Subgroups — C₅×#5550 #11755935

Order 960.

668 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	C₂×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#937	C₂	1	2	yes	maximal, complemented
5	C₅×#930	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#924	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#894	C₂	1	2	yes	maximal, complemented
8	C₅×#884	C₂	1	2	yes	maximal, complemented
9	C₅×D₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₅×#875	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#546	—	3	1	no	maximal, Hall
13	C₂³×C₅×D₃	C₂²	1	2	yes	—
14	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₅×#67	C₂²	1	2	yes	complemented
18	C₂×C₅×#67	C₂²	1	2	yes	complemented
19	C₅×#235	—	2	4	no	—
20	C₂×C₅×D₁₂	—	2	4	no	—
21	C₂×C₅×D₁₂	C₂²	1	1	yes	characteristic
22	C₂×C₅×D₁₂	C₂²	1	2	yes	—
23	C₂×C₅×D₁₂	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×D₃	C₂²	1	2	yes	complemented
25	C₂×C₄×C₅×D₃	C₂²	1	2	yes	complemented
26	C₂×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
31	C₅×#217	C₂²	1	2	yes	—
32	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	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×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
37	C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
38	#5550	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×#124	—	3	1	no	—
42	C₅×#123	—	3	2	no	—
43	C₅×C₂²⋊Q₈	—	3	1	no	—
44	C₅×#121	—	3	1	no	—
45	C₅×#121	—	3	2	no	—
46	C₅×#120	—	3	2	no	—
47	C₄×C₅×D₄	—	3	1	no	—
48	C₄×C₅×D₄	D₃	1	1	yes	characteristic, complemented
49	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
50	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
51	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₅×D₃	—	2	4	no	—
53	C₂²×C₅×D₃	—	2	4	no	—
54	C₂²×C₅×D₃	—	4	2	no	—
55	C₂²×C₅×D₃	C₂³	1	2	yes	—
56	C₂²×C₅×D₃	C₂³	1	2	yes	—
57	C₃×C₅×D₄	—	2	2	no	—
58	C₂×C₃×C₄×C₅	—	2	2	no	—
59	C₂×C₃×C₄×C₅	—	2	2	no	—
60	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₅×#67	—	2	4	no	—
66	C₅×#67	—	4	2	no	—
67	C₂×C₅×Dic₃	C₂³	1	2	yes	—
68	C₂×C₅×Dic₃	C₂³	1	2	yes	—
69	C₅×D₁₂	—	2	4	no	—
70	C₅×D₁₂	—	2	2	no	—
71	C₅×D₁₂	D₄	1	4	yes	complemented
72	C₄×C₅×D₃	—	2	4	no	—
73	C₄×C₅×D₃	—	4	2	no	—
74	C₅×Dic₆	—	2	2	no	—
75	C₂×#235	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂²×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
77	C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
78	#937	C₂×C₅	1	2	yes	complemented
79	#930	C₂×C₅	1	1	yes	characteristic, complemented
80	#924	C₂×C₅	1	1	yes	characteristic, complemented
81	#894	C₂×C₅	1	2	yes	complemented
82	#884	C₂×C₅	1	2	yes	complemented
83	D₃×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
