Subgroups — C₂×C₄×C₈×C₉×C₂₅ #72192558

Order 14400.

729 conjugacy classes of subgroups.

The subgroup lattice has 243 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₉×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×C₉×C₂₅	C₂	1	2	yes	maximal
3	C₄×C₈×C₉×C₂₅	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃×C₄×C₈×C₂₅	C₃	1	1	yes	maximal, characteristic
5	C₂²×C₄×C₉×C₂₅	C₄	1	2	yes	—
6	C₂²×C₄×C₉×C₂₅	C₂²	1	1	yes	characteristic
7	C₄²×C₉×C₂₅	C₄	1	2	yes	—
8	C₄²×C₉×C₂₅	C₂²	1	2	yes	—
9	C₂×C₈×C₉×C₂₅	C₄	1	8	yes	direct product factor
10	C₂×C₈×C₉×C₂₅	C₂²	1	4	yes	—
11	C₂×C₄×C₅×C₈×C₉	C₅	1	1	yes	maximal, characteristic
12	C₂×C₃×C₄²×C₂₅	C₂×C₃	1	1	yes	characteristic
13	C₂²×C₃×C₈×C₂₅	C₂×C₃	1	2	yes	—
14	C₃×C₄×C₈×C₂₅	C₂×C₃	1	4	yes	—
15	C₂³×C₉×C₂₅	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₉×C₂₅	C₈	1	8	yes	direct product factor
17	C₂×C₄×C₉×C₂₅	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₉×C₂₅	C₂×C₄	1	4	yes	—
19	C₂×C₄×C₉×C₂₅	C₂×C₄	1	4	yes	—
20	C₂×C₄×C₉×C₂₅	C₂³	1	1	yes	characteristic
21	C₈×C₉×C₂₅	C₂×C₄	1	8	yes	direct product factor
22	C₂×C₄×C₈×C₂₅	C₉	1	1	yes	characteristic, direct product factor, Hall
23	C₂²×C₅×C₈×C₉	C₂×C₅	1	2	yes	—
24	C₂×C₄²×C₅×C₉	C₂×C₅	1	1	yes	characteristic
25	C₄×C₅×C₈×C₉	C₂×C₅	1	4	yes	—
26	C₂²×C₃×C₄×C₂₅	C₃×C₄	1	2	yes	—
27	C₂²×C₃×C₄×C₂₅	C₂²×C₃	1	1	yes	characteristic
28	C₂×C₃×C₈×C₂₅	C₃×C₄	1	8	yes	—
29	C₂×C₃×C₈×C₂₅	C₂²×C₃	1	4	yes	—
30	C₃×C₄²×C₂₅	C₃×C₄	1	2	yes	—
31	C₃×C₄²×C₂₅	C₂²×C₃	1	2	yes	—
32	C₂×C₃×C₄×C₅×C₈	C₃×C₅	1	1	yes	characteristic
33	C₂²×C₉×C₂₅	C₄²	1	2	yes	—
34	C₂²×C₉×C₂₅	C₂×C₈	1	4	yes	—
35	C₂²×C₉×C₂₅	C₂²×C₄	1	1	yes	characteristic
36	C₄×C₉×C₂₅	C₄²	1	2	yes	—
37	C₄×C₉×C₂₅	C₂×C₈	1	8	yes	direct product factor
38	C₄×C₉×C₂₅	C₂²×C₄	1	2	yes	—
39	C₂²×C₈×C₂₅	C₂×C₉	1	2	yes	—
40	C₂×C₄²×C₂₅	C₂×C₉	1	1	yes	characteristic
41	C₄×C₈×C₂₅	C₂×C₉	1	4	yes	direct product factor
42	C₂²×C₄×C₅×C₉	C₄×C₅	1	2	yes	—
