Subgroups — C₂×C₅×#5833 #14480563

Order 1920.

3280 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5833	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅×#946	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#939	C₂	1	4	yes	maximal, complemented
6	C₂×C₅×#938	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#930	C₂	1	2	yes	maximal, complemented
8	C₂²×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#924	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#537	—	3	1	no	maximal, Hall
11	C₂×C₃×C₅×#41	—	2	8	no	—
12	C₂×C₃×C₅×#41	C₂²	1	8	yes	complemented
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
16	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
17	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
18	C₂²×C₅×#67	C₂²	1	2	yes	—
19	C₂²×C₅×#67	C₂²	1	4	yes	—
20	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
21	C₂×C₅×#235	—	2	8	no	—
22	C₂×C₅×#235	C₂²	1	8	yes	complemented
23	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
24	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
25	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
26	C₂×C₅×#217	C₂²	1	4	yes	—
27	C₅×#946	C₂²	1	16	yes	complemented
28	C₅×#939	C₂²	1	32	yes	complemented
29	C₅×#938	C₂²	1	16	yes	complemented
30	C₅×#930	C₂²	1	16	yes	complemented
31	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
32	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
33	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
34	C₂×C₅×C₄⋊Dic₃	C₂²	1	8	yes	complemented
35	C₅×#924	C₂²	1	16	yes	complemented
36	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
37	C₂×#5833	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
38	C₂²×C₅×#41	—	3	1	no	—
39	C₂²×C₅×#41	D₃	1	1	yes	characteristic, complemented
40	C₅×#537	—	3	16	no	—
41	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
42	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
43	C₂×C₅×#121	—	3	2	no	—
44	C₂×C₅×#121	—	3	4	no	—
45	C₂×C₅×#121	—	3	2	no	—
46	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
47	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
48	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
49	C₂³×C₅×D₃	C₂³	1	2	yes	—
50	C₃×C₅×#41	—	2	32	no	—
51	C₂×C₃×C₅×Q₈	—	2	4	no	—
52	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
53	C₂×C₃×C₅×D₄	—	2	8	no	—
54	C₂×C₃×C₅×D₄	—	2	4	no	—
55	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
56	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
57	C₂²×C₃×C₄×C₅	—	2	8	no	—
58	C₂²×C₃×C₄×C₅	D₄	1	8	yes	complemented
59	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
60	C₂²×C₃×C₄×C₅	C₂³	1	8	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	4	yes	—
64	C₂×C₅×#67	—	2	8	no	—
65	C₂×C₅×#67	—	4	8	no	—
66	C₂×C₅×#67	C₂³	1	8	yes	—
67	C₂×C₅×#67	C₂³	1	16	yes	—
68	C₂²×C₅×Dic₃	—	4	4	no	—
69	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
70	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
71	C₂²×C₅×Dic₃	C₂³	1	8	yes	—
72	C₅×#235	—	2	32	no	—
73	C₂×C₅×D₁₂	—	2	4	no	—
74	C₂×C₅×D₁₂	C₂³	1	4	yes	—
75	C₂×C₄×C₅×D₃	—	2	8	no	—
