Subgroups — C₂×C₃×C₅×#456 #14276051

Order 1920.

1416 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#137	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#456	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×C₅×#104	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×C₅×#101	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#456	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×C₅×2₋¹⁺⁴	—	2	4	no	—
9	C₃×C₅×2₋¹⁺⁴	—	2	2	no	—
10	C₃×C₅×2₋¹⁺⁴	C₂²	1	4	yes	—
11	C₂×C₃×C₅×#41	—	2	2	no	—
12	C₂×C₃×C₅×#41	—	2	2	no	—
13	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×Q₈	—	2	2	no	—
15	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×#137	—	2	4	no	—
18	C₃×C₅×#137	C₂²	1	8	yes	complemented
19	C₂×C₃×C₅×Q₁₆	—	2	2	no	—
20	C₂×C₃×C₅×SD₁₆	—	2	2	no	—
21	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
22	C₃×C₅×C₄⋊Q₈	—	2	2	no	—
23	C₃×C₅×C₄⋊Q₈	C₂²	1	4	yes	complemented
24	C₂×C₃×C₅×C₄⋊C₄	—	2	2	no	—
25	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₃×C₅×#104	C₂²	1	8	yes	complemented
27	C₃×C₅×#101	C₂²	1	4	yes	complemented
28	C₂×C₃×#456	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×2₋¹⁺⁴	C₂×C₃	1	1	yes	characteristic
30	C₂×C₅×#137	C₂×C₃	1	2	yes	complemented
31	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
32	C₅×#456	C₂×C₃	1	8	yes	direct product factor
33	C₂×C₅×#104	C₂×C₃	1	2	yes	complemented
34	C₂×C₅×#101	C₂×C₃	1	1	yes	characteristic, complemented
35	C₃×C₅×#41	—	2	8	no	—
36	C₃×C₅×#41	—	2	8	no	—
37	C₃×C₅×#41	—	2	8	no	—
38	C₃×C₅×#41	—	2	8	no	—
39	C₃×C₅×#41	—	2	2	no	—
40	C₃×C₅×#41	—	2	2	no	—
41	C₃×C₅×#41	D₄	1	4	yes	—
42	C₃×C₅×#41	C₂³	1	4	yes	—
43	C₂×C₃×C₅×Q₈	—	2	2	no	—
44	C₂×C₃×C₅×Q₈	—	2	8	no	—
45	C₂×C₃×C₅×Q₈	—	2	8	no	—
46	C₂×C₃×C₅×Q₈	—	2	2	no	—
47	C₂×C₃×C₅×Q₈	—	2	2	no	—
48	C₂×C₃×C₅×Q₈	—	2	1	no	—
49	C₂×C₃×C₅×Q₈	—	2	2	no	—
50	C₂×C₃×C₅×Q₈	—	2	2	no	—
51	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
52	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
53	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
54	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
55	C₂×C₃×C₅×D₄	—	2	2	no	—
56	C₂×C₃×C₅×D₄	—	2	2	no	—
57	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
58	C₂²×C₃×C₄×C₅	—	2	4	no	—
59	C₂²×C₃×C₄×C₅	—	2	1	no	—
60	C₂²×C₃×C₄×C₅	—	2	2	no	—
61	C₂²×C₃×C₄×C₅	—	2	1	no	—
62	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
63	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₃×C₅×Q₁₆	—	2	8	no	—
65	C₃×C₅×SD₁₆	—	2	8	no	—
66	C₃×C₅×M₁₆	—	2	2	no	—
67	C₃×C₅×M₁₆	C₂³	1	4	yes	—
68	C₂×C₃×C₅×C₈	—	2	2	no	—
69	C₃×C₅×C₄⋊C₄	—	2	8	no	—
70	C₃×C₄²×C₅	—	2	1	no	—
71	C₃×C₄²×C₅	C₂³	1	2	yes	—
72	C₂×C₃×2₋¹⁺⁴	C₂×C₅	1	1	yes	characteristic
73	C₂×C₃×#137	C₂×C₅	1	2	yes	complemented