43	C₂²×C₄×C₅×C₉	C₂²×C₅	1	1	yes	characteristic
44	C₂×C₅×C₈×C₉	C₄×C₅	1	8	yes	—
45	C₂×C₅×C₈×C₉	C₂²×C₅	1	4	yes	—
46	C₄²×C₅×C₉	C₄×C₅	1	2	yes	—
47	C₄²×C₅×C₉	C₂²×C₅	1	2	yes	—
48	C₂³×C₃×C₂₅	C₂×C₃×C₄	1	1	yes	characteristic
49	C₂×C₃×C₄×C₂₅	C₃×C₈	1	8	yes	—
50	C₂×C₃×C₄×C₂₅	C₂×C₃×C₄	1	1	yes	characteristic
51	C₂×C₃×C₄×C₂₅	C₂×C₃×C₄	1	4	yes	—
52	C₂×C₃×C₄×C₂₅	C₂×C₃×C₄	1	4	yes	—
53	C₂×C₃×C₄×C₂₅	C₂³×C₃	1	1	yes	characteristic
54	C₃×C₈×C₂₅	C₂×C₃×C₄	1	8	yes	—
55	C₂×C₄×C₈×C₉	C₂₅	1	1	yes	characteristic, direct product factor, Hall
56	C₂²×C₃×C₅×C₈	C₂×C₃×C₅	1	2	yes	—
57	C₂×C₃×C₄²×C₅	C₂×C₃×C₅	1	1	yes	characteristic
58	C₃×C₄×C₅×C₈	C₂×C₃×C₅	1	4	yes	—
59	C₂×C₉×C₂₅	C₄×C₈	1	4	yes	direct product factor
60	C₂×C₉×C₂₅	C₂×C₄²	1	1	yes	characteristic
61	C₂×C₉×C₂₅	C₂²×C₈	1	2	yes	—
62	C₂²×C₄×C₂₅	C₄×C₉	1	2	yes	—
63	C₂²×C₄×C₂₅	C₂²×C₉	1	1	yes	characteristic
64	C₂×C₈×C₂₅	C₄×C₉	1	8	yes	direct product factor
65	C₂×C₈×C₂₅	C₂²×C₉	1	4	yes	—
66	C₄²×C₂₅	C₄×C₉	1	2	yes	—
67	C₄²×C₂₅	C₂²×C₉	1	2	yes	—
68	C₂³×C₅×C₉	C₂×C₄×C₅	1	1	yes	characteristic
69	C₂×C₄×C₅×C₉	C₅×C₈	1	8	yes	—
70	C₂×C₄×C₅×C₉	C₂×C₄×C₅	1	1	yes	characteristic
71	C₂×C₄×C₅×C₉	C₂×C₄×C₅	1	4	yes	—
72	C₂×C₄×C₅×C₉	C₂×C₄×C₅	1	4	yes	—
73	C₂×C₄×C₅×C₉	C₂³×C₅	1	1	yes	characteristic
74	C₅×C₈×C₉	C₂×C₄×C₅	1	8	yes	—
75	C₂×C₄×C₅×C₈	C₅×C₉	1	1	yes	characteristic
76	C₂²×C₃×C₂₅	C₃×C₄²	1	2	yes	—
77	C₂²×C₃×C₂₅	C₂×C₃×C₈	1	4	yes	—
78	C₂²×C₃×C₂₅	C₂²×C₃×C₄	1	1	yes	characteristic
79	C₃×C₄×C₂₅	C₃×C₄²	1	2	yes	—
80	C₃×C₄×C₂₅	C₂×C₃×C₈	1	8	yes	—
81	C₃×C₄×C₂₅	C₂²×C₃×C₄	1	2	yes	—
82	C₂²×C₈×C₉	C₂×C₂₅	1	2	yes	—
83	C₂×C₄²×C₉	C₂×C₂₅	1	1	yes	characteristic
84	C₄×C₈×C₉	C₂×C₂₅	1	4	yes	direct product factor
85	C₂²×C₃×C₄×C₅	C₃×C₄×C₅	1	2	yes	—
86	C₂²×C₃×C₄×C₅	C₂²×C₃×C₅	1	1	yes	characteristic
87	C₂×C₃×C₅×C₈	C₃×C₄×C₅	1	8	yes	—
88	C₂×C₃×C₅×C₈	C₂²×C₃×C₅	1	4	yes	—
89	C₃×C₄²×C₅	C₃×C₄×C₅	1	2	yes	—
90	C₃×C₄²×C₅	C₂²×C₃×C₅	1	2	yes	—
