Subgroups — C₃×C₅×#2378 #14275412

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#391	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#389	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#388	C₂	1	2	yes	maximal
5	C₃×C₅×#388	C₂	1	2	yes	maximal
6	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#381	C₂	1	1	yes	maximal, characteristic
9	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic
10	C₅×#2378	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₃×C₅×C₂²⋊Q₈	C₄	1	8	yes	complemented
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
24	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
25	C₃×C₅×#95	C₂²	1	2	yes	—
26	C₃×C₅×#95	C₂²	1	1	yes	characteristic
27	C₃×C₅×#95	C₂²	1	2	yes	—
28	C₃×C₅×#95	C₂²	1	1	yes	characteristic
29	C₃×C₅×#95	C₂²	1	2	yes	—
30	C₃×C₅×#95	C₂²	1	2	yes	—
31	C₃×C₅×#95	C₂²	1	2	yes	—
32	C₃×C₅×#95	C₂²	1	2	yes	—
33	C₃×#2378	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
35	C₅×#391	C₂×C₃	1	2	yes	complemented
36	C₅×#389	C₂×C₃	1	2	yes	complemented
37	C₅×#388	C₂×C₃	1	2	yes	—
38	C₅×#388	C₂×C₃	1	2	yes	—
39	C₅×#387	C₂×C₃	1	2	yes	complemented
40	C₅×#387	C₂×C₃	1	2	yes	complemented
41	C₅×#381	C₂×C₃	1	1	yes	characteristic
42	C₅×#380	C₂×C₃	1	1	yes	characteristic
43	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
44	C₂×C₃×C₅×Q₈	—	4	2	no	—
45	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	—
46	C₂²×C₃×C₄×C₅	—	4	2	no	—
47	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₃×C₅×C₄⋊C₄	—	4	2	no	—
57	C₃×C₅×C₄⋊C₄	—	4	2	no	—
58	C₃×C₅×C₄⋊C₄	—	4	2	no	—
59	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
60	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	—
61	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
62	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
63	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
64	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	—
65	C₃×C₄²×C₅	—	4	2	no	—
66	C₃×C₄²×C₅	—	4	2	no	—
67	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
68	C₃×#391	C₂×C₅	1	2	yes	complemented
69	C₃×#389	C₂×C₅	1	2	yes	complemented
70	C₃×#388	C₂×C₅	1	2	yes	—
71	C₃×#388	C₂×C₅	1	2	yes	—
72	C₃×#387	C₂×C₅	1	2	yes	complemented
73	C₃×#387	C₂×C₅	1	2	yes	complemented
74	C₃×#381	C₂×C₅	1	1	yes	characteristic
75	C₃×#380	C₂×C₅	1	1	yes	characteristic
76	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
77	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
78	C₅×C₂²⋊Q₈	C₃×C₄	1	8	yes	complemented
79	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
80	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
81	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
82	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
84	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
87	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
88	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
89	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
90	C₅×#95	C₂²×C₃	1	2	yes	—
91	C₅×#95	C₂²×C₃	1	1	yes	characteristic
92	C₅×#95	C₂²×C₃	1	2	yes	—
93	C₅×#95	C₂²×C₃	1	1	yes	characteristic
94	C₅×#95	C₂²×C₃	1	2	yes	—
95	C₅×#95	C₂²×C₃	1	2	yes	—
96	C₅×#95	C₂²×C₃	1	2	yes	—
97	C₅×#95	C₂²×C₃	1	2	yes	—
98	#2378	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
99	C₂³×C₃×C₅	—	2	1	no	—
100	C₂³×C₃×C₅	—	2	2	no	—
101	C₂³×C₃×C₅	—	2	2	no	—
102	C₂³×C₃×C₅	—	2	1	no	—
103	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
104	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
105	C₃×C₅×Q₈	—	4	4	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	4	4	no	—
125	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
126	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
129	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
130	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
131	C₃×C₂²⋊Q₈	C₄×C₅	1	8	yes	complemented
132	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
133	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
134	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
135	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
136	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
137	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
138	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
139	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
140	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
141	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
142	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
143	C₃×#95	C₂²×C₅	1	2	yes	—
144	C₃×#95	C₂²×C₅	1	1	yes	characteristic
145	C₃×#95	C₂²×C₅	1	2	yes	—
146	C₃×#95	C₂²×C₅	1	1	yes	characteristic
147	C₃×#95	C₂²×C₅	1	2	yes	—
148	C₃×#95	C₂²×C₅	1	2	yes	—
149	C₃×#95	C₂²×C₅	1	2	yes	—
150	C₃×#95	C₂²×C₅	1	2	yes	—
151	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
152	C₂×C₅×Q₈	—	4	2	no	—
153	C₂×C₅×Q₈	C₂×C₃×C₄	1	4	yes	—
154	C₂²×C₄×C₅	—	4	2	no	—
155	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
