Subgroups — C₅×#5627 #11756012

Order 960.

660 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#239	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×C₅×D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#946	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#930	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#895	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#894	C₂	1	2	yes	maximal, complemented
8	C₅×#893	C₂	1	2	yes	maximal, complemented
9	C₅×#892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#882	C₂	1	2	yes	maximal, complemented
11	C₅×#67⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₅×#525	—	3	1	no	maximal, Hall
13	C₂³×C₅×D₃	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₅×#67	C₂²	1	2	yes	—
17	C₂²×C₅×Dic₃	C₂²	1	1	yes	characteristic
18	C₅×#239	—	2	4	no	—
19	C₂×C₅×D₁₂	C₂²	1	2	yes	—
20	C₂×C₅×D₁₂	C₂²	1	2	yes	—
21	C₂×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₄×C₅×D₃	—	2	4	no	—
23	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×D₃	C₂²	1	2	yes	complemented
28	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
30	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
32	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
33	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
34	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
35	C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
36	C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
37	C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
38	#5627	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₂×C₅×#41	—	3	1	no	—
40	C₂³×C₄×C₅	—	3	1	no	—
41	C₅×#123	—	3	2	no	—
42	C₅×C₂²⋊Q₈	—	3	1	no	—
43	C₅×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
44	C₅×#121	—	3	1	no	—
45	C₅×#121	—	3	1	no	—
46	C₅×#120	—	3	2	no	—
47	C₄×C₅×D₄	—	3	2	no	—
48	C₄×C₅×D₄	—	3	2	no	—
49	C₅×#117	—	3	1	no	—
50	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₅×D₃	—	2	2	no	—
52	C₂²×C₅×D₃	—	2	2	no	—
53	C₂²×C₅×D₃	—	2	2	no	—
54	C₂²×C₅×D₃	C₂³	1	2	yes	—
55	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
56	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
57	C₃×C₅×Q₈	—	2	2	no	—
58	C₂×C₃×C₄×C₅	—	2	2	no	—
59	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
60	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
61	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₅×#67	—	2	4	no	—
64	C₂×C₅×Dic₃	—	2	2	no	—
65	C₂×C₅×Dic₃	C₂³	1	2	yes	—
66	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
67	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
68	C₅×D₁₂	—	2	4	no	—
69	C₅×D₁₂	—	2	4	no	—
70	C₅×D₁₂	—	2	2	no	—
71	C₄×C₅×D₃	—	2	2	no	—
72	C₄×C₅×D₃	—	2	2	no	—
73	C₄×C₅×D₃	—	2	2	no	—
74	C₄×C₅×D₃	—	2	4	no	—
75	C₄×C₅×D₃	D₄	1	4	yes	complemented
76	C₂×#239	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂²×C₄×D₃	C₂×C₅	1	1	yes	characteristic, complemented