91	C₉×C₂₅	C₂×C₄×C₈	1	1	yes	characteristic, direct product factor, Hall
92	C₂³×C₂₅	C₂×C₄×C₉	1	1	yes	characteristic
93	C₂×C₄×C₂₅	C₈×C₉	1	8	yes	direct product factor
94	C₂×C₄×C₂₅	C₂×C₄×C₉	1	1	yes	characteristic
95	C₂×C₄×C₂₅	C₂×C₄×C₉	1	4	yes	—
96	C₂×C₄×C₂₅	C₂×C₄×C₉	1	4	yes	—
97	C₂×C₄×C₂₅	C₂³×C₉	1	1	yes	characteristic
98	C₈×C₂₅	C₂×C₄×C₉	1	8	yes	direct product factor
99	C₂×C₃×C₄×C₈	C₃×C₂₅	1	1	yes	characteristic
100	C₂²×C₅×C₉	C₄²×C₅	1	2	yes	—
101	C₂²×C₅×C₉	C₂×C₅×C₈	1	4	yes	—
102	C₂²×C₅×C₉	C₂²×C₄×C₅	1	1	yes	characteristic
103	C₄×C₅×C₉	C₄²×C₅	1	2	yes	—
104	C₄×C₅×C₉	C₂×C₅×C₈	1	8	yes	—
105	C₄×C₅×C₉	C₂²×C₄×C₅	1	2	yes	—
106	C₂²×C₅×C₈	C₂×C₅×C₉	1	2	yes	—
107	C₂×C₄²×C₅	C₂×C₅×C₉	1	1	yes	characteristic
108	C₄×C₅×C₈	C₂×C₅×C₉	1	4	yes	—
109	C₂×C₃×C₂₅	C₃×C₄×C₈	1	4	yes	—
110	C₂×C₃×C₂₅	C₂×C₃×C₄²	1	1	yes	characteristic
111	C₂×C₃×C₂₅	C₂²×C₃×C₈	1	2	yes	—
112	C₂²×C₄×C₉	C₄×C₂₅	1	2	yes	—
113	C₂²×C₄×C₉	C₂²×C₂₅	1	1	yes	characteristic
114	C₂×C₈×C₉	C₄×C₂₅	1	8	yes	direct product factor
115	C₂×C₈×C₉	C₂²×C₂₅	1	4	yes	—
116	C₄²×C₉	C₄×C₂₅	1	2	yes	—
117	C₄²×C₉	C₂²×C₂₅	1	2	yes	—
118	C₂³×C₃×C₅	C₂×C₃×C₄×C₅	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	C₃×C₅×C₈	1	8	yes	—
120	C₂×C₃×C₄×C₅	C₂×C₃×C₄×C₅	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	C₂×C₃×C₄×C₅	1	4	yes	—
122	C₂×C₃×C₄×C₅	C₂×C₃×C₄×C₅	1	4	yes	—
123	C₂×C₃×C₄×C₅	C₂³×C₃×C₅	1	1	yes	characteristic
124	C₃×C₅×C₈	C₂×C₃×C₄×C₅	1	8	yes	—
125	C₂²×C₂₅	C₄²×C₉	1	2	yes	—
126	C₂²×C₂₅	C₂×C₈×C₉	1	4	yes	—
127	C₂²×C₂₅	C₂²×C₄×C₉	1	1	yes	characteristic
128	C₄×C₂₅	C₄²×C₉	1	2	yes	—
129	C₄×C₂₅	C₂×C₈×C₉	1	8	yes	direct product factor
130	C₄×C₂₅	C₂²×C₄×C₉	1	2	yes	—
131	C₂²×C₃×C₈	C₂×C₃×C₂₅	1	2	yes	—
132	C₂×C₃×C₄²	C₂×C₃×C₂₅	1	1	yes	characteristic
133	C₃×C₄×C₈	C₂×C₃×C₂₅	1	4	yes	—
134	C₂×C₅×C₉	C₄×C₅×C₈	1	4	yes	—
135	C₂×C₅×C₉	C₂×C₄²×C₅	1	1	yes	characteristic
136	C₂×C₅×C₉	C₂²×C₅×C₈	1	2	yes	—
137	C₂²×C₄×C₅	C₄×C₅×C₉	1	2	yes	—
