Subgroups — C₂×C₅×#5006 #14411918

Order 1920.

1576 conjugacy classes of subgroups.

The subgroup lattice has 636 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
2	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5006	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#806	C₂	1	4	yes	maximal, complemented
6	C₂×C₅×#410	—	3	1	no	maximal, Hall
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂²×C₅×#67	C₂²	1	2	yes	—
9	C₂×C₅×#235	—	2	1	no	—
10	C₂×C₅×#235	—	2	1	no	—
11	C₂×C₅×#235	—	2	2	no	—
12	C₂×C₅×#235	—	2	1	no	—
13	C₂×C₅×#235	—	2	1	no	—
14	C₂×C₅×#235	—	2	2	no	—
15	C₂×C₅×#235	C₄	1	4	yes	complemented
16	C₂×C₅×#235	C₂²	1	4	yes	—
17	C₂²×C₅×D₁₂	C₄	1	1	yes	characteristic, complemented
18	C₂²×C₄×C₅×D₃	C₄	1	2	yes	complemented
19	C₂²×C₅×Dic₆	C₄	1	1	yes	characteristic, complemented
20	C₃×C₅×#117	—	2	2	no	—
21	C₃×C₅×#117	C₂²	1	4	yes	complemented
22	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂×C₃×C₄²×C₅	—	2	1	no	—
25	C₂×C₅×#217	C₂²	1	2	yes	—
26	C₅×#926	—	2	2	no	—
27	C₅×#926	C₂²	1	4	yes	complemented
28	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
29	C₂×C₄×C₅×Dic₃	—	2	1	no	—
30	C₅×#806	C₂²	1	16	yes	complemented
31	C₂×#5006	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂²×C₅×#41	—	3	1	no	—
33	C₂×C₅×#117	—	3	1	no	—
34	C₂×C₅×#117	D₃	1	1	yes	characteristic, complemented
35	C₅×#410	—	3	8	no	—
36	C₂×C₅×#99	—	3	4	no	—
37	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
38	C₂³×C₅×D₃	C₂×C₄	1	2	yes	—
39	C₂²×C₃×C₄×C₅	—	2	2	no	—
40	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
43	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
46	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₂×C₅×#67	—	2	2	no	—
51	C₂×C₅×#67	—	2	2	no	—
52	C₂×C₅×#67	—	2	2	no	—
53	C₂×C₅×#67	—	2	2	no	—
54	C₂×C₅×#67	C₂×C₄	1	4	yes	—
55	C₂×C₅×#67	C₂³	1	4	yes	—
56	C₂²×C₅×Dic₃	—	2	2	no	—
57	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
58	C₅×#235	—	2	4	no	—
59	C₅×#235	—	2	4	no	—
60	C₅×#235	—	2	4	no	—
61	C₅×#235	—	2	4	no	—
62	C₅×#235	—	2	4	no	—
63	C₅×#235	—	2	4	no	—
64	C₅×#235	—	2	4	no	—
65	C₅×#235	—	2	4	no	—
66	C₂×C₅×D₁₂	—	2	2	no	—
67	C₂×C₅×D₁₂	—	2	1	no	—
68	C₂×C₅×D₁₂	—	2	1	no	—
69	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	complemented
70	C₂×C₄×C₅×D₃	—	2	4	no	—
71	C₂×C₄×C₅×D₃	—	2	2	no	—
72	C₂×C₄×C₅×D₃	—	2	2	no	—
73	C₂×C₄×C₅×D₃	C₂×C₄	1	8	yes	complemented
74	C₂×C₅×Dic₆	—	2	2	no	—
75	C₂×C₅×Dic₆	—	2	1	no	—
76	C₂×C₅×Dic₆	—	2	1	no	—
77	C₂×C₅×Dic₆	C₂×C₄	1	4	yes	complemented
78	C₃×C₅×C₄⋊C₄	—	2	4	no	—
79	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
80	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
81	C₃×C₄²×C₅	—	2	4	no	—
82	C₅×#217	—	2	2	no	—
83	C₅×#217	C₂³	1	4	yes	—
84	C₅×C₄⋊Dic₃	—	2	4	no	—
85	C₄×C₅×Dic₃	—	2	4	no	—
86	C₂²×#235	C₂×C₅	1	1	yes	characteristic
87	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
88	C₂×#926	C₂×C₅	1	1	yes	characteristic, complemented
89	#5006	C₂×C₅	1	8	yes	direct product factor
90	C₂×#806	C₂×C₅	1	4	yes	complemented
91	C₂×C₅×#41	—	3	4	no	—
92	C₂×C₅×#41	—	3	4	no	—
93	C₂×C₅×#41	—	6	1	no	—
94	C₂×C₅×#41	—	6	2	no	—
95	C₂×C₅×#41	—	6	1	no	—
96	C₂×C₅×#41	—	6	1	no	—
97	C₂×C₅×#41	—	6	2	no	—
98	C₂×C₅×#41	—	6	1	no	—
99	C₂²×C₅×Q₈	—	3	1	no	—
100	C₂²×C₅×D₄	—	3	2	no	—
101	C₂²×C₅×D₄	—	3	1	no	—
102	C₂³×C₄×C₅	—	3	2	no	—
103	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
