Subgroups — C₂×C₅×#5054 #14426121

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#216	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×#214	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#835	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#832	C₂	1	1	yes	maximal, characteristic
7	C₅×#5054	C₂	1	8	yes	maximal, direct product factor
8	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#464	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
13	C₃×C₅×#124	—	2	2	no	—
14	C₃×C₅×#124	C₂²	1	4	yes	—
15	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
16	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₅×#216	—	2	4	no	—
19	C₂×C₅×#216	C₂²	1	4	yes	complemented
20	C₂×C₅×#214	—	2	4	no	—
21	C₂×C₅×#214	C₂²	1	4	yes	—
22	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
23	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
24	C₂×C₄×C₅×Dic₃	—	2	1	no	—
25	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
26	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
27	C₄×C₅×Dic₆	—	2	2	no	—
28	C₄×C₅×Dic₆	C₂²	1	4	yes	complemented
29	C₅×#835	C₂²	1	4	yes	complemented
30	C₅×#832	C₂²	1	4	yes	—
31	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
32	C₂×#5054	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂²×C₅×Q₁₆	—	3	1	no	—
34	C₂²×C₅×SD₁₆	—	3	1	no	—
35	C₂×C₅×#124	D₃	1	1	yes	characteristic
36	C₂×C₄×C₅×Q₈	—	3	1	no	—
37	C₅×#464	—	3	8	no	—
38	C₂×C₅×C₄⋊C₈	—	3	1	no	—
39	C₂×C₅×#103	—	3	1	no	—
40	C₂×C₅×#102	—	3	1	no	—
41	C₂⁴×C₃×C₅	—	2	1	no	—
42	C₂×C₃×C₅×Q₈	—	2	1	no	—
43	C₂×C₃×C₅×Q₈	—	2	2	no	—
44	C₂×C₃×C₅×Q₈	—	2	2	no	—
45	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
46	C₂×C₃×C₅×D₄	—	2	2	no	—
47	C₂×C₃×C₅×D₄	—	2	1	no	—
48	C₂×C₃×C₅×D₄	—	2	2	no	—
49	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	—	2	1	no	—
51	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₅×Dic₃	—	2	1	no	—
55	C₂²×C₅×Dic₃	—	2	1	no	—
56	C₂×C₅×Dic₆	—	2	1	no	—
57	C₂×C₅×Dic₆	—	2	2	no	—
58	C₂×C₅×Dic₆	D₄	1	4	yes	—
59	C₂×C₅×Dic₆	C₂³	1	2	yes	—
60	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
61	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
62	C₃×C₄²×C₅	D₄	1	2	yes	—
63	C₃×C₄²×C₅	C₂³	1	2	yes	—
64	C₅×#216	—	2	8	no	—
65	C₅×#214	—	2	8	no	—
66	C₅×C₄⋊Dic₃	—	2	1	no	—
67	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
68	C₅×Dic₃⋊C₄	—	2	4	no	—
69	C₄×C₅×Dic₃	—	2	4	no	—
70	C₂×C₅×C₃⋊C₈	—	2	2	no	—
71	C₂×C₅×C₃⋊C₈	—	2	2	no	—
72	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
73	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
74	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic
75	C₂²×#216	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂²×#214	C₂×C₅	1	1	yes	characteristic
77	C₂×C₄×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂×#835	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂×#832	C₂×C₅	1	1	yes	characteristic
80	#5054	C₂×C₅	1	8	yes	direct product factor
81	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
82	C₂²×C₅×Q₈	—	3	1	no	—
83	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
84	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
85	C₂×C₅×Q₁₆	—	3	4	no	—
