Subgroups — C₃×C₅×#2329 #14275363

Order 1920.

1056 conjugacy classes of subgroups.

The subgroup lattice has 520 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×#387	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#385	C₂	1	2	yes	maximal
7	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic
8	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal
9	C₂×C₃×C₅×#95	C₂	1	1	yes	maximal, characteristic
10	C₅×#2329	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	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₃×C₅×C₂²⋊Q₈	C₄	1	8	yes	complemented
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
25	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
26	C₃×C₅×#95	C₂²	1	2	yes	—
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×#2329	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×#387	C₂×C₃	1	2	yes	complemented
38	C₅×#387	C₂×C₃	1	2	yes	complemented
39	C₅×#385	C₂×C₃	1	2	yes	—
40	C₅×#380	C₂×C₃	1	1	yes	characteristic
41	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	—
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	1	no	—
45	C₂×C₃×C₅×Q₈	—	4	1	no	—
46	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
47	C₂²×C₃×C₄×C₅	—	2	2	no	—
48	C₂²×C₃×C₄×C₅	—	4	1	no	—
49	C₂²×C₃×C₄×C₅	—	4	1	no	—
50	C₂²×C₃×C₄×C₅	—	4	1	no	—
51	C₂²×C₃×C₄×C₅	—	4	1	no	—
52	C₂²×C₃×C₄×C₅	—	4	1	no	—
53	C₂²×C₃×C₄×C₅	—	4	1	no	—
54	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
55	C₂²×C₃×C₄×C₅	Q₈	1	4	yes	complemented
56	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
57	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
58	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
59	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
60	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
61	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
64	C₃×C₅×C₄⋊C₄	—	4	2	no	—
65	C₃×C₅×C₄⋊C₄	—	4	1	no	—
66	C₃×C₅×C₄⋊C₄	—	4	1	no	—
67	C₃×C₅×C₄⋊C₄	—	4	2	no	—
68	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
69	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
70	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
71	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	—
72	C₃×C₄²×C₅	—	4	2	no	—
73	C₃×C₄²×C₅	—	4	2	no	—
74	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
75	C₃×#391	C₂×C₅	1	2	yes	complemented
76	C₃×#389	C₂×C₅	1	2	yes	complemented
77	C₃×#387	C₂×C₅	1	2	yes	complemented
78	C₃×#387	C₂×C₅	1	2	yes	complemented
79	C₃×#385	C₂×C₅	1	2	yes	—
80	C₃×#380	C₂×C₅	1	1	yes	characteristic
81	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	2	yes	—
82	C₂×C₃×#95	C₂×C₅	1	1	yes	characteristic
83	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
84	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
85	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
86	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
87	C₅×C₂²⋊Q₈	C₃×C₄	1	8	yes	complemented
88	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
91	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
92	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
94	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
95	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
96	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
97	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
98	C₅×#95	C₂²×C₃	1	2	yes	—
99	C₅×#95	C₂²×C₃	1	2	yes	—
100	C₅×#95	C₂²×C₃	1	2	yes	—
101	C₅×#95	C₂²×C₃	1	2	yes	—
102	C₅×#95	C₂²×C₃	1	2	yes	—
103	C₅×#95	C₂²×C₃	1	2	yes	—
104	C₅×#95	C₂²×C₃	1	2	yes	—
105	#2329	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
106	C₂³×C₃×C₅	—	2	1	no	—
107	C₂³×C₃×C₅	—	2	1	no	—
108	C₂³×C₃×C₅	—	2	1	no	—
109	C₂³×C₃×C₅	—	2	1	no	—
110	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
111	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
112	C₂³×C₃×C₅	#41	1	2	yes	—
113	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
114	C₃×C₅×Q₈	—	4	4	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	1	no	—
