Subgroups — C₂×C₅×#5552 #14482805

Order 1920.

3240 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#939	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#930	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#924	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5552	C₂	1	16	yes	maximal, direct product factor
8	C₂×C₅×#896	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#885	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#67⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₂×C₅×#875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#548	—	3	1	no	maximal, Hall
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₂²×C₅×#67	C₂²	1	2	yes	—
18	C₂²×C₅×#67	C₂²	1	2	yes	—
19	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
20	C₂×C₅×#235	—	2	8	no	—
21	C₂×C₅×#235	C₂²	1	8	yes	complemented
22	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
23	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
24	C₂²×C₅×Dic₆	—	2	8	no	—
25	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
26	C₂²×C₅×Dic₆	C₂²	1	2	yes	—
27	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
28	C₂²×C₅×Dic₆	C₂²	1	8	yes	complemented
29	C₃×C₄×C₅×D₄	C₂²	1	8	yes	complemented
30	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
34	C₂×C₅×#217	C₂²	1	2	yes	—
35	C₅×#939	C₂²	1	16	yes	complemented
36	C₅×#930	C₂²	1	8	yes	complemented
37	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
38	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
39	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
40	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
41	C₅×#924	C₂²	1	8	yes	complemented
42	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
43	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
44	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
45	C₅×#896	C₂²	1	16	yes	complemented
46	C₅×#885	C₂²	1	16	yes	complemented
47	C₅×#67⋊C₄	C₂²	1	16	yes	complemented
48	C₅×#875	C₂²	1	8	yes	complemented
49	C₄×C₅×Dic₆	C₂²	1	8	yes	complemented
50	C₂×#5552	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
51	C₂²×C₅×#41	—	3	1	no	—
52	C₂³×C₅×Q₈	—	3	1	no	—
53	C₅×#548	—	3	16	no	—
54	C₂×C₅×#124	—	3	2	no	—
55	C₂×C₅×#124	—	3	1	no	—
56	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
57	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
58	C₂×C₅×#121	—	3	2	no	—
59	C₂×C₅×#121	—	3	1	no	—
60	C₂×C₄×C₅×Q₈	—	3	1	no	—
61	C₂×C₄×C₅×D₄	—	3	2	no	—
62	C₂×C₄×C₅×D₄	D₃	1	1	yes	characteristic, complemented
63	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
64	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
65	C₂³×C₅×D₃	C₂³	1	2	yes	—
66	C₂×C₃×C₅×D₄	—	2	4	no	—
67	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
68	C₂²×C₃×C₄×C₅	—	2	4	no	—
69	C₂²×C₃×C₄×C₅	—	2	4	no	—
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
72	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
74	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
76	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂×C₅×#67	—	2	8	no	—
78	C₂×C₅×#67	—	2	8	no	—
79	C₂×C₅×#67	C₂³	1	8	yes	—
80	C₂×C₅×#67	C₂³	1	8	yes	—
81	C₂²×C₅×Dic₃	—	2	8	no	—
82	C₂²×C₅×Dic₃	C₂³	1	8	yes	—
83	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
84	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
