Subgroups — C₃×#10615703 #14439202

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66166	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#4097	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4090	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#4088	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#4055	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65479	C₂	1	2	yes	maximal, complemented
8	C₃×#65470	C₂	1	2	yes	maximal, complemented
9	C₃×#65464	C₂	1	2	yes	maximal, complemented
10	C₃×#65456	C₂	1	2	yes	maximal, complemented
11	C₃×M₁₆×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
12	#10615703	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×#709	C₂²	1	1	yes	characteristic
16	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
17	C₃×C₅×#137	—	2	4	no	—
18	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
19	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
20	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
21	C₃×#4097	—	2	4	no	—
22	C₃×#4093	C₂²	1	1	yes	characteristic
23	C₃×#4090	—	2	2	no	—
24	C₃×#4090	C₂²	1	2	yes	—
25	C₃×#4090	C₂²	1	2	yes	—
26	C₃×#4090	C₂²	1	1	yes	characteristic
27	C₂×C₃×#689	C₂²	1	2	yes	—
28	C₂×C₃×#689	C₂²	1	2	yes	—
29	C₃×#4088	—	2	4	no	—
30	C₂×C₃×#688	C₂²	1	2	yes	—
31	C₃×#4086	C₂²	1	1	yes	characteristic
32	C₃×#4085	—	2	2	no	—
33	C₃×#4082	C₂²	1	1	yes	characteristic
34	C₂×C₃×#687	C₂²	1	2	yes	—
35	C₃×C₄×C₂²⋊D₅	—	2	2	no	—
36	C₂×C₃×#683	—	2	2	no	—
37	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
38	C₂×C₃×#681	C₂²	1	1	yes	characteristic
39	C₃×#4055	—	2	4	no	—
40	C₂×C₃×Dic₂₀	C₂²	1	2	yes	—
41	C₂×C₃×#677	C₂²	1	2	yes	—
42	C₃×#3947	C₂²	1	2	yes	—
43	C₃×C₈×Dic₅	C₂²	1	2	yes	—
44	C₃×#3152	—	5	1	no	maximal, Hall
45	C₂×C₅×#137	C₂×C₃	1	1	yes	characteristic, complemented
46	#66166	C₂×C₃	1	1	yes	characteristic
47	C₂×#4097	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂×#4090	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂×#4088	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂×#4055	C₂×C₃	1	1	yes	characteristic, complemented
51	#65479	C₂×C₃	1	2	yes	complemented
52	#65470	C₂×C₃	1	2	yes	complemented
53	#65464	C₂×C₃	1	2	yes	complemented
54	#65456	C₂×C₃	1	2	yes	complemented
55	M₁₆×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
56	C₃×C₅×#41	—	2	2	no	—
57	C₃×C₅×#41	—	2	2	no	—
58	C₂×C₃×C₅×Q₈	—	2	1	no	—
59	C₂×C₃×C₅×Q₈	—	2	2	no	—
60	C₂×C₃×C₅×Q₈	—	2	2	no	—
61	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
62	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×D₄	—	2	1	no	—
64	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	—	2	1	no	—
66	C₂²×C₃×C₄×C₅	—	2	1	no	—
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
69	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
70	C₂²×C₃×Dic₅	—	2	1	no	—
