Subgroups — C₃×C₅×#2368 #14275402

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 456 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×#387	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#385	C₂	1	2	yes	maximal
6	C₃×C₄×C₅×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal
8	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
9	C₂×C₃×C₅×#95	C₂	1	1	yes	maximal, characteristic
10	C₅×#2368	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	2	yes	—
13	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₃×C₅×C₂²⋊Q₈	C₄	1	8	yes	complemented
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	2	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄²×C₅	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	1	yes	characteristic
26	C₃×C₅×#95	C₂²	1	1	yes	characteristic
27	C₃×C₅×#95	C₂²	1	2	yes	—
28	C₃×C₅×#95	C₂²	1	2	yes	—
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×#2368	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×#387	C₂×C₃	1	2	yes	complemented
37	C₅×#387	C₂×C₃	1	2	yes	complemented
38	C₅×#385	C₂×C₃	1	2	yes	—
39	C₄×C₅×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
40	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	—
41	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
42	C₂×C₅×#95	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	complemented
46	C₂²×C₃×C₄×C₅	—	2	4	no	—
47	C₂²×C₃×C₄×C₅	—	2	4	no	—
48	C₂²×C₃×C₄×C₅	—	4	2	no	—
49	C₂²×C₃×C₄×C₅	—	4	2	no	—
50	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	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	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
58	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
59	C₃×C₅×C₄⋊C₄	—	2	4	no	—
60	C₃×C₅×C₄⋊C₄	—	4	2	no	—
61	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
62	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
63	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
64	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	—
65	C₃×C₅×C₂²⋊C₄	Q₈	1	4	yes	complemented
66	C₃×C₄²×C₅	—	2	4	no	—
67	C₃×C₄²×C₅	—	4	2	no	—
68	C₃×C₄²×C₅	—	4	2	no	—
69	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
70	C₃×#391	C₂×C₅	1	2	yes	complemented
71	C₃×#387	C₂×C₅	1	2	yes	complemented
72	C₃×#387	C₂×C₅	1	2	yes	complemented
73	C₃×#385	C₂×C₅	1	2	yes	—
74	C₃×C₄×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
75	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	2	yes	—
76	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
77	C₂×C₃×#95	C₂×C₅	1	1	yes	characteristic
78	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
79	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
80	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
81	C₅×C₂²⋊Q₈	C₃×C₄	1	8	yes	complemented
82	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
83	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
84	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
85	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
88	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
90	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
91	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
92	C₅×#95	C₂²×C₃	1	1	yes	characteristic
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	C₅×#95	C₂²×C₃	1	2	yes	—
99	C₅×#95	C₂²×C₃	1	2	yes	—
100	#2368	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
101	C₂³×C₃×C₅	—	2	2	no	—
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
104	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
105	C₂³×C₃×C₅	#41	1	2	yes	—
106	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
107	C₃×C₅×Q₈	—	4	4	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	—	4	8	no	—
126	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
131	C₂×C₃×C₄×C₅	#41	1	4	yes	—
132	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
133	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
134	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
135	C₃×C₂²⋊Q₈	C₄×C₅	1	8	yes	complemented
136	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
137	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
138	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
139	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
140	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
141	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
142	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
143	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
144	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
145	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
146	C₃×#95	C₂²×C₅	1	1	yes	characteristic
147	C₃×#95	C₂²×C₅	1	1	yes	characteristic
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	C₃×#95	C₂²×C₅	1	2	yes	—
152	C₃×#95	C₂²×C₅	1	2	yes	—
153	C₃×#95	C₂²×C₅	1	2	yes	—
154	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
155	C₂×C₅×Q₈	—	4	2	no	—
156	C₂×C₅×Q₈	C₂×C₃×C₄	1	4	yes	complemented
157	C₂²×C₄×C₅	—	2	4	no	—
158	C₂²×C₄×C₅	—	2	4	no	—
159	C₂²×C₄×C₅	—	4	2	no	—
160	C₂²×C₄×C₅	—	4	2	no	—
161	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
162	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
163	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
164	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
166	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
167	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
169	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
170	C₅×C₄⋊C₄	—	2	4	no	—
171	C₅×C₄⋊C₄	—	4	2	no	—
172	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	complemented
173	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	complemented