85	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
86	C₅×#235	—	2	32	no	—
87	C₂×C₅×D₁₂	—	2	4	no	—
88	C₂×C₅×D₁₂	C₂³	1	4	yes	—
89	C₂×C₄×C₅×D₃	—	2	8	no	—
90	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
91	C₂×C₅×Dic₆	—	2	4	no	—
92	C₂×C₅×Dic₆	—	2	8	no	—
93	C₂×C₅×Dic₆	—	2	32	no	—
94	C₂×C₅×Dic₆	D₄	1	8	yes	complemented
95	C₂×C₅×Dic₆	C₂³	1	4	yes	—
96	C₂×C₅×Dic₆	C₂³	1	8	yes	—
97	C₂×C₅×Dic₆	C₂³	1	4	yes	—
98	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
99	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
100	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
101	C₃×C₄²×C₅	C₂³	1	4	yes	—
102	C₅×#217	C₂³	1	8	yes	—
103	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
104	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
105	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
106	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
107	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
108	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
109	C₄×C₅×Dic₃	C₂³	1	8	yes	—
110	C₂²×#235	C₂×C₅	1	1	yes	characteristic, complemented
111	C₂³×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
113	C₂×#939	C₂×C₅	1	2	yes	complemented
114	C₂×#930	C₂×C₅	1	1	yes	characteristic, complemented
115	C₂×#924	C₂×C₅	1	1	yes	characteristic, complemented
116	#5552	C₂×C₅	1	16	yes	direct product factor
117	C₂×#896	C₂×C₅	1	2	yes	complemented
118	C₂×#885	C₂×C₅	1	2	yes	complemented
119	C₂×#67⋊C₄	C₂×C₅	1	2	yes	complemented
120	C₂×#875	C₂×C₅	1	1	yes	characteristic, complemented
121	C₂×C₄×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
122	C₂×C₅×#41	—	3	8	no	—
123	C₂×C₅×#41	—	6	8	no	—
124	C₂²×C₅×Q₈	—	3	1	no	—
125	C₂²×C₅×Q₈	—	3	2	no	—
126	C₂²×C₅×Q₈	—	3	1	no	—
127	C₂²×C₅×Q₈	—	3	8	no	—
128	C₂²×C₅×Q₈	—	6	8	no	—
129	C₂²×C₅×D₄	—	3	2	no	—
130	C₂²×C₅×D₄	—	3	2	no	—
131	C₂²×C₅×D₄	—	3	1	no	—
132	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
133	C₂³×C₄×C₅	—	3	2	no	—
134	C₂³×C₄×C₅	—	3	2	no	—
135	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
136	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
137	C₅×#124	—	3	16	no	—
138	C₅×#124	—	3	8	no	—
139	C₅×C₂²⋊Q₈	—	3	8	no	—
140	C₅×C₂²⋊Q₈	—	3	16	no	—
141	C₅×#121	—	3	16	no	—
142	C₅×#121	—	3	8	no	—
143	C₄×C₅×Q₈	—	3	8	no	—
144	C₄×C₅×D₄	—	3	16	no	—
145	C₄×C₅×D₄	C₂×D₃	1	8	yes	complemented
146	C₂×C₅×C₄⋊C₄	—	3	2	no	—
147	C₂×C₅×C₄⋊C₄	—	3	2	no	—
148	C₂×C₅×C₄⋊C₄	—	3	1	no	—
149	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
150	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
151	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
152	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
153	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
154	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
155	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
156	C₂×C₄²×C₅	—	3	2	no	—
157	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
158	C₂×#548	—	3	1	no	Sylow
159	C₂³×C₃×C₅	—	2	2	no	—
160	C₂³×C₃×C₅	—	2	2	no	—
161	C₂³×C₃×C₅	—	2	2	no	—
162	C₂³×C₃×C₅	—	2	2	no	—
163	C₂³×C₃×C₅	—	2	2	no	—
164	C₂³×C₃×C₅	#41	1	4	yes	complemented
165	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
166	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
167	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
168	C₂²×C₅×D₃	—	2	4	no	—
