Subgroups — C₂×C₅×#5563 #14483922

Order 1920.

2480 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×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#938	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#930	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#926	C₂	1	2	yes	maximal, complemented
5	C₅×#5563	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₅×#892	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#885	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#869	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#555	—	3	1	no	maximal, Hall
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
13	C₂²×C₅×#67	C₂²	1	4	yes	—
14	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
16	C₂²×C₅×Dic₆	C₂²	1	2	yes	—
17	C₃×C₄×C₅×D₄	C₂²	1	8	yes	complemented
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₂×C₅×#217	C₂²	1	4	yes	—
22	C₅×#938	C₂²	1	16	yes	complemented
23	C₅×#930	C₂²	1	16	yes	complemented
24	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
25	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
26	C₅×#926	C₂²	1	16	yes	complemented
27	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
28	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
29	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×Dic₃	C₂²	1	4	yes	—
31	C₅×#892	C₂²	1	16	yes	complemented
32	C₅×#885	C₂²	1	32	yes	complemented
33	C₄×C₅×D₁₂	C₂²	1	8	yes	complemented
34	C₅×#869	C₂²	1	8	yes	complemented
35	C₂×#5563	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
36	C₅×#555	—	3	16	no	—
37	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
38	C₂×C₅×#124	—	3	4	no	—
39	C₂×C₅×#121	—	3	2	no	—
40	C₂×C₅×#121	—	3	2	no	—
41	C₂×C₄×C₅×D₄	—	3	1	no	—
42	C₂×C₄×C₅×D₄	D₃	1	1	yes	characteristic, complemented
43	C₂×C₅×#117	—	3	2	no	—
44	C₂×C₅×#117	—	3	2	no	—
45	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
46	C₂³×C₅×D₃	C₂³	1	2	yes	—
47	C₂×C₃×C₅×D₄	—	2	4	no	—
48	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
49	C₂²×C₃×C₄×C₅	—	2	8	no	—
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂×C₅×#67	—	4	8	no	—
56	C₂×C₅×#67	C₂³	1	16	yes	—
57	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
58	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
59	C₂×C₅×D₁₂	—	2	4	no	—
60	C₂×C₅×D₁₂	C₂³	1	4	yes	—
61	C₂×C₄×C₅×D₃	—	2	8	no	—
62	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
63	C₂×C₅×Dic₆	—	4	4	no	—
64	C₂×C₅×Dic₆	C₂³	1	8	yes	—
65	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
66	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
67	C₃×C₄²×C₅	C₂³	1	4	yes	—
68	C₅×#217	C₂³	1	16	yes	—
69	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
70	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	—
71	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
72	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
73	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
74	C₄×C₅×Dic₃	C₂³	1	16	yes	—
75	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×#938	C₂×C₅	1	2	yes	complemented
77	C₂×#930	C₂×C₅	1	2	yes	complemented
78	C₂×#926	C₂×C₅	1	2	yes	complemented
79	#5563	C₂×C₅	1	16	yes	direct product factor
80	C₂×#892	C₂×C₅	1	2	yes	complemented
81	C₂×#885	C₂×C₅	1	4	yes	complemented
82	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂×#869	C₂×C₅	1	1	yes	characteristic, complemented
84	C₂²×C₅×Q₈	—	3	2	no	—
85	C₂²×C₅×D₄	—	3	4	no	—
86	C₂²×C₅×D₄	—	3	1	no	—
87	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
88	C₂³×C₄×C₅	—	3	2	no	—
89	C₂³×C₄×C₅	C₂×D₃	1	2	yes	—
90	C₅×C₄⋊Q₈	—	3	8	no	—
91	C₅×#124	—	3	32	no	—
92	C₅×#121	—	3	16	no	—
93	C₅×#121	—	3	16	no	—
94	C₄×C₅×D₄	—	3	8	no	—