71	C₂²×C₃×Dic₅	D₄	1	2	yes	—
72	C₃×#709	—	2	2	no	—
73	C₃×#709	—	2	2	no	—
74	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₄×D₅	—	2	1	no	—
76	C₂×C₃×Dic₁₀	—	2	2	no	—
77	C₂×C₃×Dic₁₀	—	2	2	no	—
78	C₂×C₃×Dic₁₀	—	2	1	no	—
79	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
80	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
81	C₃×C₅×Q₁₆	—	2	4	no	—
82	C₃×C₅×SD₁₆	—	2	4	no	—
83	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
84	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
85	C₃×C₂²⋊Dic₅	—	2	2	no	—
86	C₃×#689	—	2	4	no	—
87	C₃×#689	—	2	4	no	—
88	C₃×#688	—	2	4	no	—
89	C₃×#687	—	2	4	no	—
90	C₃×#685	—	2	2	no	—
91	C₃×#683	—	2	2	no	—
92	C₃×#683	—	2	4	no	—
93	C₃×#683	—	2	4	no	—
94	C₃×C₄×Dic₅	D₄	1	2	yes	—
95	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
96	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
97	C₃×#681	D₄	1	4	yes	complemented
98	C₂×C₃×#168	C₂³	1	2	yes	—
99	C₃×Dic₂₀	—	2	4	no	—
100	C₃×#677	—	2	4	no	—
101	C₂×C₃×#137	—	5	1	no	—
102	C₂×C₃×#137	—	5	1	no	—
103	C₂×C₃×#137	—	5	1	no	—
104	C₂×C₃×#137	D₅	1	1	yes	characteristic, complemented
105	C₃×#532	—	5	1	no	—
106	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
107	C₃×#497	—	5	2	no	—
108	C₃×#497	—	5	2	no	—
109	C₃×#494	—	5	2	no	—
110	C₃×#492	—	5	2	no	—
111	C₃×C₄×M₁₆	—	5	1	no	—
112	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
113	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
114	C₂×#709	C₂²×C₃	1	1	yes	characteristic
115	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
116	C₅×#137	—	2	4	no	—
117	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
118	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
119	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
120	#4097	—	2	4	no	—
121	#4093	C₂²×C₃	1	1	yes	characteristic
122	#4090	—	2	2	no	—
123	#4090	C₂²×C₃	1	2	yes	—
124	#4090	C₂²×C₃	1	2	yes	—
125	#4090	C₂²×C₃	1	1	yes	characteristic
126	C₂×#689	C₂²×C₃	1	2	yes	—
127	C₂×#689	C₂²×C₃	1	2	yes	—
128	#4088	—	2	4	no	—
129	C₂×#688	C₂²×C₃	1	2	yes	—
130	#4086	C₂²×C₃	1	1	yes	characteristic
131	#4085	—	2	2	no	—
132	#4082	C₂²×C₃	1	1	yes	characteristic
133	C₂×#687	C₂²×C₃	1	2	yes	—
134	C₄×C₂²⋊D₅	—	2	2	no	—
135	C₂×#683	—	2	2	no	—
136	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
137	C₂×#681	C₂²×C₃	1	1	yes	characteristic
138	#4055	—	2	4	no	—
139	C₂×Dic₂₀	C₂²×C₃	1	2	yes	—
140	C₂×#677	C₂²×C₃	1	2	yes	—
141	#3947	C₂²×C₃	1	2	yes	—
142	C₈×Dic₅	C₂²×C₃	1	2	yes	—
143	#3152	—	5	1	no	Sylow
144	C₂³×C₃×C₅	—	2	1	no	—
145	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₃×D₅	—	2	1	no	—
147	C₃×C₅×Q₈	—	2	2	no	—
148	C₃×C₅×Q₈	—	2	1	no	—
149	C₃×C₅×Q₈	—	2	2	no	—
150	C₃×C₅×Q₈	—	2	1	no	—
151	C₃×C₅×Q₈	—	4	2	no	—
152	C₃×C₅×D₄	—	2	1	no	—
153	C₃×C₅×D₄	—	2	1	no	—
154	C₃×C₅×D₄	—	4	2	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	2	1	no	—
