Subgroups — C₃×D₅×#550 #14482964

Order 1920.

3472 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×#41	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66168	C₂	1	2	yes	maximal, complemented
4	C₃×#66052	C₂	1	3	yes	maximal, complemented
5	C₃×D₅×#127	C₂	1	3	yes	maximal, complemented
6	C₃×D₅×#121	C₂	1	6	yes	maximal, complemented
7	C₃×#65933	C₂	1	6	yes	maximal, complemented
8	C₃×#65911	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×Q₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65887	C₂	1	3	yes	maximal, complemented
11	C₃×C₄×D₄×D₅	C₂	1	3	yes	maximal, complemented
12	D₅×#550	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
14	C₃×D₅×#41	—	2	16	no	—
15	C₂×C₃×#713	C₂²	1	2	yes	complemented
16	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic
17	C₂×C₃×#711	C₂²	1	6	yes	complemented
18	C₂×C₃×D₄×D₅	C₂²	1	3	yes	—
19	C₂×C₃×D₄×D₅	C₂²	1	6	yes	—
20	C₂×C₃×D₄×D₅	C₂²	1	6	yes	—
21	C₂×C₃×#709	C₂²	1	6	yes	complemented
22	C₂²×C₃×C₄×D₅	C₂²	1	6	yes	—
23	C₃×C₅×#127	C₂²	1	3	yes	complemented
24	C₃×C₅×#121	C₂²	1	6	yes	complemented
25	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₄×C₅×D₄	C₂²	1	3	yes	complemented
27	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
28	C₃×#4086	C₂²	1	6	yes	complemented
29	C₃×#4086	C₂²	1	6	yes	complemented
30	C₃×#4086	C₂²	1	6	yes	complemented
31	C₃×#4085	C₂²	1	12	yes	complemented
32	C₃×#4084	C₂²	1	6	yes	complemented
33	C₃×D₄×Dic₅	C₂²	1	3	yes	complemented
34	C₃×#4076	C₂²	1	6	yes	complemented
35	C₃×C₄×C₂²⋊D₅	C₂²	1	6	yes	complemented
36	C₃×#4041	C₂²	1	6	yes	complemented
37	C₃×#4039	C₂²	1	3	yes	complemented
38	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×D₅×C₄⋊C₄	C₂²	1	3	yes	—
40	C₃×#4033	C₂²	1	3	yes	complemented
41	C₃×#4030	C₂²	1	12	yes	complemented
42	C₃×#4027	C₂²	1	6	yes	complemented
43	C₃×D₅×C₂²⋊C₄	C₂²	1	6	yes	—
44	C₃×#4020	C₂²	1	3	yes	complemented
45	C₃×C₄×D₂₀	C₂²	1	3	yes	complemented
46	C₃×C₄²×D₅	C₂²	1	3	yes	—
47	C₃×C₄×Dic₁₀	C₂²	1	3	yes	complemented
48	C₂×C₃×#550	—	5	1	no	maximal, Hall
49	C₂×D₅×#41	C₂×C₃	1	2	yes	complemented
50	C₅×#550	C₂×C₃	1	1	yes	characteristic, complemented
51	#66168	C₂×C₃	1	2	yes	complemented
52	#66052	C₂×C₃	1	3	yes	complemented
53	D₅×#127	C₂×C₃	1	3	yes	complemented
54	D₅×#121	C₂×C₃	1	6	yes	complemented
55	#65933	C₂×C₃	1	6	yes	complemented
56	#65911	C₂×C₃	1	1	yes	characteristic, complemented
57	C₄×Q₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
58	#65887	C₂×C₃	1	3	yes	complemented
59	C₄×D₄×D₅	C₂×C₃	1	3	yes	complemented
60	C₂³×C₃×D₅	C₂³	1	6	yes	—
61	C₃×C₅×#41	—	2	8	no	—
62	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×D₄	C₂³	1	3	yes	—
64	C₂×C₃×C₅×D₄	C₂³	1	6	yes	—
65	C₂×C₃×C₅×D₄	C₂³	1	6	yes	—
66	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
67	C₂×C₃×C₂²⋊D₅	C₂³	1	12	yes	—
