Subgroups — C₅×D₃×#533 #14480108

Order 1920.

2336 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5728	C₂	1	2	yes	maximal, complemented
3	C₅×D₃×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
4	C₅×#5688	C₂	1	2	yes	maximal, complemented
5	C₅×D₃×#125	C₂	1	2	yes	maximal, complemented
6	C₅×D₃×C₂²⋊Q₈	C₂	1	4	yes	maximal
7	C₅×#5622	C₂	1	4	yes	maximal, complemented
8	C₅×#5578	C₂	1	4	yes	maximal, complemented
9	C₄×C₅×D₃×Q₈	C₂	1	4	yes	maximal, complemented
10	C₅×D₃×#117	C₂	1	2	yes	maximal
11	C₅×#5517	C₂	1	2	yes	maximal, complemented
12	C₂×C₄²×C₅×D₃	C₂	1	1	yes	maximal, characteristic
13	C₅×#5470	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅×#533	—	3	1	no	maximal, Hall
15	C₂×C₅×D₃×Q₈	C₂²	1	4	yes	—
16	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
17	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
18	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
19	C₃×C₅×#125	C₂²	1	2	yes	complemented
20	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
21	C₃×C₄×C₅×Q₈	C₂²	1	4	yes	complemented
22	C₃×C₅×#117	C₂²	1	2	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₅×#946	C₂²	1	4	yes	—
25	C₅×Q₈×Dic₃	C₂²	1	4	yes	complemented
26	C₅×#944	C₂²	1	4	yes	complemented
27	C₅×#926	C₂²	1	2	yes	—
28	C₅×#924	C₂²	1	4	yes	—
29	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
31	C₅×#897	C₂²	1	4	yes	—
32	C₅×#896	C₂²	1	8	yes	—
33	C₅×#892	C₂²	1	4	yes	—
34	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	—
35	C₅×D₃×C₄⋊C₄	C₂²	1	8	yes	—
36	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	—
37	C₅×#890	C₂²	1	4	yes	complemented
38	C₅×#889	C₂²	1	8	yes	complemented
39	C₅×#888	C₂²	1	4	yes	complemented
40	C₅×#888	C₂²	1	4	yes	complemented
41	C₅×#887	C₂²	1	8	yes	complemented
42	C₅×#887	C₂²	1	4	yes	complemented
43	C₅×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
44	C₅×#878	C₂²	1	8	yes	—
45	C₅×#877	C₂²	1	4	yes	—
46	C₅×#872	C₂²	1	4	yes	—
47	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
48	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
49	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
50	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
51	C₄²×C₅×D₃	C₂²	1	2	yes	—
52	C₄²×C₅×D₃	C₂²	1	2	yes	—
53	C₄²×C₅×D₃	C₂²	1	4	yes	—
54	C₅×#870	C₂²	1	2	yes	complemented
55	C₅×#869	C₂²	1	2	yes	complemented
56	C₄×C₅×Dic₆	C₂²	1	4	yes	complemented
57	C₄×C₅×Dic₆	C₂²	1	8	yes	complemented
58	D₃×#533	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
59	C₅×#533	—	3	2	no	—
60	C₅×#533	—	3	2	no	—
61	C₅×#533	—	3	4	no	—
62	C₅×#533	—	3	4	no	—
63	C₅×#533	—	3	2	no	—
64	C₅×#533	—	3	1	no	—
65	C₅×#533	D₃	1	1	yes	characteristic, direct product factor
66	C₂×C₅×C₄⋊Q₈	—	3	2	no	—
67	C₂×C₅×#125	—	3	2	no	—
68	C₂×C₅×C₂²⋊Q₈	—	3	4	no	—
69	C₂×C₄×C₅×Q₈	—	3	4	no	—
70	C₂×C₅×#117	—	3	2	no	—
71	C₂²×C₄²×C₅	—	3	1	no	—
72	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
74	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
75	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
77	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
78	C₅×D₃×Q₈	—	2	16	no	—
79	C₂×C₄×C₅×D₃	—	2	8	no	—
80	C₂×C₄×C₅×D₃	Q₈	1	8	yes	complemented