157	C₂×C₃×C₄×C₅	—	4	2	no	—
158	C₂×C₃×C₄×C₅	—	4	2	no	—
159	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
161	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
162	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
163	C₃×C₂²⋊D₅	—	4	2	no	—
164	C₃×C₂²⋊D₅	—	4	4	no	—
165	C₂×C₃×Dic₅	—	2	4	no	—
166	C₂×C₃×Dic₅	—	2	2	no	—
167	C₂×C₃×Dic₅	—	2	1	no	—
168	C₂×C₃×Dic₅	—	4	2	no	—
169	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
170	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
171	C₃×D₂₀	—	2	1	no	—
172	C₃×D₂₀	—	2	1	no	—
173	C₃×C₄×D₅	—	4	2	no	—
174	C₃×Dic₁₀	—	2	2	no	—
175	C₃×Dic₁₀	—	2	1	no	—
176	C₃×Dic₁₀	—	2	2	no	—
177	C₃×Dic₁₀	—	2	1	no	—
178	C₃×Dic₁₀	—	4	2	no	—
179	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
180	C₃×#168	C₂×D₄	1	4	yes	—
181	C₂×C₃×#41	—	5	1	no	—
182	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
183	C₂²×C₃×Q₈	—	5	1	no	—
184	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
185	C₃×#137	—	2	4	no	—
186	C₃×#137	—	10	4	no	—
187	C₃×#137	—	10	4	no	—
188	C₃×#137	—	10	4	no	—
189	C₂×C₃×Q₁₆	—	5	2	no	—
190	C₂×C₃×Q₁₆	—	5	2	no	—
191	C₂×C₃×Q₁₆	—	5	2	no	—
192	C₂×C₃×Q₁₆	C₂×D₅	1	2	yes	—
193	C₂×C₃×SD₁₆	—	5	2	no	—
194	C₂×C₃×SD₁₆	—	5	2	no	—
195	C₂×C₃×SD₁₆	—	5	2	no	—
196	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	—
197	C₂×C₃×M₁₆	—	5	1	no	—
198	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
199	C₃×C₄⋊Q₈	—	5	2	no	—
200	C₃×C₄⋊Q₈	—	5	2	no	—
201	C₃×C₄⋊Q₈	—	5	1	no	—
202	C₃×C₄⋊Q₈	—	10	2	no	—
203	C₃×#127	—	5	1	no	—
204	C₃×#124	—	5	1	no	—
205	C₃×#124	—	5	1	no	—
206	C₃×#121	—	10	2	no	—
207	C₃×C₄×D₄	—	10	2	no	—
208	C₂×C₃×C₄⋊C₄	—	10	2	no	—
209	C₂×C₃×C₄²	—	5	1	no	—
210	C₃×#97	—	5	2	no	—
211	C₃×C₄×C₈	—	5	2	no	—
212	C₅×#41	—	2	2	no	—
213	C₅×#41	—	2	2	no	—
214	C₂×C₅×Q₈	—	2	1	no	—
215	C₂×C₅×Q₈	—	2	2	no	—
216	C₂×C₅×Q₈	—	2	2	no	—
217	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
218	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
219	C₂×C₅×D₄	—	2	1	no	—
220	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
221	C₂²×C₄×C₅	—	2	1	no	—
222	C₂²×C₄×C₅	—	2	1	no	—
223	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
224	C₂×C₂²⋊D₅	—	2	1	no	—
225	C₂×C₂²⋊D₅	—	2	2	no	—
226	C₂²×Dic₅	—	2	1	no	—
227	C₂²×Dic₅	C₃×D₄	1	2	yes	—
228	#709	—	2	2	no	—
229	#709	—	2	2	no	—
230	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
231	C₂×C₄×D₅	—	2	1	no	—
232	C₂×Dic₁₀	—	2	2	no	—
233	C₂×Dic₁₀	—	2	2	no	—
234	C₂×Dic₁₀	—	2	1	no	—
235	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
236	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
237	C₅×Q₁₆	—	2	4	no	—
238	C₅×SD₁₆	—	2	4	no	—
239	C₅×M₁₆	C₃×D₄	1	4	yes	complemented
240	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
241	C₂²⋊Dic₅	—	2	2	no	—
242	#689	—	2	4	no	—
243	#689	—	2	4	no	—
244	#688	—	2	4	no	—