68	C₂×C₃×C₂²⋊D₅	C₂³	1	6	yes	—
69	C₂×C₃×C₂²⋊D₅	C₂³	1	12	yes	—
70	C₂²×C₃×Dic₅	C₂³	1	6	yes	—
71	C₃×#713	—	2	8	no	—
72	C₃×Q₈×D₅	D₄	1	8	yes	complemented
73	C₃×#711	—	2	24	no	—
74	C₃×D₄×D₅	—	2	24	no	—
75	C₃×D₄×D₅	—	2	12	no	—
76	C₃×D₄×D₅	—	4	12	no	—
77	C₃×#709	—	2	24	no	—
78	C₂×C₃×D₂₀	C₂³	1	3	yes	—
79	C₂×C₃×D₂₀	C₂³	1	6	yes	—
80	C₂×C₃×D₂₀	C₂³	1	6	yes	—
81	C₂×C₃×C₄×D₅	—	2	24	no	—
82	C₂×C₃×C₄×D₅	C₂³	1	6	yes	—
83	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
84	C₂×C₃×C₄×D₅	C₂³	1	6	yes	—
85	C₂×C₃×C₄×D₅	C₂³	1	3	yes	—
86	C₂×C₃×C₄×D₅	C₂³	1	3	yes	—
87	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
88	C₂×C₃×Dic₁₀	C₂³	1	3	yes	—
89	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₃×C₅×C₄⋊C₄	C₂³	1	3	yes	—
91	C₃×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
92	C₃×C₄²×C₅	C₂³	1	3	yes	—
93	C₃×C₂²⋊Dic₅	C₂³	1	6	yes	—
94	C₃×#685	C₂³	1	6	yes	—
95	C₃×#685	C₂³	1	6	yes	—
96	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
97	C₃×C₄⋊Dic₅	C₂³	1	3	yes	—
98	C₃×#683	C₂³	1	6	yes	—
99	C₃×#683	C₂³	1	2	yes	—
100	C₃×C₄×Dic₅	C₂³	1	3	yes	—
101	C₃×C₄×Dic₅	C₂³	1	3	yes	—
102	C₃×C₄×Dic₅	C₂³	1	3	yes	—
103	C₂²×C₃×#41	—	5	2	no	—
104	C₃×#550	—	5	2	no	—
105	C₃×#550	—	5	3	no	—
106	C₃×#550	—	5	6	no	—
107	C₃×#550	—	5	1	no	—
108	C₃×#550	—	5	3	no	—
109	C₃×#550	D₅	1	1	yes	characteristic, direct product factor
110	C₂×C₃×#127	—	5	3	no	—
111	C₂×C₃×#121	—	5	6	no	—
112	C₂×C₃×C₄×Q₈	—	5	1	no	—
113	C₂×C₃×C₄×D₄	—	5	3	no	—
114	C₂×C₅×#41	C₂²×C₃	1	2	yes	complemented
115	D₅×#41	—	2	16	no	—
116	C₂×#713	C₂²×C₃	1	2	yes	complemented
117	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic
118	C₂×#711	C₂²×C₃	1	6	yes	complemented
119	C₂×D₄×D₅	C₂²×C₃	1	3	yes	—
120	C₂×D₄×D₅	C₂²×C₃	1	6	yes	—
121	C₂×D₄×D₅	C₂²×C₃	1	6	yes	—
122	C₂×#709	C₂²×C₃	1	6	yes	complemented
123	C₂²×C₄×D₅	C₂²×C₃	1	6	yes	—
124	C₅×#127	C₂²×C₃	1	3	yes	complemented
125	C₅×#121	C₂²×C₃	1	6	yes	complemented
126	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₄×C₅×D₄	C₂²×C₃	1	3	yes	complemented
128	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
129	#4086	C₂²×C₃	1	6	yes	complemented
130	#4086	C₂²×C₃	1	6	yes	complemented
131	#4086	C₂²×C₃	1	6	yes	complemented
132	#4085	C₂²×C₃	1	12	yes	complemented
133	#4084	C₂²×C₃	1	6	yes	complemented
134	D₄×Dic₅	C₂²×C₃	1	3	yes	complemented
135	#4076	C₂²×C₃	1	6	yes	complemented
136	C₄×C₂²⋊D₅	C₂²×C₃	1	6	yes	complemented
137	#4041	C₂²×C₃	1	6	yes	complemented
138	#4039	C₂²×C₃	1	3	yes	complemented
139	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
140	D₅×C₄⋊C₄	C₂²×C₃	1	3	yes	—
141	#4033	C₂²×C₃	1	3	yes	complemented
142	#4030	C₂²×C₃	1	12	yes	complemented
143	#4027	C₂²×C₃	1	6	yes	complemented
144	D₅×C₂²⋊C₄	C₂²×C₃	1	6	yes	—
145	#4020	C₂²×C₃	1	3	yes	complemented
146	C₄×D₂₀	C₂²×C₃	1	3	yes	complemented
147	C₄²×D₅	C₂²×C₃	1	3	yes	—
