Subgroups — C₂×C₅×#5525 #14480380

Order 1920.

3792 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	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5525	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₅×#895	C₂	1	4	yes	maximal, complemented
6	C₂×C₅×#882	C₂	1	4	yes	maximal, complemented
7	C₂×C₅×#875	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#874	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#535	—	3	1	no	maximal, Hall
10	C₂⁴×C₅×D₃	C₂²	1	2	yes	—
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂²×C₅×#67	C₂²	1	2	yes	—
13	C₂×C₅×#235	—	2	8	no	—
14	C₂×C₅×#235	C₂²	1	8	yes	complemented
15	C₂²×C₅×D₁₂	—	2	8	no	—
16	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
17	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
18	C₂²×C₅×D₁₂	C₂²	1	8	yes	complemented
19	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₅×D₁₂	C₂²	1	8	yes	complemented
21	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	complemented
22	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₅×#117	C₂²	1	8	yes	complemented
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
27	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	8	yes	complemented
28	C₅×#895	C₂²	1	32	yes	complemented
29	C₅×#882	C₂²	1	32	yes	complemented
30	C₅×#875	C₂²	1	16	yes	complemented
31	C₅×#874	C₂²	1	16	yes	complemented
32	C₂×#5525	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂²×C₅×#41	—	3	1	no	—
34	C₂³×C₅×D₄	—	3	1	no	—
35	C₅×#535	—	3	16	no	—
36	C₂×C₅×#127	—	3	2	no	—
37	C₂×C₅×#124	—	3	2	no	—
38	C₂×C₅×#121	—	3	4	no	—
39	C₂×C₅×#120	—	3	4	no	—
40	C₂×C₅×#117	D₃	1	1	yes	characteristic, complemented
41	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
42	C₂³×C₅×D₃	—	2	8	no	—
43	C₂³×C₅×D₃	—	4	8	no	—
44	C₂³×C₅×D₃	C₂³	1	4	yes	—
45	C₂³×C₅×D₃	C₂³	1	2	yes	—
46	C₂³×C₅×D₃	C₂³	1	8	yes	—
47	C₂²×C₃×C₄×C₅	D₄	1	8	yes	complemented
48	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
52	C₂×C₅×#67	—	2	8	no	—
53	C₂×C₅×#67	C₂³	1	8	yes	—
54	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
55	C₅×#235	—	2	32	no	—
56	C₂×C₅×D₁₂	—	2	8	no	—
57	C₂×C₅×D₁₂	—	2	8	no	—
58	C₂×C₅×D₁₂	—	2	4	no	—
59	C₂×C₅×D₁₂	—	2	32	no	—
60	C₂×C₅×D₁₂	—	4	16	no	—
61	C₂×C₅×D₁₂	C₂³	1	8	yes	—
62	C₂×C₅×D₁₂	C₂³	1	8	yes	—
63	C₂×C₅×D₁₂	C₂³	1	4	yes	complemented
64	C₂×C₅×D₁₂	C₂³	1	32	yes	complemented
65	C₂×C₄×C₅×D₃	—	2	8	no	—
66	C₂×C₄×C₅×D₃	C₂³	1	8	yes	complemented
67	C₂×C₅×Dic₆	—	2	4	no	—
68	C₂×C₅×Dic₆	C₂³	1	4	yes	complemented
69	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	complemented
70	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
71	C₃×C₄²×C₅	C₂³	1	8	yes	complemented
72	C₅×(C₂×D₃)⋊C₄	C₂³	1	32	yes	complemented
73	C₂²×#235	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂³×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