78	C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
79	#946	C₂×C₅	1	1	yes	characteristic, complemented
80	#930	C₂×C₅	1	1	yes	characteristic, complemented
81	#895	C₂×C₅	1	1	yes	characteristic, complemented
82	#894	C₂×C₅	1	2	yes	complemented
83	#893	C₂×C₅	1	2	yes	complemented
84	#892	C₂×C₅	1	1	yes	characteristic, complemented
85	#882	C₂×C₅	1	2	yes	complemented
86	#67⋊C₄	C₂×C₅	1	2	yes	complemented
87	C₂⁴×C₅	—	3	1	no	—
88	C₅×#41	—	6	4	no	—
89	C₂×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
90	C₂×C₅×D₄	—	3	2	no	—
91	C₂×C₅×D₄	—	3	2	no	—
92	C₂×C₅×D₄	—	3	2	no	—
93	C₂×C₅×D₄	—	3	1	no	—
94	C₂²×C₄×C₅	—	3	1	no	—
95	C₂²×C₄×C₅	—	3	1	no	—
96	C₂²×C₄×C₅	—	3	1	no	—
97	C₂²×C₄×C₅	—	3	2	no	—
98	C₂²×C₄×C₅	—	3	1	no	—
99	C₂²×C₄×C₅	—	3	1	no	—
100	C₂²×C₄×C₅	—	6	4	no	—
101	C₂²×C₄×C₅	C₂×D₃	1	1	yes	characteristic
102	C₅×C₄⋊C₄	—	3	1	no	—
103	C₅×C₄⋊C₄	—	3	2	no	—
104	C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
105	C₅×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
106	C₅×C₂²⋊C₄	—	3	2	no	—
107	C₅×C₂²⋊C₄	—	3	2	no	—
108	C₅×C₂²⋊C₄	—	3	2	no	—
109	C₅×C₂²⋊C₄	—	3	2	no	—
110	C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
111	C₄²×C₅	—	3	2	no	—
112	#525	—	3	1	no	Sylow
113	C₂²×C₃×C₅	—	2	1	no	—
114	C₂²×C₃×C₅	—	2	1	no	—
115	C₂²×C₃×C₅	#41	1	2	yes	complemented
116	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
117	C₂×C₅×D₃	—	2	8	no	—
118	C₂×C₅×D₃	—	2	1	no	—
119	C₂×C₅×D₃	—	2	1	no	—
120	C₂×C₅×D₃	—	2	1	no	—
121	C₂×C₅×D₃	—	2	1	no	—
122	C₂×C₅×D₃	—	2	2	no	—
123	C₂×C₅×D₃	—	2	2	no	—
124	C₂×C₅×D₃	—	2	2	no	—
125	C₂×C₅×D₃	C₂×D₄	1	2	yes	—
126	C₂×C₅×D₃	#41	1	2	yes	complemented
127	C₃×C₄×C₅	—	2	1	no	—
128	C₃×C₄×C₅	—	2	2	no	—
129	C₃×C₄×C₅	—	2	2	no	—
130	C₃×C₄×C₅	C₂×D₄	1	2	yes	—
131	C₅×Dic₃	—	2	1	no	—
132	C₅×Dic₃	—	2	2	no	—
133	C₅×Dic₃	C₂×D₄	1	2	yes	—
134	C₂³×D₃	C₂²×C₅	1	1	yes	characteristic
135	C₂×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
136	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
137	C₂×#67	C₂²×C₅	1	2	yes	—
138	C₂²×Dic₃	C₂²×C₅	1	1	yes	characteristic
139	#239	—	2	4	no	—
140	C₂×D₁₂	C₂²×C₅	1	2	yes	—
141	C₂×D₁₂	C₂²×C₅	1	2	yes	—
142	C₂×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
143	C₂×C₄×D₃	—	2	4	no	—
144	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
145	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
147	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
148	C₂×C₄×D₃	C₂²×C₅	1	2	yes	complemented
149	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
150	C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
151	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
152	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
153	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
154	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