81	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
82	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
83	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
84	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
85	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
86	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
87	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
88	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
89	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
90	C₂×C₅×Dic₆	C₂³	1	4	yes	—
91	C₂×C₅×Dic₆	C₂³	1	8	yes	—
92	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
93	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
94	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
95	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
96	C₃×C₄²×C₅	C₂³	1	2	yes	—
97	C₃×C₄²×C₅	C₂³	1	4	yes	—
98	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
99	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
100	C₅×#217	C₂³	1	4	yes	—
101	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
102	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
103	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
104	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
105	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
106	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
107	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
108	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
109	C₄×C₅×Dic₃	C₂³	1	2	yes	—
110	C₄×C₅×Dic₃	C₂³	1	4	yes	—
111	C₄×C₅×Dic₃	C₂³	1	2	yes	—
112	C₄×C₅×Dic₃	C₂³	1	2	yes	—
113	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
114	C₄×C₅×Dic₃	C₂³	1	2	yes	—
115	C₄×C₅×Dic₃	C₂³	1	2	yes	—
116	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
117	C₄×C₅×Dic₃	C₂³	1	8	yes	—
118	C₃×#533	C₂×C₅	1	1	yes	characteristic, complemented
119	#5728	C₂×C₅	1	2	yes	complemented
120	D₃×C₄⋊Q₈	C₂×C₅	1	2	yes	complemented
121	#5688	C₂×C₅	1	2	yes	complemented
122	D₃×#125	C₂×C₅	1	2	yes	complemented
123	D₃×C₂²⋊Q₈	C₂×C₅	1	4	yes	—
124	#5622	C₂×C₅	1	4	yes	complemented
125	#5578	C₂×C₅	1	4	yes	complemented
126	C₄×D₃×Q₈	C₂×C₅	1	4	yes	complemented
127	D₃×#117	C₂×C₅	1	2	yes	—
128	#5517	C₂×C₅	1	2	yes	complemented
129	C₂×C₄²×D₃	C₂×C₅	1	1	yes	characteristic
130	#5470	C₂×C₅	1	1	yes	characteristic, complemented
131	C₂²×C₅×Q₈	—	3	4	no	—
132	C₂³×C₄×C₅	—	3	1	no	—
133	C₂³×C₄×C₅	—	3	2	no	—
134	C₅×C₄⋊Q₈	—	3	4	no	—
135	C₅×C₄⋊Q₈	—	3	4	no	—
136	C₅×C₄⋊Q₈	—	3	4	no	—
137	C₅×C₄⋊Q₈	—	3	2	no	—
138	C₅×C₄⋊Q₈	C₂×D₃	1	2	yes	complemented
139	C₅×#125	—	3	8	no	—
140	C₅×#125	—	3	4	no	—
141	C₅×#125	—	3	2	no	—
142	C₅×#125	C₂×D₃	1	2	yes	complemented
143	C₅×C₂²⋊Q₈	—	3	4	no	—
144	C₅×C₂²⋊Q₈	—	3	4	no	—
145	C₅×C₂²⋊Q₈	—	3	8	no	—
146	C₅×C₂²⋊Q₈	—	3	4	no	—
147	C₅×C₂²⋊Q₈	—	3	8	no	—
148	C₅×C₂²⋊Q₈	C₂×D₃	1	4	yes	—
149	C₄×C₅×Q₈	—	3	4	no	—
150	C₄×C₅×Q₈	—	3	4	no	—
151	C₄×C₅×Q₈	—	3	8	no	—
152	C₄×C₅×Q₈	—	3	8	no	—
153	C₄×C₅×Q₈	—	3	4	no	—
154	C₄×C₅×Q₈	C₂×D₃	1	4	yes	complemented
155	C₅×#117	—	3	2	no	—
156	C₅×#117	—	3	4	no	—
157	C₅×#117	—	3	4	no	—
158	C₅×#117	—	3	4	no	—
159	C₅×#117	C₂×D₃	1	2	yes	—
160	C₂×C₅×C₄⋊C₄	—	3	4	no	—