95	C₄×C₅×D₄	C₂×D₃	1	8	yes	complemented
96	C₅×#117	—	3	16	no	—
97	C₅×#117	—	3	16	no	—
98	C₂×C₅×C₄⋊C₄	—	3	1	no	—
99	C₂×C₅×C₄⋊C₄	—	3	2	no	—
100	C₂×C₅×C₄⋊C₄	—	3	2	no	—
101	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
102	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
103	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
104	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
105	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
106	C₂×C₄²×C₅	—	3	4	no	—
107	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
108	C₂×#555	—	3	1	no	Sylow
109	C₂³×C₃×C₅	—	2	4	no	—
110	C₂³×C₃×C₅	—	2	4	no	—
111	C₂³×C₃×C₅	—	2	4	no	—
112	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
113	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
114	C₂²×C₅×D₃	—	2	4	no	—
115	C₂²×C₅×D₃	—	2	4	no	—
116	C₂²×C₅×D₃	—	2	4	no	—
117	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
118	C₃×C₅×D₄	—	2	8	no	—
119	C₂×C₃×C₄×C₅	—	2	4	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	2	16	no	—
122	C₂×C₃×C₄×C₅	#41	1	4	yes	—
123	C₂×C₃×C₄×C₅	#41	1	4	yes	—
124	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
125	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
126	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
127	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
128	C₅×#67	—	4	16	no	—
129	C₂×C₅×Dic₃	—	2	4	no	—
130	C₂×C₅×Dic₃	—	2	8	no	—
131	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
132	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
133	C₅×D₁₂	—	2	8	no	—
134	C₄×C₅×D₃	—	2	16	no	—
135	C₅×Dic₆	—	4	8	no	—
136	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
137	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
138	C₂²×#67	C₂²×C₅	1	4	yes	—
139	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
140	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
141	C₂²×Dic₆	C₂²×C₅	1	2	yes	—
142	C₃×C₄×D₄	C₂²×C₅	1	8	yes	complemented
143	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
144	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
145	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
146	C₂×#217	C₂²×C₅	1	4	yes	—
147	#938	C₂²×C₅	1	16	yes	complemented
148	#930	C₂²×C₅	1	16	yes	complemented
149	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
150	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
151	#926	C₂²×C₅	1	16	yes	complemented
152	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
153	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
154	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
155	C₂×C₄×Dic₃	C₂²×C₅	1	4	yes	—
156	#892	C₂²×C₅	1	16	yes	complemented
157	#885	C₂²×C₅	1	32	yes	complemented
158	C₄×D₁₂	C₂²×C₅	1	8	yes	complemented
159	#869	C₂²×C₅	1	8	yes	complemented
160	C₂⁴×C₅	—	3	2	no	—
161	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
162	C₂×C₅×Q₈	—	3	8	no	—
163	C₂×C₅×Q₈	—	12	4	no	—
164	C₂×C₅×D₄	—	2	4	no	—
165	C₂×C₅×D₄	—	3	16	no	—
166	C₂×C₅×D₄	—	3	4	no	—
167	C₂×C₅×D₄	—	6	4	no	—
168	C₂×C₅×D₄	—	12	8	no	—
169	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
170	C₂²×C₄×C₅	—	2	8	no	—
171	C₂²×C₄×C₅	—	3	2	no	—
172	C₂²×C₄×C₅	—	3	4	no	—
173	C₂²×C₄×C₅	—	3	8	no	—
174	C₂²×C₄×C₅	—	6	8	no	—
175	C₂²×C₄×C₅	C₂²×D₃	1	8	yes	—
176	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
177	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
179	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
180	C₅×C₄⋊C₄	—	3	4	no	—
181	C₅×C₄⋊C₄	—	3	8	no	—
182	C₅×C₄⋊C₄	—	3	8	no	—
183	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
184	C₅×C₂²⋊C₄	—	3	16	no	—
185	C₅×C₂²⋊C₄	—	3	16	no	—
186	C₅×C₂²⋊C₄	—	3	8	no	—