76	#5525	C₂×C₅	1	16	yes	direct product factor
77	C₂×#895	C₂×C₅	1	4	yes	complemented
78	C₂×#882	C₂×C₅	1	4	yes	complemented
79	C₂×#875	C₂×C₅	1	2	yes	complemented
80	C₂×#874	C₂×C₅	1	2	yes	complemented
81	C₂⁵×C₅	—	3	2	no	—
82	C₂×C₅×#41	—	3	8	no	—
83	C₂×C₅×#41	—	6	8	no	—
84	C₂²×C₅×Q₈	—	3	1	no	—
85	C₂²×C₅×D₄	—	3	2	no	—
86	C₂²×C₅×D₄	—	3	2	no	—
87	C₂²×C₅×D₄	—	3	2	no	—
88	C₂²×C₅×D₄	—	3	1	no	—
89	C₂²×C₅×D₄	—	3	8	no	—
90	C₂²×C₅×D₄	—	3	8	no	—
91	C₂²×C₅×D₄	—	6	8	no	—
92	C₂³×C₄×C₅	—	3	2	no	—
93	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
94	C₅×#127	—	3	16	no	—
95	C₅×#124	—	3	16	no	—
96	C₅×#121	—	3	32	no	—
97	C₅×#120	—	3	32	no	—
98	C₅×#117	C₂×D₃	1	8	yes	complemented
99	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
100	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
101	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
102	C₂×C₄²×C₅	C₂×D₃	1	2	yes	complemented
103	C₂×#535	—	3	1	no	Sylow
104	C₂³×C₃×C₅	—	2	4	no	—
105	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
106	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
107	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
108	C₂²×C₅×D₃	—	2	4	no	—
109	C₂²×C₅×D₃	—	2	16	no	—
110	C₂²×C₅×D₃	—	2	8	no	—
111	C₂²×C₅×D₃	—	2	8	no	—
112	C₂²×C₅×D₃	—	2	16	no	—
113	C₂²×C₅×D₃	—	4	16	no	—
114	C₂²×C₅×D₃	—	4	32	no	—
115	C₂²×C₅×D₃	C₂⁴	1	8	yes	—
116	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
117	C₂×C₃×C₄×C₅	—	2	8	no	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
119	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
120	C₂×C₃×C₄×C₅	C₂×D₄	1	16	yes	complemented
121	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
122	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
123	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
124	C₅×#67	—	2	16	no	—
125	C₂×C₅×Dic₃	—	2	4	no	—
126	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
127	C₅×D₁₂	—	2	16	no	—
128	C₅×D₁₂	—	2	16	no	—
129	C₅×D₁₂	—	2	8	no	—
130	C₅×D₁₂	—	4	32	no	—
131	C₄×C₅×D₃	—	2	16	no	—
132	C₅×Dic₆	—	2	8	no	—
133	C₂⁴×D₃	C₂²×C₅	1	2	yes	—
134	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
135	C₂²×#67	C₂²×C₅	1	2	yes	—
136	C₂×#235	—	2	8	no	—
137	C₂×#235	C₂²×C₅	1	8	yes	complemented
138	C₂²×D₁₂	—	2	8	no	—
139	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
140	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
141	C₂²×D₁₂	C₂²×C₅	1	8	yes	complemented
142	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
143	C₂²×D₁₂	C₂²×C₅	1	8	yes	complemented
144	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	complemented
145	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
146	C₃×#117	C₂²×C₅	1	8	yes	complemented
