Subgroups — C₃×C₅×#2549 #14275583

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 460 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	2	yes	maximal
2	C₃×C₅×#398	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#395	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#391	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#389	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	1	yes	maximal, characteristic
9	C₂×C₃×C₅×#95	C₂	1	1	yes	maximal, characteristic
10	C₅×#2549	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
12	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
13	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₃×C₅×C₂²⋊Q₈	—	2	8	no	—
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	2	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
28	C₃×C₅×#95	C₂²	1	2	yes	—
29	C₃×C₅×#95	C₂²	1	1	yes	characteristic
30	C₃×C₅×#95	C₂²	1	1	yes	characteristic
31	C₃×C₅×#95	C₂²	1	2	yes	—
32	C₃×C₅×#95	C₂²	1	2	yes	—
33	C₃×#2549	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	2	yes	—
35	C₅×#398	C₂×C₃	1	2	yes	complemented
36	C₅×#395	C₂×C₃	1	2	yes	complemented
37	C₅×#391	C₂×C₃	1	2	yes	complemented
38	C₅×#389	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	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	—	2	4	no	—
45	C₂×C₃×C₅×Q₈	—	2	4	no	—
46	C₂×C₃×C₅×Q₈	—	4	2	no	—
47	C₂²×C₃×C₄×C₅	—	2	4	no	—
48	C₂²×C₃×C₄×C₅	—	2	4	no	—
49	C₂²×C₃×C₄×C₅	—	4	2	no	—
50	C₂²×C₃×C₄×C₅	—	4	2	no	—
51	C₂²×C₃×C₄×C₅	Q₈	1	4	yes	complemented
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	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	1	yes	characteristic
59	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
60	C₃×C₅×C₄⋊C₄	—	2	4	no	—
61	C₃×C₅×C₄⋊C₄	—	2	4	no	—
62	C₃×C₅×C₄⋊C₄	—	2	4	no	—
63	C₃×C₅×C₄⋊C₄	—	2	4	no	—
64	C₃×C₅×C₄⋊C₄	—	4	2	no	—
65	C₃×C₅×C₄⋊C₄	—	4	2	no	—
66	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
67	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	—
68	C₃×C₅×C₂²⋊C₄	Q₈	1	4	yes	complemented
69	C₃×C₄²×C₅	—	4	2	no	—
70	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	2	yes	—
71	C₃×#398	C₂×C₅	1	2	yes	complemented
72	C₃×#395	C₂×C₅	1	2	yes	complemented
73	C₃×#391	C₂×C₅	1	2	yes	complemented
74	C₃×#389	C₂×C₅	1	2	yes	complemented
75	C₃×#385	C₂×C₅	1	2	yes	—
76	C₃×#380	C₂×C₅	1	1	yes	characteristic
77	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
78	C₂×C₃×#95	C₂×C₅	1	1	yes	characteristic
79	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
80	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
81	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
82	C₅×C₂²⋊Q₈	—	2	8	no	—
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	2	yes	—
86	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
87	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
88	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
89	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
90	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
93	C₅×#95	C₂²×C₃	1	2	yes	—
94	C₅×#95	C₂²×C₃	1	1	yes	characteristic
95	C₅×#95	C₂²×C₃	1	1	yes	characteristic
96	C₅×#95	C₂²×C₃	1	2	yes	—
97	C₅×#95	C₂²×C₃	1	1	yes	characteristic
98	C₅×#95	C₂²×C₃	1	1	yes	characteristic
99	C₅×#95	C₂²×C₃	1	2	yes	—
100	C₅×#95	C₂²×C₃	1	2	yes	—
101	#2549	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	—	2	2	no	—
104	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
105	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
106	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
107	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
108	C₃×C₅×Q₈	—	4	8	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	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	4	4	no	—
127	C₂×C₃×C₄×C₅	—	4	8	no	—
128	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
129	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