74	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
75	C₃×#456	C₂×C₅	1	8	yes	direct product factor
76	C₂×C₃×#104	C₂×C₅	1	2	yes	complemented
77	C₂×C₃×#101	C₂×C₅	1	1	yes	characteristic, complemented
78	C₅×2₋¹⁺⁴	—	2	4	no	—
79	C₅×2₋¹⁺⁴	—	2	2	no	—
80	C₅×2₋¹⁺⁴	C₂²×C₃	1	4	yes	—
81	C₂×C₅×#41	—	2	2	no	—
82	C₂×C₅×#41	—	2	2	no	—
83	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
84	C₂²×C₅×Q₈	—	2	2	no	—
85	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
86	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
87	C₅×#137	—	2	4	no	—
88	C₅×#137	C₂²×C₃	1	8	yes	complemented
89	C₂×C₅×Q₁₆	—	2	2	no	—
90	C₂×C₅×SD₁₆	—	2	2	no	—
91	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
92	C₅×C₄⋊Q₈	—	2	2	no	—
93	C₅×C₄⋊Q₈	C₂²×C₃	1	4	yes	complemented
94	C₂×C₅×C₄⋊C₄	—	2	2	no	—
95	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
96	C₅×#104	C₂²×C₃	1	8	yes	complemented
97	C₅×#101	C₂²×C₃	1	4	yes	complemented
98	C₂×#456	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
99	C₂³×C₃×C₅	—	2	2	no	—
100	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
101	C₃×C₅×Q₈	—	2	8	no	—
102	C₃×C₅×Q₈	—	2	2	no	—
103	C₃×C₅×Q₈	—	2	4	no	—
104	C₃×C₅×Q₈	—	2	4	no	—
105	C₃×C₅×Q₈	—	2	4	no	—
106	C₃×C₅×Q₈	—	4	2	no	—
107	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
108	C₃×C₅×D₄	—	2	8	no	—
109	C₃×C₅×D₄	—	2	4	no	—
110	C₃×C₅×D₄	—	2	4	no	—
111	C₃×C₅×D₄	—	2	2	no	—
112	C₃×C₅×D₄	C₂×D₄	1	4	yes	—
113	C₂×C₃×C₄×C₅	—	2	4	no	—
114	C₂×C₃×C₄×C₅	—	2	16	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	4	no	—
120	C₂×C₃×C₄×C₅	—	2	4	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	4	1	no	—
123	C₂×C₃×C₄×C₅	—	4	1	no	—
124	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
125	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
126	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
127	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
128	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
129	C₃×C₅×C₈	—	2	4	no	—
130	C₃×2₋¹⁺⁴	—	2	4	no	—
131	C₃×2₋¹⁺⁴	—	2	2	no	—
132	C₃×2₋¹⁺⁴	C₂²×C₅	1	4	yes	—
133	C₂×C₃×#41	—	2	2	no	—
134	C₂×C₃×#41	—	2	2	no	—
135	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
136	C₂²×C₃×Q₈	—	2	2	no	—
137	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
138	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
139	C₃×#137	—	2	4	no	—
140	C₃×#137	C₂²×C₅	1	8	yes	complemented
141	C₂×C₃×Q₁₆	—	2	2	no	—
142	C₂×C₃×SD₁₆	—	2	2	no	—
143	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
144	C₃×C₄⋊Q₈	—	2	2	no	—
145	C₃×C₄⋊Q₈	C₂²×C₅	1	4	yes	complemented
146	C₂×C₃×C₄⋊C₄	—	2	2	no	—
147	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
148	C₃×#104	C₂²×C₅	1	8	yes	complemented
149	C₃×#101	C₂²×C₅	1	4	yes	complemented