155	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
156	C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
157	Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
158	C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
159	C₂³×C₅	—	3	1	no	—
160	C₂³×C₅	—	3	1	no	—
161	C₂³×C₅	—	3	2	no	—
162	C₂³×C₅	—	6	2	no	—
163	C₂³×C₅	—	6	2	no	—
164	C₂³×C₅	—	6	2	no	—
165	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
166	C₅×Q₈	—	2	2	no	—
167	C₅×D₄	—	6	4	no	—
168	C₅×D₄	—	6	4	no	—
169	C₅×D₄	—	6	4	no	—
170	C₅×D₄	—	6	2	no	—
171	C₂×C₄×C₅	—	2	2	no	—
172	C₂×C₄×C₅	—	3	1	no	—
173	C₂×C₄×C₅	—	3	4	no	—
174	C₂×C₄×C₅	—	3	2	no	—
175	C₂×C₄×C₅	—	3	1	no	—
176	C₂×C₄×C₅	—	6	2	no	—
177	C₂×C₄×C₅	—	6	4	no	—
178	C₂×C₄×C₅	—	6	2	no	—
179	C₂×C₄×C₅	—	6	2	no	—
180	C₂×C₄×C₅	—	6	2	no	—
181	C₂×C₄×C₅	C₂²×D₃	1	2	yes	—
182	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂²×D₃	1	2	yes	—
184	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
185	C₂×#41	—	3	1	no	—
186	C₂³×C₄	—	3	1	no	—
187	#123	—	3	2	no	—
188	C₂²⋊Q₈	—	3	1	no	—
189	C₂²⋊Q₈	C₅×D₃	1	1	yes	characteristic, complemented
190	#121	—	3	1	no	—
191	#121	—	3	1	no	—
192	#120	—	3	2	no	—
193	C₄×D₄	—	3	2	no	—
194	C₄×D₄	—	3	2	no	—
195	#117	—	3	1	no	—
196	C₂×C₃×C₅	—	2	2	no	—
197	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
199	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
200	C₅×D₃	—	2	2	no	—
201	C₅×D₃	—	2	2	no	—
202	C₅×D₃	—	4	2	no	—
203	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
204	C₂²×D₃	—	2	2	no	—
205	C₂²×D₃	—	2	2	no	—
206	C₂²×D₃	—	2	2	no	—
207	C₂²×D₃	C₂³×C₅	1	2	yes	—
208	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
209	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
210	C₃×Q₈	—	2	2	no	—
211	C₂×C₃×C₄	—	2	2	no	—
212	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
213	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
214	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
215	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
216	#67	—	2	4	no	—
217	C₂×Dic₃	—	2	2	no	—
218	C₂×Dic₃	C₂³×C₅	1	2	yes	—
219	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
220	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
221	D₁₂	—	2	4	no	—
222	D₁₂	—	2	4	no	—
223	D₁₂	—	2	2	no	—
224	C₄×D₃	—	2	2	no	—
225	C₄×D₃	—	2	2	no	—
226	C₄×D₃	—	2	2	no	—
227	C₄×D₃	—	2	4	no	—
228	C₄×D₃	C₅×D₄	1	4	yes	complemented
229	C₂²×C₅	—	2	1	no	—
230	C₂²×C₅	—	2	1	no	—
231	C₂²×C₅	—	3	2	no	—
232	C₂²×C₅	—	3	2	no	—
233	C₂²×C₅	—	6	8	no	—
234	C₂²×C₅	—	6	1	no	—
235	C₂²×C₅	—	6	1	no	—
236	C₂²×C₅	—	6	1	no	—
237	C₂²×C₅	—	6	1	no	—
238	C₂²×C₅	—	6	2	no	—
239	C₂²×C₅	—	6	2	no	—
240	C₂²×C₅	—	6	2	no	—
241	C₂²×C₅	#239	1	2	yes	complemented
242	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
243	C₄×C₅	—	2	1	no	—
244	C₄×C₅	—	2	2	no	—
245	C₄×C₅	—	2	2	no	—
246	C₄×C₅	—	3	2	no	—
247	C₄×C₅	—	6	1	no	—
248	C₄×C₅	—	6	2	no	—
