Subgroups — C₂×C₃×C₅×#455 #14276049

Order 1920.

1520 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#137	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#455	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×C₅×#104	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×C₅×#100	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#455	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×C₅×H(5,𝔽₂)	—	2	4	no	—
9	C₃×C₅×H(5,𝔽₂)	—	2	2	no	—
10	C₃×C₅×H(5,𝔽₂)	C₂²	1	4	yes	—
11	C₂×C₃×C₅×#41	—	2	2	no	—
12	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
14	C₂²×C₃×C₅×D₄	—	2	2	no	—
15	C₂²×C₃×C₅×D₄	—	2	2	no	—
16	C₂²×C₃×C₅×D₄	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	complemented
22	C₃×C₅×#124	—	2	2	no	—
23	C₃×C₅×#124	C₂²	1	4	yes	complemented
24	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
25	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₅×#104	C₂²	1	8	yes	complemented
27	C₃×C₅×#100	C₂²	1	4	yes	complemented
28	C₂×C₃×#455	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic
30	C₂×C₅×#137	C₂×C₃	1	2	yes	complemented
31	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic, complemented
32	C₅×#455	C₂×C₃	1	8	yes	direct product factor
33	C₂×C₅×#104	C₂×C₃	1	2	yes	complemented
34	C₂×C₅×#100	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂⁴×C₃×C₅	—	2	2	no	—
36	C₂⁴×C₃×C₅	D₄	1	2	yes	—
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	1	no	—
44	C₂×C₃×C₅×Q₈	—	2	2	no	—
45	C₂×C₃×C₅×Q₈	—	2	2	no	—
46	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
47	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	complemented
48	C₂×C₃×C₅×D₄	—	2	4	no	—
49	C₂×C₃×C₅×D₄	—	2	8	no	—
50	C₂×C₃×C₅×D₄	—	2	8	no	—
51	C₂×C₃×C₅×D₄	—	2	2	no	—
52	C₂×C₃×C₅×D₄	—	2	8	no	—
53	C₂×C₃×C₅×D₄	—	2	8	no	—
54	C₂×C₃×C₅×D₄	—	2	2	no	—
55	C₂×C₃×C₅×D₄	—	2	2	no	—
56	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
57	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
58	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
59	C₂²×C₃×C₄×C₅	—	2	2	no	—
60	C₂²×C₃×C₄×C₅	—	2	2	no	—
61	C₂²×C₃×C₄×C₅	—	2	1	no	—
62	C₂²×C₃×C₄×C₅	—	2	1	no	—
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	complemented
68	C₂×C₃×C₅×C₈	—	2	2	no	—
69	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
70	C₃×C₄²×C₅	—	2	1	no	—
71	C₃×C₄²×C₅	C₂³	1	2	yes	complemented
72	C₂×C₃×H(5,𝔽₂)	C₂×C₅	1	1	yes	characteristic
73	C₂×C₃×#137	C₂×C₅	1	2	yes	complemented
74	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic, complemented
75	C₃×#455	C₂×C₅	1	8	yes	direct product factor
76	C₂×C₃×#104	C₂×C₅	1	2	yes	complemented
77	C₂×C₃×#100	C₂×C₅	1	1	yes	characteristic, complemented
78	C₅×H(5,𝔽₂)	—	2	4	no	—
79	C₅×H(5,𝔽₂)	—	2	2	no	—
80	C₅×H(5,𝔽₂)	C₂²×C₃	1	4	yes	—
81	C₂×C₅×#41	—	2	2	no	—
82	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
83	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