104	C₅×#117	—	2	2	no	—
105	C₅×#117	—	3	4	no	—
106	C₅×#117	—	6	2	no	—
107	C₅×#117	C₂×D₃	1	4	yes	complemented
108	C₂×C₅×C₄⋊C₄	—	2	1	no	—
109	C₂×C₅×C₄⋊C₄	—	6	1	no	—
110	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
111	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
112	C₂×C₄²×C₅	—	2	1	no	—
113	C₂×C₄²×C₅	—	6	1	no	—
114	C₅×#99	—	3	16	no	—
115	C₂×#410	—	3	1	no	Sylow
116	C₂³×C₃×C₅	—	4	2	no	—
117	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
121	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
122	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
124	C₂²×C₅×D₃	—	2	2	no	—
125	C₂²×C₅×D₃	—	2	2	no	—
126	C₂²×C₅×D₃	—	4	4	no	—
127	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
128	C₂×C₃×C₄×C₅	—	2	4	no	—
129	C₂×C₃×C₄×C₅	—	4	4	no	—
130	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
133	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
134	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
136	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
137	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
138	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
139	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
141	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
143	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
144	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
145	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
146	C₅×#67	—	2	4	no	—
147	C₅×#67	—	2	4	no	—
148	C₅×#67	—	2	4	no	—
149	C₅×#67	—	2	4	no	—
150	C₂×C₅×Dic₃	—	2	2	no	—
151	C₂×C₅×Dic₃	—	2	2	no	—
152	C₂×C₅×Dic₃	—	2	4	no	—
153	C₂×C₅×Dic₃	—	4	4	no	—
154	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
155	C₅×D₁₂	—	2	4	no	—
156	C₅×D₁₂	—	2	4	no	—
157	C₄×C₅×D₃	—	2	8	no	—
158	C₄×C₅×D₃	—	2	8	no	—
159	C₅×Dic₆	—	2	4	no	—
160	C₅×Dic₆	—	2	4	no	—
161	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
162	C₂²×#67	C₂²×C₅	1	2	yes	—
163	C₂×#235	—	2	1	no	—
164	C₂×#235	—	2	1	no	—
165	C₂×#235	—	2	2	no	—
166	C₂×#235	—	2	1	no	—
167	C₂×#235	—	2	1	no	—
168	C₂×#235	—	2	2	no	—
169	C₂×#235	C₄×C₅	1	4	yes	complemented
170	C₂×#235	C₂²×C₅	1	4	yes	—
171	C₂²×D₁₂	C₄×C₅	1	1	yes	characteristic, complemented
172	C₂²×C₄×D₃	C₄×C₅	1	2	yes	complemented
173	C₂²×Dic₆	C₄×C₅	1	1	yes	characteristic, complemented
174	C₃×#117	—	2	2	no	—
175	C₃×#117	C₂²×C₅	1	4	yes	complemented
176	C₂×C₃×C₄⋊C₄	—	2	1	no	—
177	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
178	C₂×C₃×C₄²	—	2	1	no	—
179	C₂×#217	C₂²×C₅	1	2	yes	—
180	#926	—	2	2	no	—
181	#926	C₂²×C₅	1	4	yes	complemented
182	C₂×C₄⋊Dic₃	—	2	1	no	—
183	C₂×C₄×Dic₃	—	2	1	no	—
184	#806	C₂²×C₅	1	16	yes	complemented
185	C₂⁴×C₅	—	3	2	no	—
186	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
187	C₅×#41	—	6	4	no	—
188	C₅×#41	—	6	4	no	—
189	C₅×#41	—	6	4	no	—
190	C₅×#41	—	6	4	no	—
191	C₅×#41	—	6	4	no	—
192	C₅×#41	—	6	4	no	—
193	C₅×#41	—	6	4	no	—
194	C₅×#41	—	6	4	no	—
195	C₂×C₅×Q₈	—	3	4	no	—
196	C₂×C₅×Q₈	—	6	2	no	—
197	C₂×C₅×Q₈	—	6	1	no	—
198	C₂×C₅×Q₈	—	6	1	no	—
199	C₂×C₅×D₄	—	3	4	no	—
200	C₂×C₅×D₄	—	3	4	no	—
201	C₂×C₅×D₄	—	3	4	no	—
202	C₂×C₅×D₄	—	6	2	no	—
203	C₂×C₅×D₄	—	6	2	no	—
204	C₂×C₅×D₄	—	6	2	no	—
205	C₂×C₅×D₄	—	6	2	no	—
206	C₂×C₅×D₄	—	6	2	no	—
207	C₂×C₅×D₄	—	6	1	no	—
208	C₂×C₅×D₄	—	6	1	no	—
209	C₂²×C₄×C₅	—	2	2	no	—
210	C₂²×C₄×C₅	—	3	2	no	—
211	C₂²×C₄×C₅	—	3	8	no	—
212	C₂²×C₄×C₅	—	6	4	no	—
