirect
78. C₂²×#67	C₂×C₅	semidirect
79. C₂×#237	C₂×C₅	semidirect
80. C₃×#120	C₂×C₅	semidirect
81. #953	C₂×C₅	semidirect
82. #940	C₂×C₅	semidirect
83. #939	C₂×C₅	semidirect
84. #937	C₂×C₅	semidirect
85. #885	C₂×C₅	semidirect
86. #884	C₂×C₅	semidirect
87. #882	C₂×C₅	semidirect
88. #877	C₂×C₅	semidirect
102. C₂×C₅×D₄	C₂×D₃	semidirect
112. C₅×C₂²⋊C₄	C₂×D₃	semidirect
139. C₂×C₃×D₄	C₂²×C₅	semidirect
144. C₂×#67	C₂²×C₅	semidirect
145. C₂×#67	C₂²×C₅	semidirect
146. C₂×#67	C₂²×C₅	semidirect
148. C₂²×Dic₃	C₂²×C₅	semidirect
150. C₂×D₁₂	C₂²×C₅	semidirect
151. C₂×C₄×D₃	C₂²×C₅	semidirect
152. C₂×Dic₆	C₂²×C₅	semidirect
154. C₃×C₂²⋊C₄	C₂²×C₅	semidirect
156. #217	C₂²×C₅	semidirect
157. (C₂×D₃)⋊C₄	C₂²×C₅	semidirect
158. (C₂×D₃)⋊C₄	C₂²×C₅	semidirect
159. Dic₃⋊C₄	C₂²×C₅	semidirect
160. C₄×Dic₃	C₂²×C₅	semidirect
198. #120	C₅×D₃	semidirect
227. C₂×Dic₃	C₅×D₄	semidirect
269. C₂×D₄	C₂×C₅×D₃	semidirect
279. C₂²⋊C₄	C₂×C₅×D₃	semidirect
281. C₃×C₅	#535	semidirect
345. C₅	#5592	direct (N × H)
367. C₃	C₅×#535	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×#67	2
C₂×C₅×#237	2
C₃×C₅×#120	2
C₅×#953	2
C₅×#940	2
C₅×#939	2
C₅×#937	2
C₅×#885	2
C₅×#884	2
C₅×#882	2
C₅×#877	2
C₅×#535	3
#5592	5

Subgroups — C5×#5592 #11755977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5592 #11755977