169	C₂²×C₅×D₃	—	2	4	no	—
170	C₂²×C₅×D₃	—	2	4	no	—
171	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
172	C₃×C₅×D₄	—	2	8	no	—
173	C₂×C₃×C₄×C₅	—	2	2	no	—
174	C₂×C₃×C₄×C₅	—	2	2	no	—
175	C₂×C₃×C₄×C₅	—	2	2	no	—
176	C₂×C₃×C₄×C₅	—	2	2	no	—
177	C₂×C₃×C₄×C₅	—	2	8	no	—
178	C₂×C₃×C₄×C₅	—	2	8	no	—
179	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
180	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
181	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
182	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
183	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
184	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
185	C₅×#67	—	2	16	no	—
186	C₅×#67	—	2	16	no	—
187	C₂×C₅×Dic₃	—	2	4	no	—
188	C₂×C₅×Dic₃	—	2	4	no	—
189	C₂×C₅×Dic₃	—	2	16	no	—
190	C₂×C₅×Dic₃	C₂×D₄	1	8	yes	—
191	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
192	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
193	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
194	C₅×D₁₂	—	2	8	no	—
195	C₄×C₅×D₃	—	2	16	no	—
196	C₅×Dic₆	—	2	8	no	—
197	C₅×Dic₆	—	2	16	no	—
198	C₅×Dic₆	C₂×D₄	1	16	yes	complemented
199	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
200	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
201	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
202	C₂²×#67	C₂²×C₅	1	2	yes	—
203	C₂²×#67	C₂²×C₅	1	2	yes	—
204	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
205	C₂×#235	—	2	8	no	—
206	C₂×#235	C₂²×C₅	1	8	yes	complemented
207	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
208	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
209	C₂²×Dic₆	—	2	8	no	—
210	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
211	C₂²×Dic₆	C₂²×C₅	1	2	yes	—
212	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
213	C₂²×Dic₆	C₂²×C₅	1	8	yes	complemented
214	C₃×C₄×D₄	C₂²×C₅	1	8	yes	complemented
215	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
216	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
217	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
218	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
219	C₂×#217	C₂²×C₅	1	2	yes	—
220	#939	C₂²×C₅	1	16	yes	complemented
221	#930	C₂²×C₅	1	8	yes	complemented
222	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
223	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
224	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
225	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
226	#924	C₂²×C₅	1	8	yes	complemented
227	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
228	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
229	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
230	#896	C₂²×C₅	1	16	yes	complemented
231	#885	C₂²×C₅	1	16	yes	complemented
232	#67⋊C₄	C₂²×C₅	1	16	yes	complemented
233	#875	C₂²×C₅	1	8	yes	complemented
234	C₄×Dic₆	C₂²×C₅	1	8	yes	complemented
235	C₂⁴×C₅	—	3	2	no	—
236	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
237	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
238	C₅×#41	—	6	32	no	—
239	C₂×C₅×Q₈	—	3	8	no	—
240	C₂×C₅×Q₈	—	3	4	no	—
241	C₂×C₅×Q₈	—	3	8	no	—
242	C₂×C₅×Q₈	—	3	4	no	—
243	C₂×C₅×Q₈	—	6	8	no	—
244	C₂×C₅×Q₈	—	6	32	no	—
245	C₂×C₅×Q₈	—	6	4	no	—
246	C₂×C₅×D₄	—	2	4	no	—
247	C₂×C₅×D₄	—	3	8	no	—
248	C₂×C₅×D₄	—	3	8	no	—
249	C₂×C₅×D₄	—	3	4	no	—