213	C₂²×C₄×C₅	—	6	2	no	—
214	C₂²×C₄×C₅	—	6	2	no	—
215	C₂²×C₄×C₅	—	6	2	no	—
216	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
217	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
218	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
219	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
220	C₂²×C₄×C₅	D₁₂	1	2	yes	—
221	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
222	C₂²×C₄×C₅	#67	1	1	yes	characteristic
223	C₂²×C₄×C₅	#67	1	2	yes	—
224	C₂²×C₄×C₅	#67	1	1	yes	characteristic
225	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
226	C₅×C₄⋊C₄	—	2	4	no	—
227	C₅×C₄⋊C₄	—	6	4	no	—
228	C₅×C₂²⋊C₄	—	2	2	no	—
229	C₅×C₂²⋊C₄	—	3	4	no	—
230	C₅×C₂²⋊C₄	—	6	2	no	—
231	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
232	C₄²×C₅	—	2	4	no	—
233	C₄²×C₅	—	6	4	no	—
234	C₂²×#41	—	3	1	no	—
235	C₂×#117	—	3	1	no	—
236	C₂×#117	C₅×D₃	1	1	yes	characteristic, complemented
237	#410	—	3	8	no	—
238	C₂×#99	—	3	4	no	—
239	C₂²×C₃×C₅	—	2	2	no	—
240	C₂²×C₃×C₅	—	2	2	no	—
241	C₂²×C₃×C₅	—	2	2	no	—
242	C₂²×C₃×C₅	—	4	1	no	—
243	C₂²×C₃×C₅	—	4	1	no	—
244	C₂²×C₃×C₅	—	4	1	no	—
245	C₂²×C₃×C₅	—	4	1	no	—
246	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
251	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
252	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₅×D₃	—	2	4	no	—
254	C₂×C₅×D₃	—	4	4	no	—
255	C₂×C₅×D₃	—	4	4	no	—
256	C₂×C₅×D₃	—	4	4	no	—
257	C₃×C₄×C₅	—	4	4	no	—
258	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
259	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
260	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
261	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
262	C₅×Dic₃	—	2	4	no	—
263	C₅×Dic₃	—	4	4	no	—
264	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
265	C₂³×D₃	C₂×C₄×C₅	1	2	yes	—
266	C₂²×C₃×C₄	—	2	2	no	—
267	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
268	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
269	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
270	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
271	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
272	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
273	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
274	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
275	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
276	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
277	C₂×#67	—	2	2	no	—
278	C₂×#67	—	2	2	no	—
279	C₂×#67	—	2	2	no	—
280	C₂×#67	—	2	2	no	—
281	C₂×#67	C₂×C₄×C₅	1	4	yes	—
282	C₂×#67	C₂³×C₅	1	4	yes	—
283	C₂²×Dic₃	—	2	2	no	—
284	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
285	#235	—	2	4	no	—
286	#235	—	2	4	no	—
287	#235	—	2	4	no	—
288	#235	—	2	4	no	—
289	#235	—	2	4	no	—
290	#235	—	2	4	no	—
291	#235	—	2	4	no	—
292	#235	—	2	4	no	—
293	C₂×D₁₂	—	2	2	no	—
294	C₂×D₁₂	—	2	1	no	—
295	C₂×D₁₂	—	2	1	no	—
296	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	complemented
297	C₂×C₄×D₃	—	2	4	no	—
298	C₂×C₄×D₃	—	2	2	no	—
299	C₂×C₄×D₃	—	2	2	no	—
300	C₂×C₄×D₃	C₂×C₄×C₅	1	8	yes	complemented
301	C₂×Dic₆	—	2	2	no	—
302	C₂×Dic₆	—	2	1	no	—
303	C₂×Dic₆	—	2	1	no	—
304	C₂×Dic₆	C₂×C₄×C₅	1	4	yes	complemented
305	C₃×C₄⋊C₄	—	2	4	no	—
306	C₃×C₂²⋊C₄	—	2	2	no	—
307	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
308	C₃×C₄²	—	2	4	no	—
309	#217	—	2	2	no	—
310	#217	C₂³×C₅	1	4	yes	—