150	C₅×#41	—	2	8	no	—
151	C₅×#41	—	2	8	no	—
152	C₅×#41	—	2	8	no	—
153	C₅×#41	—	2	8	no	—
154	C₅×#41	—	2	2	no	—
155	C₅×#41	—	2	2	no	—
156	C₅×#41	C₃×D₄	1	4	yes	—
157	C₅×#41	C₂³×C₃	1	4	yes	—
158	C₂×C₅×Q₈	—	2	2	no	—
159	C₂×C₅×Q₈	—	2	8	no	—
160	C₂×C₅×Q₈	—	2	8	no	—
161	C₂×C₅×Q₈	—	2	2	no	—
162	C₂×C₅×Q₈	—	2	2	no	—
163	C₂×C₅×Q₈	—	2	1	no	—
164	C₂×C₅×Q₈	—	2	2	no	—
165	C₂×C₅×Q₈	—	2	2	no	—
166	C₂×C₅×Q₈	C₃×D₄	1	2	yes	—
167	C₂×C₅×Q₈	C₃×D₄	1	2	yes	—
168	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
169	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
170	C₂×C₅×D₄	—	2	2	no	—
171	C₂×C₅×D₄	—	2	2	no	—
172	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
173	C₂²×C₄×C₅	—	2	4	no	—
174	C₂²×C₄×C₅	—	2	1	no	—
175	C₂²×C₄×C₅	—	2	2	no	—
176	C₂²×C₄×C₅	—	2	1	no	—
177	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
178	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
179	C₅×Q₁₆	—	2	8	no	—
180	C₅×SD₁₆	—	2	8	no	—
181	C₅×M₁₆	—	2	2	no	—
182	C₅×M₁₆	C₂³×C₃	1	4	yes	—
183	C₂×C₅×C₈	—	2	2	no	—
184	C₅×C₄⋊C₄	—	2	8	no	—
185	C₄²×C₅	—	2	1	no	—
186	C₄²×C₅	C₂³×C₃	1	2	yes	—
187	C₂×2₋¹⁺⁴	C₂×C₃×C₅	1	1	yes	characteristic
188	C₂×#137	C₂×C₃×C₅	1	2	yes	complemented
189	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
190	#456	C₂×C₃×C₅	1	8	yes	direct product factor
191	C₂×#104	C₂×C₃×C₅	1	2	yes	complemented
192	C₂×#101	C₂×C₃×C₅	1	1	yes	characteristic, complemented
193	C₂²×C₃×C₅	—	2	2	no	—
194	C₂²×C₃×C₅	—	2	4	no	—
195	C₂²×C₃×C₅	—	4	4	no	—
196	C₂²×C₃×C₅	#120	1	1	yes	characteristic
197	C₂²×C₃×C₅	#120	1	1	yes	characteristic
198	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
199	C₃×C₄×C₅	—	2	4	no	—
200	C₃×C₄×C₅	—	2	4	no	—
201	C₃×C₄×C₅	—	2	4	no	—
202	C₃×C₄×C₅	—	4	2	no	—
203	C₃×C₄×C₅	#120	1	2	yes	—
204	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
205	C₃×#41	—	2	8	no	—
206	C₃×#41	—	2	8	no	—
207	C₃×#41	—	2	8	no	—
208	C₃×#41	—	2	8	no	—
209	C₃×#41	—	2	2	no	—
210	C₃×#41	—	2	2	no	—
211	C₃×#41	C₅×D₄	1	4	yes	—
212	C₃×#41	C₂³×C₅	1	4	yes	—
213	C₂×C₃×Q₈	—	2	2	no	—
214	C₂×C₃×Q₈	—	2	8	no	—
215	C₂×C₃×Q₈	—	2	8	no	—
216	C₂×C₃×Q₈	—	2	2	no	—
217	C₂×C₃×Q₈	—	2	2	no	—
218	C₂×C₃×Q₈	—	2	1	no	—
219	C₂×C₃×Q₈	—	2	2	no	—
220	C₂×C₃×Q₈	—	2	2	no	—
221	C₂×C₃×Q₈	C₅×D₄	1	2	yes	—
222	C₂×C₃×Q₈	C₅×D₄	1	2	yes	—
223	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
224	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
225	C₂×C₃×D₄	—	2	2	no	—
226	C₂×C₃×D₄	—	2	2	no	—
227	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
228	C₂²×C₃×C₄	—	2	4	no	—
229	C₂²×C₃×C₄	—	2	1	no	—
230	C₂²×C₃×C₄	—	2	2	no	—
231	C₂²×C₃×C₄	—	2	1	no	—
232	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
233	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
234	C₃×Q₁₆	—	2	8	no	—
