Subgroups — C₃×C₅×#2403 #14275437

Order 1920.

3128 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×D₄	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×#120	C₂	1	4	yes	maximal, complemented
3	C₃×C₅×#392	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#386	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#379	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2403	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
8	C₂⁵×C₃×C₅	C₂²	1	2	yes	complemented
9	C₂²×C₃×C₅×D₄	—	2	8	no	—
10	C₂²×C₃×C₅×D₄	—	2	16	no	—
11	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	—
12	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	complemented
13	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	complemented
14	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	complemented
15	C₃×C₅×#120	—	2	16	no	—
16	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
19	C₃×C₅×#95	C₂²	1	4	yes	complemented
20	C₃×#2403	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂³×C₅×D₄	C₂×C₃	1	2	yes	complemented
22	C₂×C₅×#120	C₂×C₃	1	4	yes	complemented
23	C₅×#392	C₂×C₃	1	4	yes	complemented
24	C₅×#386	C₂×C₃	1	4	yes	complemented
25	C₅×#379	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂⁴×C₃×C₅	—	2	8	no	—
27	C₂⁴×C₃×C₅	—	2	4	no	—
28	C₂⁴×C₃×C₅	—	2	8	no	—
29	C₂⁴×C₃×C₅	—	2	8	no	—
30	C₂⁴×C₃×C₅	—	4	2	no	—
31	C₂⁴×C₃×C₅	—	4	4	no	—
32	C₂⁴×C₃×C₅	D₄	1	4	yes	complemented
33	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
34	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
35	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
36	C₂×C₃×C₅×D₄	—	2	64	no	—
37	C₂×C₃×C₅×D₄	—	2	8	no	—
38	C₂×C₃×C₅×D₄	—	2	8	no	—
39	C₂×C₃×C₅×D₄	—	2	8	no	—
40	C₂×C₃×C₅×D₄	—	2	8	no	—
41	C₂×C₃×C₅×D₄	—	2	16	no	—
42	C₂×C₃×C₅×D₄	—	2	8	no	—
43	C₂×C₃×C₅×D₄	—	4	4	no	—
44	C₂×C₃×C₅×D₄	D₄	1	16	yes	complemented
45	C₂²×C₃×C₄×C₅	—	2	4	no	—
46	C₂²×C₃×C₄×C₅	—	2	8	no	—
47	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
49	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
50	C₃×C₅×C₂²⋊C₄	—	2	16	no	—
51	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
52	C₂³×C₃×D₄	C₂×C₅	1	2	yes	complemented
53	C₂×C₃×#120	C₂×C₅	1	4	yes	complemented
54	C₃×#392	C₂×C₅	1	4	yes	complemented
55	C₃×#386	C₂×C₅	1	4	yes	complemented
56	C₃×#379	C₂×C₅	1	1	yes	characteristic, complemented
57	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
58	C₂⁵×C₅	C₂²×C₃	1	2	yes	complemented
59	C₂²×C₅×D₄	—	2	8	no	—
60	C₂²×C₅×D₄	—	2	16	no	—
61	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	—
62	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	complemented
63	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	complemented
64	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	complemented