245	#687	—	2	4	no	—
246	#685	—	2	2	no	—
247	#683	—	2	4	no	—
248	#683	—	2	4	no	—
249	#683	—	2	2	no	—
250	C₄×Dic₅	C₃×D₄	1	2	yes	—
251	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
252	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
253	#681	C₃×D₄	1	4	yes	complemented
254	C₂×#168	C₂³×C₃	1	2	yes	—
255	Dic₂₀	—	2	4	no	—
256	#677	—	2	4	no	—
257	C₂×#137	—	5	1	no	—
258	C₂×#137	—	5	1	no	—
259	C₂×#137	—	5	1	no	—
260	C₂×#137	C₃×D₅	1	1	yes	characteristic, complemented
261	#532	—	5	1	no	—
262	C₂×C₄⋊Q₈	—	5	1	no	—
263	#497	—	5	2	no	—
264	#497	—	5	2	no	—
265	#494	—	5	2	no	—
266	#492	—	5	2	no	—
267	C₄×M₁₆	—	5	1	no	—
268	C₂²×C₃×C₅	—	2	2	no	—
269	C₂²×C₃×C₅	—	4	1	no	—
270	C₂²×C₃×C₅	—	4	2	no	—
271	C₂²×C₃×C₅	#127	1	2	yes	—
272	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₃×D₅	—	4	1	no	—
274	C₂×C₃×D₅	—	4	2	no	—
275	C₃×C₄×C₅	—	4	1	no	—
276	C₃×C₄×C₅	—	4	2	no	—
277	C₃×C₄×C₅	#127	1	2	yes	—
278	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
279	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
280	C₃×Dic₅	—	2	2	no	—
281	C₃×Dic₅	—	4	2	no	—
282	C₃×Dic₅	—	4	1	no	—
283	C₃×Dic₅	#137	1	4	yes	complemented
284	C₃×#41	—	2	2	no	—
285	C₃×#41	—	2	2	no	—
286	C₃×#41	—	10	2	no	—
287	C₃×#41	—	10	2	no	—
288	C₂×C₃×Q₈	—	2	1	no	—
289	C₂×C₃×Q₈	—	2	2	no	—
290	C₂×C₃×Q₈	—	2	2	no	—
291	C₂×C₃×Q₈	—	5	1	no	—
292	C₂×C₃×Q₈	—	5	2	no	—
293	C₂×C₃×Q₈	—	10	1	no	—
294	C₂×C₃×Q₈	—	10	2	no	—
295	C₂×C₃×Q₈	—	10	2	no	—
296	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
297	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
298	C₂×C₃×D₄	—	2	1	no	—
299	C₂×C₃×D₄	—	5	1	no	—
300	C₂×C₃×D₄	—	10	2	no	—
301	C₂×C₃×D₄	—	10	1	no	—
302	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
303	C₂²×C₃×C₄	—	2	1	no	—
304	C₂²×C₃×C₄	—	2	1	no	—
305	C₂²×C₃×C₄	—	5	2	no	—
306	C₂²×C₃×C₄	—	10	1	no	—
307	C₂²×C₃×C₄	—	10	1	no	—
308	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
309	C₃×Q₁₆	—	2	4	no	—
310	C₃×Q₁₆	—	10	4	no	—
311	C₃×Q₁₆	—	10	4	no	—
312	C₃×Q₁₆	—	10	4	no	—
313	C₃×SD₁₆	—	2	4	no	—
314	C₃×SD₁₆	—	10	4	no	—
315	C₃×SD₁₆	—	10	4	no	—
316	C₃×SD₁₆	—	10	4	no	—
317	C₃×M₁₆	—	5	4	no	—
318	C₃×M₁₆	C₂²⋊D₅	1	4	yes	complemented
319	C₂×C₃×C₈	—	5	2	no	—
320	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
321	C₃×C₄⋊C₄	—	10	4	no	—
322	C₃×C₄⋊C₄	—	10	4	no	—
323	C₃×C₄⋊C₄	—	10	2	no	—
324	C₃×C₂²⋊C₄	—	10	2	no	—
325	C₃×C₂²⋊C₄	—	10	2	no	—
326	C₃×C₄²	—	5	2	no	—
327	C₃×C₄²	—	5	1	no	—
328	C₃×C₄²	—	5	1	no	—
329	C₂³×C₅	—	2	1	no	—
330	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
331	C₂²×D₅	—	2	1	no	—
332	C₅×Q₈	—	2	2	no	—
333	C₅×Q₈	—	2	1	no	—
334	C₅×Q₈	—	2	2	no	—
335	C₅×Q₈	—	2	1	no	—
336	C₅×Q₈	—	4	2	no	—
337	C₅×D₄	—	2	1	no	—
338	C₅×D₄	—	2	1	no	—
339	C₅×D₄	—	4	2	no	—
340	C₂×C₄×C₅	—	2	2	no	—
341	C₂×C₄×C₅	—	2	1	no	—
342	C₂×C₄×C₅	—	4	2	no	—