250	C₂×C₅×D₄	—	6	8	no	—
251	C₂×C₅×D₄	—	6	8	no	—
252	C₂×C₅×D₄	—	6	4	no	—
253	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
254	C₂²×C₄×C₅	—	2	4	no	—
255	C₂²×C₄×C₅	—	2	4	no	—
256	C₂²×C₄×C₅	—	3	2	no	—
257	C₂²×C₄×C₅	—	3	8	no	—
258	C₂²×C₄×C₅	—	3	2	no	—
259	C₂²×C₄×C₅	—	3	2	no	—
260	C₂²×C₄×C₅	—	3	8	no	—
261	C₂²×C₄×C₅	—	6	8	no	—
262	C₂²×C₄×C₅	—	6	8	no	—
263	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
264	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
265	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
266	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
267	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
268	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
269	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
270	C₅×C₄⋊C₄	—	3	8	no	—
271	C₅×C₄⋊C₄	—	3	8	no	—
272	C₅×C₄⋊C₄	—	3	4	no	—
273	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
274	C₅×C₂²⋊C₄	—	3	8	no	—
275	C₅×C₂²⋊C₄	—	3	8	no	—
276	C₅×C₂²⋊C₄	—	3	8	no	—
277	C₅×C₂²⋊C₄	—	3	8	no	—
278	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
279	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
280	C₄²×C₅	—	3	8	no	—
281	C₄²×C₅	C₂²×D₃	1	4	yes	—
282	C₂²×#41	—	3	1	no	—
283	C₂³×Q₈	—	3	1	no	—
284	#548	—	3	16	no	—
285	C₂×#124	—	3	2	no	—
286	C₂×#124	—	3	1	no	—
287	C₂×C₂²⋊Q₈	—	3	1	no	—
288	C₂×C₂²⋊Q₈	—	3	2	no	—
289	C₂×#121	—	3	2	no	—
290	C₂×#121	—	3	1	no	—
291	C₂×C₄×Q₈	—	3	1	no	—
292	C₂×C₄×D₄	—	3	2	no	—
293	C₂×C₄×D₄	C₅×D₃	1	1	yes	characteristic, complemented
294	C₂²×C₃×C₅	—	2	8	no	—
295	C₂²×C₃×C₅	—	2	2	no	—
296	C₂²×C₃×C₅	—	2	2	no	—
297	C₂²×C₃×C₅	—	2	2	no	—
298	C₂²×C₃×C₅	—	2	2	no	—
299	C₂²×C₃×C₅	—	2	2	no	—
300	C₂²×C₃×C₅	—	4	4	no	—
301	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
302	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
303	C₂²×C₃×C₅	C₂×#41	1	4	yes	complemented
304	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
305	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
306	C₂×C₅×D₃	—	2	4	no	—
307	C₂×C₅×D₃	—	2	4	no	—
308	C₂×C₅×D₃	—	2	4	no	—
309	C₂×C₅×D₃	—	4	8	no	—
310	C₃×C₄×C₅	—	2	2	no	—
311	C₃×C₄×C₅	—	2	2	no	—
312	C₃×C₄×C₅	—	2	2	no	—
313	C₃×C₄×C₅	—	2	2	no	—
314	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
315	C₅×Dic₃	—	2	4	no	—
316	C₅×Dic₃	—	2	4	no	—
317	C₅×Dic₃	C₂²×D₄	1	8	yes	—
318	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
319	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
320	C₂³×D₃	C₂³×C₅	1	2	yes	—
321	C₂×C₃×D₄	—	2	4	no	—
322	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
323	C₂²×C₃×C₄	—	2	4	no	—
324	C₂²×C₃×C₄	—	2	4	no	—
325	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
326	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
327	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
328	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
329	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
330	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
331	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
332	C₂×#67	—	2	8	no	—
333	C₂×#67	—	2	8	no	—
334	C₂×#67	C₂³×C₅	1	8	yes	—
335	C₂×#67	C₂³×C₅	1	8	yes	—
336	C₂²×Dic₃	—	2	8	no	—
337	C₂²×Dic₃	C₂³×C₅	1	8	yes	—
338	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
339	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
340	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
