Subgroups — C₅×D₃×#550 #14482963

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×C₅×D₃×#41	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5834	C₂	1	2	yes	maximal, complemented
4	C₅×#5718	C₂	1	3	yes	maximal, complemented
5	C₅×D₃×#127	C₂	1	3	yes	maximal, complemented
6	C₅×D₃×#121	C₂	1	6	yes	maximal, complemented
7	C₅×#5599	C₂	1	6	yes	maximal, complemented
8	C₅×#5577	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#5553	C₂	1	3	yes	maximal, complemented
11	C₄×C₅×D₃×D₄	C₂	1	3	yes	maximal, complemented
12	C₂×C₅×#550	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
14	C₅×D₃×#41	—	2	16	no	—
15	C₂×C₅×#239	C₂²	1	2	yes	complemented
16	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×#237	C₂²	1	6	yes	complemented
18	C₂×C₅×D₃×D₄	C₂²	1	3	yes	—
19	C₂×C₅×D₃×D₄	C₂²	1	6	yes	—
20	C₂×C₅×D₃×D₄	C₂²	1	6	yes	—
21	C₂×C₅×#235	C₂²	1	6	yes	complemented
22	C₂²×C₄×C₅×D₃	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	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
28	C₅×#940	C₂²	1	6	yes	complemented
29	C₅×#940	C₂²	1	6	yes	complemented
30	C₅×#940	C₂²	1	6	yes	complemented
31	C₅×#939	C₂²	1	12	yes	complemented
32	C₅×#938	C₂²	1	6	yes	complemented
33	C₅×D₄×Dic₃	C₂²	1	3	yes	complemented
34	C₅×#930	C₂²	1	6	yes	complemented
35	C₄×C₅×#67	C₂²	1	6	yes	complemented
36	C₅×#895	C₂²	1	6	yes	complemented
37	C₅×#893	C₂²	1	3	yes	complemented
38	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₅×D₃×C₄⋊C₄	C₂²	1	3	yes	—
40	C₅×#887	C₂²	1	3	yes	complemented
41	C₅×#884	C₂²	1	12	yes	complemented
42	C₅×#67⋊C₄	C₂²	1	6	yes	complemented
43	C₅×D₃×C₂²⋊C₄	C₂²	1	6	yes	—
44	C₅×#874	C₂²	1	3	yes	complemented
45	C₄×C₅×D₁₂	C₂²	1	3	yes	complemented
46	C₄²×C₅×D₃	C₂²	1	3	yes	—
47	C₄×C₅×Dic₆	C₂²	1	3	yes	complemented
48	D₃×#550	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
49	C₂²×C₅×#41	—	3	2	no	—
50	C₅×#550	—	3	2	no	—
51	C₅×#550	—	3	3	no	—
52	C₅×#550	—	3	6	no	—
53	C₅×#550	—	3	1	no	—
54	C₅×#550	—	3	3	no	—
55	C₅×#550	D₃	1	1	yes	characteristic, direct product factor
56	C₂×C₅×#127	—	3	3	no	—
57	C₂×C₅×#121	—	3	6	no	—
58	C₂×C₄×C₅×Q₈	—	3	1	no	—
59	C₂×C₄×C₅×D₄	—	3	3	no	—
60	C₂³×C₅×D₃	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×C₅×#67	C₂³	1	6	yes	—
68	C₂×C₅×#67	C₂³	1	12	yes	—
69	C₂×C₅×#67	C₂³	1	12	yes	—
70	C₂²×C₅×Dic₃	C₂³	1	6	yes	—
71	C₅×#239	—	2	8	no	—
72	C₅×D₃×Q₈	D₄	1	8	yes	complemented
73	C₅×#237	—	2	24	no	—
74	C₅×D₃×D₄	—	2	24	no	—
75	C₅×D₃×D₄	—	2	12	no	—
76	C₅×D₃×D₄	—	4	12	no	—
77	C₅×#235	—	2	24	no	—
78	C₂×C₅×D₁₂	C₂³	1	3	yes	—
79	C₂×C₅×D₁₂	C₂³	1	6	yes	—
80	C₂×C₅×D₁₂	C₂³	1	6	yes	—
81	C₂×C₄×C₅×D₃	—	2	24	no	—
82	C₂×C₄×C₅×D₃	C₂³	1	3	yes	—