76	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
77	C₂×C₅×Dic₆	—	2	4	no	—
78	C₂×C₅×Dic₆	C₂³	1	4	yes	—
79	C₅×#217	C₂³	1	16	yes	—
80	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	—
81	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
82	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
83	C₅×Dic₃⋊C₄	C₂³	1	16	yes	—
84	C₂²×C₃×#41	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂²×#235	C₂×C₅	1	1	yes	characteristic, complemented
86	#5833	C₂×C₅	1	16	yes	direct product factor
87	C₂×#946	C₂×C₅	1	2	yes	complemented
88	C₂×#939	C₂×C₅	1	4	yes	complemented
89	C₂×#938	C₂×C₅	1	2	yes	complemented
90	C₂×#930	C₂×C₅	1	2	yes	complemented
91	C₂²×C₄⋊Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂×#924	C₂×C₅	1	2	yes	complemented
93	C₂×C₅×#41	—	2	8	no	—
94	C₂×C₅×#41	—	3	8	no	—
95	C₂×C₅×#41	—	6	8	no	—
96	C₂×C₅×#41	C₂×D₃	1	8	yes	complemented
97	C₂²×C₅×Q₈	—	3	1	no	—
98	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
99	C₂²×C₅×D₄	—	3	2	no	—
100	C₂²×C₅×D₄	—	3	4	no	—
101	C₂²×C₅×D₄	—	3	1	no	—
102	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
103	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
104	C₂³×C₄×C₅	—	3	2	no	—
105	C₂³×C₄×C₅	—	3	2	no	—
106	C₂³×C₄×C₅	C₂×D₃	1	2	yes	—
107	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
108	C₅×C₂²⋊Q₈	—	3	16	no	—
109	C₅×C₂²⋊Q₈	—	3	16	no	—
110	C₅×#121	—	3	16	no	—
111	C₅×#121	—	3	32	no	—
112	C₅×#121	—	3	16	no	—
113	C₂×C₅×C₄⋊C₄	—	3	4	no	—
114	C₂×C₅×C₄⋊C₄	—	3	2	no	—
115	C₂×C₅×C₄⋊C₄	—	3	2	no	—
116	C₂×C₅×C₄⋊C₄	—	3	8	no	—
117	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
118	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
119	C₂×#537	—	3	1	no	Sylow
120	C₂³×C₃×C₅	—	2	2	no	—
121	C₂³×C₃×C₅	—	2	2	no	—
122	C₂³×C₃×C₅	—	2	4	no	—
123	C₂³×C₃×C₅	—	2	4	no	—
124	C₂³×C₃×C₅	—	2	4	no	—
125	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
126	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
127	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
128	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
129	C₂²×C₅×D₃	—	2	4	no	—
130	C₂²×C₅×D₃	—	2	4	no	—
131	C₂²×C₅×D₃	—	2	4	no	—
132	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
133	C₃×C₅×Q₈	—	2	8	no	—
134	C₃×C₅×D₄	—	2	16	no	—
135	C₃×C₅×D₄	—	2	8	no	—
136	C₂×C₃×C₄×C₅	—	2	4	no	—
137	C₂×C₃×C₄×C₅	—	2	16	no	—
138	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
139	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
140	C₂×C₃×C₄×C₅	C₂×D₄	1	16	yes	complemented
141	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
142	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
143	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
144	C₅×#67	—	2	16	no	—
145	C₅×#67	—	4	16	no	—
146	C₂×C₅×Dic₃	—	2	4	no	—
147	C₂×C₅×Dic₃	—	2	8	no	—
148	C₂×C₅×Dic₃	—	4	8	no	—
149	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
150	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
151	C₅×D₁₂	—	2	8	no	—
152	C₄×C₅×D₃	—	2	16	no	—
153	C₅×Dic₆	—	2	8	no	—
154	C₂×C₃×#41	—	2	8	no	—
155	C₂×C₃×#41	C₂²×C₅	1	8	yes	complemented