84	#875	C₂×C₅	1	1	yes	characteristic, complemented
85	C₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂⁴×C₅	—	3	2	no	—
87	C₅×#41	—	6	4	no	—
88	C₂×C₅×Q₈	—	3	1	no	—
89	C₂×C₅×D₄	—	3	2	no	—
90	C₂×C₅×D₄	—	3	2	no	—
91	C₂×C₅×D₄	—	3	1	no	—
92	C₂×C₅×D₄	—	3	2	no	—
93	C₂×C₅×D₄	—	3	1	no	—
94	C₂×C₅×D₄	—	6	4	no	—
95	C₂×C₅×D₄	C₂×D₃	1	1	yes	characteristic
96	C₂²×C₄×C₅	—	3	2	no	—
97	C₂²×C₄×C₅	—	3	2	no	—
98	C₂²×C₄×C₅	C₂×D₃	1	1	yes	characteristic
99	C₂²×C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
100	C₅×C₄⋊C₄	—	3	1	no	—
101	C₅×C₄⋊C₄	—	3	2	no	—
102	C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
103	C₅×C₂²⋊C₄	—	3	2	no	—
104	C₅×C₂²⋊C₄	—	3	2	no	—
105	C₅×C₂²⋊C₄	—	3	2	no	—
106	C₅×C₂²⋊C₄	—	3	2	no	—
107	C₅×C₂²⋊C₄	—	3	2	no	—
108	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
109	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
110	C₄²×C₅	C₂×D₃	1	1	yes	characteristic, complemented
111	#546	—	3	1	no	Sylow
112	C₂²×C₃×C₅	—	2	1	no	—
113	C₂²×C₃×C₅	—	2	1	no	—
114	C₂²×C₃×C₅	—	2	1	no	—
115	C₂²×C₃×C₅	—	2	1	no	—
116	C₂²×C₃×C₅	—	2	1	no	—
117	C₂²×C₃×C₅	#41	1	2	yes	complemented
118	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
119	C₂×C₅×D₃	—	2	2	no	—
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	2	no	—
124	C₂×C₅×D₃	—	4	8	no	—
125	C₂×C₅×D₃	C₂×D₄	1	4	yes	—
126	C₃×C₄×C₅	—	2	1	no	—
127	C₃×C₄×C₅	—	2	1	no	—
128	C₃×C₄×C₅	—	2	1	no	—
129	C₃×C₄×C₅	—	2	1	no	—
130	C₃×C₄×C₅	C₂×D₄	1	2	yes	—
131	C₅×Dic₃	—	2	2	no	—
132	C₅×Dic₃	—	2	2	no	—
133	C₂³×D₃	C₂²×C₅	1	2	yes	—
134	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
135	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
136	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
137	C₂×#67	C₂²×C₅	1	2	yes	complemented
138	C₂×#67	C₂²×C₅	1	2	yes	complemented
139	#235	—	2	4	no	—
140	C₂×D₁₂	—	2	4	no	—
141	C₂×D₁₂	C₂²×C₅	1	1	yes	characteristic
142	C₂×D₁₂	C₂²×C₅	1	2	yes	—
143	C₂×D₁₂	C₂²×C₅	1	1	yes	characteristic
144	C₂×C₄×D₃	C₂²×C₅	1	2	yes	complemented
145	C₂×C₄×D₃	C₂²×C₅	1	2	yes	complemented
146	C₂×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
147	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
148	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
149	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
150	C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
151	#217	C₂²×C₅	1	2	yes	—
152	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
153	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
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	C₂³×C₅	—	3	2	no	—
159	C₂³×C₅	—	3	2	no	—
160	C₂³×C₅	—	6	4	no	—
161	C₂³×C₅	—	6	4	no	—
162	C₂³×C₅	—	12	2	no	—
163	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