83	C₂×C₄×C₅×D₃	C₂³	1	6	yes	—
84	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
85	C₂×C₄×C₅×D₃	C₂³	1	6	yes	—
86	C₂×C₄×C₅×D₃	C₂³	1	3	yes	—
87	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
88	C₂×C₅×Dic₆	C₂³	1	3	yes	—
89	C₃×C₅×C₄⋊C₄	C₂³	1	3	yes	—
90	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₃×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
92	C₃×C₄²×C₅	C₂³	1	3	yes	—
93	C₅×#217	C₂³	1	6	yes	—
94	C₅×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
95	C₅×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
96	C₅×C₄⋊Dic₃	C₂³	1	3	yes	—
97	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
98	C₅×Dic₃⋊C₄	C₂³	1	6	yes	—
99	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
100	C₄×C₅×Dic₃	C₂³	1	3	yes	—
101	C₄×C₅×Dic₃	C₂³	1	3	yes	—
102	C₄×C₅×Dic₃	C₂³	1	3	yes	—
103	C₂×D₃×#41	C₂×C₅	1	2	yes	complemented
104	C₃×#550	C₂×C₅	1	1	yes	characteristic, complemented
105	#5834	C₂×C₅	1	2	yes	complemented
106	#5718	C₂×C₅	1	3	yes	complemented
107	D₃×#127	C₂×C₅	1	3	yes	complemented
108	D₃×#121	C₂×C₅	1	6	yes	complemented
109	#5599	C₂×C₅	1	6	yes	complemented
110	#5577	C₂×C₅	1	1	yes	characteristic, complemented
111	C₄×D₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
112	#5553	C₂×C₅	1	3	yes	complemented
113	C₄×D₃×D₄	C₂×C₅	1	3	yes	complemented
114	C₂×C₅×#41	—	3	2	no	—
115	C₂×C₅×#41	—	3	6	no	—
116	C₂×C₅×#41	—	3	6	no	—
117	C₂×C₅×#41	—	6	16	no	—
118	C₂×C₅×#41	C₂×D₃	1	2	yes	complemented
119	C₂²×C₅×Q₈	—	3	1	no	—
120	C₂²×C₅×D₄	—	3	3	no	—
121	C₂²×C₅×D₄	—	3	6	no	—
122	C₂²×C₅×D₄	—	3	6	no	—
123	C₂³×C₄×C₅	—	3	6	no	—
124	C₅×#127	—	3	6	no	—
125	C₅×#127	—	3	6	no	—
126	C₅×#127	—	3	6	no	—
127	C₅×#127	—	3	3	no	—
128	C₅×#127	C₂×D₃	1	3	yes	complemented
129	C₅×#121	—	3	6	no	—
130	C₅×#121	—	3	12	no	—
131	C₅×#121	—	3	6	no	—
132	C₅×#121	—	3	6	no	—
133	C₅×#121	—	3	12	no	—
134	C₅×#121	C₂×D₃	1	6	yes	complemented
135	C₄×C₅×Q₈	—	3	1	no	—
136	C₄×C₅×Q₈	—	3	3	no	—
137	C₄×C₅×Q₈	—	3	3	no	—
138	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
139	C₄×C₅×D₄	—	3	3	no	—
140	C₄×C₅×D₄	—	3	6	no	—
141	C₄×C₅×D₄	—	3	3	no	—
142	C₄×C₅×D₄	—	3	6	no	—
143	C₄×C₅×D₄	—	3	3	no	—
144	C₄×C₅×D₄	C₂×D₃	1	3	yes	complemented
145	C₂×C₅×C₄⋊C₄	—	3	1	no	—
146	C₂×C₅×C₄⋊C₄	—	3	3	no	—
147	C₂×C₅×C₂²⋊C₄	—	3	6	no	—
148	C₂×C₄²×C₅	—	3	3	no	—
149	C₂×#550	—	3	1	no	Sylow
150	C₂³×C₃×C₅	C₂⁴	1	6	yes	—
151	C₂²×C₅×D₃	—	2	12	no	—
152	C₂²×C₅×D₃	—	2	12	no	—
153	C₂²×C₅×D₃	—	2	12	no	—
154	C₂²×C₅×D₃	C₂⁴	1	6	yes	—
155	C₂²×C₅×D₃	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	C₅×#67	—	2	24	no	—
166	C₅×#67	—	2	12	no	—
167	C₅×#67	—	4	12	no	—
168	C₂×C₅×Dic₃	—	2	12	no	—