138	C₂²×C₄×C₅	C₂²×C₅×C₉	1	1	yes	characteristic
139	C₂×C₅×C₈	C₄×C₅×C₉	1	8	yes	—
140	C₂×C₅×C₈	C₂²×C₅×C₉	1	4	yes	—
141	C₄²×C₅	C₄×C₅×C₉	1	2	yes	—
142	C₄²×C₅	C₂²×C₅×C₉	1	2	yes	—
143	C₃×C₂₅	C₂×C₃×C₄×C₈	1	1	yes	characteristic
144	C₂³×C₉	C₂×C₄×C₂₅	1	1	yes	characteristic
145	C₂×C₄×C₉	C₈×C₂₅	1	8	yes	direct product factor
146	C₂×C₄×C₉	C₂×C₄×C₂₅	1	1	yes	characteristic
147	C₂×C₄×C₉	C₂×C₄×C₂₅	1	4	yes	—
148	C₂×C₄×C₉	C₂×C₄×C₂₅	1	4	yes	—
149	C₂×C₄×C₉	C₂³×C₂₅	1	1	yes	characteristic
150	C₈×C₉	C₂×C₄×C₂₅	1	8	yes	direct product factor
151	C₂×C₄×C₈	C₉×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
152	C₂²×C₃×C₅	C₃×C₄²×C₅	1	2	yes	—
153	C₂²×C₃×C₅	C₂×C₃×C₅×C₈	1	4	yes	—
154	C₂²×C₃×C₅	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
155	C₃×C₄×C₅	C₃×C₄²×C₅	1	2	yes	—
156	C₃×C₄×C₅	C₂×C₃×C₅×C₈	1	8	yes	—
157	C₃×C₄×C₅	C₂²×C₃×C₄×C₅	1	2	yes	—
158	C₂×C₂₅	C₄×C₈×C₉	1	4	yes	direct product factor
159	C₂×C₂₅	C₂×C₄²×C₉	1	1	yes	characteristic
160	C₂×C₂₅	C₂²×C₈×C₉	1	2	yes	—
161	C₂²×C₃×C₄	C₃×C₄×C₂₅	1	2	yes	—
162	C₂²×C₃×C₄	C₂²×C₃×C₂₅	1	1	yes	characteristic
163	C₂×C₃×C₈	C₃×C₄×C₂₅	1	8	yes	—
164	C₂×C₃×C₈	C₂²×C₃×C₂₅	1	4	yes	—
165	C₃×C₄²	C₃×C₄×C₂₅	1	2	yes	—
166	C₃×C₄²	C₂²×C₃×C₂₅	1	2	yes	—
167	C₅×C₉	C₂×C₄×C₅×C₈	1	1	yes	characteristic
168	C₂³×C₅	C₂×C₄×C₅×C₉	1	1	yes	characteristic
169	C₂×C₄×C₅	C₅×C₈×C₉	1	8	yes	—
170	C₂×C₄×C₅	C₂×C₄×C₅×C₉	1	1	yes	characteristic
171	C₂×C₄×C₅	C₂×C₄×C₅×C₉	1	4	yes	—
172	C₂×C₄×C₅	C₂×C₄×C₅×C₉	1	4	yes	—
173	C₂×C₄×C₅	C₂³×C₅×C₉	1	1	yes	characteristic
174	C₅×C₈	C₂×C₄×C₅×C₉	1	8	yes	—
175	C₂²×C₉	C₄²×C₂₅	1	2	yes	—
176	C₂²×C₉	C₂×C₈×C₂₅	1	4	yes	—
177	C₂²×C₉	C₂²×C₄×C₂₅	1	1	yes	characteristic
178	C₄×C₉	C₄²×C₂₅	1	2	yes	—
179	C₄×C₉	C₂×C₈×C₂₅	1	8	yes	direct product factor
180	C₄×C₉	C₂²×C₄×C₂₅	1	2	yes	—
181	C₂²×C₈	C₂×C₉×C₂₅	1	2	yes	—
182	C₂×C₄²	C₂×C₉×C₂₅	1	1	yes	characteristic
183	C₄×C₈	C₂×C₉×C₂₅	1	4	yes	direct product factor
184	C₂×C₃×C₅	C₃×C₄×C₅×C₈	1	4	yes	—