147	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
148	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
149	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	complemented
150	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	8	yes	complemented
151	#895	C₂²×C₅	1	32	yes	complemented
152	#882	C₂²×C₅	1	32	yes	complemented
153	#875	C₂²×C₅	1	16	yes	complemented
154	#874	C₂²×C₅	1	16	yes	complemented
155	C₂⁴×C₅	—	3	4	no	—
156	C₂⁴×C₅	—	3	2	no	—
157	C₂⁴×C₅	—	3	8	no	—
158	C₂⁴×C₅	—	6	8	no	—
159	C₂⁴×C₅	—	12	8	no	—
160	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
161	C₅×#41	—	6	32	no	—
162	C₂×C₅×Q₈	—	3	4	no	—
163	C₂×C₅×Q₈	—	6	4	no	—
164	C₂×C₅×D₄	—	3	8	no	—
165	C₂×C₅×D₄	—	3	8	no	—
166	C₂×C₅×D₄	—	3	8	no	—
167	C₂×C₅×D₄	—	3	4	no	—
168	C₂×C₅×D₄	—	3	32	no	—
169	C₂×C₅×D₄	—	6	8	no	—
170	C₂×C₅×D₄	—	6	8	no	—
171	C₂×C₅×D₄	—	6	8	no	—
172	C₂×C₅×D₄	—	6	4	no	—
173	C₂×C₅×D₄	—	6	32	no	—
174	C₂×C₅×D₄	—	12	16	no	—
175	C₂²×C₄×C₅	—	3	2	no	—
176	C₂²×C₄×C₅	—	3	8	no	—
177	C₂²×C₄×C₅	—	6	8	no	—
178	C₂²×C₄×C₅	D₁₂	1	8	yes	complemented
179	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
180	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
181	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
183	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	complemented
184	C₅×C₂²⋊C₄	—	3	32	no	—
185	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
186	C₄²×C₅	C₂²×D₃	1	8	yes	complemented
187	C₂²×#41	—	3	1	no	—
188	C₂³×D₄	—	3	1	no	—
189	#535	—	3	16	no	—
190	C₂×#127	—	3	2	no	—
191	C₂×#124	—	3	2	no	—
192	C₂×#121	—	3	4	no	—
193	C₂×#120	—	3	4	no	—
194	C₂×#117	C₅×D₃	1	1	yes	characteristic, complemented
195	C₂²×C₃×C₅	—	2	8	no	—
196	C₂²×C₃×C₅	—	2	4	no	—
197	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
198	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
199	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
200	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
201	C₂×C₅×D₃	—	2	4	no	—
202	C₂×C₅×D₃	—	2	8	no	—
203	C₂×C₅×D₃	—	2	8	no	—
204	C₂×C₅×D₃	—	2	16	no	—
205	C₂×C₅×D₃	—	4	32	no	—
206	C₂×C₅×D₃	—	4	8	no	—
207	C₂×C₅×D₃	—	4	16	no	—
208	C₃×C₄×C₅	—	2	8	no	—
209	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
210	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
211	C₅×Dic₃	—	2	4	no	—
212	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
213	C₂³×D₃	—	2	8	no	—
214	C₂³×D₃	—	4	8	no	—
215	C₂³×D₃	C₂³×C₅	1	4	yes	—
216	C₂³×D₃	C₂³×C₅	1	2	yes	—
217	C₂³×D₃	C₂³×C₅	1	8	yes	—
218	C₂²×C₃×C₄	C₅×D₄	1	8	yes	complemented
219	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
220	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
221	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
222	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
223	C₂×#67	—	2	8	no	—