164	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
165	C₅×Q₈	—	6	2	no	—
166	C₅×D₄	—	2	2	no	—
167	C₅×D₄	—	3	4	no	—
168	C₅×D₄	—	6	4	no	—
169	C₅×D₄	—	6	4	no	—
170	C₅×D₄	—	6	2	no	—
171	C₅×D₄	—	12	2	no	—
172	C₂×C₄×C₅	—	2	2	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	3	2	no	—
175	C₂×C₄×C₅	—	3	2	no	—
176	C₂×C₄×C₅	—	6	4	no	—
177	C₂×C₄×C₅	—	12	2	no	—
178	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
179	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
180	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
181	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
183	C₂×#41	—	3	1	no	—
184	C₂²×D₄	—	3	1	no	—
185	#124	—	3	1	no	—
186	#123	—	3	2	no	—
187	C₂²⋊Q₈	—	3	1	no	—
188	#121	—	3	1	no	—
189	#121	—	3	2	no	—
190	#120	—	3	2	no	—
191	C₄×D₄	—	3	1	no	—
192	C₄×D₄	C₅×D₃	1	1	yes	characteristic, complemented
193	C₂×C₂²⋊C₄	—	3	2	no	—
194	C₂×C₃×C₅	—	2	2	no	—
195	C₂×C₃×C₅	—	4	1	no	—
196	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
198	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
199	C₅×D₃	—	2	4	no	—
200	C₅×D₃	—	4	2	no	—
201	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
202	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
203	C₂²×D₃	—	2	4	no	—
204	C₂²×D₃	—	2	4	no	—
205	C₂²×D₃	—	4	2	no	—
206	C₂²×D₃	C₂³×C₅	1	2	yes	—
207	C₂²×D₃	C₂³×C₅	1	2	yes	—
208	C₃×D₄	—	2	2	no	—
209	C₂×C₃×C₄	—	2	2	no	—
210	C₂×C₃×C₄	—	2	2	no	—
211	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
212	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
213	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
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	#67	—	4	2	no	—
218	C₂×Dic₃	C₂³×C₅	1	2	yes	—
219	C₂×Dic₃	C₂³×C₅	1	2	yes	—
220	D₁₂	—	2	4	no	—
221	D₁₂	—	2	2	no	—
222	D₁₂	C₅×D₄	1	4	yes	complemented
223	C₄×D₃	—	2	4	no	—
224	C₄×D₃	—	4	2	no	—
225	Dic₆	—	2	2	no	—
226	C₂²×C₅	—	2	1	no	—
227	C₂²×C₅	—	2	1	no	—
228	C₂²×C₅	—	2	1	no	—
229	C₂²×C₅	—	2	1	no	—
230	C₂²×C₅	—	2	1	no	—
231	C₂²×C₅	—	3	4	no	—
232	C₂²×C₅	—	6	2	no	—
233	C₂²×C₅	—	6	2	no	—
234	C₂²×C₅	—	6	2	no	—
235	C₂²×C₅	—	6	2	no	—
236	C₂²×C₅	—	6	2	no	—
237	C₂²×C₅	—	12	8	no	—
238	C₂²×C₅	#235	1	2	yes	complemented
239	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
240	C₄×C₅	—	2	1	no	—
241	C₄×C₅	—	2	1	no	—
242	C₄×C₅	—	2	1	no	—
243	C₄×C₅	—	2	1	no	—
244	C₄×C₅	—	6	2	no	—
245	C₄×C₅	—	6	2	no	—
246	C₄×C₅	D₃×D₄	1	2	yes	—
247	C₂⁴	—	3	2	no	—
248	#41	—	6	4	no	—
249	C₂×Q₈	—	3	1	no	—
250	C₂×D₄	—	3	2	no	—
251	C₂×D₄	—	3	2	no	—
252	C₂×D₄	—	3	1	no	—
253	C₂×D₄	—	3	2	no	—
254	C₂×D₄	—	3	1	no	—
255	C₂×D₄	—	6	4	no	—
256	C₂×D₄	C₂×C₅×D₃	1	1	yes	characteristic
257	C₂²×C₄	—	3	2	no	—
258	C₂²×C₄	—	3	2	no	—
259	C₂²×C₄	C₂×C₅×D₃	1	1	yes	characteristic