156	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
157	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
158	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
159	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
160	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
161	C₂²×#67	C₂²×C₅	1	2	yes	—
162	C₂²×#67	C₂²×C₅	1	4	yes	—
163	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
164	C₂×#235	—	2	8	no	—
165	C₂×#235	C₂²×C₅	1	8	yes	complemented
166	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
167	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
168	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
169	C₂×#217	C₂²×C₅	1	4	yes	—
170	#946	C₂²×C₅	1	16	yes	complemented
171	#939	C₂²×C₅	1	32	yes	complemented
172	#938	C₂²×C₅	1	16	yes	complemented
173	#930	C₂²×C₅	1	16	yes	complemented
174	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
175	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
176	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
177	C₂×C₄⋊Dic₃	C₂²×C₅	1	8	yes	complemented
178	#924	C₂²×C₅	1	16	yes	complemented
179	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
180	C₂⁴×C₅	—	3	2	no	—
181	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
182	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
183	C₅×#41	—	2	32	no	—
184	C₅×#41	—	6	32	no	—
185	C₂×C₅×Q₈	—	2	4	no	—
186	C₂×C₅×Q₈	—	3	4	no	—
187	C₂×C₅×Q₈	—	6	4	no	—
188	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
189	C₂×C₅×D₄	—	2	8	no	—
190	C₂×C₅×D₄	—	2	4	no	—
191	C₂×C₅×D₄	—	3	8	no	—
192	C₂×C₅×D₄	—	3	16	no	—
193	C₂×C₅×D₄	—	3	4	no	—
194	C₂×C₅×D₄	—	6	8	no	—
195	C₂×C₅×D₄	—	6	4	no	—
196	C₂×C₅×D₄	—	12	8	no	—
197	C₂×C₅×D₄	C₂²×D₃	1	8	yes	—
198	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
199	C₂²×C₄×C₅	—	2	8	no	—
200	C₂²×C₄×C₅	—	3	4	no	—
201	C₂²×C₄×C₅	—	3	2	no	—
202	C₂²×C₄×C₅	—	3	8	no	—
203	C₂²×C₄×C₅	—	3	8	no	—
204	C₂²×C₄×C₅	—	6	8	no	—
205	C₂²×C₄×C₅	—	12	4	no	—
206	C₂²×C₄×C₅	#67	1	8	yes	complemented
207	C₂²×C₄×C₅	C₂²×D₃	1	8	yes	—
208	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
209	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
210	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
211	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
212	C₅×C₄⋊C₄	—	3	8	no	—
213	C₅×C₄⋊C₄	—	3	8	no	—
214	C₅×C₄⋊C₄	—	3	16	no	—
215	C₅×C₂²⋊C₄	—	3	16	no	—
216	C₅×C₂²⋊C₄	—	3	16	no	—
217	C₂²×#41	—	3	1	no	—
218	C₂²×#41	C₅×D₃	1	1	yes	characteristic, complemented
219	#537	—	3	16	no	—
220	C₂×C₂²⋊Q₈	—	3	2	no	—
221	C₂×C₂²⋊Q₈	—	3	2	no	—
222	C₂×#121	—	3	2	no	—
223	C₂×#121	—	3	4	no	—
224	C₂×#121	—	3	2	no	—
225	C₂²×C₄⋊C₄	—	3	1	no	—
226	C₂²×C₃×C₅	—	2	8	no	—
227	C₂²×C₃×C₅	—	2	2	no	—
228	C₂²×C₃×C₅	—	2	2	no	—
229	C₂²×C₃×C₅	—	2	4	no	—
230	C₂²×C₃×C₅	—	2	4	no	—
231	C₂²×C₃×C₅	—	2	4	no	—
232	C₂²×C₃×C₅	—	4	8	no	—
233	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
234	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
235	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
236	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