174	C₅×C₂²⋊C₄	—	2	2	no	—
175	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
176	C₅×C₂²⋊C₄	C₃×Q₈	1	4	yes	complemented
177	C₄²×C₅	—	2	4	no	—
178	C₄²×C₅	—	4	2	no	—
179	C₄²×C₅	—	4	2	no	—
180	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
181	#391	C₂×C₃×C₅	1	2	yes	complemented
182	#387	C₂×C₃×C₅	1	2	yes	complemented
183	#387	C₂×C₃×C₅	1	2	yes	complemented
184	#385	C₂×C₃×C₅	1	2	yes	—
185	C₄×C₄⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
186	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	—
187	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
188	C₂×#95	C₂×C₃×C₅	1	1	yes	characteristic
189	C₂²×C₃×C₅	—	2	2	no	—
190	C₂²×C₃×C₅	—	2	2	no	—
191	C₂²×C₃×C₅	—	2	4	no	—
192	C₂²×C₃×C₅	—	2	4	no	—
193	C₂²×C₃×C₅	C₄×Q₈	1	4	yes	—
194	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
195	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
196	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
197	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
198	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
199	C₃×C₄×C₅	—	2	4	no	—
200	C₃×C₄×C₅	—	2	2	no	—
201	C₃×C₄×C₅	—	2	2	no	—
202	C₃×C₄×C₅	—	2	4	no	—
203	C₃×C₄×C₅	—	2	4	no	—
204	C₃×C₄×C₅	—	2	4	no	—
205	C₃×C₄×C₅	—	4	2	no	—
206	C₃×C₄×C₅	—	4	2	no	—
207	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
208	C₂×C₃×Q₈	—	4	2	no	—
209	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	complemented
210	C₂²×C₃×C₄	—	2	4	no	—
211	C₂²×C₃×C₄	—	2	4	no	—
212	C₂²×C₃×C₄	—	4	2	no	—
213	C₂²×C₃×C₄	—	4	2	no	—
214	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
215	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
216	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
217	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
220	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
221	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
222	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
223	C₃×C₄⋊C₄	—	2	4	no	—
224	C₃×C₄⋊C₄	—	4	2	no	—
225	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
226	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
227	C₃×C₂²⋊C₄	—	2	2	no	—
228	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	—
229	C₃×C₂²⋊C₄	C₅×Q₈	1	4	yes	complemented
230	C₃×C₄²	—	2	4	no	—
231	C₃×C₄²	—	4	2	no	—
232	C₃×C₄²	—	4	2	no	—
233	C₂³×C₅	—	2	2	no	—
234	C₂³×C₅	—	2	2	no	—
235	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
236	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
237	C₂³×C₅	C₃×#41	1	2	yes	—
238	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
239	C₅×Q₈	—	4	4	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	—	2	2	no	—
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	2	2	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	4	4	no	—
257	C₂×C₄×C₅	—	4	8	no	—
258	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
259	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
260	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
261	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
262	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
263	C₂×C₄×C₅	C₃×#41	1	4	yes	—
264	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
265	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
266	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
267	C₂²⋊Q₈	C₃×C₄×C₅	1	8	yes	complemented
268	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
269	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
270	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
271	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
273	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
274	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
275	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
276	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
277	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
278	#95	C₂²×C₃×C₅	1	1	yes	characteristic
279	#95	C₂²×C₃×C₅	1	1	yes	characteristic
280	#95	C₂²×C₃×C₅	1	2	yes	—
281	#95	C₂²×C₃×C₅	1	2	yes	—
282	#95	C₂²×C₃×C₅	1	2	yes	—
283	#95	C₂²×C₃×C₅	1	2	yes	—
284	#95	C₂²×C₃×C₅	1	2	yes	—
285	#95	C₂²×C₃×C₅	1	2	yes	—
286	C₂×C₃×C₅	—	2	4	no	—
287	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
288	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
289	C₂×C₃×C₅	#518	1	1	yes	characteristic
290	C₂×C₃×C₅	#551	1	2	yes	—
291	C₂×C₃×C₅	#554	1	2	yes	—
292	C₂³×C₃	—	2	2	no	—
293	C₂³×C₃	—	2	2	no	—
294	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
295	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
296	C₂³×C₃	C₅×#41	1	2	yes	—
297	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
298	C₃×Q₈	—	4	4	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	—	2	2	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	4	4	no	—
316	C₂×C₃×C₄	—	4	8	no	—
317	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
318	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
319	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
320	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
321	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
322	C₂×C₃×C₄	C₅×#41	1	4	yes	—
323	C₂²×C₅	—	2	2	no	—
324	C₂²×C₅	—	2	2	no	—
325	C₂²×C₅	—	2	4	no	—
326	C₂²×C₅	—	2	4	no	—
327	C₂²×C₅	C₃×C₄×Q₈	1	4	yes	—
328	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
329	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
330	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
331	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
332	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
333	C₄×C₅	—	2	4	no	—
334	C₄×C₅	—	2	2	no	—
335	C₄×C₅	—	2	2	no	—
336	C₄×C₅	—	2	4	no	—