120	C₂×C₃×C₄×C₅	—	2	1	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	1	no	—
123	C₂×C₃×C₄×C₅	—	2	1	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	4	4	no	—
135	C₂×C₃×C₄×C₅	—	4	4	no	—
136	C₂×C₃×C₄×C₅	—	4	4	no	—
137	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
138	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
139	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
140	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
141	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
142	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
143	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
144	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
145	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
146	C₃×C₂²⋊Q₈	C₄×C₅	1	8	yes	complemented
147	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
148	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
149	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
150	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
151	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
152	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
153	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
154	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
155	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
156	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
157	C₃×#95	C₂²×C₅	1	2	yes	—
158	C₃×#95	C₂²×C₅	1	2	yes	—
159	C₃×#95	C₂²×C₅	1	2	yes	—
160	C₃×#95	C₂²×C₅	1	2	yes	—
161	C₃×#95	C₂²×C₅	1	2	yes	—
162	C₃×#95	C₂²×C₅	1	2	yes	—
163	C₃×#95	C₂²×C₅	1	2	yes	—
164	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
165	C₂×C₅×Q₈	—	4	1	no	—
166	C₂×C₅×Q₈	—	4	1	no	—
167	C₂×C₅×Q₈	C₂×C₃×C₄	1	4	yes	complemented
168	C₂²×C₄×C₅	—	2	2	no	—
169	C₂²×C₄×C₅	—	4	1	no	—
170	C₂²×C₄×C₅	—	4	1	no	—
171	C₂²×C₄×C₅	—	4	1	no	—
172	C₂²×C₄×C₅	—	4	1	no	—
173	C₂²×C₄×C₅	—	4	1	no	—
174	C₂²×C₄×C₅	—	4	1	no	—
175	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
176	C₂²×C₄×C₅	C₃×Q₈	1	4	yes	complemented
177	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
178	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
179	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
180	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
181	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
182	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
183	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
185	C₅×C₄⋊C₄	—	4	2	no	—
186	C₅×C₄⋊C₄	—	4	1	no	—
187	C₅×C₄⋊C₄	—	4	1	no	—
188	C₅×C₄⋊C₄	—	4	2	no	—
189	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	complemented
190	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	complemented
191	C₅×C₂²⋊C₄	—	2	4	no	—
192	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
193	C₄²×C₅	—	4	2	no	—
194	C₄²×C₅	—	4	2	no	—
195	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
196	#391	C₂×C₃×C₅	1	2	yes	complemented
197	#389	C₂×C₃×C₅	1	2	yes	complemented
198	#387	C₂×C₃×C₅	1	2	yes	complemented
199	#387	C₂×C₃×C₅	1	2	yes	complemented
200	#385	C₂×C₃×C₅	1	2	yes	—
201	#380	C₂×C₃×C₅	1	1	yes	characteristic
202	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	—
203	C₂×#95	C₂×C₃×C₅	1	1	yes	characteristic
204	C₂²×C₃×C₅	—	2	2	no	—
205	C₂²×C₃×C₅	—	2	2	no	—
206	C₂²×C₃×C₅	—	2	2	no	—
207	C₂²×C₃×C₅	—	2	2	no	—
208	C₂²×C₃×C₅	—	2	2	no	—
209	C₂²×C₃×C₅	—	2	2	no	—
210	C₂²×C₃×C₅	C₄×Q₈	1	4	yes	—
211	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
212	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
213	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
214	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
215	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
217	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
218	C₃×C₄×C₅	—	2	2	no	—
219	C₃×C₄×C₅	—	2	2	no	—
220	C₃×C₄×C₅	—	2	4	no	—
221	C₃×C₄×C₅	—	2	4	no	—
222	C₃×C₄×C₅	—	2	4	no	—