161	C₂×C₅×C₄⋊C₄	—	3	8	no	—
162	C₂×C₅×C₄⋊C₄	—	3	4	no	—
163	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
164	C₂×C₄²×C₅	—	3	2	no	—
165	C₂×C₄²×C₅	—	3	1	no	—
166	C₂×C₄²×C₅	—	3	2	no	—
167	C₂×C₄²×C₅	—	3	1	no	—
168	C₂×C₄²×C₅	—	3	1	no	—
169	C₂×C₄²×C₅	—	3	1	no	—
170	C₂×C₄²×C₅	—	3	1	no	—
171	C₂×C₄²×C₅	—	3	2	no	—
172	C₂×C₄²×C₅	—	3	4	no	—
173	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
174	C₂×#533	—	3	1	no	Sylow
175	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
176	C₂²×C₅×D₃	—	2	4	no	—
177	C₂²×C₅×D₃	C₂×Q₈	1	4	yes	—
178	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
179	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
180	C₃×C₅×Q₈	—	2	8	no	—
181	C₂×C₃×C₄×C₅	—	2	4	no	—
182	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	complemented
183	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
184	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
185	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
186	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
187	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
188	C₂×C₅×Dic₃	—	2	4	no	—
189	C₂×C₅×Dic₃	C₂×Q₈	1	4	yes	complemented
190	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
191	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
192	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
193	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
194	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
195	C₄×C₅×D₃	—	2	4	no	—
196	C₄×C₅×D₃	—	2	16	no	—
197	C₄×C₅×D₃	—	2	4	no	—
198	C₄×C₅×D₃	—	2	4	no	—
199	C₄×C₅×D₃	C₂×Q₈	1	4	yes	—
200	C₄×C₅×D₃	C₂×Q₈	1	4	yes	—
201	C₄×C₅×D₃	C₂×Q₈	1	4	yes	complemented
202	C₄×C₅×D₃	C₂×Q₈	1	4	yes	complemented
203	C₄×C₅×D₃	#41	1	8	yes	—
204	C₅×Dic₆	—	2	8	no	—
205	C₅×Dic₆	—	2	16	no	—
206	C₂×D₃×Q₈	C₂²×C₅	1	4	yes	—
207	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
208	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
209	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
210	C₃×#125	C₂²×C₅	1	2	yes	complemented
211	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
212	C₃×C₄×Q₈	C₂²×C₅	1	4	yes	complemented
213	C₃×#117	C₂²×C₅	1	2	yes	—
214	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
215	#946	C₂²×C₅	1	4	yes	—
216	Q₈×Dic₃	C₂²×C₅	1	4	yes	complemented
217	#944	C₂²×C₅	1	4	yes	complemented
218	#926	C₂²×C₅	1	2	yes	—
219	#924	C₂²×C₅	1	4	yes	—
220	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
221	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
222	#897	C₂²×C₅	1	4	yes	—
223	#896	C₂²×C₅	1	8	yes	—
224	#892	C₂²×C₅	1	4	yes	—
225	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
226	D₃×C₄⋊C₄	C₂²×C₅	1	8	yes	—
227	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
228	#890	C₂²×C₅	1	4	yes	complemented
229	#889	C₂²×C₅	1	8	yes	complemented
230	#888	C₂²×C₅	1	4	yes	complemented
231	#888	C₂²×C₅	1	4	yes	complemented
232	#887	C₂²×C₅	1	8	yes	complemented
233	#887	C₂²×C₅	1	4	yes	complemented
234	D₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
235	#878	C₂²×C₅	1	8	yes	—
236	#877	C₂²×C₅	1	4	yes	—
237	#872	C₂²×C₅	1	4	yes	—
238	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