84	C₂²×C₅×D₄	—	2	2	no	—
85	C₂²×C₅×D₄	—	2	2	no	—
86	C₂²×C₅×D₄	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	complemented
92	C₅×#124	—	2	2	no	—
93	C₅×#124	C₂²×C₃	1	4	yes	complemented
94	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
95	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
96	C₅×#104	C₂²×C₃	1	8	yes	complemented
97	C₅×#100	C₂²×C₃	1	4	yes	complemented
98	C₂×#455	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
99	C₂³×C₃×C₅	—	2	8	no	—
100	C₂³×C₃×C₅	—	2	2	no	—
101	C₂³×C₃×C₅	—	2	2	no	—
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	—	4	4	no	—
104	C₂³×C₃×C₅	—	8	4	no	—
105	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
107	C₃×C₅×Q₈	—	2	2	no	—
108	C₃×C₅×Q₈	—	2	4	no	—
109	C₃×C₅×Q₈	—	4	2	no	—
110	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
111	C₃×C₅×D₄	—	2	16	no	—
112	C₃×C₅×D₄	—	2	4	no	—
113	C₃×C₅×D₄	—	2	4	no	—
114	C₃×C₅×D₄	—	2	4	no	—
115	C₃×C₅×D₄	—	2	2	no	—
116	C₃×C₅×D₄	—	2	4	no	—
117	C₃×C₅×D₄	C₂×D₄	1	4	yes	—
118	C₂×C₃×C₄×C₅	—	2	8	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	4	no	—
121	C₂×C₃×C₄×C₅	—	2	4	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	4	2	no	—
125	C₂×C₃×C₄×C₅	—	4	1	no	—
126	C₂×C₃×C₄×C₅	—	4	1	no	—
127	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
129	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
131	C₃×C₅×C₈	—	2	4	no	—
132	C₃×H(5,𝔽₂)	—	2	4	no	—
133	C₃×H(5,𝔽₂)	—	2	2	no	—
134	C₃×H(5,𝔽₂)	C₂²×C₅	1	4	yes	—
135	C₂×C₃×#41	—	2	2	no	—
136	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
137	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
138	C₂²×C₃×D₄	—	2	2	no	—
139	C₂²×C₃×D₄	—	2	2	no	—
140	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
141	C₃×#137	—	2	4	no	—
142	C₃×#137	C₂²×C₅	1	8	yes	complemented
143	C₂×C₃×Q₁₆	—	2	2	no	—
144	C₂×C₃×SD₁₆	—	2	2	no	—
145	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	complemented
146	C₃×#124	—	2	2	no	—
147	C₃×#124	C₂²×C₅	1	4	yes	complemented
148	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
149	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
150	C₃×#104	C₂²×C₅	1	8	yes	complemented
151	C₃×#100	C₂²×C₅	1	4	yes	complemented
152	C₂⁴×C₅	—	2	2	no	—
153	C₂⁴×C₅	C₃×D₄	1	2	yes	—
154	C₅×#41	—	2	8	no	—
155	C₅×#41	—	2	8	no	—
156	C₅×#41	—	2	2	no	—
157	C₅×#41	—	2	2	no	—
158	C₅×#41	C₃×D₄	1	4	yes	—
159	C₅×#41	C₂³×C₃	1	4	yes	—
160	C₂×C₅×Q₈	—	2	1	no	—
161	C₂×C₅×Q₈	—	2	2	no	—
162	C₂×C₅×Q₈	—	2	2	no	—
163	C₂×C₅×Q₈	C₃×D₄	1	2	yes	—
164	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	complemented
165	C₂×C₅×D₄	—	2	4	no	—
166	C₂×C₅×D₄	—	2	8	no	—
167	C₂×C₅×D₄	—	2	8	no	—
168	C₂×C₅×D₄	—	2	2	no	—
169	C₂×C₅×D₄	—	2	8	no	—
170	C₂×C₅×D₄	—	2	8	no	—
171	C₂×C₅×D₄	—	2	2	no	—
172	C₂×C₅×D₄	—	2	2	no	—
173	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
174	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