156	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
157	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
158	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
159	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
160	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
161	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
162	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
164	C₅×C₄⋊C₄	—	4	2	no	—
165	C₅×C₄⋊C₄	—	4	2	no	—
166	C₅×C₄⋊C₄	—	4	2	no	—
167	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
168	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
169	C₅×C₂²⋊C₄	—	4	1	no	—
170	C₅×C₂²⋊C₄	—	4	2	no	—
171	C₅×C₂²⋊C₄	—	4	1	no	—
172	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
173	C₄²×C₅	—	4	2	no	—
174	C₄²×C₅	—	4	2	no	—
175	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
176	#391	C₂×C₃×C₅	1	2	yes	complemented
177	#389	C₂×C₃×C₅	1	2	yes	complemented
178	#388	C₂×C₃×C₅	1	2	yes	—
179	#388	C₂×C₃×C₅	1	2	yes	—
180	#387	C₂×C₃×C₅	1	2	yes	complemented
181	#387	C₂×C₃×C₅	1	2	yes	complemented
182	#381	C₂×C₃×C₅	1	1	yes	characteristic
183	#380	C₂×C₃×C₅	1	1	yes	characteristic
184	C₂²×C₃×C₅	—	2	2	no	—
185	C₂²×C₃×C₅	—	2	2	no	—
186	C₂²×C₃×C₅	—	2	2	no	—
187	C₂²×C₃×C₅	—	4	2	no	—
188	C₂²×C₃×C₅	—	4	2	no	—
189	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
190	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
191	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
193	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
194	C₃×C₄×C₅	—	2	2	no	—
195	C₃×C₄×C₅	—	2	2	no	—
196	C₃×C₄×C₅	—	2	4	no	—
197	C₃×C₄×C₅	—	2	4	no	—
198	C₃×C₄×C₅	—	4	2	no	—
199	C₃×C₄×C₅	—	4	2	no	—
200	C₃×C₄×C₅	—	4	2	no	—
201	C₃×C₄×C₅	—	4	2	no	—
202	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
203	C₂×C₃×Q₈	—	4	2	no	—
204	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	—
205	C₂²×C₃×C₄	—	4	2	no	—
206	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
207	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
208	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
209	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
210	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
211	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
212	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
213	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
214	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
215	C₃×C₄⋊C₄	—	4	2	no	—
216	C₃×C₄⋊C₄	—	4	2	no	—
217	C₃×C₄⋊C₄	—	4	2	no	—
218	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
219	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	—
220	C₃×C₂²⋊C₄	—	4	1	no	—
221	C₃×C₂²⋊C₄	—	4	2	no	—
222	C₃×C₂²⋊C₄	—	4	1	no	—
223	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	—
224	C₃×C₄²	—	4	2	no	—
225	C₃×C₄²	—	4	2	no	—
226	C₂³×C₅	—	2	1	no	—
227	C₂³×C₅	—	2	2	no	—
228	C₂³×C₅	—	2	2	no	—
229	C₂³×C₅	—	2	1	no	—
230	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
231	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
232	C₅×Q₈	—	4	4	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	4	4	no	—
252	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
253	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
254	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
255	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
256	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
257	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
258	C₂²⋊Q₈	C₃×C₄×C₅	1	8	yes	complemented
259	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
260	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
261	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
262	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
264	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
267	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
268	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
269	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
270	#95	C₂²×C₃×C₅	1	2	yes	—
271	#95	C₂²×C₃×C₅	1	1	yes	characteristic
272	#95	C₂²×C₃×C₅	1	2	yes	—
273	#95	C₂²×C₃×C₅	1	1	yes	characteristic
274	#95	C₂²×C₃×C₅	1	2	yes	—
275	#95	C₂²×C₃×C₅	1	2	yes	—
276	#95	C₂²×C₃×C₅	1	2	yes	—
277	#95	C₂²×C₃×C₅	1	2	yes	—
278	C₂×C₃×C₅	—	4	2	no	—
279	C₂×C₃×C₅	#518	1	1	yes	characteristic
280	C₂×C₃×C₅	#519	1	1	yes	characteristic
281	C₂×C₃×C₅	#520	1	1	yes	characteristic
282	C₂×C₃×C₅	#562	1	2	yes	—
283	C₂×C₃×C₅	#563	1	2	yes	—
284	C₂³×C₃	—	2	1	no	—
285	C₂³×C₃	—	2	2	no	—
286	C₂³×C₃	—	2	2	no	—
287	C₂³×C₃	—	2	1	no	—
288	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
289	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
290	C₃×Q₈	—	4	4	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	—	2	2	no	—
305	C₂×C₃×C₄	—	2	2	no	—
306	C₂×C₃×C₄	—	2	2	no	—
307	C₂×C₃×C₄	—	2	2	no	—
308	C₂×C₃×C₄	—	2	2	no	—
309	C₂×C₃×C₄	—	4	4	no	—
310	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
311	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
