Subgroups — C₂×C₃×C₅×#400 #14275428

Order 1920.

1208 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#400	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×C₅×#95	C₂	1	2	yes	maximal
5	C₂×C₃×C₅×#95	C₂	1	2	yes	maximal
6	C₂×C₃×C₅×#95	C₂	1	1	yes	maximal, characteristic
7	C₂×C₅×#400	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
10	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	—	2	4	no	—
14	C₂×C₃×C₅×C₄⋊C₄	—	2	4	no	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
17	C₃×C₅×#95	C₂²	1	8	yes	—
18	C₃×C₅×#95	C₂²	1	8	yes	—
19	C₃×C₅×#95	C₂²	1	4	yes	—
20	C₂×C₃×#400	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
22	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
23	C₅×#400	C₂×C₃	1	8	yes	direct product factor
24	C₂×C₅×#95	C₂×C₃	1	1	yes	characteristic
25	C₂×C₅×#95	C₂×C₃	1	2	yes	—
26	C₂×C₅×#95	C₂×C₃	1	2	yes	—
27	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
28	C₂²×C₃×C₄×C₅	—	2	2	no	—
29	C₂²×C₃×C₄×C₅	—	2	2	no	—
30	C₂²×C₃×C₄×C₅	—	2	4	no	—
31	C₂²×C₃×C₄×C₅	—	2	2	no	—
32	C₂²×C₃×C₄×C₅	—	2	4	no	—
33	C₂²×C₃×C₄×C₅	—	2	4	no	—
34	C₂²×C₃×C₄×C₅	—	2	8	no	—
35	C₂²×C₃×C₄×C₅	—	2	4	no	—
36	C₂²×C₃×C₄×C₅	—	2	4	no	—
37	C₂²×C₃×C₄×C₅	—	2	4	no	—
38	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
39	C₂²×C₃×C₄×C₅	Q₈	1	4	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₃×C₅×C₄⋊C₄	—	2	8	no	—
46	C₃×C₅×C₄⋊C₄	—	2	8	no	—
47	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
48	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
49	C₃×#400	C₂×C₅	1	8	yes	direct product factor
50	C₂×C₃×#95	C₂×C₅	1	1	yes	characteristic
51	C₂×C₃×#95	C₂×C₅	1	2	yes	—
52	C₂×C₃×#95	C₂×C₅	1	2	yes	—
53	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
54	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
55	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
56	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
57	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
58	C₂×C₅×C₄⋊C₄	—	2	4	no	—
59	C₂×C₅×C₄⋊C₄	—	2	4	no	—
60	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
61	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
62	C₅×#95	C₂²×C₃	1	8	yes	—
63	C₅×#95	C₂²×C₃	1	8	yes	—
64	C₅×#95	C₂²×C₃	1	4	yes	—
65	C₂×#400	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
66	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
67	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
68	C₂³×C₃×C₅	#41	1	2	yes	—
69	C₂³×C₃×C₅	#41	1	4	yes	—
70	C₂³×C₃×C₅	#41	1	4	yes	—
71	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
72	C₂×C₃×C₄×C₅	—	2	8	no	—
73	C₂×C₃×C₄×C₅	—	2	8	no	—
74	C₂×C₃×C₄×C₅	—	2	2	no	—
75	C₂×C₃×C₄×C₅	—	2	2	no	—
76	C₂×C₃×C₄×C₅	—	2	4	no	—
77	C₂×C₃×C₄×C₅	—	2	2	no	—
78	C₂×C₃×C₄×C₅	—	2	4	no	—
79	C₂×C₃×C₄×C₅	—	2	4	no	—
80	C₂×C₃×C₄×C₅	—	2	8	no	—
81	C₂×C₃×C₄×C₅	—	2	4	no	—
82	C₂×C₃×C₄×C₅	—	2	4	no	—
83	C₂×C₃×C₄×C₅	—	2	4	no	—
84	C₂×C₃×C₄×C₅	—	4	4	no	—
85	C₂×C₃×C₄×C₅	—	4	8	no	—
86	C₂×C₃×C₄×C₅	—	4	8	no	—
87	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
88	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
89	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
90	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
91	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
92	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
93	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
94	C₂×C₃×C₄⋊C₄	—	2	4	no	—
95	C₂×C₃×C₄⋊C₄	—	2	4	no	—
96	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
97	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
98	C₃×#95	C₂²×C₅	1	4	yes	—
99	C₃×#95	C₂²×C₅	1	8	yes	—
100	C₃×#95	C₂²×C₅	1	8	yes	—
101	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
102	C₂²×C₄×C₅	—	2	2	no	—
103	C₂²×C₄×C₅	—	2	2	no	—
104	C₂²×C₄×C₅	—	2	4	no	—
105	C₂²×C₄×C₅	—	2	2	no	—
106	C₂²×C₄×C₅	—	2	4	no	—
107	C₂²×C₄×C₅	—	2	4	no	—
108	C₂²×C₄×C₅	—	2	8	no	—
109	C₂²×C₄×C₅	—	2	4	no	—
110	C₂²×C₄×C₅	—	2	4	no	—
111	C₂²×C₄×C₅	—	2	4	no	—
112	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
113	C₂²×C₄×C₅	C₃×Q₈	1	4	yes	—
114	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
115	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
116	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
117	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
118	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
119	C₅×C₄⋊C₄	—	2	8	no	—
120	C₅×C₄⋊C₄	—	2	8	no	—
