Subgroups — C₃×C₅×#2308 #14275342

Order 1920.

2320 conjugacy classes of subgroups.

The subgroup lattice has 352 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	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#386	C₂	1	8	yes	maximal, complemented
4	C₃×C₅×#381	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#379	C₂	1	2	yes	maximal, complemented
6	C₅×#2308	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	1	yes	characteristic
9	C₂²×C₃×C₅×D₄	—	2	8	no	—
10	C₂²×C₃×C₅×D₄	C₄	1	8	yes	complemented
11	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	—
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂³×C₃×C₄×C₅	C₂²	1	4	yes	complemented
14	C₂×C₃×C₅×C₂²⋊C₄	—	2	8	no	—
15	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
16	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
18	C₃×C₅×#95	C₂²	1	8	yes	complemented
19	C₃×#2308	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂³×C₅×D₄	C₂×C₃	1	1	yes	characteristic
21	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
22	C₅×#386	C₂×C₃	1	8	yes	complemented
23	C₅×#381	C₂×C₃	1	2	yes	complemented
24	C₅×#379	C₂×C₃	1	2	yes	complemented
25	C₂⁴×C₃×C₅	—	2	4	no	—
26	C₂⁴×C₃×C₅	—	4	4	no	—
27	C₂⁴×C₃×C₅	—	4	4	no	—
28	C₂⁴×C₃×C₅	C₂×C₄	1	4	yes	—
29	C₂⁴×C₃×C₅	C₂×C₄	1	4	yes	complemented
30	C₂⁴×C₃×C₅	D₄	1	8	yes	—
31	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
32	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
33	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
34	C₂×C₃×C₅×D₄	—	2	32	no	—
35	C₂×C₃×C₅×D₄	—	2	8	no	—
36	C₂×C₃×C₅×D₄	—	2	8	no	—
37	C₂×C₃×C₅×D₄	C₂×C₄	1	16	yes	complemented
38	C₂²×C₃×C₄×C₅	—	2	4	no	—
39	C₂²×C₃×C₄×C₅	—	2	8	no	—
40	C₂²×C₃×C₄×C₅	—	4	8	no	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	complemented
42	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
44	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
45	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
46	C₃×C₅×C₂²⋊C₄	—	4	8	no	—
47	C₂³×C₃×D₄	C₂×C₅	1	1	yes	characteristic
48	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
49	C₃×#386	C₂×C₅	1	8	yes	complemented
50	C₃×#381	C₂×C₅	1	2	yes	complemented
51	C₃×#379	C₂×C₅	1	2	yes	complemented
52	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
53	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
54	C₂²×C₅×D₄	—	2	8	no	—
55	C₂²×C₅×D₄	C₃×C₄	1	8	yes	complemented
56	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	—
57	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
58	C₂³×C₄×C₅	C₂²×C₃	1	4	yes	complemented
59	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
60	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
61	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
62	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
63	C₅×#95	C₂²×C₃	1	8	yes	complemented
64	#2308	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
65	C₂³×C₃×C₅	—	2	8	no	—
66	C₂³×C₃×C₅	—	2	4	no	—
67	C₂³×C₃×C₅	—	2	8	no	—
68	C₂³×C₃×C₅	—	2	4	no	—
69	C₂³×C₃×C₅	—	2	8	no	—
70	C₂³×C₃×C₅	—	4	8	no	—
71	C₂³×C₃×C₅	—	4	8	no	—
72	C₂³×C₃×C₅	—	4	16	no	—
73	C₂³×C₃×C₅	—	4	16	no	—
74	C₂³×C₃×C₅	C₂²⋊C₄	1	16	yes	complemented