169	C₂×C₅×Dic₃	C₂⁴	1	3	yes	—
170	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
171	C₂×C₅×Dic₃	C₂⁴	1	3	yes	—
172	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
173	C₅×D₁₂	—	2	12	no	—
174	C₅×D₁₂	—	2	6	no	—
175	C₅×D₁₂	—	4	6	no	—
176	C₄×C₅×D₃	—	2	4	no	—
177	C₄×C₅×D₃	—	2	6	no	—
178	C₄×C₅×D₃	—	2	12	no	—
179	C₄×C₅×D₃	—	2	12	no	—
180	C₄×C₅×D₃	C₂×D₄	1	12	yes	—
181	C₄×C₅×D₃	#41	1	4	yes	complemented
182	C₅×Dic₆	C₂×D₄	1	12	yes	complemented
183	C₂×C₃×#41	C₂²×C₅	1	2	yes	complemented
184	D₃×#41	—	2	16	no	—
185	C₂×#239	C₂²×C₅	1	2	yes	complemented
186	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
187	C₂×#237	C₂²×C₅	1	6	yes	complemented
188	C₂×D₃×D₄	C₂²×C₅	1	6	yes	—
189	C₂×D₃×D₄	C₂²×C₅	1	3	yes	—
190	C₂×D₃×D₄	C₂²×C₅	1	6	yes	—
191	C₂×#235	C₂²×C₅	1	6	yes	complemented
192	C₂²×C₄×D₃	C₂²×C₅	1	6	yes	—
193	C₃×#127	C₂²×C₅	1	3	yes	complemented
194	C₃×#121	C₂²×C₅	1	6	yes	complemented
195	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
196	C₃×C₄×D₄	C₂²×C₅	1	3	yes	complemented
197	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
198	#940	C₂²×C₅	1	6	yes	complemented
199	#940	C₂²×C₅	1	6	yes	complemented
200	#940	C₂²×C₅	1	6	yes	complemented
201	#939	C₂²×C₅	1	12	yes	complemented
202	#938	C₂²×C₅	1	6	yes	complemented
203	D₄×Dic₃	C₂²×C₅	1	3	yes	complemented
204	#930	C₂²×C₅	1	6	yes	complemented
205	C₄×#67	C₂²×C₅	1	6	yes	complemented
206	#895	C₂²×C₅	1	6	yes	complemented
207	#893	C₂²×C₅	1	3	yes	complemented
208	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
209	D₃×C₄⋊C₄	C₂²×C₅	1	3	yes	—
210	#887	C₂²×C₅	1	3	yes	complemented
211	#884	C₂²×C₅	1	12	yes	complemented
212	#67⋊C₄	C₂²×C₅	1	6	yes	complemented
213	D₃×C₂²⋊C₄	C₂²×C₅	1	6	yes	—
214	#874	C₂²×C₅	1	3	yes	complemented
215	C₄×D₁₂	C₂²×C₅	1	3	yes	complemented
216	C₄²×D₃	C₂²×C₅	1	3	yes	—
217	C₄×Dic₆	C₂²×C₅	1	3	yes	complemented
218	C₂⁴×C₅	—	3	6	no	—
219	C₅×#41	—	2	8	no	—
220	C₅×#41	—	6	24	no	—
221	C₅×#41	—	6	24	no	—
222	C₅×#41	—	6	8	no	—
223	C₂×C₅×Q₈	—	3	8	no	—
224	C₂×C₅×Q₈	—	3	3	no	—
225	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
226	C₂×C₅×D₄	—	3	6	no	—
227	C₂×C₅×D₄	—	3	12	no	—
228	C₂×C₅×D₄	—	3	12	no	—
229	C₂×C₅×D₄	—	3	3	no	—
230	C₂×C₅×D₄	—	3	6	no	—
231	C₂×C₅×D₄	—	3	6	no	—
232	C₂×C₅×D₄	—	6	24	no	—
233	C₂×C₅×D₄	—	6	12	no	—
234	C₂×C₅×D₄	—	12	12	no	—
235	C₂×C₅×D₄	C₂²×D₃	1	3	yes	—
236	C₂×C₅×D₄	C₂²×D₃	1	6	yes	—
237	C₂×C₅×D₄	C₂²×D₃	1	6	yes	—
238	C₂²×C₄×C₅	—	3	1	no	—
239	C₂²×C₄×C₅	—	3	3	no	—
240	C₂²×C₄×C₅	—	3	6	no	—
241	C₂²×C₄×C₅	—	3	3	no	—
242	C₂²×C₄×C₅	—	3	2	no	—
243	C₂²×C₄×C₅	—	3	6	no	—
244	C₂²×C₄×C₅	—	3	6	no	—
245	C₂²×C₄×C₅	—	6	24	no	—
246	C₂²×C₄×C₅	C₂²×D₃	1	6	yes	—