260	C₂²×C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
261	C₄⋊C₄	—	3	1	no	—
262	C₄⋊C₄	—	3	2	no	—
263	C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
264	C₂²⋊C₄	—	3	2	no	—
265	C₂²⋊C₄	—	3	2	no	—
266	C₂²⋊C₄	—	3	2	no	—
267	C₂²⋊C₄	—	3	2	no	—
268	C₂²⋊C₄	—	3	2	no	—
269	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
270	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
271	C₄²	C₂×C₅×D₃	1	1	yes	characteristic, complemented
272	C₃×C₅	#546	1	1	yes	characteristic, complemented, Hall
273	C₂²×C₃	—	2	1	no	—
274	C₂²×C₃	—	2	1	no	—
275	C₂²×C₃	—	2	1	no	—
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	2	no	—
281	C₂×D₃	—	2	2	no	—
282	C₂×D₃	—	2	2	no	—
283	C₂×D₃	—	2	2	no	—
284	C₂×D₃	—	2	2	no	—
285	C₂×D₃	—	4	8	no	—
286	C₂×D₃	C₂×C₅×D₄	1	4	yes	—
287	C₃×C₄	—	2	1	no	—
288	C₃×C₄	—	2	1	no	—
289	C₃×C₄	—	2	1	no	—
290	C₃×C₄	—	2	1	no	—
291	C₃×C₄	C₂×C₅×D₄	1	2	yes	—
292	Dic₃	—	2	2	no	—
293	Dic₃	—	2	2	no	—
294	C₂×C₅	—	2	2	no	—
295	C₂×C₅	—	4	1	no	—
296	C₂×C₅	—	6	4	no	—
297	C₂×C₅	—	12	2	no	—
298	C₂×C₅	C₂×#235	1	1	yes	characteristic
299	C₂×C₅	C₂×D₃×D₄	1	1	yes	characteristic
300	C₂×C₅	#1009	1	1	yes	characteristic
301	C₂³	—	3	2	no	—
302	C₂³	—	3	2	no	—
303	C₂³	—	6	4	no	—
304	C₂³	—	6	4	no	—
305	C₂³	—	12	2	no	—
306	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
307	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
308	Q₈	—	6	2	no	—
309	D₄	—	2	2	no	—
310	D₄	—	3	4	no	—
311	D₄	—	6	4	no	—
312	D₄	—	6	4	no	—
313	D₄	—	6	2	no	—
314	D₄	—	12	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	3	2	no	—
318	C₂×C₄	—	3	2	no	—
319	C₂×C₄	—	6	4	no	—
320	C₂×C₄	—	12	2	no	—
321	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
322	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
323	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
324	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
325	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
326	C₂×C₃	—	2	2	no	—
327	C₂×C₃	—	4	1	no	—
328	C₂×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
329	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
330	C₂×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
331	D₃	—	2	4	no	—
332	D₃	—	4	2	no	—
333	C₅	#5550	1	1	yes	characteristic, direct product factor, Sylow
334	C₂²	—	2	1	no	—
335	C₂²	—	2	1	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	3	4	no	—
340	C₂²	—	6	2	no	—
341	C₂²	—	6	2	no	—
342	C₂²	—	6	2	no	—
343	C₂²	—	6	2	no	—
344	C₂²	—	6	2	no	—
345	C₂²	—	12	8	no	—
346	C₂²	C₅×#235	1	2	yes	complemented
347	C₂²	C₂³×C₅×D₃	1	1	yes	characteristic
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	6	2	no	—
353	C₄	—	6	2	no	—
354	C₄	C₅×D₃×D₄	1	2	yes	—
355	C₃	C₅×#546	1	1	yes	characteristic, complemented, Sylow