239	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
240	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
241	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
242	C₄²×D₃	C₂²×C₅	1	2	yes	—
243	C₄²×D₃	C₂²×C₅	1	2	yes	—
244	C₄²×D₃	C₂²×C₅	1	4	yes	—
245	#870	C₂²×C₅	1	2	yes	complemented
246	#869	C₂²×C₅	1	2	yes	complemented
247	C₄×Dic₆	C₂²×C₅	1	4	yes	complemented
248	C₄×Dic₆	C₂²×C₅	1	8	yes	complemented
249	C₂⁴×C₅	—	3	1	no	—
250	C₂×C₅×Q₈	—	3	8	no	—
251	C₂×C₅×Q₈	—	3	4	no	—
252	C₂×C₅×Q₈	—	6	16	no	—
253	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
254	C₂²×C₄×C₅	—	3	1	no	—
255	C₂²×C₄×C₅	—	3	8	no	—
256	C₂²×C₄×C₅	—	3	1	no	—
257	C₂²×C₄×C₅	—	3	2	no	—
258	C₂²×C₄×C₅	—	3	1	no	—
259	C₂²×C₄×C₅	—	3	1	no	—
260	C₂²×C₄×C₅	—	3	1	no	—
261	C₂²×C₄×C₅	—	3	2	no	—
262	C₂²×C₄×C₅	—	3	2	no	—
263	C₂²×C₄×C₅	—	3	2	no	—
264	C₂²×C₄×C₅	—	3	2	no	—
265	C₂²×C₄×C₅	—	3	8	no	—
266	C₂²×C₄×C₅	—	6	8	no	—
267	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
268	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
269	C₅×C₄⋊C₄	—	3	8	no	—
270	C₅×C₄⋊C₄	—	3	4	no	—
271	C₅×C₄⋊C₄	—	3	8	no	—
272	C₅×C₄⋊C₄	—	3	8	no	—
273	C₅×C₄⋊C₄	—	3	8	no	—
274	C₅×C₄⋊C₄	—	3	8	no	—
275	C₅×C₄⋊C₄	—	3	4	no	—
276	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
277	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
278	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
279	C₅×C₂²⋊C₄	—	3	4	no	—
280	C₅×C₂²⋊C₄	—	3	8	no	—
281	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
282	C₄²×C₅	—	3	2	no	—
283	C₄²×C₅	—	3	2	no	—
284	C₄²×C₅	—	3	2	no	—
285	C₄²×C₅	—	3	1	no	—
286	C₄²×C₅	—	3	2	no	—
287	C₄²×C₅	—	3	1	no	—
288	C₄²×C₅	—	3	8	no	—
289	C₄²×C₅	—	3	2	no	—
290	C₄²×C₅	—	3	4	no	—
291	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
292	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
293	C₄²×C₅	C₂²×D₃	1	2	yes	—
294	C₄²×C₅	C₂²×D₃	1	4	yes	—
295	#533	—	3	2	no	—
296	#533	—	3	2	no	—
297	#533	—	3	4	no	—
298	#533	—	3	4	no	—
299	#533	—	3	2	no	—
300	#533	—	3	1	no	—
301	#533	C₅×D₃	1	1	yes	characteristic, direct product factor
302	C₂×C₄⋊Q₈	—	3	2	no	—
303	C₂×#125	—	3	2	no	—
304	C₂×C₂²⋊Q₈	—	3	4	no	—
305	C₂×C₄×Q₈	—	3	4	no	—
306	C₂×#117	—	3	2	no	—
307	C₂²×C₄²	—	3	1	no	—
308	C₂²×C₃×C₅	—	2	2	no	—
309	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
310	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
311	C₂×C₅×D₃	—	2	2	no	—
312	C₂×C₅×D₃	—	2	8	no	—
313	C₂×C₅×D₃	C₂²×Q₈	1	2	yes	—
314	C₂×C₅×D₃	C₂²×Q₈	1	2	yes	—
315	C₂×C₅×D₃	C₂×#41	1	4	yes	—
316	C₃×C₄×C₅	—	2	8	no	—
317	C₃×C₄×C₅	—	2	2	no	—
318	C₃×C₄×C₅	C₂²×Q₈	1	2	yes	—
319	C₃×C₄×C₅	C₂²×Q₈	1	2	yes	—
320	C₃×C₄×C₅	C₂×#41	1	4	yes	—
321	C₅×Dic₃	—	2	8	no	—
322	C₅×Dic₃	—	2	2	no	—
323	C₅×Dic₃	C₂²×Q₈	1	2	yes	—
324	C₅×Dic₃	C₂²×Q₈	1	2	yes	—
325	C₅×Dic₃	C₂×#41	1	4	yes	—
326	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
327	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
328	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
329	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
330	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
331	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
332	D₃×Q₈	—	2	16	no	—