235	C₃×SD₁₆	—	2	8	no	—
236	C₃×M₁₆	—	2	2	no	—
237	C₃×M₁₆	C₂³×C₅	1	4	yes	—
238	C₂×C₃×C₈	—	2	2	no	—
239	C₃×C₄⋊C₄	—	2	8	no	—
240	C₃×C₄²	—	2	1	no	—
241	C₃×C₄²	C₂³×C₅	1	2	yes	—
242	C₂³×C₅	—	2	2	no	—
243	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
244	C₅×Q₈	—	2	8	no	—
245	C₅×Q₈	—	2	2	no	—
246	C₅×Q₈	—	2	4	no	—
247	C₅×Q₈	—	2	4	no	—
248	C₅×Q₈	—	2	4	no	—
249	C₅×Q₈	—	4	2	no	—
250	C₅×Q₈	C₂×C₃×D₄	1	4	yes	—
251	C₅×D₄	—	2	8	no	—
252	C₅×D₄	—	2	4	no	—
253	C₅×D₄	—	2	4	no	—
254	C₅×D₄	—	2	2	no	—
255	C₅×D₄	C₂×C₃×D₄	1	4	yes	—
256	C₂×C₄×C₅	—	2	4	no	—
257	C₂×C₄×C₅	—	2	16	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	2	4	no	—
263	C₂×C₄×C₅	—	2	4	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	4	1	no	—
266	C₂×C₄×C₅	—	4	1	no	—
267	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
268	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
270	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
271	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
272	C₅×C₈	—	2	4	no	—
273	2₋¹⁺⁴	—	2	4	no	—
274	2₋¹⁺⁴	—	2	2	no	—
275	2₋¹⁺⁴	C₂²×C₃×C₅	1	4	yes	—
276	C₂×#41	—	2	2	no	—
277	C₂×#41	—	2	2	no	—
278	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
279	C₂²×Q₈	—	2	2	no	—
280	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
281	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
282	#137	—	2	4	no	—
283	#137	C₂²×C₃×C₅	1	8	yes	complemented
284	C₂×Q₁₆	—	2	2	no	—
285	C₂×SD₁₆	—	2	2	no	—
286	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
287	C₄⋊Q₈	—	2	2	no	—
288	C₄⋊Q₈	C₂²×C₃×C₅	1	4	yes	complemented
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
291	#104	C₂²×C₃×C₅	1	8	yes	complemented
292	#101	C₂²×C₃×C₅	1	4	yes	complemented
293	C₂×C₃×C₅	—	2	1	no	—
294	C₂×C₃×C₅	—	2	1	no	—
295	C₂×C₃×C₅	—	4	4	no	—
296	C₂×C₃×C₅	#456	1	2	yes	direct product factor
297	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
298	C₂³×C₃	—	2	2	no	—
299	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
300	C₃×Q₈	—	2	8	no	—
301	C₃×Q₈	—	2	2	no	—
302	C₃×Q₈	—	2	4	no	—
303	C₃×Q₈	—	2	4	no	—
304	C₃×Q₈	—	2	4	no	—
305	C₃×Q₈	—	4	2	no	—
306	C₃×Q₈	C₂×C₅×D₄	1	4	yes	—
307	C₃×D₄	—	2	8	no	—
308	C₃×D₄	—	2	4	no	—
309	C₃×D₄	—	2	4	no	—
310	C₃×D₄	—	2	2	no	—
311	C₃×D₄	C₂×C₅×D₄	1	4	yes	—
312	C₂×C₃×C₄	—	2	4	no	—
313	C₂×C₃×C₄	—	2	16	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	4	no	—
319	C₂×C₃×C₄	—	2	4	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	4	1	no	—
322	C₂×C₃×C₄	—	4	1	no	—
323	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
324	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
325	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
326	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
