Subgroups — C₅×#5653 #11756038

Order 960.

692 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#937	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#929	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#895	C₂	1	2	yes	maximal, complemented
7	C₅×#894	C₂	1	2	yes	maximal, complemented
8	C₅×#884	C₂	1	2	yes	maximal, complemented
9	C₅×#882	C₂	1	2	yes	maximal, complemented
10	C₅×#882	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#534	—	3	1	no	maximal, Hall
13	C₂³×C₅×D₃	C₂²	1	1	yes	characteristic
14	C₂³×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
15	C₂³×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₅×#67	C₂²	1	1	yes	characteristic
19	C₂×C₅×#67	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₅×#67	C₂²	1	2	yes	complemented
21	C₅×D₃×D₄	—	2	4	no	—
22	C₂×C₅×D₁₂	—	2	4	no	—
23	C₂×C₅×D₁₂	C₂²	1	2	yes	—
24	C₂×C₅×D₁₂	C₂²	1	2	yes	complemented
25	C₂×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×D₁₂	C₂²	1	2	yes	complemented
27	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₄×C₅×D₃	C₂²	1	2	yes	complemented
29	C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
30	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
32	C₅×#217	C₂²	1	1	yes	characteristic, complemented
33	C₅×(C₂×D₃)⋊C₄	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×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
37	C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
38	#5653	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₂²×C₅×D₄	—	3	1	no	—
40	C₂²×C₅×D₄	—	3	1	no	—
41	C₅×#123	—	3	1	no	—
42	C₅×#123	—	3	2	no	—
43	C₅×#123	D₃	1	1	yes	characteristic, complemented
44	C₅×#121	—	3	2	no	—
45	C₅×#121	—	3	2	no	—
46	C₅×#120	—	3	1	no	—
47	C₅×#120	—	3	2	no	—
48	C₅×#120	—	3	1	no	—
49	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
50	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
51	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₅×D₃	—	2	2	no	—
53	C₂²×C₅×D₃	—	2	2	no	—
54	C₂²×C₅×D₃	—	4	2	no	—
55	C₂²×C₅×D₃	—	4	2	no	—
56	C₂²×C₅×D₃	—	4	2	no	—
57	C₂²×C₅×D₃	D₄	1	4	yes	complemented
58	C₂²×C₅×D₃	C₂³	1	2	yes	—
59	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
60	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
61	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
62	C₃×C₅×D₄	—	2	2	no	—
63	C₂×C₃×C₄×C₅	—	2	2	no	—
64	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
65	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
66	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₅×#67	—	2	2	no	—
68	C₅×#67	—	2	2	no	—
69	C₅×#67	—	4	2	no	—
70	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
71	C₂×C₅×Dic₃	C₂³	1	2	yes	—
72	C₅×D₁₂	—	2	4	no	—
73	C₅×D₁₂	—	2	4	no	—
74	C₅×D₁₂	—	2	2	no	—
75	C₅×D₁₂	—	4	2	no	—
76	C₄×C₅×D₃	—	2	2	no	—
77	C₄×C₅×D₃	—	4	2	no	—
78	C₂×D₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂²×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