148	C₄×Dic₁₀	C₂²×C₃	1	3	yes	complemented
149	C₂×#550	—	5	1	no	Sylow
150	C₂³×C₃×C₅	C₂⁴	1	6	yes	—
151	C₂²×C₃×D₅	—	2	12	no	—
152	C₂²×C₃×D₅	—	2	12	no	—
153	C₂²×C₃×D₅	—	2	12	no	—
154	C₂²×C₃×D₅	C₂⁴	1	6	yes	—
155	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
156	C₃×C₅×Q₈	C₂×D₄	1	4	yes	complemented
157	C₃×C₅×D₄	—	2	12	no	—
158	C₃×C₅×D₄	—	2	6	no	—
159	C₃×C₅×D₄	—	4	6	no	—
160	C₂×C₃×C₄×C₅	—	2	12	no	—
161	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
162	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
163	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
164	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
165	C₃×C₂²⋊D₅	—	2	24	no	—
166	C₃×C₂²⋊D₅	—	2	12	no	—
167	C₃×C₂²⋊D₅	—	4	12	no	—
168	C₂×C₃×Dic₅	—	2	12	no	—
169	C₂×C₃×Dic₅	C₂⁴	1	3	yes	—
170	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
171	C₂×C₃×Dic₅	C₂⁴	1	3	yes	—
172	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
173	C₃×D₂₀	—	2	12	no	—
174	C₃×D₂₀	—	2	6	no	—
175	C₃×D₂₀	—	4	6	no	—
176	C₃×C₄×D₅	—	2	4	no	—
177	C₃×C₄×D₅	—	2	6	no	—
178	C₃×C₄×D₅	—	2	12	no	—
179	C₃×C₄×D₅	—	2	12	no	—
180	C₃×C₄×D₅	C₂×D₄	1	12	yes	—
181	C₃×C₄×D₅	#41	1	4	yes	complemented
182	C₃×Dic₁₀	C₂×D₄	1	12	yes	complemented
183	C₂×C₃×#41	—	5	2	no	—
184	C₂×C₃×#41	—	5	6	no	—
185	C₂×C₃×#41	—	5	6	no	—
186	C₂×C₃×#41	—	10	16	no	—
187	C₂×C₃×#41	C₂×D₅	1	2	yes	complemented
188	C₂²×C₃×Q₈	—	5	1	no	—
189	C₂²×C₃×D₄	—	5	6	no	—
190	C₂²×C₃×D₄	—	5	3	no	—
191	C₂²×C₃×D₄	—	5	6	no	—
192	C₂³×C₃×C₄	—	5	6	no	—
193	C₃×#127	—	5	6	no	—
194	C₃×#127	—	5	6	no	—
195	C₃×#127	—	5	6	no	—
196	C₃×#127	—	5	3	no	—
197	C₃×#127	C₂×D₅	1	3	yes	complemented
198	C₃×#121	—	5	6	no	—
199	C₃×#121	—	5	12	no	—
200	C₃×#121	—	5	6	no	—
201	C₃×#121	—	5	6	no	—
202	C₃×#121	—	5	12	no	—
203	C₃×#121	C₂×D₅	1	6	yes	complemented
204	C₃×C₄×Q₈	—	5	1	no	—
205	C₃×C₄×Q₈	—	5	3	no	—
206	C₃×C₄×Q₈	—	5	3	no	—
207	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
208	C₃×C₄×D₄	—	5	3	no	—
209	C₃×C₄×D₄	—	5	6	no	—
210	C₃×C₄×D₄	—	5	3	no	—
211	C₃×C₄×D₄	—	5	6	no	—
212	C₃×C₄×D₄	—	5	3	no	—
213	C₃×C₄×D₄	C₂×D₅	1	3	yes	complemented
214	C₂×C₃×C₄⋊C₄	—	5	1	no	—
215	C₂×C₃×C₄⋊C₄	—	5	3	no	—
216	C₂×C₃×C₂²⋊C₄	—	5	6	no	—
217	C₂×C₃×C₄²	—	5	3	no	—
218	C₂³×D₅	C₂³×C₃	1	6	yes	—
219	C₅×#41	—	2	8	no	—
220	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
221	C₂×C₅×D₄	C₂³×C₃	1	3	yes	—
222	C₂×C₅×D₄	C₂³×C₃	1	6	yes	—
223	C₂×C₅×D₄	C₂³×C₃	1	6	yes	—
224	C₂²×C₄×C₅	C₂³×C₃	1	6	yes	—
225	C₂×C₂²⋊D₅	C₂³×C₃	1	12	yes	—
226	C₂×C₂²⋊D₅	C₂³×C₃	1	6	yes	—
227	C₂×C₂²⋊D₅	C₂³×C₃	1	12	yes	—
228	C₂²×Dic₅	C₂³×C₃	1	6	yes	—
229	#713	—	2	8	no	—
230	Q₈×D₅	C₃×D₄	1	8	yes	complemented
231	#711	—	2	24	no	—
232	D₄×D₅	—	2	24	no	—
233	D₄×D₅	—	2	12	no	—
234	D₄×D₅	—	4	12	no	—
235	#709	—	2	24	no	—
236	C₂×D₂₀	C₂³×C₃	1	6	yes	—
237	C₂×D₂₀	C₂³×C₃	1	3	yes	—
238	C₂×D₂₀	C₂³×C₃	1	6	yes	—