130	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
132	C₂×C₃×C₄×C₅	#41	1	4	yes	—
133	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
134	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
135	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
136	C₃×C₂²⋊Q₈	—	2	8	no	—
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	2	yes	—
140	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
141	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
142	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
143	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
144	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
145	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
147	C₃×#95	C₂²×C₅	1	2	yes	—
148	C₃×#95	C₂²×C₅	1	1	yes	characteristic
149	C₃×#95	C₂²×C₅	1	1	yes	characteristic
150	C₃×#95	C₂²×C₅	1	2	yes	—
151	C₃×#95	C₂²×C₅	1	1	yes	characteristic
152	C₃×#95	C₂²×C₅	1	1	yes	characteristic
153	C₃×#95	C₂²×C₅	1	2	yes	—
154	C₃×#95	C₂²×C₅	1	2	yes	—
155	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
156	C₂×C₅×Q₈	—	2	4	no	—
157	C₂×C₅×Q₈	—	2	4	no	—
158	C₂×C₅×Q₈	—	4	2	no	—
159	C₂²×C₄×C₅	—	2	4	no	—
160	C₂²×C₄×C₅	—	2	4	no	—
161	C₂²×C₄×C₅	—	4	2	no	—
162	C₂²×C₄×C₅	—	4	2	no	—
163	C₂²×C₄×C₅	C₃×Q₈	1	4	yes	complemented
164	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
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	2	yes	—
168	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
170	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
172	C₅×C₄⋊C₄	—	2	4	no	—
173	C₅×C₄⋊C₄	—	2	4	no	—
174	C₅×C₄⋊C₄	—	2	4	no	—
175	C₅×C₄⋊C₄	—	2	4	no	—
176	C₅×C₄⋊C₄	—	4	2	no	—
177	C₅×C₄⋊C₄	—	4	2	no	—
178	C₅×C₂²⋊C₄	—	2	4	no	—
179	C₅×C₂²⋊C₄	C₃×D₄	1	4	yes	—
180	C₅×C₂²⋊C₄	C₃×Q₈	1	4	yes	complemented
181	C₄²×C₅	—	4	2	no	—
182	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	2	yes	—
183	#398	C₂×C₃×C₅	1	2	yes	complemented
184	#395	C₂×C₃×C₅	1	2	yes	complemented
185	#391	C₂×C₃×C₅	1	2	yes	complemented
186	#389	C₂×C₃×C₅	1	2	yes	complemented
187	#385	C₂×C₃×C₅	1	2	yes	—
188	#380	C₂×C₃×C₅	1	1	yes	characteristic
189	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
190	C₂×#95	C₂×C₃×C₅	1	1	yes	characteristic
191	C₂²×C₃×C₅	—	2	2	no	—
192	C₂²×C₃×C₅	—	2	2	no	—
193	C₂²×C₃×C₅	—	2	4	no	—
194	C₂²×C₃×C₅	—	2	4	no	—
195	C₂²×C₃×C₅	C₄⋊Q₈	1	4	yes	—
196	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
197	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
198	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
199	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
200	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
201	C₃×C₄×C₅	—	2	2	no	—
202	C₃×C₄×C₅	—	2	2	no	—
203	C₃×C₄×C₅	—	2	4	no	—
204	C₃×C₄×C₅	—	2	4	no	—
205	C₃×C₄×C₅	—	2	4	no	—
206	C₃×C₄×C₅	—	4	2	no	—
207	C₃×C₄×C₅	—	4	2	no	—
208	C₃×C₄×C₅	—	4	2	no	—
209	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
210	C₂×C₃×Q₈	—	2	4	no	—
211	C₂×C₃×Q₈	—	2	4	no	—
212	C₂×C₃×Q₈	—	4	2	no	—
213	C₂²×C₃×C₄	—	2	4	no	—
214	C₂²×C₃×C₄	—	2	4	no	—
215	C₂²×C₃×C₄	—	4	2	no	—
216	C₂²×C₃×C₄	—	4	2	no	—
217	C₂²×C₃×C₄	C₅×Q₈	1	4	yes	complemented
218	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
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	1	yes	characteristic
223	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
225	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
226	C₃×C₄⋊C₄	—	2	4	no	—
227	C₃×C₄⋊C₄	—	2	4	no	—
228	C₃×C₄⋊C₄	—	2	4	no	—
229	C₃×C₄⋊C₄	—	2	4	no	—
230	C₃×C₄⋊C₄	—	4	2	no	—
231	C₃×C₄⋊C₄	—	4	2	no	—
232	C₃×C₂²⋊C₄	—	2	4	no	—
233	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	—
234	C₃×C₂²⋊C₄	C₅×Q₈	1	4	yes	complemented
235	C₃×C₄²	—	4	2	no	—
236	C₂³×C₅	—	2	2	no	—
237	C₂³×C₅	—	2	2	no	—
238	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
239	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