341	#235	—	2	32	no	—
342	C₂×D₁₂	—	2	4	no	—
343	C₂×D₁₂	C₂³×C₅	1	4	yes	—
344	C₂×C₄×D₃	—	2	8	no	—
345	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
346	C₂×Dic₆	—	2	4	no	—
347	C₂×Dic₆	—	2	8	no	—
348	C₂×Dic₆	—	2	32	no	—
349	C₂×Dic₆	C₅×D₄	1	8	yes	complemented
350	C₂×Dic₆	C₂³×C₅	1	4	yes	—
351	C₂×Dic₆	C₂³×C₅	1	8	yes	—
352	C₂×Dic₆	C₂³×C₅	1	4	yes	—
353	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
354	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
355	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
356	C₃×C₄²	C₂³×C₅	1	4	yes	—
357	#217	C₂³×C₅	1	8	yes	—
358	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
359	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
360	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
361	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
362	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
363	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
364	C₄×Dic₃	C₂³×C₅	1	8	yes	—
365	C₂³×C₅	—	2	2	no	—
366	C₂³×C₅	—	2	2	no	—
367	C₂³×C₅	—	2	2	no	—
368	C₂³×C₅	—	2	2	no	—
369	C₂³×C₅	—	2	2	no	—
370	C₂³×C₅	—	3	4	no	—
371	C₂³×C₅	—	6	4	no	—
372	C₂³×C₅	—	6	4	no	—
373	C₂³×C₅	—	6	4	no	—
374	C₂³×C₅	#235	1	4	yes	complemented
375	C₂³×C₅	C₂³×D₃	1	2	yes	—
376	C₂³×C₅	C₂³×D₃	1	2	yes	—
377	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
378	C₅×Q₈	—	3	16	no	—
379	C₅×Q₈	—	6	16	no	—
380	C₅×Q₈	—	6	8	no	—
381	C₅×D₄	—	2	8	no	—
382	C₅×D₄	—	6	16	no	—
383	C₅×D₄	—	6	16	no	—
384	C₅×D₄	—	6	8	no	—
385	C₂×C₄×C₅	—	2	2	no	—
386	C₂×C₄×C₅	—	2	2	no	—
387	C₂×C₄×C₅	—	2	2	no	—
388	C₂×C₄×C₅	—	2	2	no	—
389	C₂×C₄×C₅	—	2	8	no	—
390	C₂×C₄×C₅	—	2	8	no	—
391	C₂×C₄×C₅	—	3	8	no	—
392	C₂×C₄×C₅	—	3	4	no	—
393	C₂×C₄×C₅	—	3	4	no	—
394	C₂×C₄×C₅	—	3	4	no	—
395	C₂×C₄×C₅	—	6	16	no	—
396	C₂×C₄×C₅	—	6	16	no	—
397	C₂×C₄×C₅	—	6	4	no	—
398	C₂×C₄×C₅	—	6	4	no	—
399	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
400	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
401	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
402	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
403	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
404	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
405	C₂×#41	—	3	8	no	—
406	C₂×#41	—	6	8	no	—
407	C₂²×Q₈	—	3	1	no	—
408	C₂²×Q₈	—	3	2	no	—
409	C₂²×Q₈	—	3	1	no	—
410	C₂²×Q₈	—	3	8	no	—
411	C₂²×Q₈	—	6	8	no	—
412	C₂²×D₄	—	3	2	no	—
413	C₂²×D₄	—	3	2	no	—
414	C₂²×D₄	—	3	1	no	—
415	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
416	C₂³×C₄	—	3	2	no	—
417	C₂³×C₄	—	3	2	no	—
418	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
419	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
420	#124	—	3	16	no	—
421	#124	—	3	8	no	—
422	C₂²⋊Q₈	—	3	8	no	—
423	C₂²⋊Q₈	—	3	16	no	—
424	#121	—	3	16	no	—
425	#121	—	3	8	no	—
426	C₄×Q₈	—	3	8	no	—
427	C₄×D₄	—	3	16	no	—
428	C₄×D₄	C₂×C₅×D₃	1	8	yes	complemented
429	C₂×C₄⋊C₄	—	3	2	no	—
430	C₂×C₄⋊C₄	—	3	2	no	—
431	C₂×C₄⋊C₄	—	3	1	no	—
432	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
433	C₂×C₂²⋊C₄	—	3	2	no	—
434	C₂×C₂²⋊C₄	—	3	2	no	—
435	C₂×C₂²⋊C₄	—	3	2	no	—
436	C₂×C₂²⋊C₄	—	3	2	no	—
437	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
438	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
439	C₂×C₄²	—	3	2	no	—
440	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