311	C₄⋊Dic₃	—	2	4	no	—
312	C₄×Dic₃	—	2	4	no	—
313	C₂³×C₅	—	3	4	no	—
314	C₂³×C₅	—	4	2	no	—
315	C₂³×C₅	—	6	2	no	—
316	C₂³×C₅	—	6	2	no	—
317	C₂³×C₅	—	12	4	no	—
318	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
319	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
320	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
321	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
322	C₂³×C₅	C₂×#67	1	1	yes	characteristic
323	C₂³×C₅	C₂×#67	1	1	yes	characteristic
324	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
325	C₅×Q₈	—	6	4	no	—
326	C₅×Q₈	—	6	4	no	—
327	C₅×D₄	—	6	4	no	—
328	C₅×D₄	—	6	4	no	—
329	C₅×D₄	—	6	4	no	—
330	C₅×D₄	—	6	4	no	—
331	C₅×D₄	—	6	4	no	—
332	C₅×D₄	—	6	4	no	—
333	C₂×C₄×C₅	—	2	4	no	—
334	C₂×C₄×C₅	—	3	4	no	—
335	C₂×C₄×C₅	—	4	4	no	—
336	C₂×C₄×C₅	—	6	2	no	—
337	C₂×C₄×C₅	—	6	2	no	—
338	C₂×C₄×C₅	—	6	8	no	—
339	C₂×C₄×C₅	—	6	8	no	—
340	C₂×C₄×C₅	—	6	4	no	—
341	C₂×C₄×C₅	—	12	4	no	—
342	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
343	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
344	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
345	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
346	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
347	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
348	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
349	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
350	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
351	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
352	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
353	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
354	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
355	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
356	C₂×C₄×C₅	C₂×#67	1	2	yes	—
357	C₂×C₄×C₅	C₂×#67	1	2	yes	—
358	C₂×#41	—	3	4	no	—
359	C₂×#41	—	3	4	no	—
360	C₂×#41	—	6	1	no	—
361	C₂×#41	—	6	1	no	—
362	C₂×#41	—	6	2	no	—
363	C₂×#41	—	6	1	no	—
364	C₂×#41	—	6	1	no	—
365	C₂×#41	—	6	2	no	—
366	C₂²×Q₈	—	3	1	no	—
367	C₂²×D₄	—	3	2	no	—
368	C₂²×D₄	—	3	1	no	—
369	C₂³×C₄	—	3	2	no	—
370	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
371	#117	—	2	2	no	—
372	#117	—	3	4	no	—
373	#117	—	6	2	no	—
374	#117	C₂×C₅×D₃	1	4	yes	complemented
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	6	1	no	—
377	C₂×C₂²⋊C₄	—	3	2	no	—
378	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
379	C₂×C₄²	—	2	1	no	—
380	C₂×C₄²	—	6	1	no	—
381	#99	—	3	16	no	—
382	C₂×C₃×C₅	—	2	1	no	—
383	C₂×C₃×C₅	—	2	1	no	—
384	C₂×C₃×C₅	—	2	1	no	—
385	C₂×C₃×C₅	—	2	1	no	—
386	C₂×C₃×C₅	—	2	1	no	—
387	C₂×C₃×C₅	—	2	1	no	—
388	C₂×C₃×C₅	#410	1	2	yes	complemented
389	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
390	C₅×D₃	—	4	4	no	—
391	C₂³×C₃	—	4	2	no	—
392	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
393	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
394	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
395	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
396	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
397	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
398	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
399	C₂²×D₃	—	2	2	no	—
400	C₂²×D₃	—	2	2	no	—
401	C₂²×D₃	—	4	4	no	—
402	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
403	C₂×C₃×C₄	—	2	4	no	—
404	C₂×C₃×C₄	—	4	4	no	—