239	C₂×C₄×D₅	—	2	24	no	—
240	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
241	C₂×C₄×D₅	C₂³×C₃	1	6	yes	—
242	C₂×C₄×D₅	C₂³×C₃	1	6	yes	—
243	C₂×C₄×D₅	C₂³×C₃	1	3	yes	—
244	C₂×C₄×D₅	C₂³×C₃	1	3	yes	—
245	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
246	C₂×Dic₁₀	C₂³×C₃	1	3	yes	—
247	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
248	C₅×C₄⋊C₄	C₂³×C₃	1	3	yes	—
249	C₅×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
250	C₄²×C₅	C₂³×C₃	1	3	yes	—
251	C₂²⋊Dic₅	C₂³×C₃	1	6	yes	—
252	#685	C₂³×C₃	1	6	yes	—
253	#685	C₂³×C₃	1	6	yes	—
254	C₄⋊Dic₅	C₂³×C₃	1	3	yes	—
255	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
256	#683	C₂³×C₃	1	6	yes	—
257	#683	C₂³×C₃	1	2	yes	—
258	C₄×Dic₅	C₂³×C₃	1	3	yes	—
259	C₄×Dic₅	C₂³×C₃	1	3	yes	—
260	C₄×Dic₅	C₂³×C₃	1	3	yes	—
261	C₂²×#41	—	5	2	no	—
262	#550	—	5	2	no	—
263	#550	—	5	3	no	—
264	#550	—	5	6	no	—
265	#550	—	5	1	no	—
266	#550	—	5	3	no	—
267	#550	C₃×D₅	1	1	yes	characteristic, direct product factor
268	C₂×#127	—	5	3	no	—
269	C₂×#121	—	5	6	no	—
270	C₂×C₄×Q₈	—	5	1	no	—
271	C₂×C₄×D₄	—	5	3	no	—
272	C₂²×C₃×C₅	—	2	6	no	—
273	C₂²×C₃×C₅	—	2	6	no	—
274	C₂²×C₃×C₅	—	2	6	no	—
275	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
276	C₂×C₃×D₅	—	2	6	no	—
277	C₂×C₃×D₅	—	2	6	no	—
278	C₂×C₃×D₅	—	2	6	no	—
279	C₂×C₃×D₅	—	4	24	no	—
280	C₂×C₃×D₅	C₂²×D₄	1	2	yes	—
281	C₂×C₃×D₅	C₂×#41	1	2	yes	—
282	C₂×C₃×D₅	H(5,𝔽₂)	1	2	yes	—
283	C₃×C₄×C₅	—	2	2	no	—
284	C₃×C₄×C₅	—	2	3	no	—
285	C₃×C₄×C₅	C₂²×D₄	1	6	yes	—
286	C₃×C₄×C₅	C₂×#41	1	2	yes	complemented
287	C₃×Dic₅	—	2	2	no	—
288	C₃×Dic₅	—	2	3	no	—
289	C₃×Dic₅	C₂²×D₄	1	6	yes	—
290	C₃×Dic₅	C₂×#41	1	2	yes	complemented
291	C₂⁴×C₃	—	5	6	no	—
292	C₃×#41	—	2	8	no	—
293	C₃×#41	—	10	24	no	—
294	C₃×#41	—	10	24	no	—
295	C₃×#41	—	10	8	no	—
296	C₂×C₃×Q₈	—	5	8	no	—
297	C₂×C₃×Q₈	—	5	3	no	—
298	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
299	C₂×C₃×D₄	—	5	6	no	—
300	C₂×C₃×D₄	—	5	12	no	—
301	C₂×C₃×D₄	—	5	12	no	—
302	C₂×C₃×D₄	—	5	3	no	—
303	C₂×C₃×D₄	—	5	6	no	—
304	C₂×C₃×D₄	—	5	6	no	—
305	C₂×C₃×D₄	—	10	12	no	—
306	C₂×C₃×D₄	—	10	24	no	—
307	C₂×C₃×D₄	—	20	12	no	—
308	C₂×C₃×D₄	C₂²×D₅	1	3	yes	—
309	C₂×C₃×D₄	C₂²×D₅	1	6	yes	—
310	C₂×C₃×D₄	C₂²×D₅	1	6	yes	—
311	C₂²×C₃×C₄	—	5	1	no	—
312	C₂²×C₃×C₄	—	5	3	no	—
313	C₂²×C₃×C₄	—	5	6	no	—
314	C₂²×C₃×C₄	—	5	3	no	—
315	C₂²×C₃×C₄	—	5	2	no	—
316	C₂²×C₃×C₄	—	5	6	no	—
317	C₂²×C₃×C₄	—	5	6	no	—
318	C₂²×C₃×C₄	—	10	24	no	—
319	C₂²×C₃×C₄	C₂²×D₅	1	6	yes	—
320	C₃×C₄⋊C₄	—	5	2	no	—
321	C₃×C₄⋊C₄	—	5	6	no	—
322	C₃×C₄⋊C₄	—	5	1	no	—
323	C₃×C₄⋊C₄	—	5	3	no	—
324	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
325	C₃×C₄⋊C₄	C₂²×D₅	1	3	yes	—
326	C₃×C₂²⋊C₄	—	5	6	no	—
327	C₃×C₂²⋊C₄	—	5	6	no	—
328	C₃×C₂²⋊C₄	—	5	6	no	—
329	C₃×C₂²⋊C₄	C₂²×D₅	1	6	yes	—
330	C₃×C₄²	—	5	3	no	—
331	C₃×C₄²	—	5	3	no	—