333	C₂×C₄×D₃	—	2	8	no	—
334	C₂×C₄×D₃	C₅×Q₈	1	8	yes	complemented
335	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
336	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
337	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
338	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
339	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
340	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
341	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
342	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
343	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
344	C₂×Dic₆	C₂³×C₅	1	4	yes	—
345	C₂×Dic₆	C₂³×C₅	1	8	yes	—
346	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
347	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
348	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
349	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
350	C₃×C₄²	C₂³×C₅	1	2	yes	—
351	C₃×C₄²	C₂³×C₅	1	4	yes	—
352	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
353	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
354	#217	C₂³×C₅	1	4	yes	—
355	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
356	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
357	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
358	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
359	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
360	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
361	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
362	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
363	C₄×Dic₃	C₂³×C₅	1	2	yes	—
364	C₄×Dic₃	C₂³×C₅	1	4	yes	—
365	C₄×Dic₃	C₂³×C₅	1	2	yes	—
366	C₄×Dic₃	C₂³×C₅	1	2	yes	—
367	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
368	C₄×Dic₃	C₂³×C₅	1	2	yes	—
369	C₄×Dic₃	C₂³×C₅	1	2	yes	—
370	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
371	C₄×Dic₃	C₂³×C₅	1	8	yes	—
372	C₂³×C₅	—	3	1	no	—
373	C₂³×C₅	—	3	4	no	—
374	C₂³×C₅	—	3	1	no	—
375	C₂³×C₅	—	6	4	no	—
376	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
377	C₅×Q₈	—	2	8	no	—
378	C₅×Q₈	—	6	16	no	—
379	C₅×Q₈	—	6	8	no	—
380	C₂×C₄×C₅	—	2	4	no	—
381	C₂×C₄×C₅	—	3	4	no	—
382	C₂×C₄×C₅	—	3	1	no	—
383	C₂×C₄×C₅	—	3	1	no	—
384	C₂×C₄×C₅	—	3	2	no	—
385	C₂×C₄×C₅	—	3	4	no	—
386	C₂×C₄×C₅	—	3	4	no	—
387	C₂×C₄×C₅	—	3	4	no	—
388	C₂×C₄×C₅	—	3	4	no	—
389	C₂×C₄×C₅	—	3	8	no	—
390	C₂×C₄×C₅	—	3	2	no	—
391	C₂×C₄×C₅	—	3	8	no	—
392	C₂×C₄×C₅	—	6	4	no	—
393	C₂×C₄×C₅	—	6	4	no	—
394	C₂×C₄×C₅	—	6	16	no	—
395	C₂×C₄×C₅	—	6	4	no	—
396	C₂×C₄×C₅	—	6	4	no	—
397	C₂×C₄×C₅	D₃×Q₈	1	4	yes	complemented
398	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
399	C₂×C₄×C₅	C₂³×D₃	1	8	yes	—
400	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
401	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
402	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
403	C₂²×Q₈	—	3	4	no	—
404	C₂³×C₄	—	3	1	no	—
405	C₂³×C₄	—	3	2	no	—
406	C₄⋊Q₈	—	3	4	no	—
407	C₄⋊Q₈	—	3	4	no	—
408	C₄⋊Q₈	—	3	4	no	—
409	C₄⋊Q₈	—	3	2	no	—
410	C₄⋊Q₈	C₂×C₅×D₃	1	2	yes	complemented
411	#125	—	3	8	no	—
412	#125	—	3	4	no	—
413	#125	—	3	2	no	—
414	#125	C₂×C₅×D₃	1	2	yes	complemented