65	C₅×#120	—	2	16	no	—
66	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
67	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
68	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
69	C₅×#95	C₂²×C₃	1	4	yes	complemented
70	#2403	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
71	C₂³×C₃×C₅	—	2	4	no	—
72	C₂³×C₃×C₅	—	2	4	no	—
73	C₂³×C₃×C₅	—	2	16	no	—
74	C₂³×C₃×C₅	—	2	16	no	—
75	C₂³×C₃×C₅	—	2	8	no	—
76	C₂³×C₃×C₅	—	2	4	no	—
77	C₂³×C₃×C₅	—	2	4	no	—
78	C₂³×C₃×C₅	—	2	4	no	—
79	C₂³×C₃×C₅	—	2	2	no	—
80	C₂³×C₃×C₅	—	2	8	no	—
81	C₂³×C₃×C₅	—	4	4	no	—
82	C₂³×C₃×C₅	—	4	16	no	—
83	C₂³×C₃×C₅	—	4	32	no	—
84	C₂³×C₃×C₅	—	4	8	no	—
85	C₂³×C₃×C₅	—	4	8	no	—
86	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
87	C₂³×C₃×C₅	C₂×D₄	1	8	yes	—
88	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
89	C₂³×C₃×C₅	C₂×D₄	1	8	yes	complemented
90	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
91	C₃×C₅×D₄	—	2	32	no	—
92	C₃×C₅×D₄	—	2	32	no	—
93	C₃×C₅×D₄	—	4	16	no	—
94	C₂×C₃×C₄×C₅	—	2	16	no	—
95	C₂×C₃×C₄×C₅	—	2	4	no	—
96	C₂×C₃×C₄×C₅	—	2	4	no	—
97	C₂×C₃×C₄×C₅	—	2	8	no	—
98	C₂×C₃×C₄×C₅	—	2	4	no	—
99	C₂×C₃×C₄×C₅	C₂×D₄	1	8	yes	complemented
100	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
101	C₂⁵×C₃	C₂²×C₅	1	2	yes	complemented
102	C₂²×C₃×D₄	—	2	8	no	—
103	C₂²×C₃×D₄	—	2	16	no	—
104	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	—
105	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	complemented
106	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	complemented
107	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	complemented
108	C₃×#120	—	2	16	no	—
109	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
110	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
111	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
112	C₃×#95	C₂²×C₅	1	4	yes	complemented
113	C₂⁴×C₅	—	2	8	no	—
114	C₂⁴×C₅	—	2	4	no	—
115	C₂⁴×C₅	—	2	8	no	—
116	C₂⁴×C₅	—	2	8	no	—
117	C₂⁴×C₅	—	4	2	no	—
118	C₂⁴×C₅	—	4	4	no	—
119	C₂⁴×C₅	C₃×D₄	1	4	yes	complemented
120	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
121	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
122	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
123	C₂×C₅×D₄	—	2	64	no	—
124	C₂×C₅×D₄	—	2	8	no	—
125	C₂×C₅×D₄	—	2	8	no	—
126	C₂×C₅×D₄	—	2	8	no	—
127	C₂×C₅×D₄	—	2	8	no	—
128	C₂×C₅×D₄	—	2	16	no	—
129	C₂×C₅×D₄	—	2	8	no	—
130	C₂×C₅×D₄	—	4	4	no	—
131	C₂×C₅×D₄	C₃×D₄	1	16	yes	complemented
132	C₂²×C₄×C₅	—	2	4	no	—
133	C₂²×C₄×C₅	—	2	8	no	—
134	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
135	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
136	C₅×C₂²⋊C₄	—	2	8	no	—
137	C₅×C₂²⋊C₄	—	2	16	no	—
138	C₅×C₂²⋊C₄	—	4	2	no	—
139	C₂³×D₄	C₂×C₃×C₅	1	2	yes	complemented
