Subgroups — C₃×#10615696 #14417178

Order 1920.

940 conjugacy classes of subgroups.

The subgroup lattice has 524 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
2	C₃×#66161	C₂	1	1	yes	maximal, characteristic
3	C₃×#66146	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65522	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃×#3967	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65473	C₂	1	2	yes	maximal, complemented
7	C₃×Q₁₆×Dic₅	C₂	1	2	yes	maximal, complemented
8	C₃×#65453	C₂	1	2	yes	maximal, complemented
9	C₃×SD₁₆×Dic₅	C₂	1	2	yes	maximal, complemented
10	C₃×#65411	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65410	C₂	1	1	yes	maximal, characteristic, complemented
12	#10615696	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	C₃×C₅×#137	C₄	1	8	yes	complemented
16	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
18	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
19	C₃×Q₈×Dic₅	—	2	1	no	—
20	C₃×Q₈×Dic₅	—	2	1	no	—
21	C₃×Q₈×Dic₅	C₂²	1	2	yes	—
22	C₃×Q₈×Dic₅	C₂²	1	2	yes	—
23	C₃×Q₈×Dic₅	C₂²	1	2	yes	—
24	C₃×D₄×Dic₅	—	2	2	no	—
25	C₃×D₄×Dic₅	C₂²	1	2	yes	—
26	C₃×#4072	—	2	2	no	—
27	C₃×#4072	—	2	1	no	—
28	C₃×#4072	C₂²	1	1	yes	characteristic
29	C₃×#4072	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄⋊Dic₅	—	2	1	no	—
31	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
32	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
33	C₃×#3967	C₂²	1	2	yes	—
34	C₃×#3967	C₂²	1	2	yes	—
35	C₃×#3967	C₂²	1	1	yes	characteristic
36	C₃×#3967	C₂²	1	1	yes	characteristic
37	C₃×#3964	C₂²	1	1	yes	characteristic
38	C₃×#3964	C₂²	1	1	yes	characteristic
39	C₃×#3950	C₂²	1	2	yes	—
40	C₃×#3949	C₂²	1	2	yes	—
41	C₃×#3947	C₂²	1	2	yes	—
42	C₃×C₈×Dic₅	C₂²	1	2	yes	—
43	C₃×#2947	—	5	1	no	maximal, Hall
44	C₂×C₅×#137	C₂×C₃	1	1	yes	characteristic
45	#66161	C₂×C₃	1	1	yes	characteristic
46	#66146	C₂×C₃	1	1	yes	characteristic, complemented
47	#65522	C₂×C₃	1	1	yes	characteristic
48	C₂×#3967	C₂×C₃	1	1	yes	characteristic, complemented
49	#65473	C₂×C₃	1	2	yes	complemented
50	Q₁₆×Dic₅	C₂×C₃	1	2	yes	complemented
51	#65453	C₂×C₃	1	2	yes	complemented
52	SD₁₆×Dic₅	C₂×C₃	1	2	yes	complemented
53	#65411	C₂×C₃	1	1	yes	characteristic, complemented
54	#65410	C₂×C₃	1	1	yes	characteristic, complemented
55	C₃×C₅×#41	—	2	2	no	—
56	C₃×C₅×#41	C₂×C₄	1	4	yes	—
57	C₂×C₃×C₅×Q₈	—	2	1	no	—
58	C₂×C₃×C₅×Q₈	—	2	2	no	—
59	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
60	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
61	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×D₄	—	2	1	no	—
63	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₅	—	2	1	no	—
65	C₂²×C₃×C₄×C₅	—	2	1	no	—
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂²×C₃×Dic₅	—	2	1	no	—
68	C₂²×C₃×Dic₅	—	2	2	no	—
69	C₃×C₅×Q₁₆	C₂×C₄	1	8	yes	complemented
