Subgroups — C₃×#10615704 #14439292

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 604 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, complemented
3	C₂×C₃×#4095	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4093	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#4088	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#4054	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65480	C₂	1	2	yes	maximal, complemented
8	C₃×#65479	C₂	1	2	yes	maximal, complemented
9	C₃×#65465	C₂	1	2	yes	maximal, complemented
10	C₃×#65457	C₂	1	2	yes	maximal, complemented
11	C₃×M₁₆×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
12	#10615704	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×D₂₀	C₂²	1	1	yes	characteristic
17	C₃×C₅×#137	—	2	4	no	—
18	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	complemented
19	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
20	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
21	C₃×#4095	—	2	4	no	—
22	C₃×#4093	—	2	2	no	—
23	C₃×#4093	C₂²	1	2	yes	—
24	C₃×#4093	C₂²	1	2	yes	—
25	C₃×#4093	C₂²	1	1	yes	characteristic, complemented
26	C₃×#4090	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×#689	C₂²	1	2	yes	complemented
28	C₃×#4088	—	2	4	no	—
29	C₂×C₃×#688	C₂²	1	2	yes	—
30	C₂×C₃×#688	C₂²	1	2	yes	complemented
31	C₃×#4086	C₂²	1	1	yes	characteristic, complemented
32	C₃×#4085	—	2	2	no	—
33	C₃×#4082	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₃×#686	C₂²	1	2	yes	—
35	C₃×C₄×C₂²⋊D₅	—	2	2	no	—
36	C₂×C₃×#685	—	2	2	no	—
37	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
38	C₂×C₃×#681	C₂²	1	1	yes	characteristic
39	C₃×#4054	—	2	4	no	—
40	C₂×C₃×D₄₀	C₂²	1	2	yes	—
41	C₂×C₃×#677	C₂²	1	2	yes	—
42	C₃×#3947	C₂²	1	2	yes	complemented
43	C₃×C₈×Dic₅	C₂²	1	2	yes	complemented
44	C₃×#3153	—	5	1	no	maximal, Hall
45	C₂×C₅×#137	C₂×C₃	1	1	yes	characteristic, complemented
46	#66166	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×#4095	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂×#4093	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂×#4088	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂×#4054	C₂×C₃	1	1	yes	characteristic, complemented
51	#65480	C₂×C₃	1	2	yes	complemented
52	#65479	C₂×C₃	1	2	yes	complemented
53	#65465	C₂×C₃	1	2	yes	complemented
54	#65457	C₂×C₃	1	2	yes	complemented
55	M₁₆×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂³×C₃×D₅	—	2	1	no	—
57	C₃×C₅×#41	—	2	2	no	—
58	C₃×C₅×#41	—	2	2	no	—
59	C₂×C₃×C₅×Q₈	—	2	1	no	—
60	C₂×C₃×C₅×Q₈	—	2	2	no	—
61	C₂×C₃×C₅×Q₈	—	2	2	no	—
62	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
64	C₂×C₃×C₅×D₄	—	2	1	no	—
65	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	—	2	1	no	—
67	C₂²×C₃×C₄×C₅	—	2	1	no	—
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
70	C₂×C₃×C₂²⋊D₅	—	2	2	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	—	2	2	no	—