140	C₂×#120	C₂×C₃×C₅	1	4	yes	complemented
141	#392	C₂×C₃×C₅	1	4	yes	complemented
142	#386	C₂×C₃×C₅	1	4	yes	complemented
143	#379	C₂×C₃×C₅	1	1	yes	characteristic, complemented
144	C₂²×C₃×C₅	—	2	4	no	—
145	C₂²×C₃×C₅	—	2	4	no	—
146	C₂²×C₃×C₅	—	2	16	no	—
147	C₂²×C₃×C₅	—	2	4	no	—
148	C₂²×C₃×C₅	—	2	8	no	—
149	C₂²×C₃×C₅	—	2	2	no	—
150	C₂²×C₃×C₅	—	2	16	no	—
151	C₂²×C₃×C₅	—	4	16	no	—
152	C₂²×C₃×C₅	—	4	32	no	—
153	C₂²×C₃×C₅	—	4	4	no	—
154	C₂²×C₃×C₅	—	4	4	no	—
155	C₂²×C₃×C₅	—	4	8	no	—
156	C₂²×C₃×C₅	—	4	4	no	—
157	C₂²×C₃×C₅	#120	1	8	yes	complemented
158	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
159	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
160	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
161	C₃×C₄×C₅	—	2	8	no	—
162	C₃×C₄×C₅	—	4	4	no	—
163	C₂⁴×C₃	—	2	8	no	—
164	C₂⁴×C₃	—	2	4	no	—
165	C₂⁴×C₃	—	2	8	no	—
166	C₂⁴×C₃	—	2	8	no	—
167	C₂⁴×C₃	—	4	2	no	—
168	C₂⁴×C₃	—	4	4	no	—
169	C₂⁴×C₃	C₅×D₄	1	4	yes	complemented
170	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
171	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
172	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
173	C₂×C₃×D₄	—	2	64	no	—
174	C₂×C₃×D₄	—	2	8	no	—
175	C₂×C₃×D₄	—	2	8	no	—
176	C₂×C₃×D₄	—	2	8	no	—
177	C₂×C₃×D₄	—	2	8	no	—
178	C₂×C₃×D₄	—	2	16	no	—
179	C₂×C₃×D₄	—	2	8	no	—
180	C₂×C₃×D₄	—	4	4	no	—
181	C₂×C₃×D₄	C₅×D₄	1	16	yes	complemented
182	C₂²×C₃×C₄	—	2	4	no	—
183	C₂²×C₃×C₄	—	2	8	no	—
184	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
185	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
186	C₃×C₂²⋊C₄	—	2	8	no	—
187	C₃×C₂²⋊C₄	—	2	16	no	—
188	C₃×C₂²⋊C₄	—	4	2	no	—
189	C₂³×C₅	—	2	4	no	—
190	C₂³×C₅	—	2	4	no	—
191	C₂³×C₅	—	2	16	no	—
192	C₂³×C₅	—	2	16	no	—
193	C₂³×C₅	—	2	8	no	—
194	C₂³×C₅	—	2	4	no	—
195	C₂³×C₅	—	2	4	no	—
196	C₂³×C₅	—	2	4	no	—
197	C₂³×C₅	—	2	2	no	—
198	C₂³×C₅	—	2	8	no	—
199	C₂³×C₅	—	4	4	no	—
200	C₂³×C₅	—	4	16	no	—
201	C₂³×C₅	—	4	32	no	—
202	C₂³×C₅	—	4	8	no	—
203	C₂³×C₅	—	4	8	no	—
204	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
205	C₂³×C₅	C₂×C₃×D₄	1	8	yes	—
206	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
207	C₂³×C₅	C₂×C₃×D₄	1	8	yes	complemented
208	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
209	C₅×D₄	—	2	32	no	—
210	C₅×D₄	—	2	32	no	—
211	C₅×D₄	—	4	16	no	—
212	C₂×C₄×C₅	—	2	16	no	—
213	C₂×C₄×C₅	—	2	4	no	—
214	C₂×C₄×C₅	—	2	4	no	—
215	C₂×C₄×C₅	—	2	8	no	—
216	C₂×C₄×C₅	—	2	4	no	—
217	C₂×C₄×C₅	C₂×C₃×D₄	1	8	yes	complemented
218	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
219	C₂⁵	C₂²×C₃×C₅	1	2	yes	complemented
220	C₂²×D₄	—	2	8	no	—
221	C₂²×D₄	—	2	16	no	—
222	C₂²×D₄	C₂²×C₃×C₅	1	4	yes	—
223	C₂²×D₄	C₂²×C₃×C₅	1	4	yes	complemented
224	C₂²×D₄	C₂²×C₃×C₅	1	4	yes	complemented