70	C₃×C₅×SD₁₆	C₂×C₄	1	8	yes	complemented
71	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
72	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
73	C₃×C₂²⋊Dic₅	—	2	1	no	—
74	C₃×C₂²⋊Dic₅	—	2	2	no	—
75	C₃×C₂²⋊Dic₅	D₄	1	2	yes	—
76	C₃×C₄⋊Dic₅	—	2	1	no	—
77	C₃×C₄⋊Dic₅	—	2	2	no	—
78	C₃×C₄⋊Dic₅	—	2	2	no	—
79	C₃×C₄⋊Dic₅	—	2	2	no	—
80	C₃×C₄⋊Dic₅	D₄	1	1	yes	characteristic
81	C₃×C₄⋊Dic₅	D₄	1	1	yes	characteristic
82	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
83	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
84	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
85	C₃×C₄×Dic₅	—	2	1	no	—
86	C₃×C₄×Dic₅	—	2	2	no	—
87	C₃×C₄×Dic₅	—	2	2	no	—
88	C₃×C₄×Dic₅	—	2	2	no	—
89	C₃×C₄×Dic₅	C₂³	1	2	yes	—
90	C₂×C₃×#168	—	2	2	no	—
91	C₂×C₃×#168	C₂³	1	1	yes	characteristic
92	C₂×C₃×#168	C₂³	1	1	yes	characteristic
93	C₂×C₃×#137	D₅	1	1	yes	characteristic
94	C₃×#520	—	5	1	no	—
95	C₃×#519	—	5	1	no	—
96	C₃×#441	—	5	2	no	—
97	C₃×#440	—	5	2	no	—
98	C₃×C₄×Q₁₆	—	5	2	no	—
99	C₃×C₄×SD₁₆	—	5	2	no	—
100	C₃×#428	—	5	1	no	—
101	C₃×#416	—	5	1	no	—
102	C₂×C₃×#103	—	5	1	no	—
103	C₃×#405	—	5	1	no	—
104	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
105	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
106	C₅×#137	C₃×C₄	1	8	yes	complemented
107	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
108	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
109	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
110	Q₈×Dic₅	—	2	1	no	—
111	Q₈×Dic₅	—	2	1	no	—
112	Q₈×Dic₅	C₂²×C₃	1	2	yes	—
113	Q₈×Dic₅	C₂²×C₃	1	2	yes	—
114	Q₈×Dic₅	C₂²×C₃	1	2	yes	—
115	D₄×Dic₅	—	2	2	no	—
116	D₄×Dic₅	C₂²×C₃	1	2	yes	—
117	#4072	—	2	2	no	—
118	#4072	—	2	1	no	—
119	#4072	C₂²×C₃	1	1	yes	characteristic
120	#4072	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₄⋊Dic₅	—	2	1	no	—
122	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
123	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
124	#3967	C₂²×C₃	1	2	yes	—
125	#3967	C₂²×C₃	1	2	yes	—
126	#3967	C₂²×C₃	1	1	yes	characteristic
127	#3967	C₂²×C₃	1	1	yes	characteristic
128	#3964	C₂²×C₃	1	1	yes	characteristic
129	#3964	C₂²×C₃	1	1	yes	characteristic
130	#3950	C₂²×C₃	1	2	yes	—
131	#3949	C₂²×C₃	1	2	yes	—
132	#3947	C₂²×C₃	1	2	yes	—
133	C₈×Dic₅	C₂²×C₃	1	2	yes	—
134	#2947	—	5	1	no	Sylow
135	C₂³×C₃×C₅	—	2	1	no	—
136	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
137	C₃×C₅×Q₈	—	2	4	no	—
138	C₃×C₅×Q₈	—	2	2	no	—
139	C₃×C₅×Q₈	—	2	1	no	—
140	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
141	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
142	C₃×C₅×D₄	—	2	4	no	—
143	C₃×C₅×D₄	—	2	1	no	—
144	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
145	C₂×C₃×C₄×C₅	—	2	4	no	—
146	C₂×C₃×C₄×C₅	—	2	1	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	2	4	no	—