75	C₂×C₃×D₂₀	—	2	2	no	—
76	C₂×C₃×D₂₀	—	2	1	no	—
77	C₂×C₃×D₂₀	C₂³	1	2	yes	—
78	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₄×D₅	—	2	1	no	—
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×#688	—	2	4	no	—
88	C₃×#688	—	2	4	no	—
89	C₃×#686	—	2	4	no	—
90	C₃×#685	—	2	2	no	—
91	C₃×#685	—	2	4	no	—
92	C₃×#685	—	2	4	no	—
93	C₃×#683	—	2	2	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×D₄₀	—	2	4	no	—
100	C₃×#677	—	2	4	no	—
101	C₂×C₃×#137	—	5	1	no	—
102	C₂×C₃×#137	D₅	1	1	yes	characteristic, complemented
103	C₂×C₃×AGL(1,ℤ/8)	—	5	1	no	—
104	C₂×C₃×AGL(1,ℤ/8)	—	5	1	no	—
105	C₃×#532	—	5	1	no	—
106	C₂×C₃×#124	—	5	1	no	—
107	C₃×#497	—	5	2	no	—
108	C₃×#496	—	5	2	no	—
109	C₃×#495	—	5	2	no	—
110	C₃×#495	—	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×D₂₀	C₂²×C₃	1	1	yes	characteristic
116	C₅×#137	—	2	4	no	—
117	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	complemented
118	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
119	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
120	#4095	—	2	4	no	—
121	#4093	—	2	2	no	—
122	#4093	C₂²×C₃	1	2	yes	—
123	#4093	C₂²×C₃	1	2	yes	—
124	#4093	C₂²×C₃	1	1	yes	characteristic, complemented
125	#4090	C₂²×C₃	1	1	yes	characteristic, complemented
126	C₂×#689	C₂²×C₃	1	2	yes	complemented
127	#4088	—	2	4	no	—
128	C₂×#688	C₂²×C₃	1	2	yes	—
129	C₂×#688	C₂²×C₃	1	2	yes	complemented
130	#4086	C₂²×C₃	1	1	yes	characteristic, complemented
131	#4085	—	2	2	no	—
132	#4082	C₂²×C₃	1	1	yes	characteristic, complemented
133	C₂×#686	C₂²×C₃	1	2	yes	—
134	C₄×C₂²⋊D₅	—	2	2	no	—
135	C₂×#685	—	2	2	no	—
136	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
137	C₂×#681	C₂²×C₃	1	1	yes	characteristic
138	#4054	—	2	4	no	—
139	C₂×D₄₀	C₂²×C₃	1	2	yes	—
140	C₂×#677	C₂²×C₃	1	2	yes	—
141	#3947	C₂²×C₃	1	2	yes	complemented
142	C₈×Dic₅	C₂²×C₃	1	2	yes	complemented
143	#3153	—	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	2	no	—
147	C₂²×C₃×D₅	—	2	1	no	—
148	C₂²×C₃×D₅	—	4	4	no	—
149	C₂²×C₃×D₅	—	4	2	no	—
150	C₃×C₅×Q₈	—	2	1	no	—
151	C₃×C₅×Q₈	—	2	2	no	—
152	C₃×C₅×Q₈	—	2	2	no	—
153	C₃×C₅×Q₈	—	2	1	no	—
154	C₃×C₅×Q₈	—	4	2	no	—
155	C₃×C₅×D₄	—	2	1	no	—
156	C₃×C₅×D₄	—	2	1	no	—
157	C₃×C₅×D₄	—	4	2	no	—
158	C₂×C₃×C₄×C₅	—	2	1	no	—
159	C₂×C₃×C₄×C₅	—	2	2	no	—
160	C₂×C₃×C₄×C₅	—	4	2	no	—
161	C₂×C₃×C₄×C₅	—	4	2	no	—
162	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
163	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
164	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
165	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
166	C₃×C₂²⋊D₅	—	4	4	no	—
167	C₃×C₂²⋊D₅	—	4	2	no	—
168	C₂×C₃×Dic₅	—	2	1	no	—
169	C₂×C₃×Dic₅	—	4	2	no	—
170	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
171	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
172	C₃×D₂₀	—	2	2	no	—
173	C₃×D₂₀	—	2	1	no	—
174	C₃×D₂₀	—	2	2	no	—
175	C₃×D₂₀	—	2	1	no	—
176	C₃×D₂₀	—	4	2	no	—