86	C₂×C₅×Q₁₆	—	6	4	no	—
87	C₂×C₅×SD₁₆	—	3	4	no	—
88	C₂×C₅×SD₁₆	—	6	4	no	—
89	C₂²×C₅×C₈	—	3	1	no	—
90	C₂²×C₅×C₈	—	3	1	no	—
91	C₅×#124	—	2	2	no	—
92	C₅×#124	C₂×D₃	1	4	yes	—
93	C₄×C₅×Q₈	—	3	4	no	—
94	C₄×C₅×Q₈	—	6	2	no	—
95	C₂×C₅×C₄⋊C₄	—	3	1	no	—
96	C₂×C₅×C₄⋊C₄	—	6	1	no	—
97	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₄²×C₅	—	6	1	no	—
100	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
101	C₅×C₄⋊C₈	—	3	4	no	—
102	C₅×#103	—	3	4	no	—
103	C₅×#102	—	3	4	no	—
104	C₂×#464	—	3	1	no	Sylow
105	C₂³×C₃×C₅	—	2	2	no	—
106	C₂³×C₃×C₅	—	4	2	no	—
107	C₂³×C₃×C₅	—	4	2	no	—
108	C₂³×C₃×C₅	—	4	2	no	—
109	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
110	C₃×C₅×Q₈	—	2	2	no	—
111	C₃×C₅×Q₈	—	2	2	no	—
112	C₃×C₅×Q₈	—	4	2	no	—
113	C₃×C₅×D₄	—	2	2	no	—
114	C₃×C₅×D₄	—	2	2	no	—
115	C₃×C₅×D₄	—	4	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	—	4	2	no	—
120	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
121	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
122	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
124	C₂×C₃×C₄×C₅	#41	1	2	yes	—
125	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
126	C₂×C₅×Dic₃	—	2	4	no	—
127	C₂×C₅×Dic₃	—	2	2	no	—
128	C₂×C₅×Dic₃	—	2	2	no	—
129	C₂×C₅×Dic₃	—	4	2	no	—
130	C₅×Dic₆	—	2	4	no	—
131	C₅×Dic₆	—	2	2	no	—
132	C₅×Dic₆	C₂×D₄	1	4	yes	—
133	C₅×C₃⋊C₈	—	2	2	no	—
134	C₅×C₃⋊C₈	—	2	2	no	—
135	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
136	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
137	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
138	C₃×#124	—	2	2	no	—
139	C₃×#124	C₂²×C₅	1	4	yes	—
140	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
141	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
142	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
143	C₂×#216	—	2	4	no	—
144	C₂×#216	C₂²×C₅	1	4	yes	complemented
145	C₂×#214	—	2	4	no	—
146	C₂×#214	C₂²×C₅	1	4	yes	—
147	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
148	C₂×Dic₃⋊C₄	—	2	1	no	—
149	C₂×C₄×Dic₃	—	2	1	no	—
150	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
151	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
152	C₄×Dic₆	—	2	2	no	—
153	C₄×Dic₆	C₂²×C₅	1	4	yes	complemented
154	#835	C₂²×C₅	1	4	yes	complemented
155	#832	C₂²×C₅	1	4	yes	—
156	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	4	yes	complemented
157	C₂⁴×C₅	—	2	1	no	—
158	C₂×C₅×Q₈	—	2	1	no	—
159	C₂×C₅×Q₈	—	2	2	no	—
160	C₂×C₅×Q₈	—	2	2	no	—
161	C₂×C₅×Q₈	—	3	4	no	—
162	C₂×C₅×Q₈	—	3	2	no	—
163	C₂×C₅×Q₈	—	6	2	no	—
164	C₂×C₅×Q₈	—	6	1	no	—
165	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
166	C₂×C₅×D₄	—	2	2	no	—
167	C₂×C₅×D₄	—	2	2	no	—
168	C₂×C₅×D₄	—	2	1	no	—
169	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
170	C₂²×C₄×C₅	—	2	1	no	—
171	C₂²×C₄×C₅	—	6	1	no	—
172	C₂²×C₄×C₅	—	6	1	no	—
173	C₂²×C₄×C₅	#67	1	1	yes	characteristic
174	C₂²×C₄×C₅	#67	1	1	yes	characteristic
175	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
176	C₅×Q₁₆	—	6	8	no	—
177	C₅×SD₁₆	—	6	8	no	—
178	C₂×C₅×C₈	—	3	2	no	—
179	C₂×C₅×C₈	—	3	2	no	—
180	C₂×C₅×C₈	—	6	2	no	—
181	C₂×C₅×C₈	—	6	2	no	—
182	C₅×C₄⋊C₄	—	3	2	no	—
183	C₅×C₄⋊C₄	—	6	1	no	—