415	C₂²⋊Q₈	—	3	4	no	—
416	C₂²⋊Q₈	—	3	4	no	—
417	C₂²⋊Q₈	—	3	8	no	—
418	C₂²⋊Q₈	—	3	4	no	—
419	C₂²⋊Q₈	—	3	8	no	—
420	C₂²⋊Q₈	C₂×C₅×D₃	1	4	yes	—
421	C₄×Q₈	—	3	4	no	—
422	C₄×Q₈	—	3	4	no	—
423	C₄×Q₈	—	3	8	no	—
424	C₄×Q₈	—	3	8	no	—
425	C₄×Q₈	—	3	4	no	—
426	C₄×Q₈	C₂×C₅×D₃	1	4	yes	complemented
427	#117	—	3	2	no	—
428	#117	—	3	4	no	—
429	#117	—	3	4	no	—
430	#117	—	3	4	no	—
431	#117	C₂×C₅×D₃	1	2	yes	—
432	C₂×C₄⋊C₄	—	3	4	no	—
433	C₂×C₄⋊C₄	—	3	8	no	—
434	C₂×C₄⋊C₄	—	3	4	no	—
435	C₂×C₂²⋊C₄	—	3	4	no	—
436	C₂×C₄²	—	3	2	no	—
437	C₂×C₄²	—	3	1	no	—
438	C₂×C₄²	—	3	4	no	—
439	C₂×C₄²	—	3	2	no	—
440	C₂×C₄²	—	3	1	no	—
441	C₂×C₄²	—	3	1	no	—
442	C₂×C₄²	—	3	1	no	—
443	C₂×C₄²	—	3	1	no	—
444	C₂×C₄²	—	3	2	no	—
445	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
446	C₂×C₃×C₅	—	2	2	no	—
447	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
448	C₂×C₃×C₅	C₂²×#41	1	2	yes	—
449	C₅×D₃	—	2	2	no	—
450	C₅×D₃	#533	1	4	yes	direct product factor
451	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
452	C₂²×D₃	—	2	4	no	—
453	C₂²×D₃	C₂×C₅×Q₈	1	4	yes	—
454	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
455	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
456	C₃×Q₈	—	2	8	no	—
457	C₂×C₃×C₄	—	2	4	no	—
458	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	complemented
459	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
460	C₂×C₃×C₄	C₂⁴×C₅	1	8	yes	—
461	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
462	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
463	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
464	C₂×Dic₃	—	2	4	no	—
465	C₂×Dic₃	C₂×C₅×Q₈	1	4	yes	complemented
466	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
467	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
468	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
469	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
470	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
471	C₄×D₃	—	2	4	no	—
472	C₄×D₃	—	2	16	no	—
473	C₄×D₃	—	2	4	no	—
474	C₄×D₃	—	2	4	no	—
475	C₄×D₃	C₂×C₅×Q₈	1	4	yes	—
476	C₄×D₃	C₂×C₅×Q₈	1	4	yes	—
477	C₄×D₃	C₂×C₅×Q₈	1	4	yes	complemented
478	C₄×D₃	C₂×C₅×Q₈	1	4	yes	complemented
479	C₄×D₃	C₅×#41	1	8	yes	—
480	Dic₆	—	2	8	no	—
481	Dic₆	—	2	16	no	—
482	C₂²×C₅	—	2	2	no	—
483	C₂²×C₅	—	3	2	no	—
484	C₂²×C₅	—	3	4	no	—
485	C₂²×C₅	—	3	2	no	—
486	C₂²×C₅	—	6	8	no	—
487	C₂²×C₅	—	6	2	no	—
488	C₂²×C₅	C₂×D₃×Q₈	1	2	yes	—
489	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
490	C₄×C₅	—	2	2	no	—
491	C₄×C₅	—	2	8	no	—
492	C₄×C₅	—	3	2	no	—
493	C₄×C₅	—	3	2	no	—
494	C₄×C₅	—	3	4	no	—
495	C₄×C₅	—	6	2	no	—
496	C₄×C₅	—	6	8	no	—
497	C₄×C₅	C₂×D₃×Q₈	1	2	yes	—
498	C₄×C₅	C₂×D₃×Q₈	1	2	yes	—
499	C₄×C₅	D₃×#41	1	4	yes	—
500	C₂⁴	—	3	1	no	—
501	C₂×Q₈	—	3	8	no	—
502	C₂×Q₈	—	3	4	no	—
503	C₂×Q₈	—	6	16	no	—
504	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
505	C₂²×C₄	—	3	1	no	—
506	C₂²×C₄	—	3	8	no	—
507	C₂²×C₄	—	3	1	no	—
508	C₂²×C₄	—	3	1	no	—
509	C₂²×C₄	—	3	2	no	—
510	C₂²×C₄	—	3	1	no	—
511	C₂²×C₄	—	3	1	no	—
512	C₂²×C₄	—	3	2	no	—
513	C₂²×C₄	—	3	2	no	—
514	C₂²×C₄	—	3	2	no	—
515	C₂²×C₄	—	3	2	no	—
516	C₂²×C₄	—	3	8	no	—
517	C₂²×C₄	—	6	8	no	—