75	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
76	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
77	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
78	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
79	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
80	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
81	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
82	C₃×C₅×D₄	—	2	32	no	—
83	C₂×C₃×C₄×C₅	—	2	8	no	—
84	C₂×C₃×C₄×C₅	—	2	4	no	—
85	C₂×C₃×C₄×C₅	—	2	8	no	—
86	C₂×C₃×C₄×C₅	—	2	16	no	—
87	C₂×C₃×C₄×C₅	—	4	16	no	—
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
89	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
90	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
91	C₂²×C₃×D₄	—	2	8	no	—
92	C₂²×C₃×D₄	C₄×C₅	1	8	yes	complemented
93	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	—
94	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
95	C₂³×C₃×C₄	C₂²×C₅	1	4	yes	complemented
96	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
97	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
98	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
99	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
100	C₃×#95	C₂²×C₅	1	8	yes	complemented
101	C₂⁴×C₅	—	2	4	no	—
102	C₂⁴×C₅	—	4	4	no	—
103	C₂⁴×C₅	—	4	4	no	—
104	C₂⁴×C₅	C₂×C₃×C₄	1	4	yes	—
105	C₂⁴×C₅	C₂×C₃×C₄	1	4	yes	complemented
106	C₂⁴×C₅	C₃×D₄	1	8	yes	—
107	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
108	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
109	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
110	C₂×C₅×D₄	—	2	32	no	—
111	C₂×C₅×D₄	—	2	8	no	—
112	C₂×C₅×D₄	—	2	8	no	—
113	C₂×C₅×D₄	C₂×C₃×C₄	1	16	yes	complemented
114	C₂²×C₄×C₅	—	2	4	no	—
115	C₂²×C₄×C₅	—	2	8	no	—
116	C₂²×C₄×C₅	—	4	8	no	—
117	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	complemented
118	C₂²×C₄×C₅	C₂³×C₃	1	8	yes	—
119	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
120	C₅×C₂²⋊C₄	—	2	8	no	—
121	C₅×C₂²⋊C₄	—	2	8	no	—
122	C₅×C₂²⋊C₄	—	4	8	no	—
123	C₂³×D₄	C₂×C₃×C₅	1	1	yes	characteristic
124	C₂²×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
125	#386	C₂×C₃×C₅	1	8	yes	complemented
126	#381	C₂×C₃×C₅	1	2	yes	complemented
127	#379	C₂×C₃×C₅	1	2	yes	complemented
128	C₂²×C₃×C₅	—	2	4	no	—
129	C₂²×C₃×C₅	—	2	8	no	—
130	C₂²×C₃×C₅	—	2	8	no	—
131	C₂²×C₃×C₅	—	2	8	no	—
132	C₂²×C₃×C₅	—	2	8	no	—
133	C₂²×C₃×C₅	—	2	4	no	—
134	C₂²×C₃×C₅	—	2	8	no	—
135	C₂²×C₃×C₅	—	4	16	no	—
136	C₂²×C₃×C₅	—	4	16	no	—
137	C₂²×C₃×C₅	—	4	8	no	—
138	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
139	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	8	yes	—
140	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
141	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
142	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
143	C₃×C₄×C₅	—	2	4	no	—
144	C₃×C₄×C₅	—	4	8	no	—
145	C₂⁴×C₃	—	2	4	no	—
146	C₂⁴×C₃	—	4	4	no	—
147	C₂⁴×C₃	—	4	4	no	—
148	C₂⁴×C₃	C₂×C₄×C₅	1	4	yes	—
149	C₂⁴×C₃	C₂×C₄×C₅	1	4	yes	complemented
150	C₂⁴×C₃	C₅×D₄	1	8	yes	—
151	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