224	C₂×#67	C₂³×C₅	1	8	yes	—
225	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
226	#235	—	2	32	no	—
227	C₂×D₁₂	—	2	8	no	—
228	C₂×D₁₂	—	2	8	no	—
229	C₂×D₁₂	—	2	4	no	—
230	C₂×D₁₂	—	2	32	no	—
231	C₂×D₁₂	—	4	16	no	—
232	C₂×D₁₂	C₂³×C₅	1	8	yes	—
233	C₂×D₁₂	C₂³×C₅	1	8	yes	—
234	C₂×D₁₂	C₂³×C₅	1	4	yes	complemented
235	C₂×D₁₂	C₂³×C₅	1	32	yes	complemented
236	C₂×C₄×D₃	—	2	8	no	—
237	C₂×C₄×D₃	C₂³×C₅	1	8	yes	complemented
238	C₂×Dic₆	—	2	4	no	—
239	C₂×Dic₆	C₂³×C₅	1	4	yes	complemented
240	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	complemented
241	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
242	C₃×C₄²	C₂³×C₅	1	8	yes	complemented
243	(C₂×D₃)⋊C₄	C₂³×C₅	1	32	yes	complemented
244	C₂³×C₅	—	2	4	no	—
245	C₂³×C₅	—	3	8	no	—
246	C₂³×C₅	—	3	4	no	—
247	C₂³×C₅	—	6	4	no	—
248	C₂³×C₅	—	6	16	no	—
249	C₂³×C₅	—	6	8	no	—
250	C₂³×C₅	—	6	8	no	—
251	C₂³×C₅	—	6	16	no	—
252	C₂³×C₅	—	12	16	no	—
253	C₂³×C₅	—	12	32	no	—
254	C₂³×C₅	C₂×D₁₂	1	4	yes	—
255	C₂³×C₅	C₂³×D₃	1	2	yes	—
256	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
257	C₅×Q₈	—	6	8	no	—
258	C₅×D₄	—	6	16	no	—
259	C₅×D₄	—	6	16	no	—
260	C₅×D₄	—	6	16	no	—
261	C₅×D₄	—	6	8	no	—
262	C₅×D₄	—	12	32	no	—
263	C₂×C₄×C₅	—	2	8	no	—
264	C₂×C₄×C₅	—	3	4	no	—
265	C₂×C₄×C₅	—	6	4	no	—
266	C₂×C₄×C₅	—	6	16	no	—
267	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
268	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
269	C₂×C₄×C₅	C₂×D₁₂	1	16	yes	complemented
270	C₂×C₄×C₅	C₂³×D₃	1	8	yes	—
271	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
272	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
273	C₂⁵	—	3	2	no	—
274	C₂×#41	—	3	8	no	—
275	C₂×#41	—	6	8	no	—
276	C₂²×Q₈	—	3	1	no	—
277	C₂²×D₄	—	3	2	no	—
278	C₂²×D₄	—	3	2	no	—
279	C₂²×D₄	—	3	2	no	—
280	C₂²×D₄	—	3	1	no	—
281	C₂²×D₄	—	3	8	no	—
282	C₂²×D₄	—	3	8	no	—
283	C₂²×D₄	—	6	8	no	—
284	C₂³×C₄	—	3	2	no	—
285	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
286	#127	—	3	16	no	—
287	#124	—	3	16	no	—
288	#121	—	3	32	no	—
289	#120	—	3	32	no	—
290	#117	C₂×C₅×D₃	1	8	yes	complemented
291	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
292	C₂×C₂²⋊C₄	—	3	8	no	—
293	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
294	C₂×C₄²	C₂×C₅×D₃	1	2	yes	complemented
295	C₂×C₃×C₅	—	2	4	no	—
296	C₂×C₃×C₅	#535	1	4	yes	complemented
297	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
298	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
299	C₅×D₃	—	4	4	no	—
300	C₅×D₃	—	4	8	no	—
301	C₂³×C₃	—	2	4	no	—
302	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
303	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
304	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
305	C₂²×D₃	—	2	4	no	—
306	C₂²×D₃	—	2	16	no	—
307	C₂²×D₃	—	2	8	no	—