247	C₅×C₄⋊C₄	—	3	2	no	—
248	C₅×C₄⋊C₄	—	3	1	no	—
249	C₅×C₄⋊C₄	—	3	6	no	—
250	C₅×C₄⋊C₄	—	3	3	no	—
251	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
252	C₅×C₄⋊C₄	C₂²×D₃	1	3	yes	—
253	C₅×C₂²⋊C₄	—	3	6	no	—
254	C₅×C₂²⋊C₄	—	3	6	no	—
255	C₅×C₂²⋊C₄	—	3	6	no	—
256	C₅×C₂²⋊C₄	C₂²×D₃	1	6	yes	—
257	C₄²×C₅	—	3	3	no	—
258	C₄²×C₅	—	3	3	no	—
259	C₄²×C₅	—	3	3	no	—
260	C₄²×C₅	C₂²×D₃	1	3	yes	—
261	C₂²×#41	—	3	2	no	—
262	#550	—	3	2	no	—
263	#550	—	3	3	no	—
264	#550	—	3	6	no	—
265	#550	—	3	1	no	—
266	#550	—	3	3	no	—
267	#550	C₅×D₃	1	1	yes	characteristic, direct product factor
268	C₂×#127	—	3	3	no	—
269	C₂×#121	—	3	6	no	—
270	C₂×C₄×Q₈	—	3	1	no	—
271	C₂×C₄×D₄	—	3	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×C₅×D₃	—	2	6	no	—
277	C₂×C₅×D₃	—	2	6	no	—
278	C₂×C₅×D₃	—	2	6	no	—
279	C₂×C₅×D₃	—	4	24	no	—
280	C₂×C₅×D₃	C₂²×D₄	1	2	yes	—
281	C₂×C₅×D₃	C₂×#41	1	2	yes	—
282	C₂×C₅×D₃	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	C₅×Dic₃	—	2	2	no	—
288	C₅×Dic₃	—	2	3	no	—
289	C₅×Dic₃	C₂²×D₄	1	6	yes	—
290	C₅×Dic₃	C₂×#41	1	2	yes	complemented
291	C₂³×D₃	C₂³×C₅	1	6	yes	—
292	C₃×#41	—	2	8	no	—
293	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
294	C₂×C₃×D₄	C₂³×C₅	1	3	yes	—
295	C₂×C₃×D₄	C₂³×C₅	1	6	yes	—
296	C₂×C₃×D₄	C₂³×C₅	1	6	yes	—
297	C₂²×C₃×C₄	C₂³×C₅	1	6	yes	—
298	C₂×#67	C₂³×C₅	1	6	yes	—
299	C₂×#67	C₂³×C₅	1	12	yes	—
300	C₂×#67	C₂³×C₅	1	12	yes	—
301	C₂²×Dic₃	C₂³×C₅	1	6	yes	—
302	#239	—	2	8	no	—
303	D₃×Q₈	C₅×D₄	1	8	yes	complemented
304	#237	—	2	24	no	—
305	D₃×D₄	—	2	24	no	—
306	D₃×D₄	—	2	12	no	—
307	D₃×D₄	—	4	12	no	—
308	#235	—	2	24	no	—
309	C₂×D₁₂	C₂³×C₅	1	3	yes	—
310	C₂×D₁₂	C₂³×C₅	1	6	yes	—
311	C₂×D₁₂	C₂³×C₅	1	6	yes	—
312	C₂×C₄×D₃	—	2	24	no	—
313	C₂×C₄×D₃	C₂³×C₅	1	3	yes	—
314	C₂×C₄×D₃	C₂³×C₅	1	6	yes	—
315	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
316	C₂×C₄×D₃	C₂³×C₅	1	6	yes	—
317	C₂×C₄×D₃	C₂³×C₅	1	3	yes	—
318	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
319	C₂×Dic₆	C₂³×C₅	1	3	yes	—
320	C₃×C₄⋊C₄	C₂³×C₅	1	3	yes	—
321	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
322	C₃×C₂²⋊C₄	C₂³×C₅	1	6	yes	—
323	C₃×C₄²	C₂³×C₅	1	3	yes	—
324	#217	C₂³×C₅	1	6	yes	—
325	(C₂×D₃)⋊C₄	C₂³×C₅	1	6	yes	—
326	(C₂×D₃)⋊C₄	C₂³×C₅	1	6	yes	—
327	C₄⋊Dic₃	C₂³×C₅	1	3	yes	—
328	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
329	Dic₃⋊C₄	C₂³×C₅	1	6	yes	—
330	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
331	C₄×Dic₃	C₂³×C₅	1	3	yes	—
332	C₄×Dic₃	C₂³×C₅	1	3	yes	—
333	C₄×Dic₃	C₂³×C₅	1	3	yes	—
334	C₂³×C₅	—	3	1	no	—
335	C₂³×C₅	—	3	6	no	—
336	C₂³×C₅	—	6	12	no	—
337	C₂³×C₅	—	6	12	no	—
338	C₂³×C₅	—	6	12	no	—
339	C₂³×C₅	C₂³×D₃	1	6	yes	—