332	C₃×C₄²	—	5	3	no	—
333	C₃×C₄²	C₂²×D₅	1	3	yes	—
334	C₂³×C₅	C₂⁴×C₃	1	6	yes	—
335	C₂²×D₅	—	2	12	no	—
336	C₂²×D₅	—	2	12	no	—
337	C₂²×D₅	—	2	12	no	—
338	C₂²×D₅	C₂⁴×C₃	1	6	yes	—
339	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
340	C₅×Q₈	C₂×C₃×D₄	1	4	yes	complemented
341	C₅×D₄	—	2	12	no	—
342	C₅×D₄	—	2	6	no	—
343	C₅×D₄	—	4	6	no	—
344	C₂×C₄×C₅	—	2	12	no	—
345	C₂×C₄×C₅	C₂⁴×C₃	1	3	yes	—
346	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
347	C₂×C₄×C₅	C₂⁴×C₃	1	3	yes	—
348	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
349	C₂²⋊D₅	—	2	24	no	—
350	C₂²⋊D₅	—	2	12	no	—
351	C₂²⋊D₅	—	4	12	no	—
352	C₂×Dic₅	—	2	12	no	—
353	C₂×Dic₅	C₂⁴×C₃	1	3	yes	—
354	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
355	C₂×Dic₅	C₂⁴×C₃	1	3	yes	—
356	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
357	D₂₀	—	2	12	no	—
358	D₂₀	—	2	6	no	—
359	D₂₀	—	4	6	no	—
360	C₄×D₅	—	2	4	no	—
361	C₄×D₅	—	2	6	no	—
362	C₄×D₅	—	2	12	no	—
363	C₄×D₅	—	2	12	no	—
364	C₄×D₅	C₂×C₃×D₄	1	12	yes	—
365	C₄×D₅	C₃×#41	1	4	yes	complemented
366	Dic₁₀	C₂×C₃×D₄	1	12	yes	complemented
367	C₂×#41	—	5	2	no	—
368	C₂×#41	—	5	6	no	—
369	C₂×#41	—	5	6	no	—
370	C₂×#41	—	10	16	no	—
371	C₂×#41	C₂×C₃×D₅	1	2	yes	complemented
372	C₂²×Q₈	—	5	1	no	—
373	C₂²×D₄	—	5	3	no	—
374	C₂²×D₄	—	5	6	no	—
375	C₂²×D₄	—	5	6	no	—
376	C₂³×C₄	—	5	6	no	—
377	#127	—	5	6	no	—
378	#127	—	5	6	no	—
379	#127	—	5	6	no	—
380	#127	—	5	3	no	—
381	#127	C₂×C₃×D₅	1	3	yes	complemented
382	#121	—	5	6	no	—
383	#121	—	5	12	no	—
384	#121	—	5	6	no	—
385	#121	—	5	6	no	—
386	#121	—	5	12	no	—
387	#121	C₂×C₃×D₅	1	6	yes	complemented
388	C₄×Q₈	—	5	1	no	—
389	C₄×Q₈	—	5	3	no	—
390	C₄×Q₈	—	5	3	no	—
391	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
392	C₄×D₄	—	5	3	no	—
393	C₄×D₄	—	5	6	no	—
394	C₄×D₄	—	5	3	no	—
395	C₄×D₄	—	5	6	no	—
396	C₄×D₄	—	5	3	no	—
397	C₄×D₄	C₂×C₃×D₅	1	3	yes	complemented
398	C₂×C₄⋊C₄	—	5	1	no	—
399	C₂×C₄⋊C₄	—	5	3	no	—
400	C₂×C₂²⋊C₄	—	5	6	no	—
401	C₂×C₄²	—	5	3	no	—
402	C₂×C₃×C₅	—	4	6	no	—
403	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
404	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
405	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
406	C₃×D₅	—	4	6	no	—
407	C₃×D₅	#550	1	4	yes	direct product factor
408	C₂³×C₃	—	5	1	no	—
409	C₂³×C₃	—	5	6	no	—
410	C₂³×C₃	—	10	12	no	—
411	C₂³×C₃	—	10	12	no	—
412	C₂³×C₃	—	10	12	no	—
413	C₂³×C₃	C₂³×D₅	1	6	yes	—
414	C₃×Q₈	—	5	12	no	—
415	C₃×Q₈	D₄×D₅	1	4	yes	complemented
416	C₃×D₄	—	2	12	no	—
417	C₃×D₄	—	2	6	no	—
418	C₃×D₄	—	4	6	no	—
419	C₃×D₄	—	10	12	no	—
420	C₃×D₄	—	10	24	no	—
421	C₃×D₄	—	10	12	no	—
422	C₃×D₄	—	10	6	no	—
423	C₃×D₄	—	20	6	no	—
424	C₃×D₄	—	20	12	no	—
425	C₂×C₃×C₄	—	2	12	no	—
426	C₂×C₃×C₄	—	5	1	no	—
427	C₂×C₃×C₄	—	5	3	no	—
428	C₂×C₃×C₄	—	5	12	no	—
429	C₂×C₃×C₄	—	5	4	no	—
430	C₂×C₃×C₄	—	5	3	no	—