149	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
150	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	#41	1	2	yes	—
152	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
153	C₂×C₃×Dic₅	—	2	1	no	—
154	C₂×C₃×Dic₅	—	2	1	no	—
155	C₂×C₃×Dic₅	—	2	2	no	—
156	C₂×C₃×Dic₅	—	8	2	no	—
157	C₂×C₃×Dic₅	—	8	1	no	—
158	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
159	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
160	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
161	C₃×#168	—	2	1	no	—
162	C₃×#168	—	2	1	no	—
163	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
164	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
165	C₃×#137	Dic₅	1	8	yes	complemented
166	C₂×C₃×Q₁₆	C₂×D₅	1	2	yes	—
167	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	—
168	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
169	C₂²×C₃×C₈	—	5	1	no	—
170	C₃×C₄×Q₈	—	5	2	no	—
171	C₃×C₄×Q₈	—	5	2	no	—
172	C₃×C₄×Q₈	—	5	2	no	—
173	C₃×C₄×Q₈	—	10	1	no	—
174	C₃×C₄×Q₈	—	10	1	no	—
175	C₃×C₄×D₄	—	5	2	no	—
176	C₃×C₄×D₄	—	10	2	no	—
177	C₃×#117	—	5	1	no	—
178	C₃×#117	—	5	1	no	—
179	C₃×#117	—	10	2	no	—
180	C₃×#117	—	10	1	no	—
181	C₂×C₃×C₄⋊C₄	—	5	1	no	—
182	C₂×C₃×C₄⋊C₄	—	10	1	no	—
183	C₃×#107	—	5	2	no	—
184	C₃×#106	—	5	2	no	—
185	C₃×#103	—	5	2	no	—
186	C₃×#103	—	5	2	no	—
187	C₃×#103	—	5	1	no	—
188	C₃×#103	—	5	1	no	—
189	C₃×#102	—	5	1	no	—
190	C₃×#102	—	5	1	no	—
191	C₃×#97	—	5	2	no	—
192	C₃×C₄×C₈	—	5	2	no	—
193	C₅×#41	—	2	2	no	—
194	C₅×#41	C₂×C₃×C₄	1	4	yes	—
195	C₂×C₅×Q₈	—	2	1	no	—
196	C₂×C₅×Q₈	—	2	2	no	—
197	C₂×C₅×Q₈	C₂×C₃×C₄	1	4	yes	complemented
198	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
199	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
200	C₂×C₅×D₄	—	2	1	no	—
201	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
202	C₂²×C₄×C₅	—	2	1	no	—
203	C₂²×C₄×C₅	—	2	1	no	—
204	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
205	C₂²×Dic₅	—	2	1	no	—
206	C₂²×Dic₅	—	2	2	no	—
207	C₅×Q₁₆	C₂×C₃×C₄	1	8	yes	complemented
208	C₅×SD₁₆	C₂×C₃×C₄	1	8	yes	complemented
209	C₅×M₁₆	C₂×C₃×C₄	1	4	yes	complemented
210	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
211	C₂²⋊Dic₅	—	2	1	no	—
212	C₂²⋊Dic₅	—	2	2	no	—
213	C₂²⋊Dic₅	C₃×D₄	1	2	yes	—
214	C₄⋊Dic₅	—	2	1	no	—
215	C₄⋊Dic₅	—	2	2	no	—
216	C₄⋊Dic₅	—	2	2	no	—
217	C₄⋊Dic₅	—	2	2	no	—
218	C₄⋊Dic₅	C₃×D₄	1	1	yes	characteristic
219	C₄⋊Dic₅	C₃×D₄	1	1	yes	characteristic
220	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
221	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
222	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
223	C₄×Dic₅	—	2	1	no	—
224	C₄×Dic₅	—	2	2	no	—
225	C₄×Dic₅	—	2	2	no	—
226	C₄×Dic₅	—	2	2	no	—
227	C₄×Dic₅	C₂³×C₃	1	2	yes	—
228	C₂×#168	—	2	2	no	—
229	C₂×#168	C₂³×C₃	1	1	yes	characteristic
230	C₂×#168	C₂³×C₃	1	1	yes	characteristic