177	C₃×C₄×D₅	—	4	2	no	—
178	C₃×Dic₁₀	—	2	1	no	—
179	C₃×Dic₁₀	—	2	1	no	—
180	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
181	C₃×#168	C₂×D₄	1	4	yes	—
182	C₂×C₃×#41	—	5	1	no	—
183	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
184	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
185	C₂²×C₃×D₄	—	5	1	no	—
186	C₃×#137	—	2	4	no	—
187	C₃×#137	—	10	4	no	—
188	C₃×AGL(1,ℤ/8)	—	10	4	no	—
189	C₃×AGL(1,ℤ/8)	—	10	4	no	—
190	C₂×C₃×Q₁₆	—	5	2	no	—
191	C₂×C₃×Q₁₆	C₂×D₅	1	2	yes	complemented
192	C₂×C₃×SD₁₆	—	5	2	no	—
193	C₂×C₃×SD₁₆	—	5	2	no	—
194	C₂×C₃×SD₁₆	—	5	2	no	—
195	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	complemented
196	C₂×C₃×D₈	—	5	2	no	—
197	C₂×C₃×D₈	—	5	2	no	—
198	C₂×C₃×M₁₆	—	5	1	no	—
199	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
200	C₃×C₄⋊Q₈	—	5	1	no	—
201	C₃×#127	—	5	1	no	—
202	C₃×#124	—	5	2	no	—
203	C₃×#124	—	5	2	no	—
204	C₃×#124	—	5	1	no	—
205	C₃×#124	—	5	1	no	—
206	C₃×#124	—	10	2	no	—
207	C₃×#121	—	10	2	no	—
208	C₃×C₄×D₄	—	10	2	no	—
209	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
210	C₂×C₃×C₄²	—	5	1	no	—
211	C₃×#97	—	5	2	no	—
212	C₃×C₄×C₈	—	5	2	no	—
213	C₂³×D₅	—	2	1	no	—
214	C₅×#41	—	2	2	no	—
215	C₅×#41	—	2	2	no	—
216	C₂×C₅×Q₈	—	2	1	no	—
217	C₂×C₅×Q₈	—	2	2	no	—
218	C₂×C₅×Q₈	—	2	2	no	—
219	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
220	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
221	C₂×C₅×D₄	—	2	1	no	—
222	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
223	C₂²×C₄×C₅	—	2	1	no	—
224	C₂²×C₄×C₅	—	2	1	no	—
225	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
226	C₂×C₂²⋊D₅	—	2	1	no	—
227	C₂×C₂²⋊D₅	—	2	2	no	—
228	C₂²×Dic₅	C₃×D₄	1	2	yes	—
229	#709	—	2	2	no	—
230	#709	—	2	2	no	—
231	C₂×D₂₀	—	2	2	no	—
232	C₂×D₂₀	—	2	2	no	—
233	C₂×D₂₀	—	2	1	no	—
234	C₂×D₂₀	C₂³×C₃	1	2	yes	—
235	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
236	C₂×C₄×D₅	—	2	1	no	—
237	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
238	C₅×Q₁₆	—	2	4	no	—
239	C₅×SD₁₆	—	2	4	no	—
240	C₅×M₁₆	C₃×D₄	1	4	yes	complemented
241	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
242	C₂²⋊Dic₅	—	2	2	no	—
243	#689	—	2	4	no	—
244	#688	—	2	4	no	—
245	#688	—	2	4	no	—
246	#686	—	2	4	no	—
247	#685	—	2	4	no	—
248	#685	—	2	4	no	—
249	#685	—	2	2	no	—
250	#683	—	2	2	no	—
251	C₄×Dic₅	C₃×D₄	1	2	yes	—
252	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
253	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
254	#681	C₃×D₄	1	4	yes	complemented
255	C₂×#168	C₂³×C₃	1	2	yes	—
256	D₄₀	—	2	4	no	—
257	#677	—	2	4	no	—
258	C₂×#137	—	5	1	no	—
259	C₂×#137	C₃×D₅	1	1	yes	characteristic, complemented
260	C₂×AGL(1,ℤ/8)	—	5	1	no	—
261	C₂×AGL(1,ℤ/8)	—	5	1	no	—
262	#532	—	5	1	no	—
263	C₂×#124	—	5	1	no	—
264	#497	—	5	2	no	—
265	#496	—	5	2	no	—
266	#495	—	5	2	no	—
267	#495	—	5	2	no	—
268	C₄×M₁₆	—	5	1	no	—
269	C₂²×C₃×C₅	—	2	2	no	—
270	C₂²×C₃×C₅	—	4	1	no	—