184	C₅×C₄⋊C₄	—	6	4	no	—
185	C₅×C₂²⋊C₄	—	2	4	no	—
186	C₅×C₂²⋊C₄	—	2	4	no	—
187	C₄²×C₅	—	6	4	no	—
188	C₄²×C₅	#67	1	2	yes	—
189	C₄²×C₅	C₂²×D₃	1	2	yes	—
190	C₂²×Q₁₆	—	3	1	no	—
191	C₂²×SD₁₆	—	3	1	no	—
192	C₂×#124	C₅×D₃	1	1	yes	characteristic
193	C₂×C₄×Q₈	—	3	1	no	—
194	#464	—	3	8	no	—
195	C₂×C₄⋊C₈	—	3	1	no	—
196	C₂×#103	—	3	1	no	—
197	C₂×#102	—	3	1	no	—
198	C₂²×C₃×C₅	—	4	2	no	—
199	C₂²×C₃×C₅	—	4	2	no	—
200	C₂²×C₃×C₅	—	4	2	no	—
201	C₂²×C₃×C₅	—	8	4	no	—
202	C₂²×C₃×C₅	#121	1	2	yes	—
203	C₂²×C₃×C₅	#135	1	2	yes	—
204	C₂²×C₃×C₅	#137	1	2	yes	—
205	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
206	C₃×C₄×C₅	—	2	2	no	—
207	C₃×C₄×C₅	—	2	2	no	—
208	C₃×C₄×C₅	—	4	2	no	—
209	C₃×C₄×C₅	#121	1	2	yes	—
210	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
211	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
212	C₅×Dic₃	—	2	4	no	—
213	C₅×Dic₃	—	4	2	no	—
214	C₂⁴×C₃	—	2	1	no	—
215	C₂×C₃×Q₈	—	2	1	no	—
216	C₂×C₃×Q₈	—	2	2	no	—
217	C₂×C₃×Q₈	—	2	2	no	—
218	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
219	C₂×C₃×D₄	—	2	2	no	—
220	C₂×C₃×D₄	—	2	1	no	—
221	C₂×C₃×D₄	—	2	2	no	—
222	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
223	C₂²×C₃×C₄	—	2	1	no	—
224	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
227	C₂²×Dic₃	—	2	1	no	—
228	C₂²×Dic₃	—	2	1	no	—
229	C₂×Dic₆	—	2	1	no	—
230	C₂×Dic₆	—	2	2	no	—
231	C₂×Dic₆	C₅×D₄	1	4	yes	—
232	C₂×Dic₆	C₂³×C₅	1	2	yes	—
233	C₃×C₂²⋊C₄	—	2	4	no	—
234	C₃×C₂²⋊C₄	—	2	4	no	—
235	C₃×C₄²	C₅×D₄	1	2	yes	—
236	C₃×C₄²	C₂³×C₅	1	2	yes	—
237	#216	—	2	8	no	—
238	#214	—	2	8	no	—
239	C₄⋊Dic₃	—	2	1	no	—
240	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
241	Dic₃⋊C₄	—	2	4	no	—
242	C₄×Dic₃	—	2	4	no	—
243	C₂×C₃⋊C₈	—	2	2	no	—
244	C₂×C₃⋊C₈	—	2	2	no	—
245	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
246	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
247	C₂³×C₅	—	2	2	no	—
248	C₂³×C₅	—	4	2	no	—
249	C₂³×C₅	—	4	2	no	—
250	C₂³×C₅	—	4	2	no	—
251	C₂³×C₅	C₂×#67	1	1	yes	characteristic
252	C₅×Q₈	—	2	2	no	—
253	C₅×Q₈	—	2	2	no	—
254	C₅×Q₈	—	3	4	no	—
255	C₅×Q₈	—	4	2	no	—
256	C₅×Q₈	—	6	4	no	—
257	C₅×Q₈	—	6	2	no	—
258	C₅×D₄	—	2	2	no	—
259	C₅×D₄	—	2	2	no	—
260	C₅×D₄	—	4	2	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	4	2	no	—
265	C₂×C₄×C₅	—	6	4	no	—
266	C₂×C₄×C₅	—	6	2	no	—
267	C₂×C₄×C₅	—	6	2	no	—
268	C₂×C₄×C₅	—	12	2	no	—
269	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
270	C₂×C₄×C₅	#237	1	2	yes	—
271	C₂×C₄×C₅	C₂×#67	1	2	yes	—
272	C₂×C₄×C₅	C₂×#67	1	2	yes	—
273	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
274	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
275	C₅×C₈	—	6	2	no	—
276	C₅×C₈	—	6	2	no	—
277	C₂²×Q₈	—	3	1	no	—
278	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
279	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
280	C₂×Q₁₆	—	3	4	no	—
281	C₂×Q₁₆	—	6	4	no	—
282	C₂×SD₁₆	—	3	4	no	—
283	C₂×SD₁₆	—	6	4	no	—
284	C₂²×C₈	—	3	1	no	—
285	C₂²×C₈	—	3	1	no	—
286	#124	—	2	2	no	—
287	#124	C₂×C₅×D₃	1	4	yes	—
288	C₄×Q₈	—	3	4	no	—
289	C₄×Q₈	—	6	2	no	—
290	C₂×C₄⋊C₄	—	3	1	no	—
291	C₂×C₄⋊C₄	—	6	1	no	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₄²	—	6	1	no	—