175	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
176	C₂²×C₄×C₅	—	2	2	no	—
177	C₂²×C₄×C₅	—	2	2	no	—
178	C₂²×C₄×C₅	—	2	1	no	—
179	C₂²×C₄×C₅	—	2	1	no	—
180	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
181	C₅×Q₁₆	—	2	8	no	—
182	C₅×SD₁₆	—	2	8	no	—
183	C₅×M₁₆	—	2	2	no	—
184	C₅×M₁₆	C₂³×C₃	1	4	yes	complemented
185	C₂×C₅×C₈	—	2	2	no	—
186	C₅×C₂²⋊C₄	—	2	8	no	—
187	C₄²×C₅	—	2	1	no	—
188	C₄²×C₅	C₂³×C₃	1	2	yes	complemented
189	C₂×H(5,𝔽₂)	C₂×C₃×C₅	1	1	yes	characteristic
190	C₂×#137	C₂×C₃×C₅	1	2	yes	complemented
191	C₂×#124	C₂×C₃×C₅	1	1	yes	characteristic, complemented
192	#455	C₂×C₃×C₅	1	8	yes	direct product factor
193	C₂×#104	C₂×C₃×C₅	1	2	yes	complemented
194	C₂×#100	C₂×C₃×C₅	1	1	yes	characteristic, complemented
195	C₂²×C₃×C₅	—	2	2	no	—
196	C₂²×C₃×C₅	—	2	4	no	—
197	C₂²×C₃×C₅	—	2	4	no	—
198	C₂²×C₃×C₅	—	4	4	no	—
199	C₂²×C₃×C₅	—	4	4	no	—
200	C₂²×C₃×C₅	—	4	4	no	—
201	C₂²×C₃×C₅	—	8	2	no	—
202	C₂²×C₃×C₅	—	8	8	no	—
203	C₂²×C₃×C₅	#120	1	1	yes	characteristic
204	C₂²×C₃×C₅	#120	1	1	yes	characteristic
205	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
206	C₃×C₄×C₅	—	2	4	no	—
207	C₃×C₄×C₅	—	4	2	no	—
208	C₃×C₄×C₅	—	4	2	no	—
209	C₃×C₄×C₅	#120	1	2	yes	—
210	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
211	C₂⁴×C₃	—	2	2	no	—
212	C₂⁴×C₃	C₅×D₄	1	2	yes	—
213	C₃×#41	—	2	8	no	—
214	C₃×#41	—	2	8	no	—
215	C₃×#41	—	2	2	no	—
216	C₃×#41	—	2	2	no	—
217	C₃×#41	C₅×D₄	1	4	yes	—
218	C₃×#41	C₂³×C₅	1	4	yes	—
219	C₂×C₃×Q₈	—	2	1	no	—
220	C₂×C₃×Q₈	—	2	2	no	—
221	C₂×C₃×Q₈	—	2	2	no	—
222	C₂×C₃×Q₈	C₅×D₄	1	2	yes	—
223	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	complemented
224	C₂×C₃×D₄	—	2	4	no	—
225	C₂×C₃×D₄	—	2	8	no	—
226	C₂×C₃×D₄	—	2	8	no	—
227	C₂×C₃×D₄	—	2	2	no	—
228	C₂×C₃×D₄	—	2	8	no	—
229	C₂×C₃×D₄	—	2	8	no	—
230	C₂×C₃×D₄	—	2	2	no	—
231	C₂×C₃×D₄	—	2	2	no	—
232	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
233	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
234	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
235	C₂²×C₃×C₄	—	2	2	no	—
236	C₂²×C₃×C₄	—	2	2	no	—
237	C₂²×C₃×C₄	—	2	1	no	—
238	C₂²×C₃×C₄	—	2	1	no	—
239	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
240	C₃×Q₁₆	—	2	8	no	—
241	C₃×SD₁₆	—	2	8	no	—
242	C₃×M₁₆	—	2	2	no	—
243	C₃×M₁₆	C₂³×C₅	1	4	yes	complemented
244	C₂×C₃×C₈	—	2	2	no	—
245	C₃×C₂²⋊C₄	—	2	8	no	—
246	C₃×C₄²	—	2	1	no	—
247	C₃×C₄²	C₂³×C₅	1	2	yes	complemented
248	C₂³×C₅	—	2	8	no	—
249	C₂³×C₅	—	2	2	no	—
250	C₂³×C₅	—	2	2	no	—
251	C₂³×C₅	—	2	2	no	—
252	C₂³×C₅	—	4	4	no	—
253	C₂³×C₅	—	8	4	no	—
254	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
255	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
256	C₅×Q₈	—	2	2	no	—
257	C₅×Q₈	—	2	4	no	—
258	C₅×Q₈	—	4	2	no	—
259	C₅×Q₈	C₂×C₃×D₄	1	4	yes	—
260	C₅×D₄	—	2	16	no	—
261	C₅×D₄	—	2	4	no	—
262	C₅×D₄	—	2	4	no	—
263	C₅×D₄	—	2	4	no	—
264	C₅×D₄	—	2	2	no	—
265	C₅×D₄	—	2	4	no	—
266	C₅×D₄	C₂×C₃×D₄	1	4	yes	—