152	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
153	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
154	C₂×C₃×D₄	—	2	32	no	—
155	C₂×C₃×D₄	—	2	8	no	—
156	C₂×C₃×D₄	—	2	8	no	—
157	C₂×C₃×D₄	C₂×C₄×C₅	1	16	yes	complemented
158	C₂²×C₃×C₄	—	2	4	no	—
159	C₂²×C₃×C₄	—	2	8	no	—
160	C₂²×C₃×C₄	—	4	8	no	—
161	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	complemented
162	C₂²×C₃×C₄	C₂³×C₅	1	8	yes	—
163	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
164	C₃×C₂²⋊C₄	—	2	8	no	—
165	C₃×C₂²⋊C₄	—	2	8	no	—
166	C₃×C₂²⋊C₄	—	4	8	no	—
167	C₂³×C₅	—	2	8	no	—
168	C₂³×C₅	—	2	4	no	—
169	C₂³×C₅	—	2	8	no	—
170	C₂³×C₅	—	2	4	no	—
171	C₂³×C₅	—	2	8	no	—
172	C₂³×C₅	—	4	8	no	—
173	C₂³×C₅	—	4	8	no	—
174	C₂³×C₅	—	4	16	no	—
175	C₂³×C₅	—	4	16	no	—
176	C₂³×C₅	C₃×C₂²⋊C₄	1	16	yes	complemented
177	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
178	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
179	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
180	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
181	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
182	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
183	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
184	C₅×D₄	—	2	32	no	—
185	C₂×C₄×C₅	—	2	8	no	—
186	C₂×C₄×C₅	—	2	4	no	—
187	C₂×C₄×C₅	—	2	8	no	—
188	C₂×C₄×C₅	—	2	16	no	—
189	C₂×C₄×C₅	—	4	16	no	—
190	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
191	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
192	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
193	C₂²×D₄	—	2	8	no	—
194	C₂²×D₄	C₃×C₄×C₅	1	8	yes	complemented
195	C₂²×D₄	C₂²×C₃×C₅	1	4	yes	—
196	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
197	C₂³×C₄	C₂²×C₃×C₅	1	4	yes	complemented
198	C₂×C₂²⋊C₄	—	2	8	no	—
199	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
200	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
201	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	8	yes	complemented
202	#95	C₂²×C₃×C₅	1	8	yes	complemented
203	C₂×C₃×C₅	—	2	4	no	—
204	C₂×C₃×C₅	—	2	8	no	—
205	C₂×C₃×C₅	—	4	4	no	—
206	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
207	C₂×C₃×C₅	#518	1	2	yes	—
208	C₂×C₃×C₅	#534	1	4	yes	—
209	C₂³×C₃	—	2	8	no	—
210	C₂³×C₃	—	2	4	no	—
211	C₂³×C₃	—	2	8	no	—
212	C₂³×C₃	—	2	4	no	—
213	C₂³×C₃	—	2	8	no	—
214	C₂³×C₃	—	4	8	no	—
215	C₂³×C₃	—	4	8	no	—
216	C₂³×C₃	—	4	16	no	—
217	C₂³×C₃	—	4	16	no	—
218	C₂³×C₃	C₅×C₂²⋊C₄	1	16	yes	complemented
219	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
220	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
221	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
222	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
223	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
224	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
225	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
226	C₃×D₄	—	2	32	no	—
227	C₂×C₃×C₄	—	2	8	no	—
228	C₂×C₃×C₄	—	2	4	no	—
229	C₂×C₃×C₄	—	2	8	no	—
230	C₂×C₃×C₄	—	2	16	no	—
231	C₂×C₃×C₄	—	4	16	no	—
232	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
233	C₂²×C₅	—	2	4	no	—
234	C₂²×C₅	—	2	8	no	—
235	C₂²×C₅	—	2	8	no	—
236	C₂²×C₅	—	2	8	no	—