249	C₄×C₅	D₃×D₄	1	2	yes	—
250	C₂⁴	—	3	1	no	—
251	#41	—	6	4	no	—
252	C₂×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
253	C₂×D₄	—	3	2	no	—
254	C₂×D₄	—	3	2	no	—
255	C₂×D₄	—	3	2	no	—
256	C₂×D₄	—	3	1	no	—
257	C₂²×C₄	—	3	1	no	—
258	C₂²×C₄	—	3	1	no	—
259	C₂²×C₄	—	3	1	no	—
260	C₂²×C₄	—	3	2	no	—
261	C₂²×C₄	—	3	1	no	—
262	C₂²×C₄	—	3	1	no	—
263	C₂²×C₄	—	6	4	no	—
264	C₂²×C₄	C₂×C₅×D₃	1	1	yes	characteristic
265	C₄⋊C₄	—	3	1	no	—
266	C₄⋊C₄	—	3	2	no	—
267	C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
268	C₄⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
269	C₂²⋊C₄	—	3	2	no	—
270	C₂²⋊C₄	—	3	2	no	—
271	C₂²⋊C₄	—	3	2	no	—
272	C₂²⋊C₄	—	3	2	no	—
273	C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
274	C₄²	—	3	2	no	—
275	C₃×C₅	#525	1	1	yes	characteristic, complemented, Hall
276	C₂²×C₃	—	2	1	no	—
277	C₂²×C₃	—	2	1	no	—
278	C₂²×C₃	C₅×#41	1	2	yes	complemented
279	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
280	C₂×D₃	—	2	8	no	—
281	C₂×D₃	—	2	1	no	—
282	C₂×D₃	—	2	1	no	—
283	C₂×D₃	—	2	1	no	—
284	C₂×D₃	—	2	1	no	—
285	C₂×D₃	—	2	2	no	—
286	C₂×D₃	—	2	2	no	—
287	C₂×D₃	—	2	2	no	—
288	C₂×D₃	C₂×C₅×D₄	1	2	yes	—
289	C₂×D₃	C₅×#41	1	2	yes	complemented
290	C₃×C₄	—	2	1	no	—
291	C₃×C₄	—	2	2	no	—
292	C₃×C₄	—	2	2	no	—
293	C₃×C₄	C₂×C₅×D₄	1	2	yes	—
294	Dic₃	—	2	1	no	—
295	Dic₃	—	2	2	no	—
296	Dic₃	C₂×C₅×D₄	1	2	yes	—
297	C₂×C₅	—	2	2	no	—
298	C₂×C₅	—	6	2	no	—
299	C₂×C₅	—	6	2	no	—
300	C₂×C₅	—	12	2	no	—
301	C₂×C₅	C₂×D₃×D₄	1	1	yes	characteristic
302	C₂×C₅	C₂×#239	1	1	yes	characteristic
303	C₂×C₅	D₃×#41	1	1	yes	characteristic
304	C₂³	—	3	1	no	—
305	C₂³	—	3	1	no	—
306	C₂³	—	3	2	no	—
307	C₂³	—	6	2	no	—
308	C₂³	—	6	2	no	—
309	C₂³	—	6	2	no	—
310	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
311	Q₈	—	2	2	no	—
312	D₄	—	6	4	no	—
313	D₄	—	6	4	no	—
314	D₄	—	6	4	no	—
315	D₄	—	6	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	3	1	no	—
318	C₂×C₄	—	3	4	no	—
319	C₂×C₄	—	3	2	no	—
320	C₂×C₄	—	3	1	no	—
321	C₂×C₄	—	6	2	no	—
322	C₂×C₄	—	6	4	no	—
323	C₂×C₄	—	6	2	no	—
324	C₂×C₄	—	6	2	no	—
325	C₂×C₄	—	6	2	no	—
326	C₂×C₄	C₂²×C₅×D₃	1	2	yes	—
327	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
328	C₂×C₄	C₂²×C₅×D₃	1	2	yes	—
329	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
330	C₂×C₃	—	2	2	no	—
331	C₂×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
332	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
333	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
334	D₃	—	2	2	no	—
335	D₃	—	2	2	no	—
336	D₃	—	4	2	no	—
337	C₅	#5627	1	1	yes	characteristic, direct product factor, Sylow
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	3	2	no	—
341	C₂²	—	3	2	no	—
342	C₂²	—	6	8	no	—
343	C₂²	—	6	1	no	—
344	C₂²	—	6	1	no	—
345	C₂²	—	6	1	no	—
346	C₂²	—	6	1	no	—
347	C₂²	—	6	2	no	—
348	C₂²	—	6	2	no	—
349	C₂²	—	6	2	no	—
350	C₂²	C₅×#239	1	2	yes	complemented