356	C₂	—	2	2	no	—
357	C₂	—	4	1	no	—
358	C₂	—	6	4	no	—
359	C₂	—	12	2	no	—
360	C₂	C₂×C₅×#235	1	1	yes	characteristic
361	C₂	C₂×C₅×D₃×D₄	1	1	yes	characteristic
362	C₂	C₅×#1009	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×C₄×C₅×D₄	C₂
socle	C₂²×C₃×C₅	C₂⁴
hypercenter	C₄×C₅×D₄	D₃
hypocenter	C₃	C₅×#546
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#235	C₂	semidirect
2. C₂²×C₅×D₁₂	C₂	semidirect
3. C₃×C₄×C₅×D₄	C₂	semidirect
4. C₅×#937	C₂	semidirect
5. C₅×#930	C₂	semidirect
6. C₅×#924	C₂	semidirect
7. C₅×#894	C₂	semidirect
8. C₅×#884	C₂	semidirect
9. C₅×D₃×C₂²⋊C₄	C₂	semidirect
10. C₅×#875	C₂	semidirect
11. C₄×C₅×D₁₂	C₂	semidirect
16. C₂²×C₃×C₄×C₅	C₂²	semidirect
17. C₂×C₅×#67	C₂²	semidirect
18. C₂×C₅×#67	C₂²	semidirect
24. C₂×C₄×C₅×D₃	C₂²	semidirect
25. C₂×C₄×C₅×D₃	C₂²	semidirect
26. C₂×C₅×Dic₆	C₂²	semidirect
27. C₃×C₅×C₄⋊C₄	C₂²	semidirect
29. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
30. C₃×C₄²×C₅	C₂²	semidirect
32. C₅×(C₂×D₃)⋊C₄	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×C₄⋊Dic₃	C₂²	semidirect
37. C₅×Dic₃⋊C₄	C₂²	semidirect
38. #5550	C₅	direct (N × H)
48. C₄×C₅×D₄	D₃	semidirect
71. C₅×D₁₂	D₄	semidirect
75. C₂×#235	C₂×C₅	semidirect
76. C₂²×D₁₂	C₂×C₅	semidirect
77. C₃×C₄×D₄	C₂×C₅	semidirect
78. #937	C₂×C₅	semidirect
79. #930	C₂×C₅	semidirect
80. #924	C₂×C₅	semidirect
81. #894	C₂×C₅	semidirect
82. #884	C₂×C₅	semidirect
83. D₃×C₂²⋊C₄	C₂×C₅	semidirect
84. #875	C₂×C₅	semidirect
85. C₄×D₁₂	C₂×C₅	semidirect
99. C₂²×C₄×C₅	C₂×D₃	semidirect
102. C₅×C₄⋊C₄	C₂×D₃	semidirect
109. C₅×C₂²⋊C₄	C₂×D₃	semidirect
110. C₄²×C₅	C₂×D₃	semidirect
117. C₂²×C₃×C₅	#41	semidirect
136. C₂²×C₃×C₄	C₂²×C₅	semidirect
137. C₂×#67	C₂²×C₅	semidirect
138. C₂×#67	C₂²×C₅	semidirect
144. C₂×C₄×D₃	C₂²×C₅	semidirect
145. C₂×C₄×D₃	C₂²×C₅	semidirect
146. C₂×Dic₆	C₂²×C₅	semidirect
147. C₃×C₄⋊C₄	C₂²×C₅	semidirect
149. C₃×C₂²⋊C₄	C₂²×C₅	semidirect
150. C₃×C₄²	C₂²×C₅	semidirect
152. (C₂×D₃)⋊C₄	C₂²×C₅	semidirect
153. (C₂×D₃)⋊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
192. C₄×D₄	C₅×D₃	semidirect
222. D₁₂	C₅×D₄	semidirect
238. C₂²×C₅	#235	semidirect
260. C₂²×C₄	C₂×C₅×D₃	semidirect
263. C₄⋊C₄	C₂×C₅×D₃	semidirect
270. C₂²⋊C₄	C₂×C₅×D₃	semidirect
271. C₄²	C₂×C₅×D₃	semidirect
272. C₃×C₅	#546	semidirect
278. C₂²×C₃	C₅×#41	semidirect
333. C₅	#5550	direct (N × H)
346. C₂²	C₅×#235	semidirect
355. C₃	C₅×#546	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#235	2
C₂²×C₅×D₁₂	2
C₃×C₄×C₅×D₄	2
C₅×#937	2
C₅×#930	2
C₅×#924	2
C₅×#894	2
C₅×#884	2
C₅×D₃×C₂²⋊C₄	2
C₅×#875	2
C₄×C₅×D₁₂	2
C₅×#546	3
#5550	5

Subgroups — C5×#5550 #11755935

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5550 #11755935