267	C₂×C₄×C₅	—	2	8	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	2	4	no	—
270	C₂×C₄×C₅	—	2	4	no	—
271	C₂×C₄×C₅	—	2	2	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	—	4	2	no	—
274	C₂×C₄×C₅	—	4	1	no	—
275	C₂×C₄×C₅	—	4	1	no	—
276	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
278	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
279	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
280	C₅×C₈	—	2	4	no	—
281	H(5,𝔽₂)	—	2	4	no	—
282	H(5,𝔽₂)	—	2	2	no	—
283	H(5,𝔽₂)	C₂²×C₃×C₅	1	4	yes	—
284	C₂×#41	—	2	2	no	—
285	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
286	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
287	C₂²×D₄	—	2	2	no	—
288	C₂²×D₄	—	2	2	no	—
289	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
290	#137	—	2	4	no	—
291	#137	C₂²×C₃×C₅	1	8	yes	complemented
292	C₂×Q₁₆	—	2	2	no	—
293	C₂×SD₁₆	—	2	2	no	—
294	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	complemented
295	#124	—	2	2	no	—
296	#124	C₂²×C₃×C₅	1	4	yes	complemented
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
299	#104	C₂²×C₃×C₅	1	8	yes	complemented
300	#100	C₂²×C₃×C₅	1	4	yes	complemented
301	C₂×C₃×C₅	—	2	1	no	—
302	C₂×C₃×C₅	—	2	1	no	—
303	C₂×C₃×C₅	—	4	4	no	—
304	C₂×C₃×C₅	—	4	4	no	—
305	C₂×C₃×C₅	#455	1	2	yes	direct product factor
306	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
307	C₂³×C₃	—	2	8	no	—
308	C₂³×C₃	—	2	2	no	—
309	C₂³×C₃	—	2	2	no	—
310	C₂³×C₃	—	2	2	no	—
311	C₂³×C₃	—	4	4	no	—
312	C₂³×C₃	—	8	4	no	—
313	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
314	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
315	C₃×Q₈	—	2	2	no	—
316	C₃×Q₈	—	2	4	no	—
317	C₃×Q₈	—	4	2	no	—
318	C₃×Q₈	C₂×C₅×D₄	1	4	yes	—
319	C₃×D₄	—	2	16	no	—
320	C₃×D₄	—	2	4	no	—
321	C₃×D₄	—	2	4	no	—
322	C₃×D₄	—	2	4	no	—
323	C₃×D₄	—	2	2	no	—
324	C₃×D₄	—	2	4	no	—
325	C₃×D₄	C₂×C₅×D₄	1	4	yes	—
326	C₂×C₃×C₄	—	2	8	no	—
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	—	2	4	no	—
329	C₂×C₃×C₄	—	2	4	no	—
330	C₂×C₃×C₄	—	2	2	no	—
331	C₂×C₃×C₄	—	2	2	no	—
332	C₂×C₃×C₄	—	4	2	no	—
333	C₂×C₃×C₄	—	4	1	no	—
334	C₂×C₃×C₄	—	4	1	no	—
335	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
336	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
337	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
338	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
339	C₃×C₈	—	2	4	no	—
340	C₂²×C₅	—	2	2	no	—
341	C₂²×C₅	—	2	4	no	—
342	C₂²×C₅	—	2	4	no	—
343	C₂²×C₅	—	4	4	no	—
344	C₂²×C₅	—	4	4	no	—
345	C₂²×C₅	—	4	4	no	—
346	C₂²×C₅	—	8	2	no	—
347	C₂²×C₅	—	8	8	no	—
348	C₂²×C₅	C₃×#120	1	1	yes	characteristic
349	C₂²×C₅	C₃×#120	1	1	yes	characteristic
350	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
351	C₄×C₅	—	2	4	no	—
352	C₄×C₅	—	4	2	no	—
353	C₄×C₅	—	4	2	no	—
354	C₄×C₅	C₃×#120	1	2	yes	—
355	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
356	C₂⁴	—	2	2	no	—
357	C₂⁴	C₃×C₅×D₄	1	2	yes	—