271	C₂²×C₃×C₅	—	4	2	no	—
272	C₂²×C₃×C₅	#127	1	2	yes	—
273	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₃×D₅	—	4	1	no	—
275	C₂×C₃×D₅	—	4	2	no	—
276	C₂×C₃×D₅	—	4	2	no	—
277	C₂×C₃×D₅	—	4	4	no	—
278	C₂×C₃×D₅	—	8	4	no	—
279	C₃×C₄×C₅	—	4	1	no	—
280	C₃×C₄×C₅	—	4	2	no	—
281	C₃×C₄×C₅	#127	1	2	yes	—
282	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
283	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
284	C₃×Dic₅	—	2	2	no	—
285	C₃×Dic₅	—	2	2	no	—
286	C₃×Dic₅	—	4	1	no	—
287	C₂⁴×C₃	—	10	1	no	—
288	C₃×#41	—	2	2	no	—
289	C₃×#41	—	2	2	no	—
290	C₃×#41	—	10	2	no	—
291	C₃×#41	—	10	2	no	—
292	C₂×C₃×Q₈	—	2	1	no	—
293	C₂×C₃×Q₈	—	2	2	no	—
294	C₂×C₃×Q₈	—	2	2	no	—
295	C₂×C₃×Q₈	—	5	1	no	—
296	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
297	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
298	C₂×C₃×D₄	—	2	1	no	—
299	C₂×C₃×D₄	—	5	2	no	—
300	C₂×C₃×D₄	—	5	1	no	—
301	C₂×C₃×D₄	—	10	2	no	—
302	C₂×C₃×D₄	—	10	1	no	—
303	C₂×C₃×D₄	—	10	2	no	—
304	C₂×C₃×D₄	—	10	1	no	—
305	C₂×C₃×D₄	—	10	2	no	—
306	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
307	C₂²×C₃×C₄	—	2	1	no	—
308	C₂²×C₃×C₄	—	2	1	no	—
309	C₂²×C₃×C₄	—	5	2	no	—
310	C₂²×C₃×C₄	—	10	1	no	—
311	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
312	C₃×Q₁₆	—	2	4	no	—
313	C₃×Q₁₆	—	10	4	no	—
314	C₃×SD₁₆	—	2	4	no	—
315	C₃×SD₁₆	—	10	4	no	—
316	C₃×SD₁₆	—	10	4	no	—
317	C₃×SD₁₆	—	10	4	no	—
318	C₃×D₈	—	10	4	no	—
319	C₃×D₈	—	10	4	no	—
320	C₃×M₁₆	—	5	4	no	—
321	C₃×M₁₆	C₂²⋊D₅	1	4	yes	complemented
322	C₂×C₃×C₈	—	5	2	no	—
323	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
324	C₃×C₄⋊C₄	—	10	2	no	—
325	C₃×C₂²⋊C₄	—	10	4	no	—
326	C₃×C₂²⋊C₄	—	10	4	no	—
327	C₃×C₂²⋊C₄	—	10	2	no	—
328	C₃×C₂²⋊C₄	—	10	2	no	—
329	C₃×C₄²	—	5	2	no	—
330	C₃×C₄²	—	5	1	no	—
331	C₃×C₄²	—	5	1	no	—
332	C₂³×C₅	—	2	1	no	—
333	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
334	C₂²×D₅	—	2	2	no	—
335	C₂²×D₅	—	2	1	no	—
336	C₂²×D₅	—	4	4	no	—
337	C₂²×D₅	—	4	2	no	—
338	C₅×Q₈	—	2	1	no	—
339	C₅×Q₈	—	2	2	no	—
340	C₅×Q₈	—	2	2	no	—
341	C₅×Q₈	—	2	1	no	—
342	C₅×Q₈	—	4	2	no	—
343	C₅×D₄	—	2	1	no	—
344	C₅×D₄	—	2	1	no	—
345	C₅×D₄	—	4	2	no	—
346	C₂×C₄×C₅	—	2	1	no	—
347	C₂×C₄×C₅	—	2	2	no	—
348	C₂×C₄×C₅	—	4	2	no	—
349	C₂×C₄×C₅	—	4	2	no	—
350	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
351	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
352	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
353	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
354	C₂²⋊D₅	—	4	4	no	—
355	C₂²⋊D₅	—	4	2	no	—
356	C₂×Dic₅	—	2	1	no	—
357	C₂×Dic₅	—	4	2	no	—
358	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
359	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
360	D₂₀	—	2	2	no	—
361	D₂₀	—	2	1	no	—
362	D₂₀	—	2	2	no	—
363	D₂₀	—	2	1	no	—
364	D₂₀	—	4	2	no	—
365	C₄×D₅	—	4	2	no	—
366	Dic₁₀	—	2	1	no	—
367	Dic₁₀	—	2	1	no	—