240	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
241	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
242	C₅×Q₈	—	4	8	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	—	2	2	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	4	4	no	—
261	C₂×C₄×C₅	—	4	8	no	—
262	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
263	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
264	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
265	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
266	C₂×C₄×C₅	C₃×#41	1	4	yes	—
267	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
268	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
269	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
270	C₂²⋊Q₈	—	2	8	no	—
271	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
272	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
273	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
274	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
275	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
276	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
277	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
278	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
280	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
281	#95	C₂²×C₃×C₅	1	2	yes	—
282	#95	C₂²×C₃×C₅	1	1	yes	characteristic
283	#95	C₂²×C₃×C₅	1	1	yes	characteristic
284	#95	C₂²×C₃×C₅	1	2	yes	—
285	#95	C₂²×C₃×C₅	1	1	yes	characteristic
286	#95	C₂²×C₃×C₅	1	1	yes	characteristic
287	#95	C₂²×C₃×C₅	1	2	yes	—
288	#95	C₂²×C₃×C₅	1	2	yes	—
289	C₂×C₃×C₅	—	2	4	no	—
290	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
291	C₂×C₃×C₅	#533	1	1	yes	characteristic
292	C₂×C₃×C₅	#543	1	1	yes	characteristic
293	C₂×C₃×C₅	#546	1	2	yes	—
294	C₂×C₃×C₅	#554	1	2	yes	—
295	C₂³×C₃	—	2	2	no	—
296	C₂³×C₃	—	2	2	no	—
297	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
298	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
299	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
300	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
301	C₃×Q₈	—	4	8	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	—	2	2	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	2	no	—
319	C₂×C₃×C₄	—	4	4	no	—
320	C₂×C₃×C₄	—	4	8	no	—
321	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
322	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
323	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
324	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
325	C₂×C₃×C₄	C₅×#41	1	4	yes	—
326	C₂²×C₅	—	2	2	no	—
327	C₂²×C₅	—	2	2	no	—
328	C₂²×C₅	—	2	4	no	—
329	C₂²×C₅	—	2	4	no	—
330	C₂²×C₅	C₃×C₄⋊Q₈	1	4	yes	—
331	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
332	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
333	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
334	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
335	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
336	C₄×C₅	—	2	2	no	—
337	C₄×C₅	—	2	2	no	—
338	C₄×C₅	—	2	4	no	—
339	C₄×C₅	—	2	4	no	—
340	C₄×C₅	—	2	4	no	—
341	C₄×C₅	—	4	2	no	—
342	C₄×C₅	—	4	2	no	—
343	C₄×C₅	—	4	2	no	—
344	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
345	C₂×Q₈	—	2	4	no	—
346	C₂×Q₈	—	2	4	no	—
347	C₂×Q₈	—	4	2	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	C₃×C₅×Q₈	1	4	yes	complemented
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	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
358	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
359	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
360	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	C₃×C₅×D₄	1	4	yes	—
369	C₂²⋊C₄	C₃×C₅×Q₈	1	4	yes	complemented
370	C₄²	—	4	2	no	—
371	C₃×C₅	#2549	1	1	yes	characteristic, direct product factor, Hall
372	C₂²×C₃	—	2	2	no	—
373	C₂²×C₃	—	2	2	no	—
374	C₂²×C₃	—	2	4	no	—