237	C₂²×C₅	—	2	8	no	—
238	C₂²×C₅	—	2	4	no	—
239	C₂²×C₅	—	2	8	no	—
240	C₂²×C₅	—	4	16	no	—
241	C₂²×C₅	—	4	16	no	—
242	C₂²×C₅	—	4	8	no	—
243	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
244	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	8	yes	—
245	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
246	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
247	C₂²×C₅	C₃×H(5,𝔽₂)	1	4	yes	—
248	C₄×C₅	—	2	4	no	—
249	C₄×C₅	—	4	8	no	—
250	C₂⁴	—	2	4	no	—
251	C₂⁴	—	4	4	no	—
252	C₂⁴	—	4	4	no	—
253	C₂⁴	C₂×C₃×C₄×C₅	1	4	yes	—
254	C₂⁴	C₂×C₃×C₄×C₅	1	4	yes	complemented
255	C₂⁴	C₃×C₅×D₄	1	8	yes	—
256	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
257	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
258	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
259	C₂×D₄	—	2	32	no	—
260	C₂×D₄	—	2	8	no	—
261	C₂×D₄	—	2	8	no	—
262	C₂×D₄	C₂×C₃×C₄×C₅	1	16	yes	complemented
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	8	no	—
265	C₂²×C₄	—	4	8	no	—
266	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
267	C₂²×C₄	C₂³×C₃×C₅	1	8	yes	—
268	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
269	C₂²⋊C₄	—	2	8	no	—
270	C₂²⋊C₄	—	2	8	no	—
271	C₂²⋊C₄	—	4	8	no	—
272	C₃×C₅	#2308	1	1	yes	characteristic, direct product factor, Hall
273	C₂²×C₃	—	2	4	no	—
274	C₂²×C₃	—	2	8	no	—
275	C₂²×C₃	—	2	8	no	—
276	C₂²×C₃	—	2	8	no	—
277	C₂²×C₃	—	2	8	no	—
278	C₂²×C₃	—	2	4	no	—
279	C₂²×C₃	—	2	8	no	—
280	C₂²×C₃	—	4	16	no	—
281	C₂²×C₃	—	4	16	no	—
282	C₂²×C₃	—	4	8	no	—
283	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
284	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	8	yes	—
285	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
286	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
287	C₂²×C₃	C₅×H(5,𝔽₂)	1	4	yes	—
288	C₃×C₄	—	2	4	no	—
289	C₃×C₄	—	4	8	no	—
290	C₂×C₅	—	2	4	no	—
291	C₂×C₅	—	2	8	no	—
292	C₂×C₅	—	4	4	no	—
293	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
294	C₂×C₅	C₃×#518	1	2	yes	—
295	C₂×C₅	C₃×#534	1	4	yes	—
296	C₂³	—	2	8	no	—
297	C₂³	—	2	4	no	—
298	C₂³	—	2	8	no	—
299	C₂³	—	2	4	no	—
300	C₂³	—	2	8	no	—
301	C₂³	—	4	8	no	—
302	C₂³	—	4	8	no	—
303	C₂³	—	4	16	no	—
304	C₂³	—	4	16	no	—
305	C₂³	C₃×C₅×C₂²⋊C₄	1	16	yes	complemented
306	C₂³	C₂²×C₃×C₄×C₅	1	4	yes	—
307	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
308	C₂³	C₂²×C₃×C₄×C₅	1	4	yes	—
309	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
310	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
311	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
312	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
313	D₄	—	2	32	no	—
314	C₂×C₄	—	2	8	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	2	16	no	—
318	C₂×C₄	—	4	16	no	—
319	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
320	C₂×C₃	—	2	4	no	—
321	C₂×C₃	—	2	8	no	—
322	C₂×C₃	—	4	4	no	—
323	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
324	C₂×C₃	C₅×#518	1	2	yes	—
325	C₂×C₃	C₅×#534	1	4	yes	—
326	C₅	C₃×#2308	1	1	yes	characteristic, direct product factor, Sylow
327	C₂²	—	2	4	no	—
328	C₂²	—	2	8	no	—
329	C₂²	—	2	8	no	—
330	C₂²	—	2	8	no	—
331	C₂²	—	2	8	no	—