187	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
188	C₄²×C₅	—	3	16	no	—
189	C₄²×C₅	C₂²×D₃	1	4	yes	—
190	#555	—	3	16	no	—
191	C₂×C₄⋊Q₈	—	3	1	no	—
192	C₂×#124	—	3	4	no	—
193	C₂×#121	—	3	2	no	—
194	C₂×#121	—	3	2	no	—
195	C₂×C₄×D₄	—	3	1	no	—
196	C₂×C₄×D₄	C₅×D₃	1	1	yes	characteristic, complemented
197	C₂×#117	—	3	2	no	—
198	C₂×#117	—	3	2	no	—
199	C₂²×C₃×C₅	—	2	4	no	—
200	C₂²×C₃×C₅	—	2	4	no	—
201	C₂²×C₃×C₅	—	2	4	no	—
202	C₂²×C₃×C₅	—	4	8	no	—
203	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
204	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
205	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
206	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
207	C₂×C₅×D₃	—	2	4	no	—
208	C₂×C₅×D₃	—	2	4	no	—
209	C₂×C₅×D₃	—	2	4	no	—
210	C₂×C₅×D₃	—	4	8	no	—
211	C₃×C₄×C₅	—	2	4	no	—
212	C₃×C₄×C₅	—	2	2	no	—
213	C₃×C₄×C₅	C₂×#41	1	4	yes	—
214	C₃×C₄×C₅	C₂×#41	1	4	yes	—
215	C₅×Dic₃	—	2	4	no	—
216	C₅×Dic₃	—	2	8	no	—
217	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
218	C₂³×D₃	C₂³×C₅	1	2	yes	—
219	C₂×C₃×D₄	—	2	4	no	—
220	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
221	C₂²×C₃×C₄	—	2	8	no	—
222	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
223	C₂²×C₃×C₄	C₂³×C₅	1	8	yes	—
224	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
227	C₂×#67	—	4	8	no	—
228	C₂×#67	C₂³×C₅	1	16	yes	—
229	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
230	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
231	C₂×D₁₂	—	2	4	no	—
232	C₂×D₁₂	C₂³×C₅	1	4	yes	—
233	C₂×C₄×D₃	—	2	8	no	—
234	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
235	C₂×Dic₆	—	4	4	no	—
236	C₂×Dic₆	C₂³×C₅	1	8	yes	—
237	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
238	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
239	C₃×C₄²	C₂³×C₅	1	4	yes	—
240	#217	C₂³×C₅	1	16	yes	—
241	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
242	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	—
243	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
244	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
245	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
246	C₄×Dic₃	C₂³×C₅	1	16	yes	—
247	C₂³×C₅	—	2	4	no	—
248	C₂³×C₅	—	2	4	no	—
249	C₂³×C₅	—	2	4	no	—
250	C₂³×C₅	—	3	4	no	—
251	C₂³×C₅	—	6	4	no	—
252	C₂³×C₅	—	6	4	no	—
253	C₂³×C₅	—	6	4	no	—
254	C₂³×C₅	C₂³×D₃	1	4	yes	—
255	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
256	C₅×Q₈	—	12	8	no	—
257	C₅×D₄	—	2	8	no	—
258	C₅×D₄	—	6	8	no	—
259	C₅×D₄	—	12	16	no	—
260	C₂×C₄×C₅	—	2	4	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	2	16	no	—
263	C₂×C₄×C₅	—	3	4	no	—
264	C₂×C₄×C₅	—	3	8	no	—
265	C₂×C₄×C₅	—	6	4	no	—
266	C₂×C₄×C₅	—	6	8	no	—
267	C₂×C₄×C₅	—	6	16	no	—
268	C₂×C₄×C₅	#235	1	4	yes	—
269	C₂×C₄×C₅	#237	1	4	yes	—
270	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
271	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
272	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
273	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
274	C₂²×Q₈	—	3	2	no	—
275	C₂²×D₄	—	3	4	no	—
276	C₂²×D₄	—	3	1	no	—
277	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
278	C₂³×C₄	—	3	2	no	—
279	C₂³×C₄	C₂×C₅×D₃	1	2	yes	—
280	C₄⋊Q₈	—	3	8	no	—
281	#124	—	3	32	no	—
282	#121	—	3	16	no	—
283	#121	—	3	16	no	—
284	C₄×D₄	—	3	8	no	—
285	C₄×D₄	C₂×C₅×D₃	1	8	yes	complemented
286	#117	—	3	16	no	—
287	#117	—	3	16	no	—
288	C₂×C₄⋊C₄	—	3	1	no	—
289	C₂×C₄⋊C₄	—	3	2	no	—
290	C₂×C₄⋊C₄	—	3	2	no	—
291	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	—	3	4	no	—
293	C₂×C₂²⋊C₄	—	3	4	no	—
294	C₂×C₂²⋊C₄	—	3	2	no	—
295	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