308	C₂²×D₃	—	2	8	no	—
309	C₂²×D₃	—	2	16	no	—
310	C₂²×D₃	—	4	16	no	—
311	C₂²×D₃	—	4	32	no	—
312	C₂²×D₃	C₂⁴×C₅	1	8	yes	—
313	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
314	C₂×C₃×C₄	—	2	8	no	—
315	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
316	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
317	C₂×C₃×C₄	C₂×C₅×D₄	1	16	yes	complemented
318	C₂×C₃×C₄	C₂⁴×C₅	1	8	yes	—
319	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
320	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
321	#67	—	2	16	no	—
322	C₂×Dic₃	—	2	4	no	—
323	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
324	D₁₂	—	2	16	no	—
325	D₁₂	—	2	16	no	—
326	D₁₂	—	2	8	no	—
327	D₁₂	—	4	32	no	—
328	C₄×D₃	—	2	16	no	—
329	Dic₆	—	2	8	no	—
330	C₂²×C₅	—	2	4	no	—
331	C₂²×C₅	—	2	8	no	—
332	C₂²×C₅	—	6	4	no	—
333	C₂²×C₅	—	6	8	no	—
334	C₂²×C₅	—	6	8	no	—
335	C₂²×C₅	—	6	16	no	—
336	C₂²×C₅	—	12	32	no	—
337	C₂²×C₅	—	12	8	no	—
338	C₂²×C₅	—	12	16	no	—
339	C₂²×C₅	C₂²×D₁₂	1	4	yes	—
340	C₂²×C₅	C₂²×D₁₂	1	2	yes	—
341	C₂²×C₅	#1009	1	4	yes	—
342	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
343	C₄×C₅	—	2	8	no	—
344	C₄×C₅	—	6	4	no	—
345	C₄×C₅	C₂²×D₁₂	1	4	yes	—
346	C₄×C₅	C₂²×D₁₂	1	4	yes	—
347	C₂⁴	—	3	4	no	—
348	C₂⁴	—	3	2	no	—
349	C₂⁴	—	3	8	no	—
350	C₂⁴	—	6	8	no	—
351	C₂⁴	—	12	8	no	—
352	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
353	#41	—	6	32	no	—
354	C₂×Q₈	—	3	4	no	—
355	C₂×Q₈	—	6	4	no	—
356	C₂×D₄	—	3	8	no	—
357	C₂×D₄	—	3	8	no	—
358	C₂×D₄	—	3	8	no	—
359	C₂×D₄	—	3	4	no	—
360	C₂×D₄	—	3	32	no	—
361	C₂×D₄	—	6	8	no	—
362	C₂×D₄	—	6	8	no	—
363	C₂×D₄	—	6	8	no	—
364	C₂×D₄	—	6	4	no	—
365	C₂×D₄	—	6	32	no	—
366	C₂×D₄	—	12	16	no	—
367	C₂²×C₄	—	3	2	no	—
368	C₂²×C₄	—	3	8	no	—
369	C₂²×C₄	—	6	8	no	—
370	C₂²×C₄	C₅×D₁₂	1	8	yes	complemented
371	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
372	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
373	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
374	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
375	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	complemented
376	C₂²⋊C₄	—	3	32	no	—
377	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
378	C₄²	C₂²×C₅×D₃	1	8	yes	complemented
379	C₃×C₅	C₂×#535	1	1	yes	characteristic, complemented, Hall
380	C₂²×C₃	—	2	8	no	—
381	C₂²×C₃	—	2	4	no	—
382	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
383	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
384	C₂²×C₃	C₅×H(5,𝔽₂)	1	4	yes	—
385	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
386	C₂×D₃	—	2	4	no	—
387	C₂×D₃	—	2	8	no	—
388	C₂×D₃	—	2	8	no	—
389	C₂×D₃	—	2	16	no	—
390	C₂×D₃	—	4	32	no	—
391	C₂×D₃	—	4	8	no	—
392	C₂×D₃	—	4	16	no	—
393	C₃×C₄	—	2	8	no	—
394	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