121	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
122	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
123	#400	C₂×C₃×C₅	1	8	yes	direct product factor
124	C₂×#95	C₂×C₃×C₅	1	2	yes	—
125	C₂×#95	C₂×C₃×C₅	1	2	yes	—
126	C₂×#95	C₂×C₃×C₅	1	1	yes	characteristic
127	C₂²×C₃×C₅	C₂²⋊Q₈	1	4	yes	—
128	C₂²×C₃×C₅	#123	1	4	yes	—
129	C₂²×C₃×C₅	#124	1	4	yes	—
130	C₂²×C₃×C₅	#125	1	8	yes	—
131	C₂²×C₃×C₅	#126	1	8	yes	—
132	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
133	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
134	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
135	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
136	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
137	C₃×C₄×C₅	—	2	4	no	—
138	C₃×C₄×C₅	—	2	4	no	—
139	C₃×C₄×C₅	—	4	2	no	—
140	C₃×C₄×C₅	—	4	4	no	—
141	C₃×C₄×C₅	—	4	4	no	—
142	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
143	C₂²×C₃×C₄	—	2	2	no	—
144	C₂²×C₃×C₄	—	2	2	no	—
145	C₂²×C₃×C₄	—	2	4	no	—
146	C₂²×C₃×C₄	—	2	2	no	—
147	C₂²×C₃×C₄	—	2	4	no	—
148	C₂²×C₃×C₄	—	2	4	no	—
149	C₂²×C₃×C₄	—	2	8	no	—
150	C₂²×C₃×C₄	—	2	4	no	—
151	C₂²×C₃×C₄	—	2	4	no	—
152	C₂²×C₃×C₄	—	2	4	no	—
153	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
154	C₂²×C₃×C₄	C₅×Q₈	1	4	yes	—
155	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
156	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
157	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
158	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
159	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
160	C₃×C₄⋊C₄	—	2	8	no	—
161	C₃×C₄⋊C₄	—	2	8	no	—
162	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
163	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
164	C₂³×C₅	C₃×#41	1	2	yes	—
165	C₂³×C₅	C₃×#41	1	4	yes	—
166	C₂³×C₅	C₃×#41	1	4	yes	—
167	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
168	C₂×C₄×C₅	—	2	8	no	—
169	C₂×C₄×C₅	—	2	8	no	—
170	C₂×C₄×C₅	—	2	2	no	—
171	C₂×C₄×C₅	—	2	2	no	—
172	C₂×C₄×C₅	—	2	4	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	4	no	—
175	C₂×C₄×C₅	—	2	4	no	—
176	C₂×C₄×C₅	—	2	8	no	—
177	C₂×C₄×C₅	—	2	4	no	—
178	C₂×C₄×C₅	—	2	4	no	—
179	C₂×C₄×C₅	—	2	4	no	—
180	C₂×C₄×C₅	—	4	4	no	—
181	C₂×C₄×C₅	—	4	8	no	—
182	C₂×C₄×C₅	—	4	8	no	—
183	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
184	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
185	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
186	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
187	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
188	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
189	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
190	C₂×C₄⋊C₄	—	2	4	no	—
191	C₂×C₄⋊C₄	—	2	4	no	—
192	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
193	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
194	#95	C₂²×C₃×C₅	1	4	yes	—
195	#95	C₂²×C₃×C₅	1	8	yes	—
196	#95	C₂²×C₃×C₅	1	8	yes	—
197	C₂×C₃×C₅	#400	1	8	yes	direct product factor
198	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
199	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
200	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
201	C₂×C₃×C₅	C₂×#125	1	2	yes	—
202	C₂×C₃×C₅	C₂×#126	1	2	yes	—
203	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
204	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
205	C₂³×C₃	C₅×#41	1	2	yes	—
206	C₂³×C₃	C₅×#41	1	4	yes	—
207	C₂³×C₃	C₅×#41	1	4	yes	—
208	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
209	C₂×C₃×C₄	—	2	8	no	—
210	C₂×C₃×C₄	—	2	8	no	—
211	C₂×C₃×C₄	—	2	2	no	—
212	C₂×C₃×C₄	—	2	2	no	—
213	C₂×C₃×C₄	—	2	4	no	—
214	C₂×C₃×C₄	—	2	2	no	—
215	C₂×C₃×C₄	—	2	4	no	—
216	C₂×C₃×C₄	—	2	4	no	—
217	C₂×C₃×C₄	—	2	8	no	—
218	C₂×C₃×C₄	—	2	4	no	—
219	C₂×C₃×C₄	—	2	4	no	—
220	C₂×C₃×C₄	—	2	4	no	—
221	C₂×C₃×C₄	—	4	4	no	—
222	C₂×C₃×C₄	—	4	8	no	—
223	C₂×C₃×C₄	—	4	8	no	—
224	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
225	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
226	C₂²×C₅	C₃×C₂²⋊Q₈	1	4	yes	—
227	C₂²×C₅	C₃×#123	1	4	yes	—
228	C₂²×C₅	C₃×#124	1	4	yes	—
229	C₂²×C₅	C₃×#125	1	8	yes	—
230	C₂²×C₅	C₃×#126	1	8	yes	—
231	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
232	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
233	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
234	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