80	C₃×#123	C₂×C₅	1	1	yes	characteristic, complemented
81	#937	C₂×C₅	1	1	yes	characteristic, complemented
82	#929	C₂×C₅	1	1	yes	characteristic, complemented
83	#895	C₂×C₅	1	2	yes	complemented
84	#894	C₂×C₅	1	2	yes	complemented
85	#884	C₂×C₅	1	2	yes	complemented
86	#882	C₂×C₅	1	2	yes	complemented
87	#882	C₂×C₅	1	1	yes	characteristic, complemented
88	D₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
89	C₂⁴×C₅	—	3	1	no	—
90	C₂⁴×C₅	—	3	1	no	—
91	C₂⁴×C₅	—	3	1	no	—
92	C₂×C₅×D₄	—	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	—	6	4	no	—
100	C₂×C₅×D₄	—	6	4	no	—
101	C₂×C₅×D₄	C₂×D₃	1	1	yes	characteristic
102	C₂²×C₄×C₅	—	3	1	no	—
103	C₂²×C₄×C₅	—	3	2	no	—
104	C₂²×C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
105	C₅×C₄⋊C₄	—	3	2	no	—
106	C₅×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
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	—	3	2	no	—
112	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
113	C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
114	#534	—	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	C₂×D₄	1	2	yes	—
119	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
120	C₂×C₅×D₃	—	2	2	no	—
121	C₂×C₅×D₃	—	2	2	no	—
122	C₂×C₅×D₃	—	2	2	no	—
123	C₂×C₅×D₃	—	2	1	no	—
124	C₂×C₅×D₃	—	2	2	no	—
125	C₂×C₅×D₃	—	2	2	no	—
126	C₂×C₅×D₃	—	2	2	no	—
127	C₂×C₅×D₃	—	4	4	no	—
128	C₂×C₅×D₃	—	4	4	no	—
129	C₂×C₅×D₃	—	4	4	no	—
130	C₂×C₅×D₃	C₂×D₄	1	2	yes	—
131	C₂×C₅×D₃	C₂×D₄	1	2	yes	—
132	C₃×C₄×C₅	—	2	1	no	—
133	C₃×C₄×C₅	—	2	2	no	—
134	C₃×C₄×C₅	—	2	2	no	—
135	C₅×Dic₃	—	2	1	no	—
136	C₅×Dic₃	—	2	2	no	—
137	C₂³×D₃	C₂²×C₅	1	1	yes	characteristic
138	C₂³×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
139	C₂³×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
140	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
141	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
142	C₂×#67	C₂²×C₅	1	1	yes	characteristic
143	C₂×#67	C₂²×C₅	1	1	yes	characteristic, complemented
144	C₂×#67	C₂²×C₅	1	2	yes	complemented
145	D₃×D₄	—	2	4	no	—
146	C₂×D₁₂	—	2	4	no	—
147	C₂×D₁₂	C₂²×C₅	1	2	yes	—
148	C₂×D₁₂	C₂²×C₅	1	2	yes	complemented
149	C₂×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
150	C₂×D₁₂	C₂²×C₅	1	2	yes	complemented
151	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
152	C₂×C₄×D₃	C₂²×C₅	1	2	yes	complemented
153	C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
154	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
155	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
156	#217	C₂²×C₅	1	1	yes	characteristic, complemented
157	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
158	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
159	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
160	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
161	Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
162	C₂³×C₅	—	3	1	no	—