295	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
296	C₄⋊C₈	—	3	4	no	—
297	#103	—	3	4	no	—
298	#102	—	3	4	no	—
299	C₂×C₃×C₅	—	8	2	no	—
300	C₂×C₃×C₅	#464	1	4	yes	complemented
301	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
302	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
303	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
304	C₂³×C₃	—	2	2	no	—
305	C₂³×C₃	—	4	2	no	—
306	C₂³×C₃	—	4	2	no	—
307	C₂³×C₃	—	4	2	no	—
308	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
309	C₃×Q₈	—	2	2	no	—
310	C₃×Q₈	—	2	2	no	—
311	C₃×Q₈	—	4	2	no	—
312	C₃×D₄	—	2	2	no	—
313	C₃×D₄	—	2	2	no	—
314	C₃×D₄	—	4	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	—	4	2	no	—
319	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
320	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
321	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
322	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
323	C₂×C₃×C₄	C₅×#41	1	2	yes	—
324	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
325	C₂×Dic₃	—	2	4	no	—
326	C₂×Dic₃	—	2	2	no	—
327	C₂×Dic₃	—	2	2	no	—
328	C₂×Dic₃	—	4	2	no	—
329	Dic₆	—	2	4	no	—
330	Dic₆	—	2	2	no	—
331	Dic₆	C₂×C₅×D₄	1	4	yes	—
332	C₃⋊C₈	—	2	2	no	—
333	C₃⋊C₈	—	2	2	no	—
334	C₂²×C₅	—	4	2	no	—
335	C₂²×C₅	—	4	2	no	—
336	C₂²×C₅	—	4	2	no	—
337	C₂²×C₅	—	8	4	no	—
338	C₂²×C₅	#938	1	2	yes	—
339	C₂²×C₅	#950	1	2	yes	—
340	C₂²×C₅	#951	1	2	yes	—
341	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
342	C₄×C₅	—	2	2	no	—
343	C₄×C₅	—	2	2	no	—
344	C₄×C₅	—	4	2	no	—
345	C₄×C₅	—	6	4	no	—
346	C₄×C₅	—	12	2	no	—
347	C₄×C₅	#938	1	2	yes	—
348	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
349	C₄×C₅	C₂×#237	1	1	yes	characteristic
350	C₂⁴	—	2	1	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	3	4	no	—
355	C₂×Q₈	—	3	2	no	—
356	C₂×Q₈	—	6	2	no	—
357	C₂×Q₈	—	6	1	no	—
358	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	6	1	no	—
365	C₂²×C₄	—	6	1	no	—
366	C₂²×C₄	C₅×#67	1	1	yes	characteristic
367	C₂²×C₄	C₅×#67	1	1	yes	characteristic
368	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
369	Q₁₆	—	6	8	no	—
370	SD₁₆	—	6	8	no	—
371	C₂×C₈	—	3	2	no	—
372	C₂×C₈	—	3	2	no	—
373	C₂×C₈	—	6	2	no	—
374	C₂×C₈	—	6	2	no	—
375	C₄⋊C₄	—	3	2	no	—
376	C₄⋊C₄	—	6	1	no	—
377	C₄⋊C₄	—	6	4	no	—
378	C₂²⋊C₄	—	2	4	no	—
379	C₂²⋊C₄	—	2	4	no	—
380	C₄²	—	6	4	no	—
381	C₄²	C₅×#67	1	2	yes	—
382	C₄²	C₂²×C₅×D₃	1	2	yes	—
383	C₃×C₅	C₂×#464	1	1	yes	characteristic, complemented, Hall
384	C₂²×C₃	—	4	2	no	—
385	C₂²×C₃	—	4	2	no	—
386	C₂²×C₃	—	4	2	no	—
387	C₂²×C₃	—	8	4	no	—
388	C₂²×C₃	C₅×#121	1	2	yes	—
389	C₂²×C₃	C₅×#135	1	2	yes	—
390	C₂²×C₃	C₅×#137	1	2	yes	—
391	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
392	C₃×C₄	—	2	2	no	—
393	C₃×C₄	—	2	2	no	—
394	C₃×C₄	—	4	2	no	—
395	C₃×C₄	C₅×#121	1	2	yes	—
396	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
397	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
398	Dic₃	—	2	4	no	—
399	Dic₃	—	4	2	no	—
400	C₂×C₅	—	8	2	no	—
401	C₂×C₅	#5054	1	4	yes	direct product factor
402	C₂×C₅	C₂×#938	1	1	yes	characteristic
403	C₂×C₅	C₂×#950	1	1	yes	characteristic
404	C₂×C₅	C₂×#951	1	1	yes	characteristic