395	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
396	Dic₃	—	2	4	no	—
397	C₂×C₅	—	2	4	no	—
398	C₂×C₅	—	12	8	no	—
399	C₂×C₅	—	12	4	no	—
400	C₂×C₅	#5525	1	4	yes	direct product factor
401	C₂×C₅	C₂³×D₁₂	1	1	yes	characteristic
402	C₂×C₅	C₂×#1009	1	2	yes	—
403	C₂³	—	2	4	no	—
404	C₂³	—	3	8	no	—
405	C₂³	—	3	4	no	—
406	C₂³	—	6	4	no	—
407	C₂³	—	6	16	no	—
408	C₂³	—	6	8	no	—
409	C₂³	—	6	8	no	—
410	C₂³	—	6	16	no	—
411	C₂³	—	12	16	no	—
412	C₂³	—	12	32	no	—
413	C₂³	C₂×C₅×D₁₂	1	4	yes	—
414	C₂³	C₂³×C₅×D₃	1	2	yes	—
415	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
416	Q₈	—	6	8	no	—
417	D₄	—	6	16	no	—
418	D₄	—	6	16	no	—
419	D₄	—	6	16	no	—
420	D₄	—	6	8	no	—
421	D₄	—	12	32	no	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	3	4	no	—
424	C₂×C₄	—	6	4	no	—
425	C₂×C₄	—	6	16	no	—
426	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	—
427	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	—
428	C₂×C₄	C₂×C₅×D₁₂	1	16	yes	complemented
429	C₂×C₄	C₂³×C₅×D₃	1	8	yes	—
430	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
431	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
432	C₂×C₃	—	2	4	no	—
433	C₂×C₃	C₅×#535	1	4	yes	complemented
434	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
435	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
436	D₃	—	4	8	no	—
437	D₃	—	4	4	no	—
438	C₅	C₂×#5525	1	1	yes	characteristic, direct product factor, Sylow
439	C₂²	—	2	4	no	—
440	C₂²	—	2	8	no	—
441	C₂²	—	6	4	no	—
442	C₂²	—	6	8	no	—
443	C₂²	—	6	8	no	—
444	C₂²	—	6	16	no	—
445	C₂²	—	12	32	no	—
446	C₂²	—	12	16	no	—
447	C₂²	—	12	8	no	—
448	C₂²	C₂²×C₅×D₁₂	1	4	yes	—
449	C₂²	C₂²×C₅×D₁₂	1	2	yes	—
450	C₂²	C₅×#1009	1	4	yes	—
451	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
452	C₄	—	2	8	no	—
453	C₄	—	6	4	no	—
454	C₄	C₂²×C₅×D₁₂	1	4	yes	—
455	C₄	C₂²×C₅×D₁₂	1	4	yes	—
456	C₃	C₂×C₅×#535	1	1	yes	characteristic, complemented, Sylow
457	C₂	—	2	4	no	—
458	C₂	—	12	8	no	—
459	C₂	—	12	4	no	—
460	C₂	C₅×#5525	1	4	yes	direct product factor
461	C₂	C₂³×C₅×D₁₂	1	1	yes	characteristic
462	C₂	C₂×C₅×#1009	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#117	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#117	D₃
hypocenter	C₃	C₂×C₅×#535
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#117

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#235	C₂	semidirect
2. C₂³×C₅×D₁₂	C₂	semidirect
3. C₂×C₃×C₅×#117	C₂	semidirect
4. C₅×#5525	C₂	direct (N × H)
5. C₂×C₅×#895	C₂	semidirect
6. C₂×C₅×#882	C₂	semidirect
7. C₂×C₅×#875	C₂	semidirect
8. C₂×C₅×#874	C₂	semidirect
14. C₂×C₅×#235	C₂²	semidirect
18. C₂²×C₅×D₁₂	C₂²	semidirect
19. C₂²×C₅×D₁₂	C₂²	semidirect
20. C₂²×C₅×D₁₂	C₂²	semidirect
21. C₂²×C₄×C₅×D₃	C₂²	semidirect
22. C₂²×C₅×Dic₆	C₂²	semidirect