185	C₂×C₃×C₅	C₂×C₃×C₄²×C₅	1	1	yes	characteristic
186	C₂×C₃×C₅	C₂²×C₃×C₅×C₈	1	2	yes	—
187	C₂₅	C₂×C₄×C₈×C₉	1	1	yes	characteristic, direct product factor, Sylow
188	C₂³×C₃	C₂×C₃×C₄×C₂₅	1	1	yes	characteristic
189	C₂×C₃×C₄	C₃×C₈×C₂₅	1	8	yes	—
190	C₂×C₃×C₄	C₂×C₃×C₄×C₂₅	1	1	yes	characteristic
191	C₂×C₃×C₄	C₂×C₃×C₄×C₂₅	1	4	yes	—
192	C₂×C₃×C₄	C₂×C₃×C₄×C₂₅	1	4	yes	—
193	C₂×C₃×C₄	C₂³×C₃×C₂₅	1	1	yes	characteristic
194	C₃×C₈	C₂×C₃×C₄×C₂₅	1	8	yes	—
195	C₂²×C₅	C₄²×C₅×C₉	1	2	yes	—
196	C₂²×C₅	C₂×C₅×C₈×C₉	1	4	yes	—
197	C₂²×C₅	C₂²×C₄×C₅×C₉	1	1	yes	characteristic
198	C₄×C₅	C₄²×C₅×C₉	1	2	yes	—
199	C₄×C₅	C₂×C₅×C₈×C₉	1	8	yes	—
200	C₄×C₅	C₂²×C₄×C₅×C₉	1	2	yes	—
201	C₂×C₉	C₄×C₈×C₂₅	1	4	yes	direct product factor
202	C₂×C₉	C₂×C₄²×C₂₅	1	1	yes	characteristic
203	C₂×C₉	C₂²×C₈×C₂₅	1	2	yes	—
204	C₂²×C₄	C₄×C₉×C₂₅	1	2	yes	—
205	C₂²×C₄	C₂²×C₉×C₂₅	1	1	yes	characteristic
206	C₂×C₈	C₄×C₉×C₂₅	1	8	yes	direct product factor
207	C₂×C₈	C₂²×C₉×C₂₅	1	4	yes	—
208	C₄²	C₄×C₉×C₂₅	1	2	yes	—
209	C₄²	C₂²×C₉×C₂₅	1	2	yes	—
210	C₃×C₅	C₂×C₃×C₄×C₅×C₈	1	1	yes	characteristic
211	C₂²×C₃	C₃×C₄²×C₂₅	1	2	yes	—
212	C₂²×C₃	C₂×C₃×C₈×C₂₅	1	4	yes	—
213	C₂²×C₃	C₂²×C₃×C₄×C₂₅	1	1	yes	characteristic
214	C₃×C₄	C₃×C₄²×C₂₅	1	2	yes	—
215	C₃×C₄	C₂×C₃×C₈×C₂₅	1	8	yes	—
216	C₃×C₄	C₂²×C₃×C₄×C₂₅	1	2	yes	—
217	C₂×C₅	C₄×C₅×C₈×C₉	1	4	yes	—
218	C₂×C₅	C₂×C₄²×C₅×C₉	1	1	yes	characteristic
219	C₂×C₅	C₂²×C₅×C₈×C₉	1	2	yes	—
220	C₉	C₂×C₄×C₈×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
221	C₂³	C₂×C₄×C₉×C₂₅	1	1	yes	characteristic
222	C₂×C₄	C₈×C₉×C₂₅	1	8	yes	direct product factor
223	C₂×C₄	C₂×C₄×C₉×C₂₅	1	1	yes	characteristic
224	C₂×C₄	C₂×C₄×C₉×C₂₅	1	4	yes	—
225	C₂×C₄	C₂×C₄×C₉×C₂₅	1	4	yes	—
226	C₂×C₄	C₂³×C₉×C₂₅	1	1	yes	characteristic
227	C₈	C₂×C₄×C₉×C₂₅	1	8	yes	direct product factor
228	C₂×C₃	C₃×C₄×C₈×C₂₅	1	4	yes	—
229	C₂×C₃	C₂²×C₃×C₈×C₂₅	1	2	yes	—
230	C₂×C₃	C₂×C₃×C₄²×C₂₅	1	1	yes	characteristic