351	C₂²	C₂³×C₅×D₃	1	1	yes	characteristic
352	C₄	—	2	1	no	—
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	3	2	no	—
356	C₄	—	6	1	no	—
357	C₄	—	6	2	no	—
358	C₄	C₅×D₃×D₄	1	2	yes	—
359	C₃	C₅×#525	1	1	yes	characteristic, complemented, Sylow
360	C₂	—	2	2	no	—
361	C₂	—	6	2	no	—
362	C₂	—	6	2	no	—
363	C₂	—	12	2	no	—
364	C₂	C₂×C₅×D₃×D₄	1	1	yes	characteristic
365	C₂	C₂×C₅×#239	1	1	yes	characteristic
366	C₂	C₅×D₃×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₅
Frattini	C₂²	C₂³×C₅×D₃
Fitting	C₃×C₅×C₂²⋊Q₈	C₂
socle	C₂²×C₃×C₅	C₂⁴
hypercenter	C₅×C₂²⋊Q₈	D₃
hypocenter	C₃	C₅×#525
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#239	C₂	semidirect
2. C₂²×C₄×C₅×D₃	C₂	semidirect
3. C₃×C₅×C₂²⋊Q₈	C₂	semidirect
4. C₅×#946	C₂	semidirect
5. C₅×#930	C₂	semidirect
6. C₅×#895	C₂	semidirect
7. C₅×#894	C₂	semidirect
8. C₅×#893	C₂	semidirect
9. C₅×#892	C₂	semidirect
10. C₅×#882	C₂	semidirect
11. C₅×#67⋊C₄	C₂	semidirect
14. C₂×C₃×C₅×Q₈	C₂²	semidirect
21. C₂×C₅×D₁₂	C₂²	semidirect
27. C₂×C₄×C₅×D₃	C₂²	semidirect
28. C₃×C₅×C₄⋊C₄	C₂²	semidirect
29. C₃×C₅×C₄⋊C₄	C₂²	semidirect
33. C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
34. C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
35. C₅×C₄⋊Dic₃	C₂²	semidirect
36. C₅×Dic₃⋊C₄	C₂²	semidirect
37. C₄×C₅×Dic₃	C₂²	semidirect
38. #5627	C₅	direct (N × H)
43. C₅×C₂²⋊Q₈	D₃	semidirect
75. C₄×C₅×D₃	D₄	semidirect
76. C₂×#239	C₂×C₅	semidirect
77. C₂²×C₄×D₃	C₂×C₅	semidirect
78. C₃×C₂²⋊Q₈	C₂×C₅	semidirect
79. #946	C₂×C₅	semidirect
80. #930	C₂×C₅	semidirect
81. #895	C₂×C₅	semidirect
82. #894	C₂×C₅	semidirect
83. #893	C₂×C₅	semidirect
84. #892	C₂×C₅	semidirect
85. #882	C₂×C₅	semidirect
86. #67⋊C₄	C₂×C₅	semidirect
89. C₂×C₅×Q₈	C₂×D₃	semidirect
104. C₅×C₄⋊C₄	C₂×D₃	semidirect
105. C₅×C₄⋊C₄	C₂×D₃	semidirect
115. C₂²×C₃×C₅	#41	semidirect
126. C₂×C₅×D₃	#41	semidirect
135. C₂×C₃×Q₈	C₂²×C₅	semidirect
142. C₂×D₁₂	C₂²×C₅	semidirect
148. C₂×C₄×D₃	C₂²×C₅	semidirect
149. C₃×C₄⋊C₄	C₂²×C₅	semidirect
150. C₃×C₄⋊C₄	C₂²×C₅	semidirect
154. (C₂×D₃)⋊C₄	C₂²×C₅	semidirect
155. (C₂×D₃)⋊C₄	C₂²×C₅	semidirect
156. C₄⋊Dic₃	C₂²×C₅	semidirect
157. Dic₃⋊C₄	C₂²×C₅	semidirect
158. C₄×Dic₃	C₂²×C₅	semidirect
189. C₂²⋊Q₈	C₅×D₃	semidirect
228. C₄×D₃	C₅×D₄	semidirect
241. C₂²×C₅	#239	semidirect
252. C₂×Q₈	C₂×C₅×D₃	semidirect
267. C₄⋊C₄	C₂×C₅×D₃	semidirect
268. C₄⋊C₄	C₂×C₅×D₃	semidirect
275. C₃×C₅	#525	semidirect
278. C₂²×C₃	C₅×#41	semidirect
289. C₂×D₃	C₅×#41	semidirect
337. C₅	#5627	direct (N × H)
350. C₂²	C₅×#239	semidirect
359. C₃	C₅×#525	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#239	2
C₂²×C₄×C₅×D₃	2
C₃×C₅×C₂²⋊Q₈	2
C₅×#946	2
C₅×#930	2
C₅×#895	2
C₅×#894	2
C₅×#893	2
C₅×#892	2
C₅×#882	2
C₅×#67⋊C₄	2
C₅×#525	3
#5627	5

Subgroups — C5×#5627 #11756012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5627 #11756012