368	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
369	#168	C₂×C₃×D₄	1	4	yes	—
370	C₂×#41	—	5	1	no	—
371	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
372	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
373	C₂²×D₄	—	5	1	no	—
374	#137	—	2	4	no	—
375	#137	—	10	4	no	—
376	AGL(1,ℤ/8)	—	10	4	no	—
377	AGL(1,ℤ/8)	—	10	4	no	—
378	C₂×Q₁₆	—	5	2	no	—
379	C₂×Q₁₆	C₂×C₃×D₅	1	2	yes	complemented
380	C₂×SD₁₆	—	5	2	no	—
381	C₂×SD₁₆	—	5	2	no	—
382	C₂×SD₁₆	—	5	2	no	—
383	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	complemented
384	C₂×D₈	—	5	2	no	—
385	C₂×D₈	—	5	2	no	—
386	C₂×M₁₆	—	5	1	no	—
387	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
388	C₄⋊Q₈	—	5	1	no	—
389	#127	—	5	1	no	—
390	#124	—	5	2	no	—
391	#124	—	5	2	no	—
392	#124	—	5	1	no	—
393	#124	—	5	1	no	—
394	#124	—	10	2	no	—
395	#121	—	10	2	no	—
396	C₄×D₄	—	10	2	no	—
397	C₂×C₂²⋊C₄	—	10	2	no	—
398	C₂×C₄²	—	5	1	no	—
399	#97	—	5	2	no	—
400	C₄×C₈	—	5	2	no	—
401	C₂×C₃×C₅	—	2	2	no	—
402	C₂×C₃×C₅	—	8	1	no	—
403	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
404	C₂×C₃×C₅	#575	1	2	yes	—
405	C₃×D₅	—	8	1	no	—
406	C₃×D₅	—	8	2	no	—
407	C₂³×C₃	—	2	1	no	—
408	C₂³×C₃	—	10	2	no	—
409	C₂³×C₃	—	10	1	no	—
410	C₂³×C₃	—	20	4	no	—
411	C₂³×C₃	—	20	2	no	—
412	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
413	C₃×Q₈	—	2	1	no	—
414	C₃×Q₈	—	2	2	no	—
415	C₃×Q₈	—	2	2	no	—
416	C₃×Q₈	—	2	1	no	—
417	C₃×Q₈	—	4	2	no	—
418	C₃×Q₈	—	10	1	no	—
419	C₃×Q₈	—	10	1	no	—
420	C₃×D₄	—	2	1	no	—
421	C₃×D₄	—	2	1	no	—
422	C₃×D₄	—	4	2	no	—
423	C₃×D₄	—	10	2	no	—
424	C₃×D₄	—	10	1	no	—
425	C₃×D₄	—	10	1	no	—
426	C₃×D₄	—	10	2	no	—
427	C₃×D₄	—	20	4	no	—
428	C₃×D₄	—	20	2	no	—
429	C₃×D₄	—	20	2	no	—
430	C₂×C₃×C₄	—	2	2	no	—
431	C₂×C₃×C₄	—	2	1	no	—
432	C₂×C₃×C₄	—	4	2	no	—
433	C₂×C₃×C₄	—	4	2	no	—
434	C₂×C₃×C₄	—	5	2	no	—
435	C₂×C₃×C₄	—	5	2	no	—
436	C₂×C₃×C₄	—	10	1	no	—
437	C₂×C₃×C₄	—	20	2	no	—
438	C₂×C₃×C₄	—	20	2	no	—
439	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
440	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
441	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
442	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
443	C₃×C₈	—	5	4	no	—
444	C₃×C₈	C₂×C₂²⋊D₅	1	4	yes	—
445	C₂²×C₅	—	2	2	no	—
446	C₂²×C₅	—	4	2	no	—
447	C₂²×C₅	—	4	1	no	—
448	C₂²×C₅	C₃×#127	1	2	yes	—
449	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
450	C₂×D₅	—	4	2	no	—
451	C₂×D₅	—	4	4	no	—
452	C₂×D₅	—	4	1	no	—
453	C₂×D₅	—	4	2	no	—
454	C₂×D₅	—	8	4	no	—
455	C₄×C₅	—	4	1	no	—
456	C₄×C₅	—	4	2	no	—
457	C₄×C₅	C₃×#127	1	2	yes	—
458	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
459	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
460	Dic₅	—	2	2	no	—
461	Dic₅	—	2	2	no	—
462	Dic₅	—	4	1	no	—
463	C₂⁴	—	10	1	no	—
464	#41	—	2	2	no	—
465	#41	—	2	2	no	—
466	#41	—	10	2	no	—
467	#41	—	10	2	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	2	no	—
470	C₂×Q₈	—	2	2	no	—