343	C₂×C₄×C₅	—	4	2	no	—
344	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
345	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
346	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
347	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
348	C₂²⋊D₅	—	4	2	no	—
349	C₂²⋊D₅	—	4	4	no	—
350	C₂×Dic₅	—	2	4	no	—
351	C₂×Dic₅	—	2	2	no	—
352	C₂×Dic₅	—	2	1	no	—
353	C₂×Dic₅	—	4	2	no	—
354	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
355	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
356	D₂₀	—	2	1	no	—
357	D₂₀	—	2	1	no	—
358	C₄×D₅	—	4	2	no	—
359	Dic₁₀	—	2	2	no	—
360	Dic₁₀	—	2	1	no	—
361	Dic₁₀	—	2	2	no	—
362	Dic₁₀	—	2	1	no	—
363	Dic₁₀	—	4	2	no	—
364	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
365	#168	C₂×C₃×D₄	1	4	yes	—
366	C₂×#41	—	5	1	no	—
367	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
368	C₂²×Q₈	—	5	1	no	—
369	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
370	#137	—	2	4	no	—
371	#137	—	10	4	no	—
372	#137	—	10	4	no	—
373	#137	—	10	4	no	—
374	C₂×Q₁₆	—	5	2	no	—
375	C₂×Q₁₆	—	5	2	no	—
376	C₂×Q₁₆	—	5	2	no	—
377	C₂×Q₁₆	C₂×C₃×D₅	1	2	yes	—
378	C₂×SD₁₆	—	5	2	no	—
379	C₂×SD₁₆	—	5	2	no	—
380	C₂×SD₁₆	—	5	2	no	—
381	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	—
382	C₂×M₁₆	—	5	1	no	—
383	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
384	C₄⋊Q₈	—	5	2	no	—
385	C₄⋊Q₈	—	5	2	no	—
386	C₄⋊Q₈	—	5	1	no	—
387	C₄⋊Q₈	—	10	2	no	—
388	#127	—	5	1	no	—
389	#124	—	5	1	no	—
390	#124	—	5	1	no	—
391	#121	—	10	2	no	—
392	C₄×D₄	—	10	2	no	—
393	C₂×C₄⋊C₄	—	10	2	no	—
394	C₂×C₄²	—	5	1	no	—
395	#97	—	5	2	no	—
396	C₄×C₈	—	5	2	no	—
397	C₂×C₃×C₅	—	2	2	no	—
398	C₂×C₃×C₅	—	8	1	no	—
399	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
400	C₂×C₃×C₅	C₂×#137	1	2	yes	—
401	C₃×D₅	—	8	1	no	—
402	C₂³×C₃	—	2	1	no	—
403	C₂³×C₃	—	10	1	no	—
404	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
405	C₃×Q₈	—	2	2	no	—
406	C₃×Q₈	—	2	1	no	—
407	C₃×Q₈	—	2	2	no	—
408	C₃×Q₈	—	2	1	no	—
409	C₃×Q₈	—	4	2	no	—
410	C₃×Q₈	—	10	2	no	—
411	C₃×Q₈	—	10	1	no	—
412	C₃×Q₈	—	10	2	no	—
413	C₃×Q₈	—	10	1	no	—
414	C₃×Q₈	—	20	2	no	—
415	C₃×D₄	—	2	1	no	—
416	C₃×D₄	—	2	1	no	—
417	C₃×D₄	—	4	2	no	—
418	C₃×D₄	—	10	1	no	—
419	C₃×D₄	—	10	1	no	—
420	C₃×D₄	—	20	4	no	—
421	C₃×D₄	—	20	2	no	—
422	C₂×C₃×C₄	—	2	1	no	—
423	C₂×C₃×C₄	—	2	2	no	—
424	C₂×C₃×C₄	—	4	2	no	—
425	C₂×C₃×C₄	—	4	2	no	—
426	C₂×C₃×C₄	—	5	2	no	—
427	C₂×C₃×C₄	—	5	2	no	—
428	C₂×C₃×C₄	—	10	4	no	—
429	C₂×C₃×C₄	—	10	1	no	—
430	C₂×C₃×C₄	—	10	2	no	—
431	C₂×C₃×C₄	—	20	2	no	—
432	C₂×C₃×C₄	—	20	2	no	—
433	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
434	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
435	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
436	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
437	C₃×C₈	—	5	4	no	—
438	C₃×C₈	C₂×C₂²⋊D₅	1	4	yes	—