235	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
236	C₄×C₅	—	2	4	no	—
237	C₄×C₅	—	2	4	no	—
238	C₄×C₅	—	4	2	no	—
239	C₄×C₅	—	4	4	no	—
240	C₄×C₅	—	4	4	no	—
241	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	—	2	2	no	—
244	C₂²×C₄	—	2	4	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	8	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
253	C₂²×C₄	C₃×C₅×Q₈	1	4	yes	—
254	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
255	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
256	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
257	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
258	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
259	C₄⋊C₄	—	2	8	no	—
260	C₄⋊C₄	—	2	8	no	—
261	C₃×C₅	C₂×#400	1	1	yes	characteristic, direct product factor, Hall
262	C₂²×C₃	C₅×C₂²⋊Q₈	1	4	yes	—
263	C₂²×C₃	C₅×#123	1	4	yes	—
264	C₂²×C₃	C₅×#124	1	4	yes	—
265	C₂²×C₃	C₅×#125	1	8	yes	—
266	C₂²×C₃	C₅×#126	1	8	yes	—
267	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
268	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
269	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
270	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
271	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
272	C₃×C₄	—	2	4	no	—
273	C₃×C₄	—	2	4	no	—
274	C₃×C₄	—	4	2	no	—
275	C₃×C₄	—	4	4	no	—
276	C₃×C₄	—	4	4	no	—
277	C₂×C₅	C₃×#400	1	8	yes	direct product factor
278	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
279	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
280	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
281	C₂×C₅	C₂×C₃×#125	1	2	yes	—
282	C₂×C₅	C₂×C₃×#126	1	2	yes	—
283	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
284	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
285	C₂³	C₃×C₅×#41	1	2	yes	—
286	C₂³	C₃×C₅×#41	1	4	yes	—
287	C₂³	C₃×C₅×#41	1	4	yes	—
288	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	8	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	2	8	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	2	8	no	—
298	C₂×C₄	—	2	4	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	4	4	no	—
302	C₂×C₄	—	4	8	no	—
303	C₂×C₄	—	4	8	no	—
304	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
305	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
306	C₂×C₃	C₅×#400	1	8	yes	direct product factor
307	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
308	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
309	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
310	C₂×C₃	C₂×C₅×#125	1	2	yes	—
311	C₂×C₃	C₂×C₅×#126	1	2	yes	—
312	C₅	C₂×C₃×#400	1	1	yes	characteristic, direct product factor, Sylow
313	C₂²	C₃×C₅×C₂²⋊Q₈	1	4	yes	—
314	C₂²	C₃×C₅×#123	1	4	yes	—
315	C₂²	C₃×C₅×#124	1	4	yes	—
316	C₂²	C₃×C₅×#125	1	8	yes	—
317	C₂²	C₃×C₅×#126	1	8	yes	—
318	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
319	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
320	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
321	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
322	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
323	C₄	—	2	4	no	—
324	C₄	—	2	4	no	—
325	C₄	—	4	2	no	—
326	C₄	—	4	4	no	—
327	C₄	—	4	4	no	—
328	C₃	C₂×C₅×#400	1	1	yes	characteristic, direct product factor, Sylow
329	C₂	C₃×C₅×#400	1	8	yes	direct product factor
330	C₂	C₂×C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
331	C₂	C₂×C₃×C₅×#123	1	1	yes	characteristic
332	C₂	C₂×C₃×C₅×#124	1	1	yes	characteristic
333	C₂	C₂×C₃×C₅×#125	1	2	yes	—
334	C₂	C₂×C₃×C₅×#126	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₃×C₅	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#400	C₂	direct (N × H)
7. C₂×C₅×#400	C₃	direct (N × H)
20. C₂×C₃×#400	C₅	direct (N × H)
23. C₅×#400	C₂×C₃	direct (N × H)
49. C₃×#400	C₂×C₅	direct (N × H)
65. C₂×#400	C₃×C₅	direct (N × H)
123. #400	C₂×C₃×C₅	direct (N × H)
197. C₂×C₃×C₅	#400	direct (N × H)
261. C₃×C₅	C₂×#400	direct (N × H)
277. C₂×C₅	C₃×#400	direct (N × H)
306. C₂×C₃	C₅×#400	direct (N × H)
312. C₅	C₂×C₃×#400	direct (N × H)
328. C₃	C₂×C₅×#400	direct (N × H)
329. C₂	C₃×C₅×#400	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×C₃×C₅×C₄⋊C₄	2
C₃×C₅×#400	2
C₂×C₃×C₅×#95	2
C₂×C₅×#400	3
C₂×C₃×#400	5

Subgroups — C2×C3×C5×#400 #14275428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#400 #14275428