296	C₂×C₄²	—	3	4	no	—
297	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
298	C₂×C₃×C₅	—	4	4	no	—
299	C₂×C₃×C₅	#555	1	4	yes	complemented
300	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
301	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
302	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
303	C₅×D₃	—	4	4	no	—
304	C₂³×C₃	—	2	4	no	—
305	C₂³×C₃	—	2	4	no	—
306	C₂³×C₃	—	2	4	no	—
307	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
308	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
309	C₂²×D₃	—	2	4	no	—
310	C₂²×D₃	—	2	4	no	—
311	C₂²×D₃	—	2	4	no	—
312	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
313	C₃×D₄	—	2	8	no	—
314	C₂×C₃×C₄	—	2	4	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	16	no	—
317	C₂×C₃×C₄	C₅×#41	1	4	yes	—
318	C₂×C₃×C₄	C₅×#41	1	4	yes	—
319	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
320	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
321	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
322	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
323	#67	—	4	16	no	—
324	C₂×Dic₃	—	2	4	no	—
325	C₂×Dic₃	—	2	8	no	—
326	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
327	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
328	D₁₂	—	2	8	no	—
329	C₄×D₃	—	2	16	no	—
330	Dic₆	—	4	8	no	—
331	C₂²×C₅	—	2	4	no	—
332	C₂²×C₅	—	2	4	no	—
333	C₂²×C₅	—	2	4	no	—
334	C₂²×C₅	—	4	8	no	—
335	C₂²×C₅	—	6	4	no	—
336	C₂²×C₅	—	6	4	no	—
337	C₂²×C₅	—	6	4	no	—
338	C₂²×C₅	—	12	8	no	—
339	C₂²×C₅	C₂×#235	1	2	yes	—
340	C₂²×C₅	C₂×#237	1	2	yes	—
341	C₂²×C₅	#1009	1	2	yes	—
342	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
343	C₄×C₅	—	2	4	no	—
344	C₄×C₅	—	2	2	no	—
345	C₄×C₅	—	6	4	no	—
346	C₄×C₅	—	6	8	no	—
347	C₄×C₅	C₂×#235	1	4	yes	—
348	C₄×C₅	C₂×#237	1	4	yes	—
349	C₂⁴	—	3	2	no	—
350	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
351	C₂×Q₈	—	3	8	no	—
352	C₂×Q₈	—	12	4	no	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	3	16	no	—
355	C₂×D₄	—	3	4	no	—
356	C₂×D₄	—	6	4	no	—
357	C₂×D₄	—	12	8	no	—
358	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
359	C₂²×C₄	—	2	8	no	—
360	C₂²×C₄	—	3	2	no	—
361	C₂²×C₄	—	3	4	no	—
362	C₂²×C₄	—	3	8	no	—
363	C₂²×C₄	—	6	8	no	—
364	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
365	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
366	C₂²×C₄	C₂²×C₅×D₃	1	8	yes	—
367	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
368	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
369	C₄⋊C₄	—	3	4	no	—
370	C₄⋊C₄	—	3	8	no	—
371	C₄⋊C₄	—	3	8	no	—
372	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
373	C₂²⋊C₄	—	3	16	no	—
374	C₂²⋊C₄	—	3	16	no	—
375	C₂²⋊C₄	—	3	8	no	—
376	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
377	C₄²	—	3	16	no	—
378	C₄²	C₂²×C₅×D₃	1	4	yes	—
379	C₃×C₅	C₂×#555	1	1	yes	characteristic, complemented, Hall
380	C₂²×C₃	—	2	4	no	—
381	C₂²×C₃	—	2	4	no	—
382	C₂²×C₃	—	2	4	no	—
383	C₂²×C₃	—	4	8	no	—
384	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
385	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
386	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
387	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
388	C₂×D₃	—	2	4	no	—
389	C₂×D₃	—	2	4	no	—
390	C₂×D₃	—	2	4	no	—
391	C₂×D₃	—	4	8	no	—
392	C₃×C₄	—	2	4	no	—
393	C₃×C₄	—	2	2	no	—
394	C₃×C₄	C₂×C₅×#41	1	4	yes	—
395	C₃×C₄	C₂×C₅×#41	1	4	yes	—
396	Dic₃	—	2	4	no	—
397	Dic₃	—	2	8	no	—
398	C₂×C₅	—	4	4	no	—
399	C₂×C₅	—	12	4	no	—
400	C₂×C₅	#5563	1	4	yes	direct product factor
401	C₂×C₅	C₂²×#235	1	1	yes	characteristic
402	C₂×C₅	C₂²×#237	1	1	yes	characteristic
403	C₂×C₅	C₂×#1009	1	1	yes	characteristic
404	C₂³	—	2	4	no	—