471	C₂×Q₈	—	5	1	no	—
472	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
473	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	5	2	no	—
476	C₂×D₄	—	5	1	no	—
477	C₂×D₄	—	10	2	no	—
478	C₂×D₄	—	10	1	no	—
479	C₂×D₄	—	10	2	no	—
480	C₂×D₄	—	10	1	no	—
481	C₂×D₄	—	10	2	no	—
482	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	5	2	no	—
486	C₂²×C₄	—	10	1	no	—
487	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
488	Q₁₆	—	2	4	no	—
489	Q₁₆	—	10	4	no	—
490	SD₁₆	—	2	4	no	—
491	SD₁₆	—	10	4	no	—
492	SD₁₆	—	10	4	no	—
493	SD₁₆	—	10	4	no	—
494	D₈	—	10	4	no	—
495	D₈	—	10	4	no	—
496	M₁₆	—	5	4	no	—
497	M₁₆	C₃×C₂²⋊D₅	1	4	yes	complemented
498	C₂×C₈	—	5	2	no	—
499	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
500	C₄⋊C₄	—	10	2	no	—
501	C₂²⋊C₄	—	10	4	no	—
502	C₂²⋊C₄	—	10	4	no	—
503	C₂²⋊C₄	—	10	2	no	—
504	C₂²⋊C₄	—	10	2	no	—
505	C₄²	—	5	2	no	—
506	C₄²	—	5	1	no	—
507	C₄²	—	5	1	no	—
508	C₃×C₅	#3153	1	1	yes	characteristic, complemented, Hall
509	C₂²×C₃	—	2	2	no	—
510	C₂²×C₃	—	4	2	no	—
511	C₂²×C₃	—	4	1	no	—
512	C₂²×C₃	—	20	2	no	—
513	C₂²×C₃	—	20	4	no	—
514	C₂²×C₃	—	20	1	no	—
515	C₂²×C₃	—	20	2	no	—
516	C₂²×C₃	—	40	4	no	—
517	C₂²×C₃	#4086	1	2	yes	—
518	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
519	C₃×C₄	—	4	1	no	—
520	C₃×C₄	—	4	2	no	—
521	C₃×C₄	—	10	2	no	—
522	C₃×C₄	—	10	2	no	—
523	C₃×C₄	—	20	1	no	—
524	C₃×C₄	#4086	1	2	yes	—
525	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
526	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
527	C₂×C₅	—	2	2	no	—
528	C₂×C₅	—	8	1	no	—
529	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
530	C₂×C₅	C₃×#575	1	2	yes	—
531	D₅	—	8	2	no	—
532	D₅	—	8	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	10	2	no	—
535	C₂³	—	10	1	no	—
536	C₂³	—	20	4	no	—
537	C₂³	—	20	2	no	—
538	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
539	Q₈	—	2	1	no	—
540	Q₈	—	2	2	no	—
541	Q₈	—	2	2	no	—
542	Q₈	—	2	1	no	—
543	Q₈	—	4	2	no	—
544	Q₈	—	10	1	no	—
545	Q₈	—	10	1	no	—
546	D₄	—	2	1	no	—
547	D₄	—	2	1	no	—
548	D₄	—	4	2	no	—
549	D₄	—	10	2	no	—
550	D₄	—	10	1	no	—
551	D₄	—	10	1	no	—
552	D₄	—	10	2	no	—
553	D₄	—	20	4	no	—
554	D₄	—	20	2	no	—
555	D₄	—	20	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	5	2	no	—
561	C₂×C₄	—	5	2	no	—
562	C₂×C₄	—	10	1	no	—
563	C₂×C₄	—	20	2	no	—
564	C₂×C₄	—	20	2	no	—
565	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
566	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
567	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
568	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
569	C₈	—	5	4	no	—
570	C₈	C₂×C₃×C₂²⋊D₅	1	4	yes	—
571	C₂×C₃	—	2	2	no	—
572	C₂×C₃	—	8	1	no	—
573	C₂×C₃	—	40	2	no	—
574	C₂×C₃	—	40	1	no	—
575	C₂×C₃	#66111	1	2	yes	—
576	C₂×C₃	C₂×#4086	1	1	yes	characteristic
577	C₅	C₃×#3153	1	1	yes	characteristic, complemented, Sylow
578	C₂²	—	2	2	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	20	2	no	—