225	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	complemented
226	#120	—	2	16	no	—
227	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
228	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	8	yes	complemented
229	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
230	#95	C₂²×C₃×C₅	1	4	yes	complemented
231	C₂×C₃×C₅	—	2	8	no	—
232	C₂×C₃×C₅	—	4	2	no	—
233	C₂×C₃×C₅	—	4	8	no	—
234	C₂×C₃×C₅	C₂×#120	1	2	yes	—
235	C₂×C₃×C₅	#534	1	1	yes	characteristic
236	C₂×C₃×C₅	D₄²	1	4	yes	—
237	C₂³×C₃	—	2	4	no	—
238	C₂³×C₃	—	2	4	no	—
239	C₂³×C₃	—	2	16	no	—
240	C₂³×C₃	—	2	16	no	—
241	C₂³×C₃	—	2	8	no	—
242	C₂³×C₃	—	2	4	no	—
243	C₂³×C₃	—	2	4	no	—
244	C₂³×C₃	—	2	4	no	—
245	C₂³×C₃	—	2	2	no	—
246	C₂³×C₃	—	2	8	no	—
247	C₂³×C₃	—	4	4	no	—
248	C₂³×C₃	—	4	16	no	—
249	C₂³×C₃	—	4	32	no	—
250	C₂³×C₃	—	4	8	no	—
251	C₂³×C₃	—	4	8	no	—
252	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
253	C₂³×C₃	C₂×C₅×D₄	1	8	yes	—
254	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
255	C₂³×C₃	C₂×C₅×D₄	1	8	yes	complemented
256	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
257	C₃×D₄	—	2	32	no	—
258	C₃×D₄	—	2	32	no	—
259	C₃×D₄	—	4	16	no	—
260	C₂×C₃×C₄	—	2	16	no	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	2	8	no	—
264	C₂×C₃×C₄	—	2	4	no	—
265	C₂×C₃×C₄	C₂×C₅×D₄	1	8	yes	complemented
266	C₂²×C₅	—	2	4	no	—
267	C₂²×C₅	—	2	4	no	—
268	C₂²×C₅	—	2	16	no	—
269	C₂²×C₅	—	2	4	no	—
270	C₂²×C₅	—	2	8	no	—
271	C₂²×C₅	—	2	2	no	—
272	C₂²×C₅	—	2	16	no	—
273	C₂²×C₅	—	4	16	no	—
274	C₂²×C₅	—	4	32	no	—
275	C₂²×C₅	—	4	4	no	—
276	C₂²×C₅	—	4	4	no	—
277	C₂²×C₅	—	4	8	no	—
278	C₂²×C₅	—	4	4	no	—
279	C₂²×C₅	C₃×#120	1	8	yes	complemented
280	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
281	C₂²×C₅	C₂²×C₃×D₄	1	4	yes	—
282	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
283	C₄×C₅	—	2	8	no	—
284	C₄×C₅	—	4	4	no	—
285	C₂⁴	—	2	8	no	—
286	C₂⁴	—	2	4	no	—
287	C₂⁴	—	2	8	no	—
288	C₂⁴	—	2	8	no	—
289	C₂⁴	—	4	2	no	—
290	C₂⁴	—	4	4	no	—
291	C₂⁴	C₃×C₅×D₄	1	4	yes	complemented
292	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
293	C₂⁴	C₂³×C₃×C₅	1	4	yes	—
294	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
295	C₂×D₄	—	2	64	no	—
296	C₂×D₄	—	2	8	no	—
297	C₂×D₄	—	2	8	no	—
298	C₂×D₄	—	2	8	no	—
299	C₂×D₄	—	2	8	no	—
300	C₂×D₄	—	2	16	no	—
301	C₂×D₄	—	2	8	no	—
302	C₂×D₄	—	4	4	no	—
303	C₂×D₄	C₃×C₅×D₄	1	16	yes	complemented
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	8	no	—
306	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
307	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
308	C₂²⋊C₄	—	2	8	no	—
309	C₂²⋊C₄	—	2	16	no	—
310	C₂²⋊C₄	—	4	2	no	—
311	C₃×C₅	#2403	1	1	yes	characteristic, direct product factor, Hall
312	C₂²×C₃	—	2	4	no	—
313	C₂²×C₃	—	2	4	no	—