340	C₅×Q₈	—	3	12	no	—
341	C₅×Q₈	D₃×D₄	1	4	yes	complemented
342	C₅×D₄	—	2	12	no	—
343	C₅×D₄	—	2	6	no	—
344	C₅×D₄	—	4	6	no	—
345	C₅×D₄	—	6	12	no	—
346	C₅×D₄	—	6	24	no	—
347	C₅×D₄	—	6	12	no	—
348	C₅×D₄	—	6	6	no	—
349	C₅×D₄	—	12	6	no	—
350	C₅×D₄	—	12	12	no	—
351	C₂×C₄×C₅	—	2	12	no	—
352	C₂×C₄×C₅	—	3	1	no	—
353	C₂×C₄×C₅	—	3	3	no	—
354	C₂×C₄×C₅	—	3	12	no	—
355	C₂×C₄×C₅	—	3	4	no	—
356	C₂×C₄×C₅	—	3	3	no	—
357	C₂×C₄×C₅	—	3	2	no	—
358	C₂×C₄×C₅	—	6	12	no	—
359	C₂×C₄×C₅	—	6	4	no	—
360	C₂×C₄×C₅	—	6	6	no	—
361	C₂×C₄×C₅	—	6	12	no	—
362	C₂×C₄×C₅	—	6	12	no	—
363	C₂×C₄×C₅	C₂³×D₃	1	3	yes	—
364	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
365	C₂×C₄×C₅	C₂³×D₃	1	3	yes	—
366	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
367	C₂×#41	—	3	2	no	—
368	C₂×#41	—	3	6	no	—
369	C₂×#41	—	3	6	no	—
370	C₂×#41	—	6	16	no	—
371	C₂×#41	C₂×C₅×D₃	1	2	yes	complemented
372	C₂²×Q₈	—	3	1	no	—
373	C₂²×D₄	—	3	3	no	—
374	C₂²×D₄	—	3	6	no	—
375	C₂²×D₄	—	3	6	no	—
376	C₂³×C₄	—	3	6	no	—
377	#127	—	3	6	no	—
378	#127	—	3	6	no	—
379	#127	—	3	6	no	—
380	#127	—	3	3	no	—
381	#127	C₂×C₅×D₃	1	3	yes	complemented
382	#121	—	3	6	no	—
383	#121	—	3	12	no	—
384	#121	—	3	6	no	—
385	#121	—	3	6	no	—
386	#121	—	3	12	no	—
387	#121	C₂×C₅×D₃	1	6	yes	complemented
388	C₄×Q₈	—	3	1	no	—
389	C₄×Q₈	—	3	3	no	—
390	C₄×Q₈	—	3	3	no	—
391	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
392	C₄×D₄	—	3	3	no	—
393	C₄×D₄	—	3	6	no	—
394	C₄×D₄	—	3	3	no	—
395	C₄×D₄	—	3	6	no	—
396	C₄×D₄	—	3	3	no	—
397	C₄×D₄	C₂×C₅×D₃	1	3	yes	complemented
398	C₂×C₄⋊C₄	—	3	1	no	—
399	C₂×C₄⋊C₄	—	3	3	no	—
400	C₂×C₂²⋊C₄	—	3	6	no	—
401	C₂×C₄²	—	3	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	C₅×D₃	—	4	6	no	—
407	C₅×D₃	#550	1	4	yes	direct product factor
408	C₂³×C₃	C₂⁴×C₅	1	6	yes	—
409	C₂²×D₃	—	2	12	no	—
410	C₂²×D₃	—	2	12	no	—
411	C₂²×D₃	—	2	12	no	—
412	C₂²×D₃	C₂⁴×C₅	1	6	yes	—
413	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
414	C₃×Q₈	C₂×C₅×D₄	1	4	yes	complemented
415	C₃×D₄	—	2	12	no	—
416	C₃×D₄	—	2	6	no	—
417	C₃×D₄	—	4	6	no	—
418	C₂×C₃×C₄	—	2	12	no	—
419	C₂×C₃×C₄	C₂⁴×C₅	1	3	yes	—
420	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
421	C₂×C₃×C₄	C₂⁴×C₅	1	3	yes	—
422	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
423	#67	—	2	24	no	—
424	#67	—	2	12	no	—
425	#67	—	4	12	no	—
426	C₂×Dic₃	—	2	12	no	—
427	C₂×Dic₃	C₂⁴×C₅	1	3	yes	—
428	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
429	C₂×Dic₃	C₂⁴×C₅	1	3	yes	—
430	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
431	D₁₂	—	2	12	no	—
432	D₁₂	—	2	6	no	—
433	D₁₂	—	4	6	no	—
434	C₄×D₃	—	2	4	no	—
435	C₄×D₃	—	2	6	no	—
436	C₄×D₃	—	2	12	no	—