441	C₂×C₃×C₅	—	2	4	no	—
442	C₂×C₃×C₅	—	4	2	no	—
443	C₂×C₃×C₅	#548	1	4	yes	complemented
444	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
445	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
446	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
447	C₅×D₃	—	4	4	no	—
448	C₂³×C₃	—	2	2	no	—
449	C₂³×C₃	—	2	2	no	—
450	C₂³×C₃	—	2	2	no	—
451	C₂³×C₃	—	2	2	no	—
452	C₂³×C₃	—	2	2	no	—
453	C₂³×C₃	C₅×#41	1	4	yes	complemented
454	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
455	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
456	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
457	C₂²×D₃	—	2	4	no	—
458	C₂²×D₃	—	2	4	no	—
459	C₂²×D₃	—	2	4	no	—
460	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
461	C₃×D₄	—	2	8	no	—
462	C₂×C₃×C₄	—	2	2	no	—
463	C₂×C₃×C₄	—	2	2	no	—
464	C₂×C₃×C₄	—	2	2	no	—
465	C₂×C₃×C₄	—	2	2	no	—
466	C₂×C₃×C₄	—	2	8	no	—
467	C₂×C₃×C₄	—	2	8	no	—
468	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
469	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
470	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
471	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
472	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
473	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
474	#67	—	2	16	no	—
475	#67	—	2	16	no	—
476	C₂×Dic₃	—	2	4	no	—
477	C₂×Dic₃	—	2	4	no	—
478	C₂×Dic₃	—	2	16	no	—
479	C₂×Dic₃	C₂×C₅×D₄	1	8	yes	—
480	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
481	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
482	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
483	D₁₂	—	2	8	no	—
484	C₄×D₃	—	2	16	no	—
485	Dic₆	—	2	8	no	—
486	Dic₆	—	2	16	no	—
487	Dic₆	C₂×C₅×D₄	1	16	yes	complemented
488	C₂²×C₅	—	2	2	no	—
489	C₂²×C₅	—	2	2	no	—
490	C₂²×C₅	—	2	8	no	—
491	C₂²×C₅	—	2	2	no	—
492	C₂²×C₅	—	2	2	no	—
493	C₂²×C₅	—	2	2	no	—
494	C₂²×C₅	—	4	4	no	—
495	C₂²×C₅	—	6	4	no	—
496	C₂²×C₅	—	6	4	no	—
497	C₂²×C₅	—	6	4	no	—
498	C₂²×C₅	—	12	8	no	—
499	C₂²×C₅	C₂×#235	1	2	yes	—
500	C₂²×C₅	C₂×#235	1	4	yes	complemented
501	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
502	C₂²×C₅	#1010	1	2	yes	—
503	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
504	C₄×C₅	—	2	2	no	—
505	C₄×C₅	—	2	2	no	—
506	C₄×C₅	—	2	2	no	—
507	C₄×C₅	—	2	2	no	—
508	C₄×C₅	—	3	8	no	—
509	C₄×C₅	—	6	4	no	—
510	C₄×C₅	—	6	4	no	—
511	C₄×C₅	C₂×D₃×D₄	1	4	yes	—
512	C₂⁴	—	3	2	no	—
513	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
514	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
515	#41	—	6	32	no	—
516	C₂×Q₈	—	3	8	no	—
517	C₂×Q₈	—	3	4	no	—
518	C₂×Q₈	—	3	8	no	—
519	C₂×Q₈	—	3	4	no	—
520	C₂×Q₈	—	6	8	no	—
521	C₂×Q₈	—	6	32	no	—
522	C₂×Q₈	—	6	4	no	—
523	C₂×D₄	—	2	4	no	—
524	C₂×D₄	—	3	8	no	—
525	C₂×D₄	—	3	8	no	—
526	C₂×D₄	—	3	4	no	—
527	C₂×D₄	—	6	8	no	—
528	C₂×D₄	—	6	8	no	—
529	C₂×D₄	—	6	4	no	—
530	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	3	2	no	—
534	C₂²×C₄	—	3	2	no	—
535	C₂²×C₄	—	3	2	no	—
536	C₂²×C₄	—	3	8	no	—
537	C₂²×C₄	—	3	8	no	—
538	C₂²×C₄	—	6	8	no	—
539	C₂²×C₄	—	6	8	no	—
540	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
541	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
542	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
543	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