237	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
238	C₂×C₅×D₃	—	2	4	no	—
239	C₂×C₅×D₃	—	2	4	no	—
240	C₂×C₅×D₃	—	2	4	no	—
241	C₂×C₅×D₃	—	4	8	no	—
242	C₃×C₄×C₅	—	2	4	no	—
243	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
244	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
245	C₅×Dic₃	—	2	4	no	—
246	C₅×Dic₃	—	2	8	no	—
247	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
248	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
249	C₂³×D₃	C₂³×C₅	1	2	yes	—
250	C₃×#41	—	2	32	no	—
251	C₂×C₃×Q₈	—	2	4	no	—
252	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
253	C₂×C₃×D₄	—	2	8	no	—
254	C₂×C₃×D₄	—	2	4	no	—
255	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
256	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
257	C₂²×C₃×C₄	—	2	8	no	—
258	C₂²×C₃×C₄	C₅×D₄	1	8	yes	complemented
259	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
260	C₂²×C₃×C₄	C₂³×C₅	1	8	yes	—
261	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
262	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
263	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
264	C₂×#67	—	2	8	no	—
265	C₂×#67	—	4	8	no	—
266	C₂×#67	C₂³×C₅	1	8	yes	—
267	C₂×#67	C₂³×C₅	1	16	yes	—
268	C₂²×Dic₃	—	4	4	no	—
269	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
270	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
271	C₂²×Dic₃	C₂³×C₅	1	8	yes	—
272	#235	—	2	32	no	—
273	C₂×D₁₂	—	2	4	no	—
274	C₂×D₁₂	C₂³×C₅	1	4	yes	—
275	C₂×C₄×D₃	—	2	8	no	—
276	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
277	C₂×Dic₆	—	2	4	no	—
278	C₂×Dic₆	C₂³×C₅	1	4	yes	—
279	#217	C₂³×C₅	1	16	yes	—
280	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	—
281	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
282	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
283	Dic₃⋊C₄	C₂³×C₅	1	16	yes	—
284	C₂³×C₅	—	2	2	no	—
285	C₂³×C₅	—	2	2	no	—
286	C₂³×C₅	—	2	4	no	—
287	C₂³×C₅	—	2	4	no	—
288	C₂³×C₅	—	2	4	no	—
289	C₂³×C₅	—	3	4	no	—
290	C₂³×C₅	—	6	4	no	—
291	C₂³×C₅	—	6	4	no	—
292	C₂³×C₅	—	6	4	no	—
293	C₂³×C₅	C₂×#67	1	4	yes	—
294	C₂³×C₅	C₂³×D₃	1	4	yes	—
295	C₂³×C₅	C₂³×D₃	1	2	yes	—
296	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
297	C₅×Q₈	—	2	8	no	—
298	C₅×Q₈	—	6	8	no	—
299	C₅×D₄	—	2	16	no	—
300	C₅×D₄	—	2	8	no	—
301	C₅×D₄	—	6	16	no	—
302	C₅×D₄	—	6	8	no	—
303	C₅×D₄	—	12	16	no	—
304	C₂×C₄×C₅	—	2	4	no	—
305	C₂×C₄×C₅	—	2	16	no	—
306	C₂×C₄×C₅	—	3	8	no	—
307	C₂×C₄×C₅	—	3	4	no	—
308	C₂×C₄×C₅	—	6	8	no	—
309	C₂×C₄×C₅	—	6	4	no	—
310	C₂×C₄×C₅	—	6	16	no	—
311	C₂×C₄×C₅	—	12	8	no	—
312	C₂×C₄×C₅	C₂×#67	1	4	yes	—
313	C₂×C₄×C₅	C₂×#67	1	4	yes	—
314	C₂×C₄×C₅	C₂×#67	1	16	yes	complemented
315	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
316	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
317	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
318	C₂×#41	—	2	8	no	—
319	C₂×#41	—	3	8	no	—
320	C₂×#41	—	6	8	no	—
321	C₂×#41	C₂×C₅×D₃	1	8	yes	complemented
322	C₂²×Q₈	—	3	1	no	—
323	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
324	C₂²×D₄	—	3	2	no	—
325	C₂²×D₄	—	3	4	no	—