405	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
406	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
407	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
408	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
409	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
410	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
411	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
412	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
413	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
414	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
415	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
416	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
417	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
418	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
419	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
420	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
421	#67	—	2	4	no	—
422	#67	—	2	4	no	—
423	#67	—	2	4	no	—
424	#67	—	2	4	no	—
425	C₂×Dic₃	—	2	2	no	—
426	C₂×Dic₃	—	2	2	no	—
427	C₂×Dic₃	—	2	4	no	—
428	C₂×Dic₃	—	4	4	no	—
429	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
430	D₁₂	—	2	4	no	—
431	D₁₂	—	2	4	no	—
432	C₄×D₃	—	2	8	no	—
433	C₄×D₃	—	2	8	no	—
434	Dic₆	—	2	4	no	—
435	Dic₆	—	2	4	no	—
436	C₂²×C₅	—	2	2	no	—
437	C₂²×C₅	—	2	2	no	—
438	C₂²×C₅	—	2	2	no	—
439	C₂²×C₅	—	4	1	no	—
440	C₂²×C₅	—	4	1	no	—
441	C₂²×C₅	—	4	1	no	—
442	C₂²×C₅	—	4	1	no	—
443	C₂²×C₅	—	6	4	no	—
444	C₂²×C₅	—	12	4	no	—
445	C₂²×C₅	—	12	4	no	—
446	C₂²×C₅	—	12	4	no	—
447	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
448	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
449	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
450	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
451	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
452	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
453	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
454	C₄×C₅	—	4	4	no	—
455	C₄×C₅	—	6	4	no	—
456	C₄×C₅	—	12	4	no	—
457	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
458	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
459	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
460	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
461	C₂⁴	—	3	2	no	—
462	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
463	#41	—	6	4	no	—
464	#41	—	6	4	no	—
465	#41	—	6	4	no	—
466	#41	—	6	4	no	—
467	#41	—	6	4	no	—
468	#41	—	6	4	no	—
469	#41	—	6	4	no	—
470	#41	—	6	4	no	—
471	C₂×Q₈	—	3	4	no	—
472	C₂×Q₈	—	6	2	no	—
473	C₂×Q₈	—	6	1	no	—
474	C₂×Q₈	—	6	1	no	—
475	C₂×D₄	—	3	4	no	—
476	C₂×D₄	—	3	4	no	—
477	C₂×D₄	—	3	4	no	—
478	C₂×D₄	—	6	2	no	—
479	C₂×D₄	—	6	2	no	—
480	C₂×D₄	—	6	2	no	—
481	C₂×D₄	—	6	2	no	—
482	C₂×D₄	—	6	2	no	—
483	C₂×D₄	—	6	1	no	—
484	C₂×D₄	—	6	1	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	3	2	no	—
487	C₂²×C₄	—	3	8	no	—
488	C₂²×C₄	—	6	4	no	—
489	C₂²×C₄	—	6	2	no	—
490	C₂²×C₄	—	6	2	no	—
491	C₂²×C₄	—	6	2	no	—
492	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
493	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
494	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
495	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
496	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
497	C₂²×C₄	C₅×D₁₂	1	2	yes	—
498	C₂²×C₄	C₅×#67	1	1	yes	characteristic