544	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
545	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
546	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
547	C₄⋊C₄	—	3	8	no	—
548	C₄⋊C₄	—	3	8	no	—
549	C₄⋊C₄	—	3	4	no	—
550	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
551	C₂²⋊C₄	—	3	8	no	—
552	C₂²⋊C₄	—	3	8	no	—
553	C₂²⋊C₄	—	3	8	no	—
554	C₂²⋊C₄	—	3	8	no	—
555	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
556	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
557	C₄²	—	3	8	no	—
558	C₄²	C₂²×C₅×D₃	1	4	yes	—
559	C₃×C₅	C₂×#548	1	1	yes	characteristic, complemented, Hall
560	C₂²×C₃	—	2	8	no	—
561	C₂²×C₃	—	2	2	no	—
562	C₂²×C₃	—	2	2	no	—
563	C₂²×C₃	—	2	2	no	—
564	C₂²×C₃	—	2	2	no	—
565	C₂²×C₃	—	2	2	no	—
566	C₂²×C₃	—	4	4	no	—
567	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
568	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
569	C₂²×C₃	C₂×C₅×#41	1	4	yes	complemented
570	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
571	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
572	C₂×D₃	—	2	4	no	—
573	C₂×D₃	—	2	4	no	—
574	C₂×D₃	—	2	4	no	—
575	C₂×D₃	—	4	8	no	—
576	C₃×C₄	—	2	2	no	—
577	C₃×C₄	—	2	2	no	—
578	C₃×C₄	—	2	2	no	—
579	C₃×C₄	—	2	2	no	—
580	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
581	Dic₃	—	2	4	no	—
582	Dic₃	—	2	4	no	—
583	Dic₃	C₂²×C₅×D₄	1	8	yes	—
584	C₂×C₅	—	2	4	no	—
585	C₂×C₅	—	4	2	no	—
586	C₂×C₅	—	12	4	no	—
587	C₂×C₅	#5552	1	4	yes	direct product factor
588	C₂×C₅	C₂²×#235	1	1	yes	characteristic
589	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
590	C₂×C₅	C₂×#1010	1	1	yes	characteristic
591	C₂³	—	2	2	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	2	no	—
596	C₂³	—	3	4	no	—
597	C₂³	—	6	4	no	—
598	C₂³	—	6	4	no	—
599	C₂³	—	6	4	no	—
600	C₂³	C₅×#235	1	4	yes	complemented
601	C₂³	C₂³×C₅×D₃	1	2	yes	—
602	C₂³	C₂³×C₅×D₃	1	2	yes	—
603	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
604	Q₈	—	3	16	no	—
605	Q₈	—	6	16	no	—
606	Q₈	—	6	8	no	—
607	D₄	—	2	8	no	—
608	D₄	—	6	16	no	—
609	D₄	—	6	16	no	—
610	D₄	—	6	8	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	8	no	—
616	C₂×C₄	—	2	8	no	—
617	C₂×C₄	—	3	8	no	—
618	C₂×C₄	—	3	4	no	—
619	C₂×C₄	—	3	4	no	—
620	C₂×C₄	—	3	4	no	—
621	C₂×C₄	—	6	16	no	—
622	C₂×C₄	—	6	16	no	—
623	C₂×C₄	—	6	4	no	—
624	C₂×C₄	—	6	4	no	—
625	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
626	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
627	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
628	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
629	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
630	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
631	C₂×C₃	—	2	4	no	—
632	C₂×C₃	—	4	2	no	—
633	C₂×C₃	C₅×#548	1	4	yes	complemented
634	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
635	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
636	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
637	D₃	—	4	4	no	—
638	C₅	C₂×#5552	1	1	yes	characteristic, direct product factor, Sylow
639	C₂²	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	8	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	4	4	no	—
646	C₂²	—	6	4	no	—
647	C₂²	—	6	4	no	—
648	C₂²	—	6	4	no	—
649	C₂²	—	12	8	no	—
650	C₂²	C₂×C₅×#235	1	2	yes	—
651	C₂²	C₂×C₅×#235	1	4	yes	complemented