326	C₂²×D₄	—	3	1	no	—
327	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
328	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
329	C₂³×C₄	—	3	2	no	—
330	C₂³×C₄	—	3	2	no	—
331	C₂³×C₄	C₂×C₅×D₃	1	2	yes	—
332	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
333	C₂²⋊Q₈	—	3	16	no	—
334	C₂²⋊Q₈	—	3	16	no	—
335	#121	—	3	16	no	—
336	#121	—	3	32	no	—
337	#121	—	3	16	no	—
338	C₂×C₄⋊C₄	—	3	2	no	—
339	C₂×C₄⋊C₄	—	3	2	no	—
340	C₂×C₄⋊C₄	—	3	8	no	—
341	C₂×C₄⋊C₄	—	3	4	no	—
342	C₂×C₂²⋊C₄	—	3	4	no	—
343	C₂×C₂²⋊C₄	—	3	4	no	—
344	C₂×C₃×C₅	—	2	4	no	—
345	C₂×C₃×C₅	—	4	4	no	—
346	C₂×C₃×C₅	#537	1	4	yes	complemented
347	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
348	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
349	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
350	C₅×D₃	—	4	4	no	—
351	C₂³×C₃	—	2	2	no	—
352	C₂³×C₃	—	2	2	no	—
353	C₂³×C₃	—	2	4	no	—
354	C₂³×C₃	—	2	4	no	—
355	C₂³×C₃	—	2	4	no	—
356	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
357	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
358	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
359	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
360	C₂²×D₃	—	2	4	no	—
361	C₂²×D₃	—	2	4	no	—
362	C₂²×D₃	—	2	4	no	—
363	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
364	C₃×Q₈	—	2	8	no	—
365	C₃×D₄	—	2	16	no	—
366	C₃×D₄	—	2	8	no	—
367	C₂×C₃×C₄	—	2	4	no	—
368	C₂×C₃×C₄	—	2	16	no	—
369	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
370	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
371	C₂×C₃×C₄	C₂×C₅×D₄	1	16	yes	complemented
372	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
373	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
374	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
375	#67	—	2	16	no	—
376	#67	—	4	16	no	—
377	C₂×Dic₃	—	2	4	no	—
378	C₂×Dic₃	—	2	8	no	—
379	C₂×Dic₃	—	4	8	no	—
380	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
381	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
382	D₁₂	—	2	8	no	—
383	C₄×D₃	—	2	16	no	—
384	Dic₆	—	2	8	no	—
385	C₂²×C₅	—	2	2	no	—
386	C₂²×C₅	—	2	2	no	—
387	C₂²×C₅	—	2	8	no	—
388	C₂²×C₅	—	2	4	no	—
389	C₂²×C₅	—	2	4	no	—
390	C₂²×C₅	—	2	4	no	—
391	C₂²×C₅	—	4	8	no	—
392	C₂²×C₅	—	6	4	no	—
393	C₂²×C₅	—	6	4	no	—
394	C₂²×C₅	—	6	4	no	—
395	C₂²×C₅	—	12	8	no	—
396	C₂²×C₅	#1009	1	2	yes	—
397	C₂²×C₅	#1010	1	2	yes	—
398	C₂²×C₅	C₂²×#67	1	4	yes	—
399	C₂²×C₅	C₂²×#67	1	2	yes	—
400	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
401	C₄×C₅	—	2	4	no	—
402	C₄×C₅	—	6	8	no	—
403	C₄×C₅	—	6	4	no	—
404	C₄×C₅	C₂²×#67	1	4	yes	—
405	C₄×C₅	C₂²×#67	1	4	yes	—
406	C₂⁴	—	3	2	no	—
407	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
408	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
409	#41	—	2	32	no	—
410	#41	—	6	32	no	—
411	C₂×Q₈	—	2	4	no	—
412	C₂×Q₈	—	3	4	no	—
413	C₂×Q₈	—	6	4	no	—
414	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
415	C₂×D₄	—	2	8	no	—
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	—	3	8	no	—
418	C₂×D₄	—	3	16	no	—
419	C₂×D₄	—	3	4	no	—
420	C₂×D₄	—	6	8	no	—