405	C₂³	—	2	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	C₂×C₅×#67	1	1	yes	characteristic
410	Q₈	—	2	2	no	—
411	Q₈	—	2	2	no	—
412	Q₈	—	3	4	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	6	4	no	—
415	Q₈	—	6	2	no	—
416	D₄	—	2	2	no	—
417	D₄	—	2	2	no	—
418	D₄	—	4	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	6	4	no	—
424	C₂×C₄	—	6	2	no	—
425	C₂×C₄	—	6	2	no	—
426	C₂×C₄	—	12	2	no	—
427	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
428	C₂×C₄	C₅×#237	1	2	yes	—
429	C₂×C₄	C₂×C₅×#67	1	2	yes	—
430	C₂×C₄	C₂×C₅×#67	1	2	yes	—
431	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
432	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
433	C₈	—	6	2	no	—
434	C₈	—	6	2	no	—
435	C₂×C₃	—	8	2	no	—
436	C₂×C₃	C₅×#464	1	4	yes	complemented
437	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
438	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
439	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
440	C₅	C₂×#5054	1	1	yes	characteristic, direct product factor, Sylow
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	8	4	no	—
445	C₂²	C₅×#938	1	2	yes	—
446	C₂²	C₅×#950	1	2	yes	—
447	C₂²	C₅×#951	1	2	yes	—
448	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	6	4	no	—
453	C₄	—	12	2	no	—
454	C₄	C₅×#938	1	2	yes	—
455	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
456	C₄	C₂×C₅×#237	1	1	yes	characteristic
457	C₃	C₂×C₅×#464	1	1	yes	characteristic, complemented, Sylow
458	C₂	—	8	2	no	—
459	C₂	C₅×#5054	1	4	yes	direct product factor
460	C₂	C₂×C₅×#938	1	1	yes	characteristic
461	C₂	C₂×C₅×#950	1	1	yes	characteristic
462	C₂	C₂×C₅×#951	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#124	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×C₅×D₄	C₂²
hypercenter	C₂×C₅×#124	D₃
hypocenter	C₃	C₂×C₅×#464
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₅×#124

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×#216	C₂	semidirect
4. C₂×C₄×C₅×Dic₆	C₂	semidirect
5. C₂×C₅×#835	C₂	semidirect
7. C₅×#5054	C₂	direct (N × H)
8. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
19. C₂×C₅×#216	C₂²	semidirect
28. C₄×C₅×Dic₆	C₂²	semidirect
29. C₅×#835	C₂²	semidirect
31. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
32. C₂×#5054	C₅	direct (N × H)
75. C₂²×#216	C₂×C₅	semidirect
77. C₂×C₄×Dic₆	C₂×C₅	semidirect
78. C₂×#835	C₂×C₅	semidirect
80. #5054	C₂×C₅	direct (N × H)
81. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
144. C₂×#216	C₂²×C₅	semidirect
153. C₄×Dic₆	C₂²×C₅	semidirect
154. #835	C₂²×C₅	semidirect
156. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
300. C₂×C₃×C₅	#464	semidirect
383. C₃×C₅	C₂×#464	semidirect
401. C₂×C₅	#5054	direct (N × H)
436. C₂×C₃	C₅×#464	semidirect
440. C₅	C₂×#5054	direct (N × H)
457. C₃	C₂×C₅×#464	semidirect
459. C₂	C₅×#5054	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×#124	2
C₂²×C₅×#216	2
C₂²×C₅×#214	2
C₂×C₄×C₅×Dic₆	2
C₂×C₅×#835	2
C₂×C₅×#832	2
C₅×#5054	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₂×C₅×#464	3
C₂×#5054	5

Subgroups — C2×C5×#5054 #14426121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5054 #14426121