358	#41	—	2	8	no	—
359	#41	—	2	8	no	—
360	#41	—	2	2	no	—
361	#41	—	2	2	no	—
362	#41	C₃×C₅×D₄	1	4	yes	—
363	#41	C₂³×C₃×C₅	1	4	yes	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	C₃×C₅×D₄	1	2	yes	—
368	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	complemented
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	8	no	—
371	C₂×D₄	—	2	8	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	8	no	—
374	C₂×D₄	—	2	8	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
378	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
379	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
385	Q₁₆	—	2	8	no	—
386	SD₁₆	—	2	8	no	—
387	M₁₆	—	2	2	no	—
388	M₁₆	C₂³×C₃×C₅	1	4	yes	complemented
389	C₂×C₈	—	2	2	no	—
390	C₂²⋊C₄	—	2	8	no	—
391	C₄²	—	2	1	no	—
392	C₄²	C₂³×C₃×C₅	1	2	yes	complemented
393	C₃×C₅	C₂×#455	1	1	yes	characteristic, direct product factor, Hall
394	C₂²×C₃	—	2	2	no	—
395	C₂²×C₃	—	2	4	no	—
396	C₂²×C₃	—	2	4	no	—
397	C₂²×C₃	—	4	4	no	—
398	C₂²×C₃	—	4	4	no	—
399	C₂²×C₃	—	4	4	no	—
400	C₂²×C₃	—	8	2	no	—
401	C₂²×C₃	—	8	8	no	—
402	C₂²×C₃	C₅×#120	1	1	yes	characteristic
403	C₂²×C₃	C₅×#120	1	1	yes	characteristic
404	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
405	C₃×C₄	—	2	4	no	—
406	C₃×C₄	—	4	2	no	—
407	C₃×C₄	—	4	2	no	—
408	C₃×C₄	C₅×#120	1	2	yes	—
409	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
410	C₂×C₅	—	2	1	no	—
411	C₂×C₅	—	2	1	no	—
412	C₂×C₅	—	4	4	no	—
413	C₂×C₅	—	4	4	no	—
414	C₂×C₅	C₃×#455	1	2	yes	direct product factor
415	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
416	C₂³	—	2	8	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	4	4	no	—
421	C₂³	—	8	4	no	—
422	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
423	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
424	Q₈	—	2	2	no	—
425	Q₈	—	2	4	no	—
426	Q₈	—	4	2	no	—
427	Q₈	C₂×C₃×C₅×D₄	1	4	yes	—
428	D₄	—	2	16	no	—
429	D₄	—	2	4	no	—
430	D₄	—	2	4	no	—
431	D₄	—	2	4	no	—
432	D₄	—	2	2	no	—
433	D₄	—	2	4	no	—
434	D₄	C₂×C₃×C₅×D₄	1	4	yes	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
445	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
446	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
447	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
448	C₈	—	2	4	no	—
449	C₂×C₃	—	2	1	no	—
450	C₂×C₃	—	2	1	no	—
451	C₂×C₃	—	4	4	no	—
452	C₂×C₃	—	4	4	no	—
453	C₂×C₃	C₅×#455	1	2	yes	direct product factor
454	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
455	C₅	C₂×C₃×#455	1	1	yes	characteristic, direct product factor, Sylow
456	C₂²	—	2	2	no	—
457	C₂²	—	2	4	no	—
458	C₂²	—	2	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	8	2	no	—
463	C₂²	—	8	8	no	—
464	C₂²	C₃×C₅×#120	1	1	yes	characteristic
465	C₂²	C₃×C₅×#120	1	1	yes	characteristic
466	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
467	C₄	—	2	4	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	C₃×C₅×#120	1	2	yes	—