314	C₂²×C₃	—	2	16	no	—
315	C₂²×C₃	—	2	4	no	—
316	C₂²×C₃	—	2	8	no	—
317	C₂²×C₃	—	2	2	no	—
318	C₂²×C₃	—	2	16	no	—
319	C₂²×C₃	—	4	16	no	—
320	C₂²×C₃	—	4	32	no	—
321	C₂²×C₃	—	4	4	no	—
322	C₂²×C₃	—	4	4	no	—
323	C₂²×C₃	—	4	8	no	—
324	C₂²×C₃	—	4	4	no	—
325	C₂²×C₃	C₅×#120	1	8	yes	complemented
326	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
327	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
328	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
329	C₃×C₄	—	2	8	no	—
330	C₃×C₄	—	4	4	no	—
331	C₂×C₅	—	2	8	no	—
332	C₂×C₅	—	4	2	no	—
333	C₂×C₅	—	4	8	no	—
334	C₂×C₅	C₂×C₃×#120	1	2	yes	—
335	C₂×C₅	C₃×#534	1	1	yes	characteristic
336	C₂×C₅	C₃×D₄²	1	4	yes	—
337	C₂³	—	2	4	no	—
338	C₂³	—	2	4	no	—
339	C₂³	—	2	16	no	—
340	C₂³	—	2	16	no	—
341	C₂³	—	2	8	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	2	4	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	8	no	—
347	C₂³	—	4	4	no	—
348	C₂³	—	4	16	no	—
349	C₂³	—	4	32	no	—
350	C₂³	—	4	8	no	—
351	C₂³	—	4	8	no	—
352	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
353	C₂³	C₂×C₃×C₅×D₄	1	8	yes	—
354	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
355	C₂³	C₂×C₃×C₅×D₄	1	8	yes	complemented
356	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
357	D₄	—	2	32	no	—
358	D₄	—	2	32	no	—
359	D₄	—	4	16	no	—
360	C₂×C₄	—	2	16	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	C₂×C₃×C₅×D₄	1	8	yes	complemented
366	C₂×C₃	—	2	8	no	—
367	C₂×C₃	—	4	2	no	—
368	C₂×C₃	—	4	8	no	—
369	C₂×C₃	C₂×C₅×#120	1	2	yes	—
370	C₂×C₃	C₅×#534	1	1	yes	characteristic
371	C₂×C₃	C₅×D₄²	1	4	yes	—
372	C₅	C₃×#2403	1	1	yes	characteristic, direct product factor, Sylow
373	C₂²	—	2	4	no	—
374	C₂²	—	2	4	no	—
375	C₂²	—	2	16	no	—
376	C₂²	—	2	4	no	—
377	C₂²	—	2	8	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	16	no	—
380	C₂²	—	4	16	no	—
381	C₂²	—	4	32	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	8	no	—
385	C₂²	—	4	4	no	—
386	C₂²	C₃×C₅×#120	1	8	yes	complemented
387	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
388	C₂²	C₂²×C₃×C₅×D₄	1	4	yes	—
389	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
390	C₄	—	2	8	no	—
391	C₄	—	4	4	no	—
392	C₃	C₅×#2403	1	1	yes	characteristic, direct product factor, Sylow
393	C₂	—	2	8	no	—
394	C₂	—	4	2	no	—
395	C₂	—	4	8	no	—
396	C₂	C₂×C₃×C₅×#120	1	2	yes	—
397	C₂	C₃×C₅×#534	1	1	yes	characteristic
398	C₂	C₃×C₅×D₄²	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₅×D₄	C₂	semidirect
2. C₂×C₃×C₅×#120	C₂	semidirect
3. C₃×C₅×#392	C₂	semidirect
4. C₃×C₅×#386	C₂	semidirect
5. C₃×C₅×#379	C₂	semidirect
6. C₅×#2403	C₃	direct (N × H)
8. C₂⁵×C₃×C₅	C₂²	semidirect
12. C₂²×C₃×C₅×D₄	C₂²	semidirect
13. C₂²×C₃×C₅×D₄	C₂²	semidirect
14. C₂³×C₃×C₄×C₅	C₂²	semidirect
16. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
17. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
18. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
19. C₃×C₅×#95	C₂²	semidirect
20. C₃×#2403	C₅	direct (N × H)
21. C₂³×C₅×D₄	C₂×C₃	semidirect
22. C₂×C₅×#120	C₂×C₃	semidirect
23. C₅×#392	C₂×C₃	semidirect
24. C₅×#386	C₂×C₃	semidirect
25. C₅×#379	C₂×C₃	semidirect
32. C₂⁴×C₃×C₅	D₄	semidirect
44. C₂×C₃×C₅×D₄	D₄	semidirect
52. C₂³×C₃×D₄	C₂×C₅	semidirect
53. C₂×C₃×#120	C₂×C₅	semidirect
54. C₃×#392	C₂×C₅	semidirect
55. C₃×#386	C₂×C₅	semidirect
56. C₃×#379	C₂×C₅	semidirect
58. C₂⁵×C₅	C₂²×C₃	semidirect
62. C₂²×C₅×D₄	C₂²×C₃	semidirect
63. C₂²×C₅×D₄	C₂²×C₃	semidirect
64. C₂³×C₄×C₅	C₂²×C₃	semidirect
66. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
67. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
68. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
69. C₅×#95	C₂²×C₃	semidirect
70. #2403	C₃×C₅	direct (N × H)
89. C₂³×C₃×C₅	C₂×D₄	semidirect
99. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
101. C₂⁵×C₃	C₂²×C₅	semidirect
105. C₂²×C₃×D₄	C₂²×C₅	semidirect
106. C₂²×C₃×D₄	C₂²×C₅	semidirect
107. C₂³×C₃×C₄	C₂²×C₅	semidirect
109. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
110. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
111. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
112. C₃×#95	C₂²×C₅	semidirect
119. C₂⁴×C₅	C₃×D₄	semidirect
131. C₂×C₅×D₄	C₃×D₄	semidirect
139. C₂³×D₄	C₂×C₃×C₅	semidirect
140. C₂×#120	C₂×C₃×C₅	semidirect
141. #392	C₂×C₃×C₅	semidirect
142. #386	C₂×C₃×C₅	semidirect
143. #379	C₂×C₃×C₅	semidirect
157. C₂²×C₃×C₅	#120	semidirect
169. C₂⁴×C₃	C₅×D₄	semidirect
181. C₂×C₃×D₄	C₅×D₄	semidirect
207. C₂³×C₅	C₂×C₃×D₄	semidirect
217. C₂×C₄×C₅	C₂×C₃×D₄	semidirect
219. C₂⁵	C₂²×C₃×C₅	semidirect
223. C₂²×D₄	C₂²×C₃×C₅	semidirect
224. C₂²×D₄	C₂²×C₃×C₅	semidirect
225. C₂³×C₄	C₂²×C₃×C₅	semidirect
227. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
228. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
229. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
230. #95	C₂²×C₃×C₅	semidirect
255. C₂³×C₃	C₂×C₅×D₄	semidirect
265. C₂×C₃×C₄	C₂×C₅×D₄	semidirect
279. C₂²×C₅	C₃×#120	semidirect
291. C₂⁴	C₃×C₅×D₄	semidirect
303. C₂×D₄	C₃×C₅×D₄	semidirect
311. C₃×C₅	#2403	direct (N × H)
325. C₂²×C₃	C₅×#120	semidirect
355. C₂³	C₂×C₃×C₅×D₄	semidirect
365. C₂×C₄	C₂×C₃×C₅×D₄	semidirect
372. C₅	C₃×#2403	direct (N × H)
386. C₂²	C₃×C₅×#120	semidirect
392. C₃	C₅×#2403	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₅×D₄	2
C₂×C₃×C₅×#120	2
C₃×C₅×#392	2
C₃×C₅×#386	2
C₃×C₅×#379	2
C₅×#2403	3
C₃×#2403	5

Subgroups — C3×C5×#2403 #14275437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2403 #14275437