499	C₂²×C₄	C₅×#67	1	1	yes	characteristic
500	C₂²×C₄	C₅×#67	1	2	yes	—
501	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
502	C₄⋊C₄	—	2	4	no	—
503	C₄⋊C₄	—	6	4	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	3	4	no	—
506	C₂²⋊C₄	—	6	2	no	—
507	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
508	C₄²	—	2	4	no	—
509	C₄²	—	6	4	no	—
510	C₃×C₅	C₂×#410	1	1	yes	characteristic, complemented, Hall
511	C₂²×C₃	—	2	2	no	—
512	C₂²×C₃	—	2	2	no	—
513	C₂²×C₃	—	2	2	no	—
514	C₂²×C₃	—	4	1	no	—
515	C₂²×C₃	—	4	1	no	—
516	C₂²×C₃	—	4	1	no	—
517	C₂²×C₃	—	4	1	no	—
518	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
519	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
520	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
521	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
522	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
523	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
524	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
525	C₂×D₃	—	2	4	no	—
526	C₂×D₃	—	4	4	no	—
527	C₂×D₃	—	4	4	no	—
528	C₂×D₃	—	4	4	no	—
529	C₃×C₄	—	4	4	no	—
530	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
531	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
532	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
533	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
534	Dic₃	—	2	4	no	—
535	Dic₃	—	4	4	no	—
536	C₂×C₅	—	2	1	no	—
537	C₂×C₅	—	2	1	no	—
538	C₂×C₅	—	2	1	no	—
539	C₂×C₅	—	2	1	no	—
540	C₂×C₅	—	2	1	no	—
541	C₂×C₅	—	2	1	no	—
542	C₂×C₅	—	12	4	no	—
543	C₂×C₅	#5006	1	2	yes	direct product factor
544	C₂×C₅	C₂²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
545	C₂³	—	3	4	no	—
546	C₂³	—	4	2	no	—
547	C₂³	—	6	2	no	—
548	C₂³	—	6	2	no	—
549	C₂³	—	12	4	no	—
550	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
551	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
552	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
553	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
554	C₂³	C₂×C₅×#67	1	1	yes	characteristic
555	C₂³	C₂×C₅×#67	1	1	yes	characteristic
556	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
557	Q₈	—	6	4	no	—
558	Q₈	—	6	4	no	—
559	D₄	—	6	4	no	—
560	D₄	—	6	4	no	—
561	D₄	—	6	4	no	—
562	D₄	—	6	4	no	—
563	D₄	—	6	4	no	—
564	D₄	—	6	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	3	4	no	—
567	C₂×C₄	—	4	4	no	—
568	C₂×C₄	—	6	2	no	—
569	C₂×C₄	—	6	2	no	—
570	C₂×C₄	—	6	8	no	—
571	C₂×C₄	—	6	8	no	—
572	C₂×C₄	—	6	4	no	—
573	C₂×C₄	—	12	4	no	—
574	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
575	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
576	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
577	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
578	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
579	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
580	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
581	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
582	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
583	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
584	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
585	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
586	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
587	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
588	C₂×C₄	C₂×C₅×#67	1	2	yes	—