471	C₄	C₂²×C₃×C₅×D₄	1	2	yes	—
472	C₃	C₂×C₅×#455	1	1	yes	characteristic, direct product factor, Sylow
473	C₂	—	2	1	no	—
474	C₂	—	2	1	no	—
475	C₂	—	4	4	no	—
476	C₂	—	4	4	no	—
477	C₂	C₃×C₅×#455	1	2	yes	direct product factor
478	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×H(5,𝔽₂)	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×#124	C₂	semidirect
4. C₃×C₅×#455	C₂	direct (N × H)
5. C₂×C₃×C₅×#104	C₂	semidirect
6. C₂×C₃×C₅×#100	C₂	semidirect
7. C₂×C₅×#455	C₃	direct (N × H)
13. C₂²×C₃×C₅×Q₈	C₂²	semidirect
18. C₃×C₅×#137	C₂²	semidirect
21. C₂×C₃×C₅×M₁₆	C₂²	semidirect
23. C₃×C₅×#124	C₂²	semidirect
25. C₂×C₃×C₄²×C₅	C₂²	semidirect
26. C₃×C₅×#104	C₂²	semidirect
27. C₃×C₅×#100	C₂²	semidirect
28. C₂×C₃×#455	C₅	direct (N × H)
30. C₂×C₅×#137	C₂×C₃	semidirect
31. C₂×C₅×#124	C₂×C₃	semidirect
32. C₅×#455	C₂×C₃	direct (N × H)
33. C₂×C₅×#104	C₂×C₃	semidirect
34. C₂×C₅×#100	C₂×C₃	semidirect
47. C₂×C₃×C₅×Q₈	C₂³	semidirect
67. C₃×C₅×M₁₆	C₂³	semidirect
71. C₃×C₄²×C₅	C₂³	semidirect
73. C₂×C₃×#137	C₂×C₅	semidirect
74. C₂×C₃×#124	C₂×C₅	semidirect
75. C₃×#455	C₂×C₅	direct (N × H)
76. C₂×C₃×#104	C₂×C₅	semidirect
77. C₂×C₃×#100	C₂×C₅	semidirect
83. C₂²×C₅×Q₈	C₂²×C₃	semidirect
88. C₅×#137	C₂²×C₃	semidirect
91. C₂×C₅×M₁₆	C₂²×C₃	semidirect
93. C₅×#124	C₂²×C₃	semidirect
95. C₂×C₄²×C₅	C₂²×C₃	semidirect
96. C₅×#104	C₂²×C₃	semidirect
97. C₅×#100	C₂²×C₃	semidirect
98. C₂×#455	C₃×C₅	direct (N × H)
137. C₂²×C₃×Q₈	C₂²×C₅	semidirect
142. C₃×#137	C₂²×C₅	semidirect
145. C₂×C₃×M₁₆	C₂²×C₅	semidirect
147. C₃×#124	C₂²×C₅	semidirect
149. C₂×C₃×C₄²	C₂²×C₅	semidirect
150. C₃×#104	C₂²×C₅	semidirect
151. C₃×#100	C₂²×C₅	semidirect
164. C₂×C₅×Q₈	C₂³×C₃	semidirect
184. C₅×M₁₆	C₂³×C₃	semidirect
188. C₄²×C₅	C₂³×C₃	semidirect
190. C₂×#137	C₂×C₃×C₅	semidirect
191. C₂×#124	C₂×C₃×C₅	semidirect
192. #455	C₂×C₃×C₅	direct (N × H)
193. C₂×#104	C₂×C₃×C₅	semidirect
194. C₂×#100	C₂×C₃×C₅	semidirect
223. C₂×C₃×Q₈	C₂³×C₅	semidirect
243. C₃×M₁₆	C₂³×C₅	semidirect
247. C₃×C₄²	C₂³×C₅	semidirect
286. C₂²×Q₈	C₂²×C₃×C₅	semidirect
291. #137	C₂²×C₃×C₅	semidirect
294. C₂×M₁₆	C₂²×C₃×C₅	semidirect
296. #124	C₂²×C₃×C₅	semidirect
298. C₂×C₄²	C₂²×C₃×C₅	semidirect
299. #104	C₂²×C₃×C₅	semidirect
300. #100	C₂²×C₃×C₅	semidirect
305. C₂×C₃×C₅	#455	direct (N × H)
368. C₂×Q₈	C₂³×C₃×C₅	semidirect
388. M₁₆	C₂³×C₃×C₅	semidirect
392. C₄²	C₂³×C₃×C₅	semidirect
393. C₃×C₅	C₂×#455	direct (N × H)
414. C₂×C₅	C₃×#455	direct (N × H)
453. C₂×C₃	C₅×#455	direct (N × H)
455. C₅	C₂×C₃×#455	direct (N × H)
472. C₃	C₂×C₅×#455	direct (N × H)
477. C₂	C₃×C₅×#455	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×H(5,𝔽₂)	2
C₂×C₃×C₅×#137	2
C₂×C₃×C₅×#124	2
C₃×C₅×#455	2
C₂×C₃×C₅×#104	2
C₂×C₃×C₅×#100	2
C₂×C₅×#455	3
C₂×C₃×#455	5

Subgroups — C2×C3×C5×#455 #14276049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#455 #14276049