405	C₂³	—	2	4	no	—
406	C₂³	—	2	4	no	—
407	C₂³	—	3	4	no	—
408	C₂³	—	6	4	no	—
409	C₂³	—	6	4	no	—
410	C₂³	—	6	4	no	—
411	C₂³	C₂³×C₅×D₃	1	4	yes	—
412	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
413	Q₈	—	12	8	no	—
414	D₄	—	2	8	no	—
415	D₄	—	6	8	no	—
416	D₄	—	12	16	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	16	no	—
420	C₂×C₄	—	3	4	no	—
421	C₂×C₄	—	3	8	no	—
422	C₂×C₄	—	6	4	no	—
423	C₂×C₄	—	6	8	no	—
424	C₂×C₄	—	6	16	no	—
425	C₂×C₄	C₅×#235	1	4	yes	—
426	C₂×C₄	C₅×#237	1	4	yes	—
427	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
428	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
429	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
430	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
431	C₂×C₃	—	4	4	no	—
432	C₂×C₃	C₅×#555	1	4	yes	complemented
433	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
434	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
435	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
436	D₃	—	4	4	no	—
437	C₅	C₂×#5563	1	1	yes	characteristic, direct product factor, Sylow
438	C₂²	—	2	4	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	4	8	no	—
442	C₂²	—	6	4	no	—
443	C₂²	—	6	4	no	—
444	C₂²	—	6	4	no	—
445	C₂²	—	12	8	no	—
446	C₂²	C₂×C₅×#235	1	2	yes	—
447	C₂²	C₂×C₅×#237	1	2	yes	—
448	C₂²	C₅×#1009	1	2	yes	—
449	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
450	C₄	—	2	4	no	—
451	C₄	—	2	2	no	—
452	C₄	—	6	4	no	—
453	C₄	—	6	8	no	—
454	C₄	C₂×C₅×#235	1	4	yes	—
455	C₄	C₂×C₅×#237	1	4	yes	—
456	C₃	C₂×C₅×#555	1	1	yes	characteristic, complemented, Sylow
457	C₂	—	4	4	no	—
458	C₂	—	12	4	no	—
459	C₂	C₅×#5563	1	4	yes	direct product factor
460	C₂	C₂²×C₅×#235	1	1	yes	characteristic
461	C₂	C₂²×C₅×#237	1	1	yes	characteristic
462	C₂	C₂×C₅×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₄×C₅×D₄	D₃
hypocenter	C₃	C₂×C₅×#555
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄×C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
2. C₂×C₅×#938	C₂	semidirect
3. C₂×C₅×#930	C₂	semidirect
4. C₂×C₅×#926	C₂	semidirect
5. C₅×#5563	C₂	direct (N × H)
6. C₂×C₅×#892	C₂	semidirect
7. C₂×C₅×#885	C₂	semidirect
8. C₂×C₄×C₅×D₁₂	C₂	semidirect
9. C₂×C₅×#869	C₂	semidirect
17. C₃×C₄×C₅×D₄	C₂²	semidirect
22. C₅×#938	C₂²	semidirect
23. C₅×#930	C₂²	semidirect
26. C₅×#926	C₂²	semidirect
31. C₅×#892	C₂²	semidirect
32. C₅×#885	C₂²	semidirect
33. C₄×C₅×D₁₂	C₂²	semidirect
34. C₅×#869	C₂²	semidirect
35. C₂×#5563	C₅	direct (N × H)
42. C₂×C₄×C₅×D₄	D₃	semidirect
75. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
76. C₂×#938	C₂×C₅	semidirect
77. C₂×#930	C₂×C₅	semidirect
78. C₂×#926	C₂×C₅	semidirect
79. #5563	C₂×C₅	direct (N × H)
80. C₂×#892	C₂×C₅	semidirect
81. C₂×#885	C₂×C₅	semidirect
82. C₂×C₄×D₁₂	C₂×C₅	semidirect
83. C₂×#869	C₂×C₅	semidirect
95. C₄×C₅×D₄	C₂×D₃	semidirect
142. C₃×C₄×D₄	C₂²×C₅	semidirect
147. #938	C₂²×C₅	semidirect
148. #930	C₂²×C₅	semidirect
151. #926	C₂²×C₅	semidirect
156. #892	C₂²×C₅	semidirect
157. #885	C₂²×C₅	semidirect
158. C₄×D₁₂	C₂²×C₅	semidirect
159. #869	C₂²×C₅	semidirect
196. C₂×C₄×D₄	C₅×D₃	semidirect
285. C₄×D₄	C₂×C₅×D₃	semidirect
299. C₂×C₃×C₅	#555	semidirect
379. C₃×C₅	C₂×#555	semidirect
400. C₂×C₅	#5563	direct (N × H)
432. C₂×C₃	C₅×#555	semidirect
437. C₅	C₂×#5563	direct (N × H)
456. C₃	C₂×C₅×#555	semidirect
459. C₂	C₅×#5563	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×C₄×C₅×D₄	2
C₂×C₅×#938	2
C₂×C₅×#930	2
C₂×C₅×#926	2
C₅×#5563	2
C₂×C₅×#892	2
C₂×C₅×#885	2
C₂×C₄×C₅×D₁₂	2
C₂×C₅×#869	2
C₂×C₅×#555	3
C₂×#5563	5

Subgroups — C2×C5×#5563 #14483922

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5563 #14483922