589	C₂×C₄	C₂×C₅×#67	1	2	yes	—
590	C₂×C₃	—	2	1	no	—
591	C₂×C₃	—	2	1	no	—
592	C₂×C₃	—	2	1	no	—
593	C₂×C₃	—	2	1	no	—
594	C₂×C₃	—	2	1	no	—
595	C₂×C₃	—	2	1	no	—
596	C₂×C₃	C₅×#410	1	2	yes	complemented
597	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
598	D₃	—	4	4	no	—
599	C₅	C₂×#5006	1	1	yes	characteristic, direct product factor, Sylow
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	6	4	no	—
608	C₂²	—	12	4	no	—
609	C₂²	—	12	4	no	—
610	C₂²	—	12	4	no	—
611	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
612	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
613	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
614	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
615	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
616	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
617	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
618	C₄	—	4	4	no	—
619	C₄	—	6	4	no	—
620	C₄	—	12	4	no	—
621	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
622	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
623	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
624	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
625	C₃	C₂×C₅×#410	1	1	yes	characteristic, complemented, Sylow
626	C₂	—	2	1	no	—
627	C₂	—	2	1	no	—
628	C₂	—	2	1	no	—
629	C₂	—	2	1	no	—
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	12	4	no	—
633	C₂	C₅×#5006	1	2	yes	direct product factor
634	C₂	C₂²×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	(C₂×D₃)⋊C₄
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#117	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂²×C₅×#235	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₂×C₅×#117	D₃
hypocenter	C₃	C₂×C₅×#410
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂³×C₄×C₅ ◁ C₂×C₅×#117

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#117	C₂	semidirect
3. C₂×C₅×#926	C₂	semidirect
4. C₅×#5006	C₂	direct (N × H)
5. C₂×C₅×#806	C₂	semidirect
15. C₂×C₅×#235	C₄	semidirect
17. C₂²×C₅×D₁₂	C₄	semidirect
18. C₂²×C₄×C₅×D₃	C₄	semidirect
19. C₂²×C₅×Dic₆	C₄	semidirect
21. C₃×C₅×#117	C₂²	semidirect
27. C₅×#926	C₂²	semidirect
30. C₅×#806	C₂²	semidirect
31. C₂×#5006	C₅	direct (N × H)
34. C₂×C₅×#117	D₃	semidirect
69. C₂×C₅×D₁₂	C₂×C₄	semidirect
73. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
77. C₂×C₅×Dic₆	C₂×C₄	semidirect
87. C₂×C₃×#117	C₂×C₅	semidirect
88. C₂×#926	C₂×C₅	semidirect
89. #5006	C₂×C₅	direct (N × H)
90. C₂×#806	C₂×C₅	semidirect
107. C₅×#117	C₂×D₃	semidirect
169. C₂×#235	C₄×C₅	semidirect
171. C₂²×D₁₂	C₄×C₅	semidirect
172. C₂²×C₄×D₃	C₄×C₅	semidirect
173. C₂²×Dic₆	C₄×C₅	semidirect
175. C₃×#117	C₂²×C₅	semidirect
181. #926	C₂²×C₅	semidirect
184. #806	C₂²×C₅	semidirect
236. C₂×#117	C₅×D₃	semidirect
296. C₂×D₁₂	C₂×C₄×C₅	semidirect
300. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
304. C₂×Dic₆	C₂×C₄×C₅	semidirect
374. #117	C₂×C₅×D₃	semidirect
388. C₂×C₃×C₅	#410	semidirect
510. C₃×C₅	C₂×#410	semidirect
543. C₂×C₅	#5006	direct (N × H)
596. C₂×C₃	C₅×#410	semidirect
599. C₅	C₂×#5006	direct (N × H)
625. C₃	C₂×C₅×#410	semidirect
633. C₂	C₅×#5006	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
C₂×C₃×C₅×#117	2
C₂×C₅×#926	2
C₅×#5006	2
C₂×C₅×#806	2
C₂×C₅×#410	3
C₂×#5006	5

Subgroups — C2×C5×#5006 #14411918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5006 #14411918