431	C₂×C₃×C₄	—	5	2	no	—
432	C₂×C₃×C₄	—	10	12	no	—
433	C₂×C₃×C₄	—	10	4	no	—
434	C₂×C₃×C₄	—	10	6	no	—
435	C₂×C₃×C₄	—	10	12	no	—
436	C₂×C₃×C₄	—	10	12	no	—
437	C₂×C₃×C₄	C₂³×D₅	1	3	yes	—
438	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
439	C₂×C₃×C₄	C₂³×D₅	1	3	yes	—
440	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
441	C₂²×C₅	—	2	6	no	—
442	C₂²×C₅	—	2	6	no	—
443	C₂²×C₅	—	2	6	no	—
444	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
445	C₂×D₅	—	2	6	no	—
446	C₂×D₅	—	2	6	no	—
447	C₂×D₅	—	2	6	no	—
448	C₂×D₅	—	4	24	no	—
449	C₂×D₅	C₂²×C₃×D₄	1	2	yes	—
450	C₂×D₅	C₂×C₃×#41	1	2	yes	—
451	C₂×D₅	C₃×H(5,𝔽₂)	1	2	yes	—
452	C₄×C₅	—	2	2	no	—
453	C₄×C₅	—	2	3	no	—
454	C₄×C₅	C₂²×C₃×D₄	1	6	yes	—
455	C₄×C₅	C₂×C₃×#41	1	2	yes	complemented
456	Dic₅	—	2	2	no	—
457	Dic₅	—	2	3	no	—
458	Dic₅	C₂²×C₃×D₄	1	6	yes	—
459	Dic₅	C₂×C₃×#41	1	2	yes	complemented
460	C₂⁴	—	5	6	no	—
461	#41	—	2	8	no	—
462	#41	—	10	24	no	—
463	#41	—	10	24	no	—
464	#41	—	10	8	no	—
465	C₂×Q₈	—	5	8	no	—
466	C₂×Q₈	—	5	3	no	—
467	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
468	C₂×D₄	—	5	6	no	—
469	C₂×D₄	—	5	12	no	—
470	C₂×D₄	—	5	12	no	—
471	C₂×D₄	—	5	3	no	—
472	C₂×D₄	—	5	6	no	—
473	C₂×D₄	—	5	6	no	—
474	C₂×D₄	—	10	24	no	—
475	C₂×D₄	—	10	12	no	—
476	C₂×D₄	—	20	12	no	—
477	C₂×D₄	C₂²×C₃×D₅	1	3	yes	—
478	C₂×D₄	C₂²×C₃×D₅	1	6	yes	—
479	C₂×D₄	C₂²×C₃×D₅	1	6	yes	—
480	C₂²×C₄	—	5	1	no	—
481	C₂²×C₄	—	5	3	no	—
482	C₂²×C₄	—	5	6	no	—
483	C₂²×C₄	—	5	3	no	—
484	C₂²×C₄	—	5	2	no	—
485	C₂²×C₄	—	5	6	no	—
486	C₂²×C₄	—	5	6	no	—
487	C₂²×C₄	—	10	24	no	—
488	C₂²×C₄	C₂²×C₃×D₅	1	6	yes	—
489	C₄⋊C₄	—	5	2	no	—
490	C₄⋊C₄	—	5	1	no	—
491	C₄⋊C₄	—	5	6	no	—
492	C₄⋊C₄	—	5	3	no	—
493	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×C₃×D₅	1	3	yes	—
495	C₂²⋊C₄	—	5	6	no	—
496	C₂²⋊C₄	—	5	6	no	—
497	C₂²⋊C₄	—	5	6	no	—
498	C₂²⋊C₄	C₂²×C₃×D₅	1	6	yes	—
499	C₄²	—	5	3	no	—
500	C₄²	—	5	3	no	—
501	C₄²	—	5	3	no	—
502	C₄²	C₂²×C₃×D₅	1	3	yes	—
503	C₃×C₅	C₂×#550	1	1	yes	characteristic, complemented, Hall
504	C₂²×C₃	—	2	6	no	—
505	C₂²×C₃	—	2	6	no	—
506	C₂²×C₃	—	2	6	no	—
507	C₂²×C₃	—	5	2	no	—
508	C₂²×C₃	—	5	2	no	—
509	C₂²×C₃	—	5	2	no	—
510	C₂²×C₃	—	10	6	no	—
511	C₂²×C₃	—	10	6	no	—
512	C₂²×C₃	—	10	6	no	—
513	C₂²×C₃	—	20	24	no	—
514	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
515	C₃×C₄	—	2	2	no	—
516	C₃×C₄	—	2	3	no	—
517	C₃×C₄	—	5	6	no	—
518	C₃×C₄	—	5	2	no	—
519	C₃×C₄	—	10	2	no	—
520	C₃×C₄	—	10	3	no	—
521	C₃×C₄	C₂×D₄×D₅	1	6	yes	—
522	C₃×C₄	D₅×#41	1	2	yes	complemented
523	C₂×C₅	—	4	6	no	—
524	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
525	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
526	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
527	D₅	—	4	6	no	—
528	D₅	C₃×#550	1	4	yes	direct product factor
529	C₂³	—	5	1	no	—
530	C₂³	—	5	6	no	—
531	C₂³	—	10	12	no	—