231	C₅	C₂×C₄×C₅×C₈×C₉	1	1	yes	characteristic
232	C₂²	C₂×C₈×C₉×C₂₅	1	4	yes	—
233	C₂²	C₄²×C₉×C₂₅	1	2	yes	—
234	C₂²	C₂²×C₄×C₉×C₂₅	1	1	yes	characteristic
235	C₄	C₂×C₈×C₉×C₂₅	1	8	yes	direct product factor
236	C₄	C₄²×C₉×C₂₅	1	2	yes	—
237	C₄	C₂²×C₄×C₉×C₂₅	1	2	yes	—
238	C₃	C₂×C₃×C₄×C₈×C₂₅	1	1	yes	characteristic
239	C₂	C₄×C₈×C₉×C₂₅	1	4	yes	direct product factor
240	C₂	C₂²×C₈×C₉×C₂₅	1	2	yes	—
241	C₂	C₂×C₄²×C₉×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃×C₄×C₅	C₂³×C₃×C₅
socle, prime radical	C₂³×C₃×C₅	C₂×C₃×C₄×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄×C₈×C₉×C₂₅	C₂	direct (N × H)
9. C₂×C₈×C₉×C₂₅	C₄	direct (N × H)
16. C₂×C₄×C₉×C₂₅	C₈	direct (N × H)
21. C₈×C₉×C₂₅	C₂×C₄	direct (N × H)
22. C₂×C₄×C₈×C₂₅	C₉	direct (N × H)
37. C₄×C₉×C₂₅	C₂×C₈	direct (N × H)
41. C₄×C₈×C₂₅	C₂×C₉	direct (N × H)
55. C₂×C₄×C₈×C₉	C₂₅	direct (N × H)
59. C₂×C₉×C₂₅	C₄×C₈	direct (N × H)
64. C₂×C₈×C₂₅	C₄×C₉	direct (N × H)
84. C₄×C₈×C₉	C₂×C₂₅	direct (N × H)
91. C₉×C₂₅	C₂×C₄×C₈	direct (N × H)
93. C₂×C₄×C₂₅	C₈×C₉	direct (N × H)
98. C₈×C₂₅	C₂×C₄×C₉	direct (N × H)
114. C₂×C₈×C₉	C₄×C₂₅	direct (N × H)
129. C₄×C₂₅	C₂×C₈×C₉	direct (N × H)
145. C₂×C₄×C₉	C₈×C₂₅	direct (N × H)
150. C₈×C₉	C₂×C₄×C₂₅	direct (N × H)
151. C₂×C₄×C₈	C₉×C₂₅	direct (N × H)
158. C₂×C₂₅	C₄×C₈×C₉	direct (N × H)
179. C₄×C₉	C₂×C₈×C₂₅	direct (N × H)
183. C₄×C₈	C₂×C₉×C₂₅	direct (N × H)
187. C₂₅	C₂×C₄×C₈×C₉	direct (N × H)
201. C₂×C₉	C₄×C₈×C₂₅	direct (N × H)
206. C₂×C₈	C₄×C₉×C₂₅	direct (N × H)
220. C₉	C₂×C₄×C₈×C₂₅	direct (N × H)
222. C₂×C₄	C₈×C₉×C₂₅	direct (N × H)
227. C₈	C₂×C₄×C₉×C₂₅	direct (N × H)
235. C₄	C₂×C₈×C₉×C₂₅	direct (N × H)
239. C₂	C₄×C₈×C₉×C₂₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄²×C₉×C₂₅	2
C₂²×C₈×C₉×C₂₅	2
C₄×C₈×C₉×C₂₅	2
C₂×C₃×C₄×C₈×C₂₅	3
C₂×C₄×C₅×C₈×C₉	5

Subgroups — C2×C4×C8×C9×C25 #72192558

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₈×C₉×C₂₅ #72192558