652	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
653	C₂²	C₅×#1010	1	2	yes	—
654	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
655	C₄	—	2	2	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	2	no	—
659	C₄	—	3	8	no	—
660	C₄	—	6	4	no	—
661	C₄	—	6	4	no	—
662	C₄	C₂×C₅×D₃×D₄	1	4	yes	—
663	C₃	C₂×C₅×#548	1	1	yes	characteristic, complemented, Sylow
664	C₂	—	2	4	no	—
665	C₂	—	4	2	no	—
666	C₂	—	12	4	no	—
667	C₂	C₅×#5552	1	4	yes	direct product factor
668	C₂	C₂²×C₅×#235	1	1	yes	characteristic
669	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
670	C₂	C₂×C₅×#1010	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₄×C₅×D₄	D₃
hypocenter	C₃	C₂×C₅×#548
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄×C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#235	C₂	semidirect
2. C₂³×C₅×Dic₆	C₂	semidirect
3. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
4. C₂×C₅×#939	C₂	semidirect
5. C₂×C₅×#930	C₂	semidirect
6. C₂×C₅×#924	C₂	semidirect
7. C₅×#5552	C₂	direct (N × H)
8. C₂×C₅×#896	C₂	semidirect
9. C₂×C₅×#885	C₂	semidirect
10. C₂×C₅×#67⋊C₄	C₂	semidirect
11. C₂×C₅×#875	C₂	semidirect
12. C₂×C₄×C₅×Dic₆	C₂	semidirect
21. C₂×C₅×#235	C₂²	semidirect
28. C₂²×C₅×Dic₆	C₂²	semidirect
29. C₃×C₄×C₅×D₄	C₂²	semidirect
35. C₅×#939	C₂²	semidirect
36. C₅×#930	C₂²	semidirect
41. C₅×#924	C₂²	semidirect
45. C₅×#896	C₂²	semidirect
46. C₅×#885	C₂²	semidirect
47. C₅×#67⋊C₄	C₂²	semidirect
48. C₅×#875	C₂²	semidirect
49. C₄×C₅×Dic₆	C₂²	semidirect
50. C₂×#5552	C₅	direct (N × H)
62. C₂×C₄×C₅×D₄	D₃	semidirect
94. C₂×C₅×Dic₆	D₄	semidirect
110. C₂²×#235	C₂×C₅	semidirect
111. C₂³×Dic₆	C₂×C₅	semidirect
112. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
113. C₂×#939	C₂×C₅	semidirect
114. C₂×#930	C₂×C₅	semidirect
115. C₂×#924	C₂×C₅	semidirect
116. #5552	C₂×C₅	direct (N × H)
117. C₂×#896	C₂×C₅	semidirect
118. C₂×#885	C₂×C₅	semidirect
119. C₂×#67⋊C₄	C₂×C₅	semidirect
120. C₂×#875	C₂×C₅	semidirect
121. C₂×C₄×Dic₆	C₂×C₅	semidirect
145. C₄×C₅×D₄	C₂×D₃	semidirect
164. C₂³×C₃×C₅	#41	semidirect
198. C₅×Dic₆	C₂×D₄	semidirect
206. C₂×#235	C₂²×C₅	semidirect
213. C₂²×Dic₆	C₂²×C₅	semidirect
214. C₃×C₄×D₄	C₂²×C₅	semidirect
220. #939	C₂²×C₅	semidirect
221. #930	C₂²×C₅	semidirect
226. #924	C₂²×C₅	semidirect
230. #896	C₂²×C₅	semidirect
231. #885	C₂²×C₅	semidirect
232. #67⋊C₄	C₂²×C₅	semidirect
233. #875	C₂²×C₅	semidirect
234. C₄×Dic₆	C₂²×C₅	semidirect
293. C₂×C₄×D₄	C₅×D₃	semidirect
303. C₂²×C₃×C₅	C₂×#41	semidirect
349. C₂×Dic₆	C₅×D₄	semidirect
374. C₂³×C₅	#235	semidirect
428. C₄×D₄	C₂×C₅×D₃	semidirect
443. C₂×C₃×C₅	#548	semidirect
453. C₂³×C₃	C₅×#41	semidirect
487. Dic₆	C₂×C₅×D₄	semidirect
500. C₂²×C₅	C₂×#235	semidirect
559. C₃×C₅	C₂×#548	semidirect
569. C₂²×C₃	C₂×C₅×#41	semidirect
587. C₂×C₅	#5552	direct (N × H)
600. C₂³	C₅×#235	semidirect
633. C₂×C₃	C₅×#548	semidirect
638. C₅	C₂×#5552	direct (N × H)
651. C₂²	C₂×C₅×#235	semidirect
663. C₃	C₂×C₅×#548	semidirect
667. C₂	C₅×#5552	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×#235	2
C₂³×C₅×Dic₆	2
C₂×C₃×C₄×C₅×D₄	2
C₂×C₅×#939	2
C₂×C₅×#930	2
C₂×C₅×#924	2
C₅×#5552	2
C₂×C₅×#896	2
C₂×C₅×#885	2
C₂×C₅×#67⋊C₄	2
C₂×C₅×#875	2
C₂×C₄×C₅×Dic₆	2
C₂×C₅×#548	3
C₂×#5552	5

Subgroups — C2×C5×#5552 #14482805

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5552 #14482805