337	C₄×C₅	—	2	4	no	—
338	C₄×C₅	—	2	4	no	—
339	C₄×C₅	—	4	2	no	—
340	C₄×C₅	—	4	2	no	—
341	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
342	C₂×Q₈	—	4	2	no	—
343	C₂×Q₈	C₂×C₃×C₄×C₅	1	4	yes	complemented
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
349	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
350	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
351	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
352	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
353	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
354	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
355	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
356	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
360	C₄⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	complemented
361	C₂²⋊C₄	—	2	2	no	—
362	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
363	C₂²⋊C₄	C₃×C₅×Q₈	1	4	yes	complemented
364	C₄²	—	2	4	no	—
365	C₄²	—	4	2	no	—
366	C₄²	—	4	2	no	—
367	C₃×C₅	#2368	1	1	yes	characteristic, direct product factor, Hall
368	C₂²×C₃	—	2	2	no	—
369	C₂²×C₃	—	2	2	no	—
370	C₂²×C₃	—	2	4	no	—
371	C₂²×C₃	—	2	4	no	—
372	C₂²×C₃	C₄×C₅×Q₈	1	4	yes	—
373	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
374	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
375	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
376	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
377	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
378	C₃×C₄	—	2	4	no	—
379	C₃×C₄	—	2	2	no	—
380	C₃×C₄	—	2	2	no	—
381	C₃×C₄	—	2	4	no	—
382	C₃×C₄	—	2	4	no	—
383	C₃×C₄	—	2	4	no	—
384	C₃×C₄	—	4	2	no	—
385	C₃×C₄	—	4	2	no	—
386	C₂×C₅	—	2	4	no	—
387	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
388	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
389	C₂×C₅	C₃×#518	1	1	yes	characteristic
390	C₂×C₅	C₃×#551	1	2	yes	—
391	C₂×C₅	C₃×#554	1	2	yes	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
395	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
396	C₂³	C₃×C₅×#41	1	2	yes	—
397	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
398	Q₈	—	4	4	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	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	8	no	—
417	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
418	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
419	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
420	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
421	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
422	C₂×C₄	C₃×C₅×#41	1	4	yes	—
423	C₂×C₃	—	2	4	no	—
424	C₂×C₃	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
425	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
426	C₂×C₃	C₅×#518	1	1	yes	characteristic
427	C₂×C₃	C₅×#551	1	2	yes	—
428	C₂×C₃	C₅×#554	1	2	yes	—
429	C₅	C₃×#2368	1	1	yes	characteristic, direct product factor, Sylow
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	2	4	no	—
434	C₂²	C₃×C₄×C₅×Q₈	1	4	yes	—
435	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
436	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
437	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
438	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
439	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
440	C₄	—	2	4	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	4	no	—
444	C₄	—	2	4	no	—
445	C₄	—	2	4	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₃	C₅×#2368	1	1	yes	characteristic, direct product factor, Sylow
449	C₂	—	2	4	no	—
450	C₂	C₂×C₃×C₄×C₅×Q₈	1	1	yes	characteristic
451	C₂	C₃×C₄×C₅×#41	1	1	yes	characteristic
452	C₂	C₃×C₅×#518	1	1	yes	characteristic
453	C₂	C₃×C₅×#551	1	2	yes	—
454	C₂	C₃×C₅×#554	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×#387	C₂	semidirect
4. C₃×C₅×#387	C₂	semidirect
6. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
10. C₅×#2368	C₃	direct (N × H)
14. C₃×C₅×C₂²⋊Q₈	C₄	semidirect
33. C₃×#2368	C₅	direct (N × H)
35. C₅×#391	C₂×C₃	semidirect
36. C₅×#387	C₂×C₃	semidirect
37. C₅×#387	C₂×C₃	semidirect
39. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
45. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
61. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
62. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
65. C₃×C₅×C₂²⋊C₄	Q₈	semidirect
70. C₃×#391	C₂×C₅	semidirect
71. C₃×#387	C₂×C₅	semidirect
72. C₃×#387	C₂×C₅	semidirect
74. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
81. C₅×C₂²⋊Q₈	C₃×C₄	semidirect
100. #2368	C₃×C₅	direct (N × H)
135. C₃×C₂²⋊Q₈	C₄×C₅	semidirect
156. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
172. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
173. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
176. C₅×C₂²⋊C₄	C₃×Q₈	semidirect
181. #391	C₂×C₃×C₅	semidirect
182. #387	C₂×C₃×C₅	semidirect
183. #387	C₂×C₃×C₅	semidirect
185. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
209. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
225. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
226. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
229. C₃×C₂²⋊C₄	C₅×Q₈	semidirect
267. C₂²⋊Q₈	C₃×C₄×C₅	semidirect
343. C₂×Q₈	C₂×C₃×C₄×C₅	semidirect
359. C₄⋊C₄	C₂×C₃×C₄×C₅	semidirect
360. C₄⋊C₄	C₂×C₃×C₄×C₅	semidirect
363. C₂²⋊C₄	C₃×C₅×Q₈	semidirect
367. C₃×C₅	#2368	direct (N × H)
429. C₅	C₃×#2368	direct (N × H)
448. C₃	C₅×#2368	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×#387	2
C₃×C₅×#385	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₂×C₃×C₅×#95	2
C₅×#2368	3
C₃×#2368	5

Subgroups — C3×C5×#2368 #14275402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2368 #14275402