23. C₃×C₅×#117	C₂²	semidirect
24. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
26. C₂×C₃×C₄²×C₅	C₂²	semidirect
27. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
28. C₅×#895	C₂²	semidirect
29. C₅×#882	C₂²	semidirect
30. C₅×#875	C₂²	semidirect
31. C₅×#874	C₂²	semidirect
32. C₂×#5525	C₅	direct (N × H)
40. C₂×C₅×#117	D₃	semidirect
47. C₂²×C₃×C₄×C₅	D₄	semidirect
63. C₂×C₅×D₁₂	C₂³	semidirect
64. C₂×C₅×D₁₂	C₂³	semidirect
66. C₂×C₄×C₅×D₃	C₂³	semidirect
68. C₂×C₅×Dic₆	C₂³	semidirect
69. C₃×C₅×C₄⋊C₄	C₂³	semidirect
71. C₃×C₄²×C₅	C₂³	semidirect
72. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
73. C₂²×#235	C₂×C₅	semidirect
74. C₂³×D₁₂	C₂×C₅	semidirect
75. C₂×C₃×#117	C₂×C₅	semidirect
76. #5525	C₂×C₅	direct (N × H)
77. C₂×#895	C₂×C₅	semidirect
78. C₂×#882	C₂×C₅	semidirect
79. C₂×#875	C₂×C₅	semidirect
80. C₂×#874	C₂×C₅	semidirect
98. C₅×#117	C₂×D₃	semidirect
99. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
102. C₂×C₄²×C₅	C₂×D₃	semidirect
120. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
137. C₂×#235	C₂²×C₅	semidirect
141. C₂²×D₁₂	C₂²×C₅	semidirect
142. C₂²×D₁₂	C₂²×C₅	semidirect
143. C₂²×D₁₂	C₂²×C₅	semidirect
144. C₂²×C₄×D₃	C₂²×C₅	semidirect
145. C₂²×Dic₆	C₂²×C₅	semidirect
146. C₃×#117	C₂²×C₅	semidirect
147. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
149. C₂×C₃×C₄²	C₂²×C₅	semidirect
150. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
151. #895	C₂²×C₅	semidirect
152. #882	C₂²×C₅	semidirect
153. #875	C₂²×C₅	semidirect
154. #874	C₂²×C₅	semidirect
178. C₂²×C₄×C₅	D₁₂	semidirect
183. C₅×C₄⋊C₄	C₂²×D₃	semidirect
186. C₄²×C₅	C₂²×D₃	semidirect
194. C₂×#117	C₅×D₃	semidirect
218. C₂²×C₃×C₄	C₅×D₄	semidirect
234. C₂×D₁₂	C₂³×C₅	semidirect
235. C₂×D₁₂	C₂³×C₅	semidirect
237. C₂×C₄×D₃	C₂³×C₅	semidirect
239. C₂×Dic₆	C₂³×C₅	semidirect
240. C₃×C₄⋊C₄	C₂³×C₅	semidirect
242. C₃×C₄²	C₂³×C₅	semidirect
243. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
269. C₂×C₄×C₅	C₂×D₁₂	semidirect
290. #117	C₂×C₅×D₃	semidirect
291. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
294. C₂×C₄²	C₂×C₅×D₃	semidirect
296. C₂×C₃×C₅	#535	semidirect
317. C₂×C₃×C₄	C₂×C₅×D₄	semidirect
370. C₂²×C₄	C₅×D₁₂	semidirect
375. C₄⋊C₄	C₂²×C₅×D₃	semidirect
378. C₄²	C₂²×C₅×D₃	semidirect
379. C₃×C₅	C₂×#535	semidirect
400. C₂×C₅	#5525	direct (N × H)
428. C₂×C₄	C₂×C₅×D₁₂	semidirect
433. C₂×C₃	C₅×#535	semidirect
438. C₅	C₂×#5525	direct (N × H)
456. C₃	C₂×C₅×#535	semidirect
460. C₂	C₅×#5525	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×C₅×#235	2
C₂³×C₅×D₁₂	2
C₂×C₃×C₅×#117	2
C₅×#5525	2
C₂×C₅×#895	2
C₂×C₅×#882	2
C₂×C₅×#875	2
C₂×C₅×#874	2
C₂×C₅×#535	3
C₂×#5525	5

Subgroups — C2×C5×#5525 #14480380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5525 #14480380