163	C₂³×C₅	—	3	1	no	—
164	C₂³×C₅	—	3	4	no	—
165	C₂³×C₅	—	3	1	no	—
166	C₂³×C₅	—	3	2	no	—
167	C₂³×C₅	—	6	2	no	—
168	C₂³×C₅	—	6	2	no	—
169	C₂³×C₅	—	12	2	no	—
170	C₂³×C₅	—	12	2	no	—
171	C₂³×C₅	—	12	2	no	—
172	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
173	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
174	C₅×D₄	—	2	2	no	—
175	C₅×D₄	—	6	4	no	—
176	C₅×D₄	—	6	4	no	—
177	C₅×D₄	—	6	2	no	—
178	C₅×D₄	—	6	2	no	—
179	C₅×D₄	—	6	2	no	—
180	C₅×D₄	—	12	2	no	—
181	C₅×D₄	—	12	2	no	—
182	C₂×C₄×C₅	—	2	2	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	—	12	2	no	—
187	C₂×C₄×C₅	C₂²×D₃	1	2	yes	—
188	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
189	C₂×C₄×C₅	C₂²×D₃	1	2	yes	—
190	C₂²×D₄	—	3	1	no	—
191	C₂²×D₄	—	3	1	no	—
192	#123	—	3	1	no	—
193	#123	—	3	2	no	—
194	#123	C₅×D₃	1	1	yes	characteristic, complemented
195	#121	—	3	2	no	—
196	#121	—	3	2	no	—
197	#120	—	3	1	no	—
198	#120	—	3	2	no	—
199	#120	—	3	1	no	—
200	C₂×C₂²⋊C₄	—	3	1	no	—
201	C₂×C₃×C₅	—	2	2	no	—
202	C₂×C₃×C₅	—	4	1	no	—
203	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
205	C₅×D₃	—	2	2	no	—
206	C₅×D₃	—	2	2	no	—
207	C₅×D₃	—	4	2	no	—
208	C₅×D₃	—	4	1	no	—
209	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
210	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
211	C₂²×D₃	—	2	2	no	—
212	C₂²×D₃	—	2	2	no	—
213	C₂²×D₃	—	4	2	no	—
214	C₂²×D₃	—	4	2	no	—
215	C₂²×D₃	—	4	2	no	—
216	C₂²×D₃	C₅×D₄	1	4	yes	complemented
217	C₂²×D₃	C₂³×C₅	1	2	yes	—
218	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
219	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
220	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
221	C₃×D₄	—	2	2	no	—
222	C₂×C₃×C₄	—	2	2	no	—
223	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
224	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
225	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
226	#67	—	2	2	no	—
227	#67	—	2	2	no	—
228	#67	—	4	2	no	—
229	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
230	C₂×Dic₃	C₂³×C₅	1	2	yes	—
231	D₁₂	—	2	4	no	—
232	D₁₂	—	2	4	no	—
233	D₁₂	—	2	2	no	—
234	D₁₂	—	4	2	no	—
235	C₄×D₃	—	2	2	no	—
236	C₄×D₃	—	4	2	no	—
237	C₂²×C₅	—	2	2	no	—
238	C₂²×C₅	—	2	1	no	—
239	C₂²×C₅	—	2	2	no	—
240	C₂²×C₅	—	3	2	no	—
241	C₂²×C₅	—	3	2	no	—
242	C₂²×C₅	—	6	2	no	—
243	C₂²×C₅	—	6	2	no	—
244	C₂²×C₅	—	6	2	no	—
245	C₂²×C₅	—	6	1	no	—
246	C₂²×C₅	—	6	2	no	—
247	C₂²×C₅	—	6	2	no	—
248	C₂²×C₅	—	6	2	no	—
249	C₂²×C₅	—	12	4	no	—
250	C₂²×C₅	—	12	4	no	—
251	C₂²×C₅	—	12	4	no	—
252	C₂²×C₅	D₃×D₄	1	2	yes	—
253	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
254	C₄×C₅	—	2	2	no	—
255	C₄×C₅	—	2	1	no	—
256	C₄×C₅	—	2	2	no	—
257	C₄×C₅	—	6	1	no	—
258	C₄×C₅	—	6	2	no	—
259	C₂⁴	—	3	1	no	—
260	C₂⁴	—	3	1	no	—
261	C₂⁴	—	3	1	no	—
262	C₂×D₄	—	3	1	no	—
263	C₂×D₄	—	3	1	no	—
264	C₂×D₄	—	3	2	no	—
265	C₂×D₄	—	3	2	no	—
266	C₂×D₄	—	3	1	no	—
267	C₂×D₄	—	3	2	no	—
268	C₂×D₄	—	3	2	no	—
269	C₂×D₄	—	6	4	no	—