518	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
519	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
520	C₄⋊C₄	—	3	8	no	—
521	C₄⋊C₄	—	3	4	no	—
522	C₄⋊C₄	—	3	8	no	—
523	C₄⋊C₄	—	3	8	no	—
524	C₄⋊C₄	—	3	8	no	—
525	C₄⋊C₄	—	3	8	no	—
526	C₄⋊C₄	—	3	4	no	—
527	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
528	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
529	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
530	C₂²⋊C₄	—	3	4	no	—
531	C₂²⋊C₄	—	3	8	no	—
532	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
533	C₄²	—	3	2	no	—
534	C₄²	—	3	2	no	—
535	C₄²	—	3	2	no	—
536	C₄²	—	3	2	no	—
537	C₄²	—	3	1	no	—
538	C₄²	—	3	2	no	—
539	C₄²	—	3	1	no	—
540	C₄²	—	3	8	no	—
541	C₄²	—	3	4	no	—
542	C₄²	C₂²×C₅×D₃	1	2	yes	—
543	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
544	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
545	C₄²	C₂²×C₅×D₃	1	4	yes	—
546	C₃×C₅	C₂×#533	1	1	yes	characteristic, complemented, Hall
547	C₂²×C₃	—	2	2	no	—
548	C₂²×C₃	C₂²×C₅×Q₈	1	2	yes	—
549	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
550	C₂×D₃	—	2	2	no	—
551	C₂×D₃	—	2	8	no	—
552	C₂×D₃	C₂²×C₅×Q₈	1	2	yes	—
553	C₂×D₃	C₂²×C₅×Q₈	1	2	yes	—
554	C₂×D₃	C₂×C₅×#41	1	4	yes	—
555	C₃×C₄	—	2	8	no	—
556	C₃×C₄	—	2	2	no	—
557	C₃×C₄	C₂²×C₅×Q₈	1	2	yes	—
558	C₃×C₄	C₂²×C₅×Q₈	1	2	yes	—
559	C₃×C₄	C₂×C₅×#41	1	4	yes	—
560	Dic₃	—	2	8	no	—
561	Dic₃	—	2	2	no	—
562	Dic₃	C₂²×C₅×Q₈	1	2	yes	—
563	Dic₃	C₂²×C₅×Q₈	1	2	yes	—
564	Dic₃	C₂×C₅×#41	1	4	yes	—
565	C₂×C₅	—	2	2	no	—
566	C₂×C₅	—	3	4	no	—
567	C₂×C₅	—	6	2	no	—
568	C₂×C₅	C₂²×D₃×Q₈	1	1	yes	characteristic
569	C₂×C₅	C₂×D₃×#41	1	2	yes	—
570	C₂³	—	3	1	no	—
571	C₂³	—	3	4	no	—
572	C₂³	—	3	1	no	—
573	C₂³	—	6	4	no	—
574	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
575	Q₈	—	2	8	no	—
576	Q₈	—	6	16	no	—
577	Q₈	—	6	8	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	3	4	no	—
580	C₂×C₄	—	3	1	no	—
581	C₂×C₄	—	3	1	no	—
582	C₂×C₄	—	3	2	no	—
583	C₂×C₄	—	3	4	no	—
584	C₂×C₄	—	3	4	no	—
585	C₂×C₄	—	3	4	no	—
586	C₂×C₄	—	3	4	no	—
587	C₂×C₄	—	3	8	no	—
588	C₂×C₄	—	3	2	no	—
589	C₂×C₄	—	3	8	no	—
590	C₂×C₄	—	6	4	no	—
591	C₂×C₄	—	6	4	no	—
592	C₂×C₄	—	6	16	no	—
593	C₂×C₄	—	6	4	no	—
594	C₂×C₄	—	6	4	no	—
595	C₂×C₄	C₅×D₃×Q₈	1	4	yes	complemented
596	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
597	C₂×C₄	C₂³×C₅×D₃	1	8	yes	—
598	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
599	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
600	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
601	C₂×C₃	—	2	2	no	—
602	C₂×C₃	C₂³×C₅×Q₈	1	1	yes	characteristic
603	C₂×C₃	C₂²×C₅×#41	1	2	yes	—
604	D₃	—	2	2	no	—
605	D₃	C₅×#533	1	4	yes	direct product factor
606	C₅	D₃×#533	1	1	yes	characteristic, direct product factor, Sylow
607	C₂²	—	2	2	no	—
608	C₂²	—	3	2	no	—
609	C₂²	—	3	4	no	—
610	C₂²	—	3	2	no	—
611	C₂²	—	6	8	no	—
612	C₂²	—	6	2	no	—
613	C₂²	C₂×C₅×D₃×Q₈	1	2	yes	—
614	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
615	C₄	—	2	2	no	—
616	C₄	—	2	8	no	—
617	C₄	—	3	2	no	—
618	C₄	—	3	2	no	—
619	C₄	—	3	4	no	—
620	C₄	—	6	2	no	—
621	C₄	—	6	8	no	—
622	C₄	C₂×C₅×D₃×Q₈	1	2	yes	—
623	C₄	C₂×C₅×D₃×Q₈	1	2	yes	—