437	C₄×D₃	—	2	12	no	—
438	C₄×D₃	C₂×C₅×D₄	1	12	yes	—
439	C₄×D₃	C₅×#41	1	4	yes	complemented
440	Dic₆	C₂×C₅×D₄	1	12	yes	complemented
441	C₂²×C₅	—	2	6	no	—
442	C₂²×C₅	—	2	6	no	—
443	C₂²×C₅	—	2	6	no	—
444	C₂²×C₅	—	3	2	no	—
445	C₂²×C₅	—	3	2	no	—
446	C₂²×C₅	—	3	2	no	—
447	C₂²×C₅	—	6	6	no	—
448	C₂²×C₅	—	6	6	no	—
449	C₂²×C₅	—	6	6	no	—
450	C₂²×C₅	—	12	24	no	—
451	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
452	C₄×C₅	—	2	2	no	—
453	C₄×C₅	—	2	3	no	—
454	C₄×C₅	—	3	6	no	—
455	C₄×C₅	—	3	2	no	—
456	C₄×C₅	—	6	2	no	—
457	C₄×C₅	—	6	3	no	—
458	C₄×C₅	C₂×D₃×D₄	1	6	yes	—
459	C₄×C₅	D₃×#41	1	2	yes	complemented
460	C₂⁴	—	3	6	no	—
461	#41	—	2	8	no	—
462	#41	—	6	24	no	—
463	#41	—	6	24	no	—
464	#41	—	6	8	no	—
465	C₂×Q₈	—	3	8	no	—
466	C₂×Q₈	—	3	3	no	—
467	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
468	C₂×D₄	—	3	6	no	—
469	C₂×D₄	—	3	12	no	—
470	C₂×D₄	—	3	12	no	—
471	C₂×D₄	—	3	3	no	—
472	C₂×D₄	—	3	6	no	—
473	C₂×D₄	—	3	6	no	—
474	C₂×D₄	—	6	24	no	—
475	C₂×D₄	—	6	12	no	—
476	C₂×D₄	—	12	12	no	—
477	C₂×D₄	C₂²×C₅×D₃	1	3	yes	—
478	C₂×D₄	C₂²×C₅×D₃	1	6	yes	—
479	C₂×D₄	C₂²×C₅×D₃	1	6	yes	—
480	C₂²×C₄	—	3	1	no	—
481	C₂²×C₄	—	3	3	no	—
482	C₂²×C₄	—	3	6	no	—
483	C₂²×C₄	—	3	3	no	—
484	C₂²×C₄	—	3	2	no	—
485	C₂²×C₄	—	3	6	no	—
486	C₂²×C₄	—	3	6	no	—
487	C₂²×C₄	—	6	24	no	—
488	C₂²×C₄	C₂²×C₅×D₃	1	6	yes	—
489	C₄⋊C₄	—	3	2	no	—
490	C₄⋊C₄	—	3	1	no	—
491	C₄⋊C₄	—	3	6	no	—
492	C₄⋊C₄	—	3	3	no	—
493	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×C₅×D₃	1	3	yes	—
495	C₂²⋊C₄	—	3	6	no	—
496	C₂²⋊C₄	—	3	6	no	—
497	C₂²⋊C₄	—	3	6	no	—
498	C₂²⋊C₄	C₂²×C₅×D₃	1	6	yes	—
499	C₄²	—	3	3	no	—
500	C₄²	—	3	3	no	—
501	C₄²	—	3	3	no	—
502	C₄²	C₂²×C₅×D₃	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	C₂⁵×C₅	1	1	yes	characteristic
508	C₂×D₃	—	2	6	no	—
509	C₂×D₃	—	2	6	no	—
510	C₂×D₃	—	2	6	no	—
511	C₂×D₃	—	4	24	no	—
512	C₂×D₃	C₂²×C₅×D₄	1	2	yes	—
513	C₂×D₃	C₂×C₅×#41	1	2	yes	—
514	C₂×D₃	C₅×H(5,𝔽₂)	1	2	yes	—
515	C₃×C₄	—	2	2	no	—
516	C₃×C₄	—	2	3	no	—
517	C₃×C₄	C₂²×C₅×D₄	1	6	yes	—
518	C₃×C₄	C₂×C₅×#41	1	2	yes	complemented
519	Dic₃	—	2	2	no	—
520	Dic₃	—	2	3	no	—
521	Dic₃	C₂²×C₅×D₄	1	6	yes	—
522	Dic₃	C₂×C₅×#41	1	2	yes	complemented
523	C₂×C₅	—	3	4	no	—
524	C₂×C₅	—	4	6	no	—
525	C₂×C₅	—	12	6	no	—
526	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
527	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
528	C₂×C₅	D₃×H(5,𝔽₂)	1	1	yes	characteristic
529	C₂³	—	3	1	no	—
530	C₂³	—	3	6	no	—
531	C₂³	—	6	12	no	—
532	C₂³	—	6	12	no	—
533	C₂³	—	6	12	no	—
534	C₂³	C₂³×C₅×D₃	1	6	yes	—
535	Q₈	—	3	12	no	—
536	Q₈	C₅×D₃×D₄	1	4	yes	complemented
537	D₄	—	2	12	no	—
538	D₄	—	2	6	no	—
539	D₄	—	4	6	no	—