532	C₂³	—	10	12	no	—
533	C₂³	—	10	12	no	—
534	C₂³	C₂³×C₃×D₅	1	6	yes	—
535	Q₈	—	5	12	no	—
536	Q₈	C₃×D₄×D₅	1	4	yes	complemented
537	D₄	—	2	12	no	—
538	D₄	—	2	6	no	—
539	D₄	—	4	6	no	—
540	D₄	—	10	24	no	—
541	D₄	—	10	12	no	—
542	D₄	—	10	12	no	—
543	D₄	—	10	6	no	—
544	D₄	—	20	6	no	—
545	D₄	—	20	12	no	—
546	C₂×C₄	—	2	12	no	—
547	C₂×C₄	—	5	1	no	—
548	C₂×C₄	—	5	3	no	—
549	C₂×C₄	—	5	12	no	—
550	C₂×C₄	—	5	4	no	—
551	C₂×C₄	—	5	3	no	—
552	C₂×C₄	—	5	2	no	—
553	C₂×C₄	—	10	12	no	—
554	C₂×C₄	—	10	4	no	—
555	C₂×C₄	—	10	6	no	—
556	C₂×C₄	—	10	12	no	—
557	C₂×C₄	—	10	12	no	—
558	C₂×C₄	C₂³×C₃×D₅	1	3	yes	—
559	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
560	C₂×C₄	C₂³×C₃×D₅	1	3	yes	—
561	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
562	C₂×C₃	—	4	6	no	—
563	C₂×C₃	—	5	4	no	—
564	C₂×C₃	—	20	6	no	—
565	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
566	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
567	C₂×C₃	D₅×H(5,𝔽₂)	1	1	yes	characteristic
568	C₅	C₂×C₃×#550	1	1	yes	characteristic, complemented, Sylow
569	C₂²	—	2	6	no	—
570	C₂²	—	2	6	no	—
571	C₂²	—	2	6	no	—
572	C₂²	—	5	2	no	—
573	C₂²	—	5	2	no	—
574	C₂²	—	5	2	no	—
575	C₂²	—	10	6	no	—
576	C₂²	—	10	6	no	—
577	C₂²	—	10	6	no	—
578	C₂²	—	20	24	no	—
579	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
580	C₄	—	2	2	no	—
581	C₄	—	2	3	no	—
582	C₄	—	5	6	no	—
583	C₄	—	5	2	no	—
584	C₄	—	10	2	no	—
585	C₄	—	10	3	no	—
586	C₄	C₂×C₃×D₄×D₅	1	6	yes	—
587	C₄	C₃×D₅×#41	1	2	yes	complemented
588	C₃	D₅×#550	1	1	yes	characteristic, direct product factor, Sylow
589	C₂	—	4	6	no	—
590	C₂	—	5	4	no	—
591	C₂	—	20	6	no	—
592	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
593	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
594	C₂	C₃×D₅×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₅×#550	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₃×#550	D₅
hypocenter	C₅	C₂×C₃×#550
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#550

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₅×#41	C₂	semidirect
2. C₃×C₅×#550	C₂	semidirect
3. C₃×#66168	C₂	semidirect
4. C₃×#66052	C₂	semidirect
5. C₃×D₅×#127	C₂	semidirect
6. C₃×D₅×#121	C₂	semidirect
7. C₃×#65933	C₂	semidirect
8. C₃×#65911	C₂	semidirect
9. C₃×C₄×Q₈×D₅	C₂	semidirect
10. C₃×#65887	C₂	semidirect
11. C₃×C₄×D₄×D₅	C₂	semidirect
12. D₅×#550	C₃	direct (N × H)
13. C₂×C₃×C₅×#41	C₂²	semidirect
15. C₂×C₃×#713	C₂²	semidirect
17. C₂×C₃×#711	C₂²	semidirect
21. C₂×C₃×#709	C₂²	semidirect
23. C₃×C₅×#127	C₂²	semidirect
24. C₃×C₅×#121	C₂²	semidirect
25. C₃×C₄×C₅×Q₈	C₂²	semidirect
26. C₃×C₄×C₅×D₄	C₂²	semidirect
27. C₃×Q₈×Dic₅	C₂²	semidirect
28. C₃×#4086	C₂²	semidirect
29. C₃×#4086	C₂²	semidirect
30. C₃×#4086	C₂²	semidirect
31. C₃×#4085	C₂²	semidirect
32. C₃×#4084	C₂²	semidirect