375	C₂²×C₃	—	2	4	no	—
376	C₂²×C₃	C₅×C₄⋊Q₈	1	4	yes	—
377	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
378	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
379	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
380	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
381	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
382	C₃×C₄	—	2	2	no	—
383	C₃×C₄	—	2	2	no	—
384	C₃×C₄	—	2	4	no	—
385	C₃×C₄	—	2	4	no	—
386	C₃×C₄	—	2	4	no	—
387	C₃×C₄	—	4	2	no	—
388	C₃×C₄	—	4	2	no	—
389	C₃×C₄	—	4	2	no	—
390	C₂×C₅	—	2	4	no	—
391	C₂×C₅	C₂×C₃×C₄⋊Q₈	1	1	yes	characteristic
392	C₂×C₅	C₃×#533	1	1	yes	characteristic
393	C₂×C₅	C₃×#543	1	1	yes	characteristic
394	C₂×C₅	C₃×#546	1	2	yes	—
395	C₂×C₅	C₃×#554	1	2	yes	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
399	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
400	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
401	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
402	Q₈	—	4	8	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	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	8	no	—
422	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
423	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
424	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
425	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
426	C₂×C₄	C₃×C₅×#41	1	4	yes	—
427	C₂×C₃	—	2	4	no	—
428	C₂×C₃	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
429	C₂×C₃	C₅×#533	1	1	yes	characteristic
430	C₂×C₃	C₅×#543	1	1	yes	characteristic
431	C₂×C₃	C₅×#546	1	2	yes	—
432	C₂×C₃	C₅×#554	1	2	yes	—
433	C₅	C₃×#2549	1	1	yes	characteristic, direct product factor, Sylow
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	4	no	—
438	C₂²	C₃×C₅×C₄⋊Q₈	1	4	yes	—
439	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
440	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
441	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
442	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
443	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
444	C₄	—	2	2	no	—
445	C₄	—	2	2	no	—
446	C₄	—	2	4	no	—
447	C₄	—	2	4	no	—
448	C₄	—	2	4	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₃	C₅×#2549	1	1	yes	characteristic, direct product factor, Sylow
453	C₂	—	2	4	no	—
454	C₂	C₂×C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
455	C₂	C₃×C₅×#533	1	1	yes	characteristic
456	C₂	C₃×C₅×#543	1	1	yes	characteristic
457	C₂	C₃×C₅×#546	1	2	yes	—
458	C₂	C₃×C₅×#554	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁴×C₃×C₅	C₂³
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
2. C₃×C₅×#398	C₂	semidirect
3. C₃×C₅×#395	C₂	semidirect
4. C₃×C₅×#391	C₂	semidirect
5. C₃×C₅×#389	C₂	semidirect
10. C₅×#2549	C₃	direct (N × H)
33. C₃×#2549	C₅	direct (N × H)
35. C₅×#398	C₂×C₃	semidirect
36. C₅×#395	C₂×C₃	semidirect
37. C₅×#391	C₂×C₃	semidirect
38. C₅×#389	C₂×C₃	semidirect
51. C₂²×C₃×C₄×C₅	Q₈	semidirect
68. C₃×C₅×C₂²⋊C₄	Q₈	semidirect
71. C₃×#398	C₂×C₅	semidirect
72. C₃×#395	C₂×C₅	semidirect
73. C₃×#391	C₂×C₅	semidirect
74. C₃×#389	C₂×C₅	semidirect
101. #2549	C₃×C₅	direct (N × H)
163. C₂²×C₄×C₅	C₃×Q₈	semidirect
180. C₅×C₂²⋊C₄	C₃×Q₈	semidirect
183. #398	C₂×C₃×C₅	semidirect
184. #395	C₂×C₃×C₅	semidirect
185. #391	C₂×C₃×C₅	semidirect
186. #389	C₂×C₃×C₅	semidirect
217. C₂²×C₃×C₄	C₅×Q₈	semidirect
234. C₃×C₂²⋊C₄	C₅×Q₈	semidirect
352. C₂²×C₄	C₃×C₅×Q₈	semidirect
369. C₂²⋊C₄	C₃×C₅×Q₈	semidirect
371. C₃×C₅	#2549	direct (N × H)
433. C₅	C₃×#2549	direct (N × H)
452. C₃	C₅×#2549	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×#398	2
C₃×C₅×#395	2
C₃×C₅×#391	2
C₃×C₅×#389	2
C₃×C₅×#385	2
C₃×C₅×#380	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₂×C₃×C₅×#95	2
C₅×#2549	3
C₃×#2549	5

Subgroups — C3×C5×#2549 #14275583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2549 #14275583