327	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
328	C₃×C₈	—	2	4	no	—
329	C₂²×C₅	—	2	2	no	—
330	C₂²×C₅	—	2	4	no	—
331	C₂²×C₅	—	4	4	no	—
332	C₂²×C₅	C₃×#120	1	1	yes	characteristic
333	C₂²×C₅	C₃×#120	1	1	yes	characteristic
334	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
335	C₄×C₅	—	2	4	no	—
336	C₄×C₅	—	2	4	no	—
337	C₄×C₅	—	2	4	no	—
338	C₄×C₅	—	4	2	no	—
339	C₄×C₅	C₃×#120	1	2	yes	—
340	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
341	#41	—	2	8	no	—
342	#41	—	2	8	no	—
343	#41	—	2	8	no	—
344	#41	—	2	8	no	—
345	#41	—	2	2	no	—
346	#41	—	2	2	no	—
347	#41	C₃×C₅×D₄	1	4	yes	—
348	#41	C₂³×C₃×C₅	1	4	yes	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	8	no	—
351	C₂×Q₈	—	2	8	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	C₃×C₅×D₄	1	2	yes	—
358	C₂×Q₈	C₃×C₅×D₄	1	2	yes	—
359	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
360	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
369	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
370	Q₁₆	—	2	8	no	—
371	SD₁₆	—	2	8	no	—
372	M₁₆	—	2	2	no	—
373	M₁₆	C₂³×C₃×C₅	1	4	yes	—
374	C₂×C₈	—	2	2	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄²	—	2	1	no	—
377	C₄²	C₂³×C₃×C₅	1	2	yes	—
378	C₃×C₅	C₂×#456	1	1	yes	characteristic, direct product factor, Hall
379	C₂²×C₃	—	2	2	no	—
380	C₂²×C₃	—	2	4	no	—
381	C₂²×C₃	—	4	4	no	—
382	C₂²×C₃	C₅×#120	1	1	yes	characteristic
383	C₂²×C₃	C₅×#120	1	1	yes	characteristic
384	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
385	C₃×C₄	—	2	4	no	—
386	C₃×C₄	—	2	4	no	—
387	C₃×C₄	—	2	4	no	—
388	C₃×C₄	—	4	2	no	—
389	C₃×C₄	C₅×#120	1	2	yes	—
390	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
391	C₂×C₅	—	2	1	no	—
392	C₂×C₅	—	2	1	no	—
393	C₂×C₅	—	4	4	no	—
394	C₂×C₅	C₃×#456	1	2	yes	direct product factor
395	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
396	C₂³	—	2	2	no	—
397	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
398	Q₈	—	2	8	no	—
399	Q₈	—	2	2	no	—
400	Q₈	—	2	4	no	—
401	Q₈	—	2	4	no	—
402	Q₈	—	2	4	no	—
403	Q₈	—	4	2	no	—
404	Q₈	C₂×C₃×C₅×D₄	1	4	yes	—
405	D₄	—	2	8	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	4	no	—
408	D₄	—	2	2	no	—
409	D₄	C₂×C₃×C₅×D₄	1	4	yes	—
410	C₂×C₄	—	2	16	no	—
411	C₂×C₄	—	2	4	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	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
422	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
423	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
424	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
425	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
426	C₈	—	2	4	no	—
427	C₂×C₃	—	2	1	no	—
428	C₂×C₃	—	2	1	no	—
429	C₂×C₃	—	4	4	no	—
430	C₂×C₃	C₅×#456	1	2	yes	direct product factor
431	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