270	C₂×D₄	—	6	4	no	—
271	C₂×D₄	C₂×C₅×D₃	1	1	yes	characteristic
272	C₂²×C₄	—	3	1	no	—
273	C₂²×C₄	—	3	2	no	—
274	C₂²×C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
275	C₄⋊C₄	—	3	2	no	—
276	C₄⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
277	C₂²⋊C₄	—	3	1	no	—
278	C₂²⋊C₄	—	3	2	no	—
279	C₂²⋊C₄	—	3	2	no	—
280	C₂²⋊C₄	—	3	2	no	—
281	C₂²⋊C₄	—	3	2	no	—
282	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
283	C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
284	C₃×C₅	#534	1	1	yes	characteristic, complemented, Hall
285	C₂²×C₃	—	2	2	no	—
286	C₂²×C₃	—	2	1	no	—
287	C₂²×C₃	—	2	2	no	—
288	C₂²×C₃	C₂×C₅×D₄	1	2	yes	—
289	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
290	C₂×D₃	—	2	2	no	—
291	C₂×D₃	—	2	2	no	—
292	C₂×D₃	—	2	2	no	—
293	C₂×D₃	—	2	1	no	—
294	C₂×D₃	—	2	2	no	—
295	C₂×D₃	—	2	2	no	—
296	C₂×D₃	—	2	2	no	—
297	C₂×D₃	—	4	4	no	—
298	C₂×D₃	—	4	4	no	—
299	C₂×D₃	—	4	4	no	—
300	C₂×D₃	C₂×C₅×D₄	1	2	yes	—
301	C₂×D₃	C₂×C₅×D₄	1	2	yes	—
302	C₃×C₄	—	2	1	no	—
303	C₃×C₄	—	2	2	no	—
304	C₃×C₄	—	2	2	no	—
305	Dic₃	—	2	1	no	—
306	Dic₃	—	2	2	no	—
307	C₂×C₅	—	2	2	no	—
308	C₂×C₅	—	4	1	no	—
309	C₂×C₅	—	6	2	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	C₂×C₅	#1009	1	2	yes	—
315	C₂³	—	3	1	no	—
316	C₂³	—	3	1	no	—
317	C₂³	—	3	4	no	—
318	C₂³	—	3	1	no	—
319	C₂³	—	3	2	no	—
320	C₂³	—	6	2	no	—
321	C₂³	—	6	2	no	—
322	C₂³	—	12	2	no	—
323	C₂³	—	12	2	no	—
324	C₂³	—	12	2	no	—
325	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
326	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
327	D₄	—	2	2	no	—
328	D₄	—	6	4	no	—
329	D₄	—	6	4	no	—
330	D₄	—	6	2	no	—
331	D₄	—	6	2	no	—
332	D₄	—	6	2	no	—
333	D₄	—	12	2	no	—
334	D₄	—	12	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	3	2	no	—
337	C₂×C₄	—	3	1	no	—
338	C₂×C₄	—	6	2	no	—
339	C₂×C₄	—	12	2	no	—
340	C₂×C₄	C₂²×C₅×D₃	1	2	yes	—
341	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
342	C₂×C₄	C₂²×C₅×D₃	1	2	yes	—
343	C₂×C₃	—	2	2	no	—
344	C₂×C₃	—	4	1	no	—
345	C₂×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
346	C₂×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
347	D₃	—	2	2	no	—
348	D₃	—	2	2	no	—
349	D₃	—	4	2	no	—
350	D₃	—	4	1	no	—
351	C₅	#5653	1	1	yes	characteristic, direct product factor, Sylow
352	C₂²	—	2	2	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	3	2	no	—
356	C₂²	—	3	2	no	—
357	C₂²	—	6	2	no	—
358	C₂²	—	6	2	no	—
359	C₂²	—	6	2	no	—
360	C₂²	—	6	1	no	—
361	C₂²	—	6	2	no	—
362	C₂²	—	6	2	no	—
363	C₂²	—	6	2	no	—
364	C₂²	—	12	4	no	—
365	C₂²	—	12	4	no	—
366	C₂²	—	12	4	no	—
367	C₂²	C₅×D₃×D₄	1	2	yes	—
368	C₂²	C₂³×C₅×D₃	1	1	yes	characteristic
369	C₄	—	2	2	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	2	no	—
372	C₄	—	6	1	no	—
373	C₄	—	6	2	no	—
374	C₃	C₅×#534	1	1	yes	characteristic, complemented, Sylow
375	C₂	—	2	2	no	—
376	C₂	—	4	1	no	—
377	C₂	—	6	2	no	—
378	C₂	—	6	2	no	—
379	C₂	—	12	2	no	—
380	C₂	—	12	1	no	—