312	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
313	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
314	C₂²×C₅	—	2	2	no	—
315	C₂²×C₅	—	2	2	no	—
316	C₂²×C₅	—	2	2	no	—
317	C₂²×C₅	—	4	2	no	—
318	C₂²×C₅	—	4	2	no	—
319	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
320	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
321	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
322	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
323	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
324	C₄×C₅	—	2	2	no	—
325	C₄×C₅	—	2	2	no	—
326	C₄×C₅	—	2	4	no	—
327	C₄×C₅	—	2	4	no	—
328	C₄×C₅	—	4	2	no	—
329	C₄×C₅	—	4	2	no	—
330	C₄×C₅	—	4	2	no	—
331	C₄×C₅	—	4	2	no	—
332	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
333	C₂×Q₈	—	4	2	no	—
334	C₂×Q₈	C₂×C₃×C₄×C₅	1	4	yes	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
337	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
338	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
339	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
340	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
341	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
342	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
343	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
344	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
349	C₄⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
350	C₂²⋊C₄	—	4	1	no	—
351	C₂²⋊C₄	—	4	2	no	—
352	C₂²⋊C₄	—	4	1	no	—
353	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
354	C₄²	—	4	2	no	—
355	C₄²	—	4	2	no	—
356	C₃×C₅	#2378	1	1	yes	characteristic, direct product factor, Hall
357	C₂²×C₃	—	2	2	no	—
358	C₂²×C₃	—	2	2	no	—
359	C₂²×C₃	—	2	2	no	—
360	C₂²×C₃	—	4	2	no	—
361	C₂²×C₃	—	4	2	no	—
362	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
363	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
364	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
365	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
366	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
367	C₃×C₄	—	2	2	no	—
368	C₃×C₄	—	2	2	no	—
369	C₃×C₄	—	2	4	no	—
370	C₃×C₄	—	2	4	no	—
371	C₃×C₄	—	4	2	no	—
372	C₃×C₄	—	4	2	no	—
373	C₃×C₄	—	4	2	no	—
374	C₃×C₄	—	4	2	no	—
375	C₂×C₅	—	4	2	no	—
376	C₂×C₅	C₃×#518	1	1	yes	characteristic
377	C₂×C₅	C₃×#519	1	1	yes	characteristic
378	C₂×C₅	C₃×#520	1	1	yes	characteristic
379	C₂×C₅	C₃×#562	1	2	yes	—
380	C₂×C₅	C₃×#563	1	2	yes	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	1	no	—
385	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
386	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
387	Q₈	—	4	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
408	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
409	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
410	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
411	C₂×C₃	—	4	2	no	—
412	C₂×C₃	C₅×#518	1	1	yes	characteristic
413	C₂×C₃	C₅×#519	1	1	yes	characteristic
414	C₂×C₃	C₅×#520	1	1	yes	characteristic
415	C₂×C₃	C₅×#562	1	2	yes	—
416	C₂×C₃	C₅×#563	1	2	yes	—
417	C₅	C₃×#2378	1	1	yes	characteristic, direct product factor, Sylow
418	C₂²	—	2	2	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
424	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
425	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
426	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
427	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	2	4	no	—
431	C₄	—	2	4	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₃	C₅×#2378	1	1	yes	characteristic, direct product factor, Sylow
437	C₂	—	4	2	no	—
438	C₂	C₃×C₅×#518	1	1	yes	characteristic
439	C₂	C₃×C₅×#519	1	1	yes	characteristic
440	C₂	C₃×C₅×#520	1	1	yes	characteristic
441	C₂	C₃×C₅×#562	1	2	yes	—
442	C₂	C₃×C₅×#563	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁴×C₃×C₅	C₂³
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. C₃×C₅×#391	C₂	semidirect
3. C₃×C₅×#389	C₂	semidirect
6. C₃×C₅×#387	C₂	semidirect
7. C₃×C₅×#387	C₂	semidirect
10. C₅×#2378	C₃	direct (N × H)
13. C₃×C₅×C₂²⋊Q₈	C₄	semidirect
33. C₃×#2378	C₅	direct (N × H)
35. C₅×#391	C₂×C₃	semidirect
36. C₅×#389	C₂×C₃	semidirect
39. C₅×#387	C₂×C₃	semidirect
40. C₅×#387	C₂×C₃	semidirect
68. C₃×#391	C₂×C₅	semidirect
69. C₃×#389	C₂×C₅	semidirect
72. C₃×#387	C₂×C₅	semidirect
73. C₃×#387	C₂×C₅	semidirect
78. C₅×C₂²⋊Q₈	C₃×C₄	semidirect
98. #2378	C₃×C₅	direct (N × H)
131. C₃×C₂²⋊Q₈	C₄×C₅	semidirect
176. #391	C₂×C₃×C₅	semidirect
177. #389	C₂×C₃×C₅	semidirect
180. #387	C₂×C₃×C₅	semidirect
181. #387	C₂×C₃×C₅	semidirect
258. C₂²⋊Q₈	C₃×C₄×C₅	semidirect
356. C₃×C₅	#2378	direct (N × H)
417. C₅	C₃×#2378	direct (N × H)
436. C₃	C₅×#2378	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×C₃×C₅×C₂²⋊Q₈	2
C₃×C₅×#391	2
C₃×C₅×#389	2
C₃×C₅×#388	2
C₃×C₅×#387	2
C₃×C₅×#381	2
C₃×C₅×#380	2
C₅×#2378	3
C₃×#2378	5

Subgroups — C3×C5×#2378 #14275412

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2378 #14275412