231	C₂×#137	C₃×D₅	1	1	yes	characteristic
232	#520	—	5	1	no	—
233	#519	—	5	1	no	—
234	#441	—	5	2	no	—
235	#440	—	5	2	no	—
236	C₄×Q₁₆	—	5	2	no	—
237	C₄×SD₁₆	—	5	2	no	—
238	#428	—	5	1	no	—
239	#416	—	5	1	no	—
240	C₂×#103	—	5	1	no	—
241	#405	—	5	1	no	—
242	C₂²×C₃×C₅	—	2	1	no	—
243	C₂²×C₃×C₅	—	2	1	no	—
244	C₂²×C₃×C₅	—	2	2	no	—
245	C₂²×C₃×C₅	—	4	1	no	—
246	C₂²×C₃×C₅	—	4	1	no	—
247	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
248	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
249	C₃×C₄×C₅	—	2	2	no	—
250	C₃×C₄×C₅	—	2	4	no	—
251	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
252	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
253	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
254	C₃×Dic₅	—	2	2	no	—
255	C₃×Dic₅	—	2	2	no	—
256	C₃×Dic₅	—	4	1	no	—
257	C₃×Dic₅	—	4	2	no	—
258	C₃×Dic₅	—	4	1	no	—
259	C₃×#41	—	2	2	no	—
260	C₃×#41	C₂×Dic₅	1	4	yes	—
261	C₂×C₃×Q₈	—	2	1	no	—
262	C₂×C₃×Q₈	—	2	2	no	—
263	C₂×C₃×Q₈	C₂×Dic₅	1	4	yes	complemented
264	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
265	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
266	C₂×C₃×D₄	—	2	1	no	—
267	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
268	C₂²×C₃×C₄	—	2	1	no	—
269	C₂²×C₃×C₄	—	2	1	no	—
270	C₂²×C₃×C₄	—	10	2	no	—
271	C₂²×C₃×C₄	—	10	1	no	—
272	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
273	C₃×Q₁₆	C₂×Dic₅	1	8	yes	complemented
274	C₃×SD₁₆	C₂×Dic₅	1	8	yes	complemented
275	C₃×M₁₆	C₂×Dic₅	1	4	yes	complemented
276	C₂×C₃×C₈	—	5	1	no	—
277	C₂×C₃×C₈	—	5	1	no	—
278	C₂×C₃×C₈	—	10	2	no	—
279	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
280	C₃×C₄⋊C₄	—	5	1	no	—
281	C₃×C₄⋊C₄	—	5	1	no	—
282	C₃×C₄⋊C₄	—	5	1	no	—
283	C₃×C₄⋊C₄	—	5	1	no	—
284	C₃×C₄⋊C₄	—	5	2	no	—
285	C₃×C₄⋊C₄	—	10	2	no	—
286	C₃×C₄⋊C₄	—	10	2	no	—
287	C₃×C₄⋊C₄	—	10	2	no	—
288	C₃×C₄⋊C₄	—	10	1	no	—
289	C₃×C₂²⋊C₄	—	5	2	no	—
290	C₃×C₂²⋊C₄	—	10	2	no	—
291	C₃×C₂²⋊C₄	—	10	1	no	—
292	C₃×C₄²	—	5	2	no	—
293	C₃×C₄²	—	10	2	no	—
294	C₃×C₄²	—	10	2	no	—
295	C₃×C₄²	—	10	2	no	—
296	C₃×C₄²	—	10	1	no	—
297	C₂³×C₅	—	2	1	no	—
298	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
299	C₅×Q₈	—	2	4	no	—
300	C₅×Q₈	—	2	2	no	—
301	C₅×Q₈	—	2	1	no	—
302	C₅×Q₈	C₂²×C₃×C₄	1	4	yes	—
303	C₅×Q₈	C₂²×C₃×C₄	1	2	yes	—
304	C₅×D₄	—	2	4	no	—
305	C₅×D₄	—	2	1	no	—
306	C₅×D₄	C₂²×C₃×C₄	1	2	yes	—
307	C₂×C₄×C₅	—	2	4	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	2	2	no	—
310	C₂×C₄×C₅	—	2	4	no	—
311	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
312	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
313	C₂×C₄×C₅	C₃×#41	1	2	yes	—
314	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
315	C₂×Dic₅	—	2	1	no	—
316	C₂×Dic₅	—	2	1	no	—
317	C₂×Dic₅	—	2	2	no	—
318	C₂×Dic₅	—	8	2	no	—
319	C₂×Dic₅	—	8	1	no	—
320	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