223	C₃×C₄×C₅	—	4	2	no	—
224	C₃×C₄×C₅	—	4	2	no	—
225	C₃×C₄×C₅	—	4	2	no	—
226	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
227	C₂×C₃×Q₈	—	4	1	no	—
228	C₂×C₃×Q₈	—	4	1	no	—
229	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	complemented
230	C₂²×C₃×C₄	—	2	2	no	—
231	C₂²×C₃×C₄	—	4	1	no	—
232	C₂²×C₃×C₄	—	4	1	no	—
233	C₂²×C₃×C₄	—	4	1	no	—
234	C₂²×C₃×C₄	—	4	1	no	—
235	C₂²×C₃×C₄	—	4	1	no	—
236	C₂²×C₃×C₄	—	4	1	no	—
237	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
238	C₂²×C₃×C₄	C₅×Q₈	1	4	yes	complemented
239	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
240	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
241	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
242	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
243	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
244	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
245	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
246	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
247	C₃×C₄⋊C₄	—	4	2	no	—
248	C₃×C₄⋊C₄	—	4	1	no	—
249	C₃×C₄⋊C₄	—	4	1	no	—
250	C₃×C₄⋊C₄	—	4	2	no	—
251	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
252	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
253	C₃×C₂²⋊C₄	—	2	4	no	—
254	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	—
255	C₃×C₄²	—	4	2	no	—
256	C₃×C₄²	—	4	2	no	—
257	C₂³×C₅	—	2	1	no	—
258	C₂³×C₅	—	2	1	no	—
259	C₂³×C₅	—	2	1	no	—
260	C₂³×C₅	—	2	1	no	—
261	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
262	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
263	C₂³×C₅	C₃×#41	1	2	yes	—
264	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
265	C₅×Q₈	—	4	4	no	—
266	C₂×C₄×C₅	—	2	2	no	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	2	2	no	—
270	C₂×C₄×C₅	—	2	1	no	—
271	C₂×C₄×C₅	—	2	1	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	—	2	1	no	—
274	C₂×C₄×C₅	—	2	1	no	—
275	C₂×C₄×C₅	—	2	2	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	4	4	no	—
286	C₂×C₄×C₅	—	4	4	no	—
287	C₂×C₄×C₅	—	4	4	no	—
288	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
289	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
290	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
291	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
292	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
293	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
294	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
295	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
296	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
297	C₂²⋊Q₈	C₃×C₄×C₅	1	8	yes	complemented
298	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
301	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
302	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
304	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
305	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
306	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
307	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
308	#95	C₂²×C₃×C₅	1	2	yes	—
309	#95	C₂²×C₃×C₅	1	2	yes	—
310	#95	C₂²×C₃×C₅	1	2	yes	—
311	#95	C₂²×C₃×C₅	1	2	yes	—
312	#95	C₂²×C₃×C₅	1	2	yes	—
313	#95	C₂²×C₃×C₅	1	2	yes	—
314	#95	C₂²×C₃×C₅	1	2	yes	—
315	C₂×C₃×C₅	—	2	4	no	—
316	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
317	C₂×C₃×C₅	#518	1	1	yes	characteristic
318	C₂×C₃×C₅	#520	1	1	yes	characteristic
319	C₂×C₃×C₅	#538	1	1	yes	characteristic
320	C₂×C₃×C₅	#539	1	1	yes	characteristic
321	C₂×C₃×C₅	#543	1	1	yes	characteristic
322	C₂×C₃×C₅	#544	1	1	yes	characteristic
323	C₂³×C₃	—	2	1	no	—
324	C₂³×C₃	—	2	1	no	—
325	C₂³×C₃	—	2	1	no	—
326	C₂³×C₃	—	2	1	no	—
327	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
328	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
329	C₂³×C₃	C₅×#41	1	2	yes	—
330	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
331	C₃×Q₈	—	4	4	no	—
332	C₂×C₃×C₄	—	2	2	no	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	2	2	no	—