421	C₂×D₄	—	6	4	no	—
422	C₂×D₄	—	12	8	no	—
423	C₂×D₄	C₂²×C₅×D₃	1	8	yes	—
424	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
425	C₂²×C₄	—	2	8	no	—
426	C₂²×C₄	—	3	4	no	—
427	C₂²×C₄	—	3	2	no	—
428	C₂²×C₄	—	3	8	no	—
429	C₂²×C₄	—	3	8	no	—
430	C₂²×C₄	—	6	8	no	—
431	C₂²×C₄	—	12	4	no	—
432	C₂²×C₄	C₅×#67	1	8	yes	complemented
433	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
434	C₂²×C₄	C₂²×C₅×D₃	1	8	yes	—
435	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
436	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
437	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
438	C₄⋊C₄	—	3	8	no	—
439	C₄⋊C₄	—	3	8	no	—
440	C₄⋊C₄	—	3	16	no	—
441	C₂²⋊C₄	—	3	16	no	—
442	C₂²⋊C₄	—	3	16	no	—
443	C₃×C₅	C₂×#537	1	1	yes	characteristic, complemented, Hall
444	C₂²×C₃	—	2	8	no	—
445	C₂²×C₃	—	2	2	no	—
446	C₂²×C₃	—	2	2	no	—
447	C₂²×C₃	—	2	4	no	—
448	C₂²×C₃	—	2	4	no	—
449	C₂²×C₃	—	2	4	no	—
450	C₂²×C₃	—	4	8	no	—
451	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
452	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
453	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
454	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
455	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
456	C₂×D₃	—	2	4	no	—
457	C₂×D₃	—	2	4	no	—
458	C₂×D₃	—	2	4	no	—
459	C₂×D₃	—	4	8	no	—
460	C₃×C₄	—	2	4	no	—
461	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
462	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
463	Dic₃	—	2	4	no	—
464	Dic₃	—	2	8	no	—
465	C₂×C₅	—	2	4	no	—
466	C₂×C₅	—	4	4	no	—
467	C₂×C₅	—	12	4	no	—
468	C₂×C₅	#5833	1	4	yes	direct product factor
469	C₂×C₅	C₂×#1009	1	1	yes	characteristic
470	C₂×C₅	C₂×#1010	1	1	yes	characteristic
471	C₂×C₅	C₂³×#67	1	1	yes	characteristic
472	C₂³	—	2	2	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	4	no	—
476	C₂³	—	2	4	no	—
477	C₂³	—	3	4	no	—
478	C₂³	—	6	4	no	—
479	C₂³	—	6	4	no	—
480	C₂³	—	6	4	no	—
481	C₂³	C₂×C₅×#67	1	4	yes	—
482	C₂³	C₂³×C₅×D₃	1	4	yes	—
483	C₂³	C₂³×C₅×D₃	1	2	yes	—
484	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
485	Q₈	—	2	8	no	—
486	Q₈	—	6	8	no	—
487	D₄	—	2	16	no	—
488	D₄	—	2	8	no	—
489	D₄	—	6	16	no	—
490	D₄	—	6	8	no	—
491	D₄	—	12	16	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	16	no	—
494	C₂×C₄	—	3	8	no	—
495	C₂×C₄	—	3	4	no	—
496	C₂×C₄	—	6	8	no	—
497	C₂×C₄	—	6	4	no	—
498	C₂×C₄	—	6	16	no	—
499	C₂×C₄	—	12	8	no	—
500	C₂×C₄	C₂×C₅×#67	1	4	yes	—
501	C₂×C₄	C₂×C₅×#67	1	4	yes	—
502	C₂×C₄	C₂×C₅×#67	1	16	yes	complemented
503	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
504	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
505	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
506	C₂×C₃	—	2	4	no	—
507	C₂×C₃	—	4	4	no	—
508	C₂×C₃	C₅×#537	1	4	yes	complemented
509	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
510	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
511	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
512	D₃	—	4	4	no	—
513	C₅	C₂×#5833	1	1	yes	characteristic, direct product factor, Sylow
514	C₂²	—	2	2	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	8	no	—