439	C₂²×C₅	—	2	2	no	—
440	C₂²×C₅	—	4	2	no	—
441	C₂²×C₅	—	4	1	no	—
442	C₂²×C₅	C₃×#127	1	2	yes	—
443	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
444	C₂×D₅	—	4	2	no	—
445	C₂×D₅	—	4	1	no	—
446	C₄×C₅	—	4	1	no	—
447	C₄×C₅	—	4	2	no	—
448	C₄×C₅	C₃×#127	1	2	yes	—
449	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
450	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
451	Dic₅	—	2	2	no	—
452	Dic₅	—	4	2	no	—
453	Dic₅	—	4	1	no	—
454	Dic₅	C₃×#137	1	4	yes	complemented
455	#41	—	2	2	no	—
456	#41	—	2	2	no	—
457	#41	—	10	2	no	—
458	#41	—	10	2	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	2	no	—
461	C₂×Q₈	—	2	2	no	—
462	C₂×Q₈	—	5	1	no	—
463	C₂×Q₈	—	5	2	no	—
464	C₂×Q₈	—	10	1	no	—
465	C₂×Q₈	—	10	2	no	—
466	C₂×Q₈	—	10	2	no	—
467	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
468	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	5	1	no	—
471	C₂×D₄	—	10	2	no	—
472	C₂×D₄	—	10	1	no	—
473	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	5	2	no	—
477	C₂²×C₄	—	10	1	no	—
478	C₂²×C₄	—	10	1	no	—
479	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
480	Q₁₆	—	2	4	no	—
481	Q₁₆	—	10	4	no	—
482	Q₁₆	—	10	4	no	—
483	Q₁₆	—	10	4	no	—
484	SD₁₆	—	2	4	no	—
485	SD₁₆	—	10	4	no	—
486	SD₁₆	—	10	4	no	—
487	SD₁₆	—	10	4	no	—
488	M₁₆	—	5	4	no	—
489	M₁₆	C₃×C₂²⋊D₅	1	4	yes	complemented
490	C₂×C₈	—	5	2	no	—
491	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
492	C₄⋊C₄	—	10	4	no	—
493	C₄⋊C₄	—	10	4	no	—
494	C₄⋊C₄	—	10	2	no	—
495	C₂²⋊C₄	—	10	2	no	—
496	C₂²⋊C₄	—	10	2	no	—
497	C₄²	—	5	2	no	—
498	C₄²	—	5	1	no	—
499	C₄²	—	5	1	no	—
500	C₃×C₅	#3152	1	1	yes	characteristic, complemented, Hall
501	C₂²×C₃	—	2	2	no	—
502	C₂²×C₃	—	4	2	no	—
503	C₂²×C₃	—	4	1	no	—
504	C₂²×C₃	—	20	2	no	—
505	C₂²×C₃	—	20	1	no	—
506	C₂²×C₃	#4086	1	2	yes	—
507	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
508	C₃×C₄	—	4	1	no	—
509	C₃×C₄	—	4	2	no	—
510	C₃×C₄	—	5	4	no	—
511	C₃×C₄	—	10	2	no	—
512	C₃×C₄	—	20	1	no	—
513	C₃×C₄	—	20	2	no	—
514	C₃×C₄	#4086	1	2	yes	—
515	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
516	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
517	C₂×C₅	—	2	2	no	—
518	C₂×C₅	—	8	1	no	—
519	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
520	C₂×C₅	C₂×C₃×#137	1	2	yes	—
521	D₅	—	8	1	no	—
522	C₂³	—	2	1	no	—
523	C₂³	—	10	1	no	—
524	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
525	Q₈	—	2	2	no	—
526	Q₈	—	2	1	no	—
527	Q₈	—	2	2	no	—
528	Q₈	—	2	1	no	—
529	Q₈	—	4	2	no	—
530	Q₈	—	10	2	no	—
531	Q₈	—	10	1	no	—
532	Q₈	—	10	2	no	—
533	Q₈	—	10	1	no	—
534	Q₈	—	20	2	no	—
535	D₄	—	2	1	no	—
536	D₄	—	2	1	no	—
537	D₄	—	4	2	no	—
538	D₄	—	10	1	no	—
539	D₄	—	10	1	no	—
540	D₄	—	20	4	no	—
541	D₄	—	20	2	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	5	2	no	—
547	C₂×C₄	—	5	2	no	—
548	C₂×C₄	—	10	4	no	—