381	C₂	C₂×C₅×D₃×D₄	1	1	yes	characteristic
382	C₂	C₅×#1009	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×#123	C₂
socle	C₂²×C₃×C₅	C₂⁴
hypercenter	C₅×#123	D₃
hypocenter	C₃	C₅×#534
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#123

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×D₄	C₂	semidirect
2. C₂²×C₅×D₁₂	C₂	semidirect
3. C₃×C₅×#123	C₂	semidirect
4. C₅×#937	C₂	semidirect
5. C₅×#929	C₂	semidirect
6. C₅×#895	C₂	semidirect
7. C₅×#894	C₂	semidirect
8. C₅×#884	C₂	semidirect
9. C₅×#882	C₂	semidirect
10. C₅×#882	C₂	semidirect
11. C₅×D₃×C₂²⋊C₄	C₂	semidirect
14. C₂³×C₅×D₃	C₂²	semidirect
15. C₂³×C₅×D₃	C₂²	semidirect
17. C₂²×C₃×C₄×C₅	C₂²	semidirect
19. C₂×C₅×#67	C₂²	semidirect
20. C₂×C₅×#67	C₂²	semidirect
24. C₂×C₅×D₁₂	C₂²	semidirect
25. C₂×C₅×D₁₂	C₂²	semidirect
26. C₂×C₅×D₁₂	C₂²	semidirect
27. C₂×C₄×C₅×D₃	C₂²	semidirect
28. C₂×C₄×C₅×D₃	C₂²	semidirect
29. C₃×C₅×C₄⋊C₄	C₂²	semidirect
30. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
31. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
32. C₅×#217	C₂²	semidirect
33. C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
34. C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
35. C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
37. C₅×Dic₃⋊C₄	C₂²	semidirect
38. #5653	C₅	direct (N × H)
43. C₅×#123	D₃	semidirect
57. C₂²×C₅×D₃	D₄	semidirect
78. C₂×D₃×D₄	C₂×C₅	semidirect
79. C₂²×D₁₂	C₂×C₅	semidirect
80. C₃×#123	C₂×C₅	semidirect
81. #937	C₂×C₅	semidirect
82. #929	C₂×C₅	semidirect
83. #895	C₂×C₅	semidirect
84. #894	C₂×C₅	semidirect
85. #884	C₂×C₅	semidirect
86. #882	C₂×C₅	semidirect
87. #882	C₂×C₅	semidirect
88. D₃×C₂²⋊C₄	C₂×C₅	semidirect
104. C₂²×C₄×C₅	C₂×D₃	semidirect
106. C₅×C₄⋊C₄	C₂×D₃	semidirect
112. C₅×C₂²⋊C₄	C₂×D₃	semidirect
113. C₅×C₂²⋊C₄	C₂×D₃	semidirect
138. C₂³×D₃	C₂²×C₅	semidirect
139. C₂³×D₃	C₂²×C₅	semidirect
141. C₂²×C₃×C₄	C₂²×C₅	semidirect
143. C₂×#67	C₂²×C₅	semidirect
144. C₂×#67	C₂²×C₅	semidirect
148. C₂×D₁₂	C₂²×C₅	semidirect
149. C₂×D₁₂	C₂²×C₅	semidirect
150. C₂×D₁₂	C₂²×C₅	semidirect
151. C₂×C₄×D₃	C₂²×C₅	semidirect
152. C₂×C₄×D₃	C₂²×C₅	semidirect
153. C₃×C₄⋊C₄	C₂²×C₅	semidirect
154. C₃×C₂²⋊C₄	C₂²×C₅	semidirect
155. 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. (C₂×D₃)⋊C₄	C₂²×C₅	semidirect
160. (C₂×D₃)⋊C₄	C₂²×C₅	semidirect
161. Dic₃⋊C₄	C₂²×C₅	semidirect
194. #123	C₅×D₃	semidirect
216. C₂²×D₃	C₅×D₄	semidirect
274. C₂²×C₄	C₂×C₅×D₃	semidirect
276. C₄⋊C₄	C₂×C₅×D₃	semidirect
282. C₂²⋊C₄	C₂×C₅×D₃	semidirect
283. C₂²⋊C₄	C₂×C₅×D₃	semidirect
284. C₃×C₅	#534	semidirect
351. C₅	#5653	direct (N × H)
374. C₃	C₅×#534	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×D₄	2
C₂²×C₅×D₁₂	2
C₃×C₅×#123	2
C₅×#937	2
C₅×#929	2
C₅×#895	2
C₅×#894	2
C₅×#884	2
C₅×#882	2
C₅×D₃×C₂²⋊C₄	2
C₅×#534	3
#5653	5

Subgroups — C5×#5653 #11756038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5653 #11756038