540	D₄	—	6	24	no	—
541	D₄	—	6	12	no	—
542	D₄	—	6	12	no	—
543	D₄	—	6	6	no	—
544	D₄	—	12	6	no	—
545	D₄	—	12	12	no	—
546	C₂×C₄	—	2	12	no	—
547	C₂×C₄	—	3	1	no	—
548	C₂×C₄	—	3	3	no	—
549	C₂×C₄	—	3	12	no	—
550	C₂×C₄	—	3	4	no	—
551	C₂×C₄	—	3	3	no	—
552	C₂×C₄	—	3	2	no	—
553	C₂×C₄	—	6	12	no	—
554	C₂×C₄	—	6	4	no	—
555	C₂×C₄	—	6	6	no	—
556	C₂×C₄	—	6	12	no	—
557	C₂×C₄	—	6	12	no	—
558	C₂×C₄	C₂³×C₅×D₃	1	3	yes	—
559	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
560	C₂×C₄	C₂³×C₅×D₃	1	3	yes	—
561	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
562	C₂×C₃	—	4	6	no	—
563	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
564	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
565	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
566	D₃	—	4	6	no	—
567	D₃	C₅×#550	1	4	yes	direct product factor
568	C₅	D₃×#550	1	1	yes	characteristic, direct product factor, Sylow
569	C₂²	—	2	6	no	—
570	C₂²	—	2	6	no	—
571	C₂²	—	2	6	no	—
572	C₂²	—	3	2	no	—
573	C₂²	—	3	2	no	—
574	C₂²	—	3	2	no	—
575	C₂²	—	6	6	no	—
576	C₂²	—	6	6	no	—
577	C₂²	—	6	6	no	—
578	C₂²	—	12	24	no	—
579	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
580	C₄	—	2	2	no	—
581	C₄	—	2	3	no	—
582	C₄	—	3	6	no	—
583	C₄	—	3	2	no	—
584	C₄	—	6	2	no	—
585	C₄	—	6	3	no	—
586	C₄	C₂×C₅×D₃×D₄	1	6	yes	—
587	C₄	C₅×D₃×#41	1	2	yes	complemented
588	C₃	C₂×C₅×#550	1	1	yes	characteristic, complemented, Sylow
589	C₂	—	3	4	no	—
590	C₂	—	4	6	no	—
591	C₂	—	12	6	no	—
592	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
593	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
594	C₂	C₅×D₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#550	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#550	D₃
hypocenter	C₃	C₂×C₅×#550
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#550

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×#41	C₂	semidirect
2. C₃×C₅×#550	C₂	semidirect
3. C₅×#5834	C₂	semidirect
4. C₅×#5718	C₂	semidirect
5. C₅×D₃×#127	C₂	semidirect
6. C₅×D₃×#121	C₂	semidirect
7. C₅×#5599	C₂	semidirect
8. C₅×#5577	C₂	semidirect
9. C₄×C₅×D₃×Q₈	C₂	semidirect
10. C₅×#5553	C₂	semidirect
11. C₄×C₅×D₃×D₄	C₂	semidirect
13. C₂×C₃×C₅×#41	C₂²	semidirect
15. C₂×C₅×#239	C₂²	semidirect
17. C₂×C₅×#237	C₂²	semidirect
21. C₂×C₅×#235	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. C₅×Q₈×Dic₃	C₂²	semidirect
28. C₅×#940	C₂²	semidirect
29. C₅×#940	C₂²	semidirect
30. C₅×#940	C₂²	semidirect
31. C₅×#939	C₂²	semidirect
32. C₅×#938	C₂²	semidirect
33. C₅×D₄×Dic₃	C₂²	semidirect
34. C₅×#930	C₂²	semidirect
35. C₄×C₅×#67	C₂²	semidirect
36. C₅×#895	C₂²	semidirect
37. C₅×#893	C₂²	semidirect