517	C₂²	—	2	4	no	—
518	C₂²	—	2	4	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	4	8	no	—
521	C₂²	—	6	4	no	—
522	C₂²	—	6	4	no	—
523	C₂²	—	6	4	no	—
524	C₂²	—	12	8	no	—
525	C₂²	C₅×#1009	1	2	yes	—
526	C₂²	C₅×#1010	1	2	yes	—
527	C₂²	C₂²×C₅×#67	1	4	yes	—
528	C₂²	C₂²×C₅×#67	1	2	yes	—
529	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
530	C₄	—	2	4	no	—
531	C₄	—	6	8	no	—
532	C₄	—	6	4	no	—
533	C₄	C₂²×C₅×#67	1	4	yes	—
534	C₄	C₂²×C₅×#67	1	4	yes	—
535	C₃	C₂×C₅×#537	1	1	yes	characteristic, complemented, Sylow
536	C₂	—	2	4	no	—
537	C₂	—	4	4	no	—
538	C₂	—	12	4	no	—
539	C₂	C₅×#5833	1	4	yes	direct product factor
540	C₂	C₂×C₅×#1009	1	1	yes	characteristic
541	C₂	C₂×C₅×#1010	1	1	yes	characteristic
542	C₂	C₂³×C₅×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂²×C₃×C₅×#41	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂²×C₅×#41	D₃
hypocenter	C₃	C₂×C₅×#537
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₅×#41

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×#41	C₂	semidirect
2. C₂²×C₅×#235	C₂	semidirect
3. C₅×#5833	C₂	direct (N × H)
4. C₂×C₅×#946	C₂	semidirect
5. C₂×C₅×#939	C₂	semidirect
6. C₂×C₅×#938	C₂	semidirect
7. C₂×C₅×#930	C₂	semidirect
8. C₂²×C₅×C₄⋊Dic₃	C₂	semidirect
9. C₂×C₅×#924	C₂	semidirect
12. C₂×C₃×C₅×#41	C₂²	semidirect
22. C₂×C₅×#235	C₂²	semidirect
27. C₅×#946	C₂²	semidirect
28. C₅×#939	C₂²	semidirect
29. C₅×#938	C₂²	semidirect
30. C₅×#930	C₂²	semidirect
34. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
35. C₅×#924	C₂²	semidirect
37. C₂×#5833	C₅	direct (N × H)
39. C₂²×C₅×#41	D₃	semidirect
58. C₂²×C₃×C₄×C₅	D₄	semidirect
84. C₂²×C₃×#41	C₂×C₅	semidirect
85. C₂²×#235	C₂×C₅	semidirect
86. #5833	C₂×C₅	direct (N × H)
87. C₂×#946	C₂×C₅	semidirect
88. C₂×#939	C₂×C₅	semidirect
89. C₂×#938	C₂×C₅	semidirect
90. C₂×#930	C₂×C₅	semidirect
91. C₂²×C₄⋊Dic₃	C₂×C₅	semidirect
92. C₂×#924	C₂×C₅	semidirect
96. C₂×C₅×#41	C₂×D₃	semidirect
140. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
155. C₂×C₃×#41	C₂²×C₅	semidirect
165. C₂×#235	C₂²×C₅	semidirect
170. #946	C₂²×C₅	semidirect
171. #939	C₂²×C₅	semidirect
172. #938	C₂²×C₅	semidirect
173. #930	C₂²×C₅	semidirect
177. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
178. #924	C₂²×C₅	semidirect
206. C₂²×C₄×C₅	#67	semidirect
218. C₂²×#41	C₅×D₃	semidirect
258. C₂²×C₃×C₄	C₅×D₄	semidirect
314. C₂×C₄×C₅	C₂×#67	semidirect
321. C₂×#41	C₂×C₅×D₃	semidirect
346. C₂×C₃×C₅	#537	semidirect
371. C₂×C₃×C₄	C₂×C₅×D₄	semidirect
432. C₂²×C₄	C₅×#67	semidirect
443. C₃×C₅	C₂×#537	semidirect
468. C₂×C₅	#5833	direct (N × H)
502. C₂×C₄	C₂×C₅×#67	semidirect
508. C₂×C₃	C₅×#537	semidirect
513. C₅	C₂×#5833	direct (N × H)
535. C₃	C₂×C₅×#537	semidirect
539. C₂	C₅×#5833	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₅×#41	2
C₂²×C₅×#235	2
C₅×#5833	2
C₂×C₅×#946	2
C₂×C₅×#939	2
C₂×C₅×#938	2
C₂×C₅×#930	2
C₂²×C₅×C₄⋊Dic₃	2
C₂×C₅×#924	2
C₂×C₅×#537	3
C₂×#5833	5

Subgroups — C2×C5×#5833 #14480563

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5833 #14480563