332	C₂²	—	2	4	no	—
333	C₂²	—	2	8	no	—
334	C₂²	—	4	16	no	—
335	C₂²	—	4	16	no	—
336	C₂²	—	4	8	no	—
337	C₂²	C₂×C₃×C₅×C₂²⋊C₄	1	4	yes	—
338	C₂²	C₂×C₃×C₅×C₂²⋊C₄	1	8	yes	—
339	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
340	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
341	C₂²	C₃×C₅×H(5,𝔽₂)	1	4	yes	—
342	C₄	—	2	4	no	—
343	C₄	—	4	8	no	—
344	C₃	C₅×#2308	1	1	yes	characteristic, direct product factor, Sylow
345	C₂	—	2	4	no	—
346	C₂	—	2	8	no	—
347	C₂	—	4	4	no	—
348	C₂	C₂²×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
349	C₂	C₃×C₅×#518	1	2	yes	—
350	C₂	C₃×C₅×#534	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂³×C₃×C₅×D₄	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₅×C₂²⋊C₄	C₂	semidirect
3. C₃×C₅×#386	C₂	semidirect
4. C₃×C₅×#381	C₂	semidirect
5. C₃×C₅×#379	C₂	semidirect
6. C₅×#2308	C₃	direct (N × H)
10. C₂²×C₃×C₅×D₄	C₄	semidirect
13. C₂³×C₃×C₄×C₅	C₂²	semidirect
16. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
17. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
18. C₃×C₅×#95	C₂²	semidirect
19. C₃×#2308	C₅	direct (N × H)
21. C₂²×C₅×C₂²⋊C₄	C₂×C₃	semidirect
22. C₅×#386	C₂×C₃	semidirect
23. C₅×#381	C₂×C₃	semidirect
24. C₅×#379	C₂×C₃	semidirect
29. C₂⁴×C₃×C₅	C₂×C₄	semidirect
37. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
41. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
48. C₂²×C₃×C₂²⋊C₄	C₂×C₅	semidirect
49. C₃×#386	C₂×C₅	semidirect
50. C₃×#381	C₂×C₅	semidirect
51. C₃×#379	C₂×C₅	semidirect
55. C₂²×C₅×D₄	C₃×C₄	semidirect
58. C₂³×C₄×C₅	C₂²×C₃	semidirect
61. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
62. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
63. C₅×#95	C₂²×C₃	semidirect
64. #2308	C₃×C₅	direct (N × H)
74. C₂³×C₃×C₅	C₂²⋊C₄	semidirect
92. C₂²×C₃×D₄	C₄×C₅	semidirect
95. C₂³×C₃×C₄	C₂²×C₅	semidirect
98. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
99. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
100. C₃×#95	C₂²×C₅	semidirect
105. C₂⁴×C₅	C₂×C₃×C₄	semidirect
113. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
117. C₂²×C₄×C₅	C₂×C₃×C₄	semidirect
124. C₂²×C₂²⋊C₄	C₂×C₃×C₅	semidirect
125. #386	C₂×C₃×C₅	semidirect
126. #381	C₂×C₃×C₅	semidirect
127. #379	C₂×C₃×C₅	semidirect
149. C₂⁴×C₃	C₂×C₄×C₅	semidirect
157. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
161. C₂²×C₃×C₄	C₂×C₄×C₅	semidirect
176. C₂³×C₅	C₃×C₂²⋊C₄	semidirect
194. C₂²×D₄	C₃×C₄×C₅	semidirect
197. C₂³×C₄	C₂²×C₃×C₅	semidirect
200. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
201. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
202. #95	C₂²×C₃×C₅	semidirect
218. C₂³×C₃	C₅×C₂²⋊C₄	semidirect
254. C₂⁴	C₂×C₃×C₄×C₅	semidirect
262. C₂×D₄	C₂×C₃×C₄×C₅	semidirect
266. C₂²×C₄	C₂×C₃×C₄×C₅	semidirect
272. C₃×C₅	#2308	direct (N × H)
305. C₂³	C₃×C₅×C₂²⋊C₄	semidirect
326. C₅	C₃×#2308	direct (N × H)
344. C₃	C₅×#2308	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
C₂²×C₃×C₅×C₂²⋊C₄	2
C₃×C₅×#386	2
C₃×C₅×#381	2
C₃×C₅×#379	2
C₅×#2308	3
C₃×#2308	5

Subgroups — C3×C5×#2308 #14275342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2308 #14275342