40. C₅×#887	C₂²	semidirect
41. C₅×#884	C₂²	semidirect
42. C₅×#67⋊C₄	C₂²	semidirect
44. C₅×#874	C₂²	semidirect
45. C₄×C₅×D₁₂	C₂²	semidirect
47. C₄×C₅×Dic₆	C₂²	semidirect
48. D₃×#550	C₅	direct (N × H)
55. C₅×#550	D₃	direct (N × H)
72. C₅×D₃×Q₈	D₄	semidirect
103. C₂×D₃×#41	C₂×C₅	semidirect
104. C₃×#550	C₂×C₅	semidirect
105. #5834	C₂×C₅	semidirect
106. #5718	C₂×C₅	semidirect
107. D₃×#127	C₂×C₅	semidirect
108. D₃×#121	C₂×C₅	semidirect
109. #5599	C₂×C₅	semidirect
110. #5577	C₂×C₅	semidirect
111. C₄×D₃×Q₈	C₂×C₅	semidirect
112. #5553	C₂×C₅	semidirect
113. C₄×D₃×D₄	C₂×C₅	semidirect
118. C₂×C₅×#41	C₂×D₃	semidirect
128. C₅×#127	C₂×D₃	semidirect
134. C₅×#121	C₂×D₃	semidirect
138. C₄×C₅×Q₈	C₂×D₃	semidirect
144. C₄×C₅×D₄	C₂×D₃	semidirect
156. C₃×C₅×Q₈	C₂×D₄	semidirect
181. C₄×C₅×D₃	#41	semidirect
182. C₅×Dic₆	C₂×D₄	semidirect
183. C₂×C₃×#41	C₂²×C₅	semidirect
185. C₂×#239	C₂²×C₅	semidirect
187. C₂×#237	C₂²×C₅	semidirect
191. C₂×#235	C₂²×C₅	semidirect
193. C₃×#127	C₂²×C₅	semidirect
194. C₃×#121	C₂²×C₅	semidirect
195. C₃×C₄×Q₈	C₂²×C₅	semidirect
196. C₃×C₄×D₄	C₂²×C₅	semidirect
197. Q₈×Dic₃	C₂²×C₅	semidirect
198. #940	C₂²×C₅	semidirect
199. #940	C₂²×C₅	semidirect
200. #940	C₂²×C₅	semidirect
201. #939	C₂²×C₅	semidirect
202. #938	C₂²×C₅	semidirect
203. D₄×Dic₃	C₂²×C₅	semidirect
204. #930	C₂²×C₅	semidirect
205. C₄×#67	C₂²×C₅	semidirect
206. #895	C₂²×C₅	semidirect
207. #893	C₂²×C₅	semidirect
210. #887	C₂²×C₅	semidirect
211. #884	C₂²×C₅	semidirect
212. #67⋊C₄	C₂²×C₅	semidirect
214. #874	C₂²×C₅	semidirect
215. C₄×D₁₂	C₂²×C₅	semidirect
217. C₄×Dic₆	C₂²×C₅	semidirect
267. #550	C₅×D₃	direct (N × H)
286. C₃×C₄×C₅	C₂×#41	semidirect
290. C₅×Dic₃	C₂×#41	semidirect
303. D₃×Q₈	C₅×D₄	semidirect
341. C₅×Q₈	D₃×D₄	semidirect
371. C₂×#41	C₂×C₅×D₃	semidirect
381. #127	C₂×C₅×D₃	semidirect
387. #121	C₂×C₅×D₃	semidirect
391. C₄×Q₈	C₂×C₅×D₃	semidirect
397. C₄×D₄	C₂×C₅×D₃	semidirect
407. C₅×D₃	#550	direct (N × H)
414. C₃×Q₈	C₂×C₅×D₄	semidirect
439. C₄×D₃	C₅×#41	semidirect
440. Dic₆	C₂×C₅×D₄	semidirect
459. C₄×C₅	D₃×#41	semidirect
503. C₃×C₅	C₂×#550	semidirect
518. C₃×C₄	C₂×C₅×#41	semidirect
522. Dic₃	C₂×C₅×#41	semidirect
536. Q₈	C₅×D₃×D₄	semidirect
567. D₃	C₅×#550	direct (N × H)
568. C₅	D₃×#550	direct (N × H)
587. C₄	C₅×D₃×#41	semidirect
588. C₃	C₂×C₅×#550	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×#41	2
C₃×C₅×#550	2
C₅×#5834	2
C₅×#5718	2
C₅×D₃×#127	2
C₅×D₃×#121	2
C₅×#5599	2
C₅×#5577	2
C₄×C₅×D₃×Q₈	2
C₅×#5553	2
C₄×C₅×D₃×D₄	2
C₂×C₅×#550	3
D₃×#550	5

Subgroups — C5×D3×#550 #14482963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#550 #14482963