336	C₂×C₃×C₄	—	2	1	no	—
337	C₂×C₃×C₄	—	2	1	no	—
338	C₂×C₃×C₄	—	2	2	no	—
339	C₂×C₃×C₄	—	2	1	no	—
340	C₂×C₃×C₄	—	2	1	no	—
341	C₂×C₃×C₄	—	2	2	no	—
342	C₂×C₃×C₄	—	2	2	no	—
343	C₂×C₃×C₄	—	2	2	no	—
344	C₂×C₃×C₄	—	2	2	no	—
345	C₂×C₃×C₄	—	2	2	no	—
346	C₂×C₃×C₄	—	2	2	no	—
347	C₂×C₃×C₄	—	2	2	no	—
348	C₂×C₃×C₄	—	2	2	no	—
349	C₂×C₃×C₄	—	2	2	no	—
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	—	4	4	no	—
352	C₂×C₃×C₄	—	4	4	no	—
353	C₂×C₃×C₄	—	4	4	no	—
354	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
355	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
356	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
357	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
358	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
359	C₂²×C₅	—	2	2	no	—
360	C₂²×C₅	—	2	2	no	—
361	C₂²×C₅	—	2	2	no	—
362	C₂²×C₅	—	2	2	no	—
363	C₂²×C₅	—	2	2	no	—
364	C₂²×C₅	—	2	2	no	—
365	C₂²×C₅	C₃×C₄×Q₈	1	4	yes	—
366	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
367	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
368	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
369	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
370	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
371	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
372	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
373	C₄×C₅	—	2	2	no	—
374	C₄×C₅	—	2	2	no	—
375	C₄×C₅	—	2	4	no	—
376	C₄×C₅	—	2	4	no	—
377	C₄×C₅	—	2	4	no	—
378	C₄×C₅	—	4	2	no	—
379	C₄×C₅	—	4	2	no	—
380	C₄×C₅	—	4	2	no	—
381	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
382	C₂×Q₈	—	4	1	no	—
383	C₂×Q₈	—	4	1	no	—
384	C₂×Q₈	C₂×C₃×C₄×C₅	1	4	yes	complemented
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	4	1	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	—	4	1	no	—
389	C₂²×C₄	—	4	1	no	—
390	C₂²×C₄	—	4	1	no	—
391	C₂²×C₄	—	4	1	no	—
392	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
393	C₂²×C₄	C₃×C₅×Q₈	1	4	yes	complemented
394	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
395	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
396	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
397	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
398	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
399	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
400	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
401	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
402	C₄⋊C₄	—	4	2	no	—
403	C₄⋊C₄	—	4	1	no	—
404	C₄⋊C₄	—	4	1	no	—
405	C₄⋊C₄	—	4	2	no	—
406	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
407	C₄⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	complemented
408	C₂²⋊C₄	—	2	4	no	—
409	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
410	C₄²	—	4	2	no	—
411	C₄²	—	4	2	no	—
412	C₃×C₅	#2329	1	1	yes	characteristic, direct product factor, Hall
413	C₂²×C₃	—	2	2	no	—
414	C₂²×C₃	—	2	2	no	—
415	C₂²×C₃	—	2	2	no	—
416	C₂²×C₃	—	2	2	no	—
417	C₂²×C₃	—	2	2	no	—
418	C₂²×C₃	—	2	2	no	—
419	C₂²×C₃	C₄×C₅×Q₈	1	4	yes	—
420	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
421	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
422	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
423	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
424	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
425	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
426	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
427	C₃×C₄	—	2	2	no	—
428	C₃×C₄	—	2	2	no	—
429	C₃×C₄	—	2	4	no	—
430	C₃×C₄	—	2	4	no	—
431	C₃×C₄	—	2	4	no	—
432	C₃×C₄	—	4	2	no	—
433	C₃×C₄	—	4	2	no	—
434	C₃×C₄	—	4	2	no	—
435	C₂×C₅	—	2	4	no	—
436	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
437	C₂×C₅	C₃×#518	1	1	yes	characteristic
438	C₂×C₅	C₃×#520	1	1	yes	characteristic
439	C₂×C₅	C₃×#538	1	1	yes	characteristic
440	C₂×C₅	C₃×#539	1	1	yes	characteristic
441	C₂×C₅	C₃×#543	1	1	yes	characteristic