549	C₂×C₄	—	10	1	no	—
550	C₂×C₄	—	10	2	no	—
551	C₂×C₄	—	20	2	no	—
552	C₂×C₄	—	20	2	no	—
553	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
554	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
555	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
556	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
557	C₈	—	5	4	no	—
558	C₈	C₂×C₃×C₂²⋊D₅	1	4	yes	—
559	C₂×C₃	—	2	2	no	—
560	C₂×C₃	—	8	1	no	—
561	C₂×C₃	—	40	1	no	—
562	C₂×C₃	D₅×#137	1	2	yes	—
563	C₂×C₃	C₂×#4086	1	1	yes	characteristic
564	C₅	C₃×#3152	1	1	yes	characteristic, complemented, Sylow
565	C₂²	—	2	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	20	2	no	—
569	C₂²	—	20	1	no	—
570	C₂²	C₃×#4086	1	2	yes	—
571	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
572	C₄	—	4	1	no	—
573	C₄	—	4	2	no	—
574	C₄	—	5	4	no	—
575	C₄	—	10	2	no	—
576	C₄	—	20	1	no	—
577	C₄	—	20	2	no	—
578	C₄	C₃×#4086	1	2	yes	—
579	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
580	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
581	C₃	#10615703	1	1	yes	characteristic, direct product factor, Sylow
582	C₂	—	2	2	no	—
583	C₂	—	8	1	no	—
584	C₂	—	40	1	no	—
585	C₂	C₃×D₅×#137	1	2	yes	—
586	C₂	C₂×C₃×#4086	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#137	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₃×#66166	C₂
hypercenter	C₂×C₃×#137	D₅
hypocenter	C₅	C₃×#3152
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#137

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#137	C₂	semidirect
3. C₂×C₃×#4097	C₂	semidirect
4. C₂×C₃×#4090	C₂	semidirect
5. C₂×C₃×#4088	C₂	semidirect
6. C₂×C₃×#4055	C₂	semidirect
7. C₃×#65479	C₂	semidirect
8. C₃×#65470	C₂	semidirect
9. C₃×#65464	C₂	semidirect
10. C₃×#65456	C₂	semidirect
11. C₃×M₁₆×Dic₅	C₂	semidirect
12. #10615703	C₃	direct (N × H)
45. C₂×C₅×#137	C₂×C₃	semidirect
47. C₂×#4097	C₂×C₃	semidirect
48. C₂×#4090	C₂×C₃	semidirect
49. C₂×#4088	C₂×C₃	semidirect
50. C₂×#4055	C₂×C₃	semidirect
51. #65479	C₂×C₃	semidirect
52. #65470	C₂×C₃	semidirect
53. #65464	C₂×C₃	semidirect
54. #65456	C₂×C₃	semidirect
55. M₁₆×Dic₅	C₂×C₃	semidirect
83. C₃×C₅×M₁₆	D₄	semidirect
97. C₃×#681	D₄	semidirect
104. C₂×C₃×#137	D₅	semidirect
239. C₅×M₁₆	C₃×D₄	semidirect
253. #681	C₃×D₄	semidirect
260. C₂×#137	C₃×D₅	semidirect
283. C₃×Dic₅	#137	semidirect
318. C₃×M₁₆	C₂²⋊D₅	semidirect
454. Dic₅	C₃×#137	semidirect
489. M₁₆	C₃×C₂²⋊D₅	semidirect
500. C₃×C₅	#3152	semidirect
564. C₅	C₃×#3152	semidirect
581. C₃	#10615703	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×C₅×#137	2
C₃×#66166	2
C₂×C₃×#4097	2
C₂×C₃×#4090	2
C₂×C₃×#4088	2
C₂×C₃×#4055	2
C₃×#65479	2
C₃×#65470	2
C₃×#65464	2
C₃×#65456	2
C₃×M₁₆×Dic₅	2
#10615703	3
C₃×#3152	5

Subgroups — C3×#10615703 #14439202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615703 #14439202