582	C₂²	—	20	4	no	—
583	C₂²	—	20	1	no	—
584	C₂²	—	20	2	no	—
585	C₂²	—	40	4	no	—
586	C₂²	C₃×#4086	1	2	yes	—
587	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
588	C₄	—	4	1	no	—
589	C₄	—	4	2	no	—
590	C₄	—	10	2	no	—
591	C₄	—	10	2	no	—
592	C₄	—	20	1	no	—
593	C₄	C₃×#4086	1	2	yes	—
594	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
595	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
596	C₃	#10615704	1	1	yes	characteristic, direct product factor, Sylow
597	C₂	—	2	2	no	—
598	C₂	—	8	1	no	—
599	C₂	—	40	2	no	—
600	C₂	—	40	1	no	—
601	C₂	C₃×#66111	1	2	yes	—
602	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
hypercenter	C₂×C₃×#137	D₅
hypocenter	C₅	C₃×#3153
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
2. C₃×#66166	C₂	semidirect
3. C₂×C₃×#4095	C₂	semidirect
4. C₂×C₃×#4093	C₂	semidirect
5. C₂×C₃×#4088	C₂	semidirect
6. C₂×C₃×#4054	C₂	semidirect
7. C₃×#65480	C₂	semidirect
8. C₃×#65479	C₂	semidirect
9. C₃×#65465	C₂	semidirect
10. C₃×#65457	C₂	semidirect
11. C₃×M₁₆×Dic₅	C₂	semidirect
12. #10615704	C₃	direct (N × H)
18. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
19. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
25. C₃×#4093	C₂²	semidirect
26. C₃×#4090	C₂²	semidirect
27. C₂×C₃×#689	C₂²	semidirect
30. C₂×C₃×#688	C₂²	semidirect
31. C₃×#4086	C₂²	semidirect
33. C₃×#4082	C₂²	semidirect
42. C₃×#3947	C₂²	semidirect
43. C₃×C₈×Dic₅	C₂²	semidirect
45. C₂×C₅×#137	C₂×C₃	semidirect
46. #66166	C₂×C₃	semidirect
47. C₂×#4095	C₂×C₃	semidirect
48. C₂×#4093	C₂×C₃	semidirect
49. C₂×#4088	C₂×C₃	semidirect
50. C₂×#4054	C₂×C₃	semidirect
51. #65480	C₂×C₃	semidirect
52. #65479	C₂×C₃	semidirect
53. #65465	C₂×C₃	semidirect
54. #65457	C₂×C₃	semidirect
55. M₁₆×Dic₅	C₂×C₃	semidirect
83. C₃×C₅×M₁₆	D₄	semidirect
97. C₃×#681	D₄	semidirect
102. C₂×C₃×#137	D₅	semidirect
117. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
118. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
124. #4093	C₂²×C₃	semidirect
125. #4090	C₂²×C₃	semidirect
126. C₂×#689	C₂²×C₃	semidirect
129. C₂×#688	C₂²×C₃	semidirect
130. #4086	C₂²×C₃	semidirect
132. #4082	C₂²×C₃	semidirect
141. #3947	C₂²×C₃	semidirect
142. C₈×Dic₅	C₂²×C₃	semidirect
191. C₂×C₃×Q₁₆	C₂×D₅	semidirect
195. C₂×C₃×SD₁₆	C₂×D₅	semidirect
240. C₅×M₁₆	C₃×D₄	semidirect
254. #681	C₃×D₄	semidirect
259. C₂×#137	C₃×D₅	semidirect
321. C₃×M₁₆	C₂²⋊D₅	semidirect
379. C₂×Q₁₆	C₂×C₃×D₅	semidirect
383. C₂×SD₁₆	C₂×C₃×D₅	semidirect
497. M₁₆	C₃×C₂²⋊D₅	semidirect
508. C₃×C₅	#3153	semidirect
577. C₅	C₃×#3153	semidirect
596. C₃	#10615704	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×#4095	2
C₂×C₃×#4093	2
C₂×C₃×#4088	2
C₂×C₃×#4054	2
C₃×#65480	2
C₃×#65479	2
C₃×#65465	2
C₃×#65457	2
C₃×M₁₆×Dic₅	2
#10615704	3
C₃×#3153	5

Subgroups — C3×#10615704 #14439292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615704 #14439292