33. C₃×D₄×Dic₅	C₂²	semidirect
34. C₃×#4076	C₂²	semidirect
35. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
36. C₃×#4041	C₂²	semidirect
37. C₃×#4039	C₂²	semidirect
40. C₃×#4033	C₂²	semidirect
41. C₃×#4030	C₂²	semidirect
42. C₃×#4027	C₂²	semidirect
44. C₃×#4020	C₂²	semidirect
45. C₃×C₄×D₂₀	C₂²	semidirect
47. C₃×C₄×Dic₁₀	C₂²	semidirect
49. C₂×D₅×#41	C₂×C₃	semidirect
50. C₅×#550	C₂×C₃	semidirect
51. #66168	C₂×C₃	semidirect
52. #66052	C₂×C₃	semidirect
53. D₅×#127	C₂×C₃	semidirect
54. D₅×#121	C₂×C₃	semidirect
55. #65933	C₂×C₃	semidirect
56. #65911	C₂×C₃	semidirect
57. C₄×Q₈×D₅	C₂×C₃	semidirect
58. #65887	C₂×C₃	semidirect
59. C₄×D₄×D₅	C₂×C₃	semidirect
72. C₃×Q₈×D₅	D₄	semidirect
109. C₃×#550	D₅	direct (N × H)
114. C₂×C₅×#41	C₂²×C₃	semidirect
116. C₂×#713	C₂²×C₃	semidirect
118. C₂×#711	C₂²×C₃	semidirect
122. C₂×#709	C₂²×C₃	semidirect
124. C₅×#127	C₂²×C₃	semidirect
125. C₅×#121	C₂²×C₃	semidirect
126. C₄×C₅×Q₈	C₂²×C₃	semidirect
127. C₄×C₅×D₄	C₂²×C₃	semidirect
128. Q₈×Dic₅	C₂²×C₃	semidirect
129. #4086	C₂²×C₃	semidirect
130. #4086	C₂²×C₃	semidirect
131. #4086	C₂²×C₃	semidirect
132. #4085	C₂²×C₃	semidirect
133. #4084	C₂²×C₃	semidirect
134. D₄×Dic₅	C₂²×C₃	semidirect
135. #4076	C₂²×C₃	semidirect
136. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
137. #4041	C₂²×C₃	semidirect
138. #4039	C₂²×C₃	semidirect
141. #4033	C₂²×C₃	semidirect
142. #4030	C₂²×C₃	semidirect
143. #4027	C₂²×C₃	semidirect
145. #4020	C₂²×C₃	semidirect
146. C₄×D₂₀	C₂²×C₃	semidirect
148. C₄×Dic₁₀	C₂²×C₃	semidirect
156. C₃×C₅×Q₈	C₂×D₄	semidirect
181. C₃×C₄×D₅	#41	semidirect
182. C₃×Dic₁₀	C₂×D₄	semidirect
187. C₂×C₃×#41	C₂×D₅	semidirect
197. C₃×#127	C₂×D₅	semidirect
203. C₃×#121	C₂×D₅	semidirect
207. C₃×C₄×Q₈	C₂×D₅	semidirect
213. C₃×C₄×D₄	C₂×D₅	semidirect
230. Q₈×D₅	C₃×D₄	semidirect
267. #550	C₃×D₅	direct (N × H)
286. C₃×C₄×C₅	C₂×#41	semidirect
290. C₃×Dic₅	C₂×#41	semidirect
340. C₅×Q₈	C₂×C₃×D₄	semidirect
365. C₄×D₅	C₃×#41	semidirect
366. Dic₁₀	C₂×C₃×D₄	semidirect
371. C₂×#41	C₂×C₃×D₅	semidirect
381. #127	C₂×C₃×D₅	semidirect
387. #121	C₂×C₃×D₅	semidirect
391. C₄×Q₈	C₂×C₃×D₅	semidirect
397. C₄×D₄	C₂×C₃×D₅	semidirect
407. C₃×D₅	#550	direct (N × H)
415. C₃×Q₈	D₄×D₅	semidirect
455. C₄×C₅	C₂×C₃×#41	semidirect
459. Dic₅	C₂×C₃×#41	semidirect
503. C₃×C₅	C₂×#550	semidirect
522. C₃×C₄	D₅×#41	semidirect
528. D₅	C₃×#550	direct (N × H)
536. Q₈	C₃×D₄×D₅	semidirect
568. C₅	C₂×C₃×#550	semidirect
587. C₄	C₃×D₅×#41	semidirect
588. C₃	D₅×#550	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×D₅×#41	2
C₃×C₅×#550	2
C₃×#66168	2
C₃×#66052	2
C₃×D₅×#127	2
C₃×D₅×#121	2
C₃×#65933	2
C₃×#65911	2
C₃×C₄×Q₈×D₅	2
C₃×#65887	2
C₃×C₄×D₄×D₅	2
D₅×#550	3
C₂×C₃×#550	5

Subgroups — C3×D5×#550 #14482964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#550 #14482964