624	C₄	C₅×D₃×#41	1	4	yes	—
625	C₃	C₂×C₅×#533	1	1	yes	characteristic, complemented, Sylow
626	C₂	—	2	2	no	—
627	C₂	—	3	4	no	—
628	C₂	—	6	2	no	—
629	C₂	C₂²×C₅×D₃×Q₈	1	1	yes	characteristic
630	C₂	C₂×C₅×D₃×#41	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#533	C₂
socle	C₂²×C₃×C₅	C₂⁵
prime radical	C₂³×C₅×D₃	C₂³
hypercenter	C₅×#533	D₃
hypocenter	C₃	C₂×C₅×#533
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#533

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#533	C₂	semidirect
2. C₅×#5728	C₂	semidirect
3. C₅×D₃×C₄⋊Q₈	C₂	semidirect
4. C₅×#5688	C₂	semidirect
5. C₅×D₃×#125	C₂	semidirect
7. C₅×#5622	C₂	semidirect
8. C₅×#5578	C₂	semidirect
9. C₄×C₅×D₃×Q₈	C₂	semidirect
11. C₅×#5517	C₂	semidirect
13. C₅×#5470	C₂	semidirect
18. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
19. C₃×C₅×#125	C₂²	semidirect
21. C₃×C₄×C₅×Q₈	C₂²	semidirect
25. C₅×Q₈×Dic₃	C₂²	semidirect
26. C₅×#944	C₂²	semidirect
37. C₅×#890	C₂²	semidirect
38. C₅×#889	C₂²	semidirect
39. C₅×#888	C₂²	semidirect
40. C₅×#888	C₂²	semidirect
41. C₅×#887	C₂²	semidirect
42. C₅×#887	C₂²	semidirect
54. C₅×#870	C₂²	semidirect
55. C₅×#869	C₂²	semidirect
56. C₄×C₅×Dic₆	C₂²	semidirect
57. C₄×C₅×Dic₆	C₂²	semidirect
58. D₃×#533	C₅	direct (N × H)
65. C₅×#533	D₃	direct (N × H)
80. C₂×C₄×C₅×D₃	Q₈	semidirect
118. C₃×#533	C₂×C₅	semidirect
119. #5728	C₂×C₅	semidirect
120. D₃×C₄⋊Q₈	C₂×C₅	semidirect
121. #5688	C₂×C₅	semidirect
122. D₃×#125	C₂×C₅	semidirect
124. #5622	C₂×C₅	semidirect
125. #5578	C₂×C₅	semidirect
126. C₄×D₃×Q₈	C₂×C₅	semidirect
128. #5517	C₂×C₅	semidirect
130. #5470	C₂×C₅	semidirect
138. C₅×C₄⋊Q₈	C₂×D₃	semidirect
142. C₅×#125	C₂×D₃	semidirect
154. C₄×C₅×Q₈	C₂×D₃	semidirect
182. C₂×C₃×C₄×C₅	C₂×Q₈	semidirect
189. C₂×C₅×Dic₃	C₂×Q₈	semidirect
201. C₄×C₅×D₃	C₂×Q₈	semidirect
202. C₄×C₅×D₃	C₂×Q₈	semidirect
209. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
210. C₃×#125	C₂²×C₅	semidirect
212. C₃×C₄×Q₈	C₂²×C₅	semidirect
216. Q₈×Dic₃	C₂²×C₅	semidirect
217. #944	C₂²×C₅	semidirect
228. #890	C₂²×C₅	semidirect
229. #889	C₂²×C₅	semidirect
230. #888	C₂²×C₅	semidirect
231. #888	C₂²×C₅	semidirect
232. #887	C₂²×C₅	semidirect
233. #887	C₂²×C₅	semidirect
245. #870	C₂²×C₅	semidirect
246. #869	C₂²×C₅	semidirect
247. C₄×Dic₆	C₂²×C₅	semidirect
248. C₄×Dic₆	C₂²×C₅	semidirect
301. #533	C₅×D₃	direct (N × H)
334. C₂×C₄×D₃	C₅×Q₈	semidirect
397. C₂×C₄×C₅	D₃×Q₈	semidirect
410. C₄⋊Q₈	C₂×C₅×D₃	semidirect
414. #125	C₂×C₅×D₃	semidirect
426. C₄×Q₈	C₂×C₅×D₃	semidirect
450. C₅×D₃	#533	direct (N × H)
458. C₂×C₃×C₄	C₂×C₅×Q₈	semidirect
465. C₂×Dic₃	C₂×C₅×Q₈	semidirect
477. C₄×D₃	C₂×C₅×Q₈	semidirect
478. C₄×D₃	C₂×C₅×Q₈	semidirect
546. C₃×C₅	C₂×#533	semidirect
595. C₂×C₄	C₅×D₃×Q₈	semidirect
605. D₃	C₅×#533	direct (N × H)
606. C₅	D₃×#533	direct (N × H)
625. C₃	C₂×C₅×#533	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#533	2
C₅×#5728	2
C₅×D₃×C₄⋊Q₈	2
C₅×#5688	2
C₅×D₃×#125	2
C₅×D₃×C₂²⋊Q₈	2
C₅×#5622	2
C₅×#5578	2
C₄×C₅×D₃×Q₈	2
C₅×D₃×#117	2
C₅×#5517	2
C₂×C₄²×C₅×D₃	2
C₅×#5470	2
C₂×C₅×#533	3
D₃×#533	5

Subgroups — C5×D3×#533 #14480108

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#533 #14480108