442	C₂×C₅	C₃×#544	1	1	yes	characteristic
443	C₂³	—	2	1	no	—
444	C₂³	—	2	1	no	—
445	C₂³	—	2	1	no	—
446	C₂³	—	2	1	no	—
447	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
448	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
449	C₂³	C₃×C₅×#41	1	2	yes	—
450	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
451	Q₈	—	4	4	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	—	4	4	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
475	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
476	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
477	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
478	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
479	C₂×C₃	—	2	4	no	—
480	C₂×C₃	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
481	C₂×C₃	C₅×#518	1	1	yes	characteristic
482	C₂×C₃	C₅×#520	1	1	yes	characteristic
483	C₂×C₃	C₅×#538	1	1	yes	characteristic
484	C₂×C₃	C₅×#539	1	1	yes	characteristic
485	C₂×C₃	C₅×#543	1	1	yes	characteristic
486	C₂×C₃	C₅×#544	1	1	yes	characteristic
487	C₅	C₃×#2329	1	1	yes	characteristic, direct product factor, Sylow
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	C₃×C₄×C₅×Q₈	1	4	yes	—
495	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
496	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
497	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
498	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
499	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
500	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
501	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	2	4	no	—
505	C₄	—	2	4	no	—
506	C₄	—	2	4	no	—
507	C₄	—	4	2	no	—
508	C₄	—	4	2	no	—
509	C₄	—	4	2	no	—
510	C₃	C₅×#2329	1	1	yes	characteristic, direct product factor, Sylow
511	C₂	—	2	4	no	—
512	C₂	C₂×C₃×C₄×C₅×Q₈	1	1	yes	characteristic
513	C₂	C₃×C₅×#518	1	1	yes	characteristic
514	C₂	C₃×C₅×#520	1	1	yes	characteristic
515	C₂	C₃×C₅×#538	1	1	yes	characteristic
516	C₂	C₃×C₅×#539	1	1	yes	characteristic
517	C₂	C₃×C₅×#543	1	1	yes	characteristic
518	C₂	C₃×C₅×#544	1	1	yes	characteristic

	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
4. C₃×C₅×#387	C₂	semidirect
5. C₃×C₅×#387	C₂	semidirect
10. C₅×#2329	C₃	direct (N × H)
15. C₃×C₅×C₂²⋊Q₈	C₄	semidirect
33. C₃×#2329	C₅	direct (N × H)
35. C₅×#391	C₂×C₃	semidirect
36. C₅×#389	C₂×C₃	semidirect
37. C₅×#387	C₂×C₃	semidirect
38. C₅×#387	C₂×C₃	semidirect
46. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
55. C₂²×C₃×C₄×C₅	Q₈	semidirect
68. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
69. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
75. C₃×#391	C₂×C₅	semidirect
76. C₃×#389	C₂×C₅	semidirect
77. C₃×#387	C₂×C₅	semidirect
78. C₃×#387	C₂×C₅	semidirect
87. C₅×C₂²⋊Q₈	C₃×C₄	semidirect
105. #2329	C₃×C₅	direct (N × H)
146. C₃×C₂²⋊Q₈	C₄×C₅	semidirect
167. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
176. C₂²×C₄×C₅	C₃×Q₈	semidirect
189. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
190. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
196. #391	C₂×C₃×C₅	semidirect
197. #389	C₂×C₃×C₅	semidirect
198. #387	C₂×C₃×C₅	semidirect
199. #387	C₂×C₃×C₅	semidirect
229. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
238. C₂²×C₃×C₄	C₅×Q₈	semidirect
251. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
252. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
297. C₂²⋊Q₈	C₃×C₄×C₅	semidirect
384. C₂×Q₈	C₂×C₃×C₄×C₅	semidirect
393. C₂²×C₄	C₃×C₅×Q₈	semidirect
406. C₄⋊C₄	C₂×C₃×C₄×C₅	semidirect
407. C₄⋊C₄	C₂×C₃×C₄×C₅	semidirect
412. C₃×C₅	#2329	direct (N × H)
487. C₅	C₃×#2329	direct (N × H)
510. C₃	C₅×#2329	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×#387	2
C₃×C₅×#385	2
C₃×C₅×#380	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₂×C₃×C₅×#95	2
C₅×#2329	3
C₃×#2329	5

Subgroups — C3×C5×#2329 #14275363

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2329 #14275363