432	C₅	C₂×C₃×#456	1	1	yes	characteristic, direct product factor, Sylow
433	C₂²	—	2	2	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	4	4	no	—
436	C₂²	C₃×C₅×#120	1	1	yes	characteristic
437	C₂²	C₃×C₅×#120	1	1	yes	characteristic
438	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
439	C₄	—	2	4	no	—
440	C₄	—	2	4	no	—
441	C₄	—	2	4	no	—
442	C₄	—	4	2	no	—
443	C₄	C₃×C₅×#120	1	2	yes	—
444	C₄	C₂²×C₃×C₅×D₄	1	2	yes	—
445	C₃	C₂×C₅×#456	1	1	yes	characteristic, direct product factor, Sylow
446	C₂	—	2	1	no	—
447	C₂	—	2	1	no	—
448	C₂	—	4	4	no	—
449	C₂	C₃×C₅×#456	1	2	yes	direct product factor
450	C₂	C₂×C₃×C₅×#120	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×2₋¹⁺⁴	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#137	C₂	semidirect
3. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
4. C₃×C₅×#456	C₂	direct (N × H)
5. C₂×C₃×C₅×#104	C₂	semidirect
6. C₂×C₃×C₅×#101	C₂	semidirect
7. C₂×C₅×#456	C₃	direct (N × H)
18. C₃×C₅×#137	C₂²	semidirect
23. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
26. C₃×C₅×#104	C₂²	semidirect
27. C₃×C₅×#101	C₂²	semidirect
28. C₂×C₃×#456	C₅	direct (N × H)
30. C₂×C₅×#137	C₂×C₃	semidirect
31. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
32. C₅×#456	C₂×C₃	direct (N × H)
33. C₂×C₅×#104	C₂×C₃	semidirect
34. C₂×C₅×#101	C₂×C₃	semidirect
73. C₂×C₃×#137	C₂×C₅	semidirect
74. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
75. C₃×#456	C₂×C₅	direct (N × H)
76. C₂×C₃×#104	C₂×C₅	semidirect
77. C₂×C₃×#101	C₂×C₅	semidirect
88. C₅×#137	C₂²×C₃	semidirect
93. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
96. C₅×#104	C₂²×C₃	semidirect
97. C₅×#101	C₂²×C₃	semidirect
98. C₂×#456	C₃×C₅	direct (N × H)
140. C₃×#137	C₂²×C₅	semidirect
145. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
148. C₃×#104	C₂²×C₅	semidirect
149. C₃×#101	C₂²×C₅	semidirect
188. C₂×#137	C₂×C₃×C₅	semidirect
189. C₂×C₄⋊Q₈	C₂×C₃×C₅	semidirect
190. #456	C₂×C₃×C₅	direct (N × H)
191. C₂×#104	C₂×C₃×C₅	semidirect
192. C₂×#101	C₂×C₃×C₅	semidirect
283. #137	C₂²×C₃×C₅	semidirect
288. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
291. #104	C₂²×C₃×C₅	semidirect
292. #101	C₂²×C₃×C₅	semidirect
296. C₂×C₃×C₅	#456	direct (N × H)
378. C₃×C₅	C₂×#456	direct (N × H)
394. C₂×C₅	C₃×#456	direct (N × H)
430. C₂×C₃	C₅×#456	direct (N × H)
432. C₅	C₂×C₃×#456	direct (N × H)
445. C₃	C₂×C₅×#456	direct (N × H)
449. C₂	C₃×C₅×#456	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×C₅×2₋¹⁺⁴	2
C₂×C₃×C₅×#137	2
C₂×C₃×C₅×C₄⋊Q₈	2
C₃×C₅×#456	2
C₂×C₃×C₅×#104	2
C₂×C₃×C₅×#101	2
C₂×C₅×#456	3
C₂×C₃×#456	5

Subgroups — C2×C3×C5×#456 #14276051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#456 #14276051