321	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
322	C₅×C₈	C₂²×C₃×C₄	1	4	yes	—
323	#168	—	2	1	no	—
324	#168	—	2	1	no	—
325	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
326	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
327	#137	C₃×Dic₅	1	8	yes	complemented
328	C₂×Q₁₆	C₂×C₃×D₅	1	2	yes	—
329	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	—
330	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
331	C₂²×C₈	—	5	1	no	—
332	C₄×Q₈	—	5	2	no	—
333	C₄×Q₈	—	5	2	no	—
334	C₄×Q₈	—	5	2	no	—
335	C₄×Q₈	—	10	1	no	—
336	C₄×Q₈	—	10	1	no	—
337	C₄×D₄	—	5	2	no	—
338	C₄×D₄	—	10	2	no	—
339	#117	—	5	1	no	—
340	#117	—	5	1	no	—
341	#117	—	10	2	no	—
342	#117	—	10	1	no	—
343	C₂×C₄⋊C₄	—	5	1	no	—
344	C₂×C₄⋊C₄	—	10	1	no	—
345	#107	—	5	2	no	—
346	#106	—	5	2	no	—
347	#103	—	5	2	no	—
348	#103	—	5	2	no	—
349	#103	—	5	1	no	—
350	#103	—	5	1	no	—
351	#102	—	5	1	no	—
352	#102	—	5	1	no	—
353	#97	—	5	2	no	—
354	C₄×C₈	—	5	2	no	—
355	C₂×C₃×C₅	—	2	2	no	—
356	C₂×C₃×C₅	—	4	2	no	—
357	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
358	C₂×C₃×C₅	#577	1	1	yes	characteristic
359	C₂×C₃×C₅	#578	1	1	yes	characteristic
360	C₂³×C₃	—	2	1	no	—
361	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
362	C₃×Q₈	—	2	2	no	—
363	C₃×Q₈	—	2	1	no	—
364	C₃×Q₈	—	2	4	no	—
365	C₃×Q₈	C₂²×Dic₅	1	4	yes	—
366	C₃×Q₈	C₂²×Dic₅	1	2	yes	—
367	C₃×D₄	—	2	4	no	—
368	C₃×D₄	—	2	1	no	—
369	C₃×D₄	C₂²×Dic₅	1	2	yes	—
370	C₂×C₃×C₄	—	2	1	no	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	2	4	no	—
373	C₂×C₃×C₄	—	2	4	no	—
374	C₂×C₃×C₄	—	5	2	no	—
375	C₂×C₃×C₄	—	5	2	no	—
376	C₂×C₃×C₄	—	10	1	no	—
377	C₂×C₃×C₄	—	10	1	no	—
378	C₂×C₃×C₄	—	10	2	no	—
379	C₂×C₃×C₄	—	40	2	no	—
380	C₂×C₃×C₄	—	40	1	no	—
381	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
382	C₂×C₃×C₄	#711	1	2	yes	—
383	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
384	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
385	C₃×C₈	—	10	1	no	—
386	C₃×C₈	—	10	1	no	—
387	C₃×C₈	C₂²×Dic₅	1	4	yes	—
388	C₂²×C₅	—	2	1	no	—
389	C₂²×C₅	—	2	1	no	—
390	C₂²×C₅	—	2	2	no	—
391	C₂²×C₅	—	4	1	no	—
392	C₂²×C₅	—	4	1	no	—
393	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
394	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
395	C₄×C₅	—	2	2	no	—
396	C₄×C₅	—	2	4	no	—
397	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
398	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
399	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
400	Dic₅	—	2	2	no	—
401	Dic₅	—	2	2	no	—
402	Dic₅	—	4	1	no	—
403	Dic₅	—	4	2	no	—
404	Dic₅	—	4	1	no	—
405	#41	—	2	2	no	—
406	#41	C₂×C₃×Dic₅	1	4	yes	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	C₂×C₃×Dic₅	1	4	yes	complemented
410	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
411	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	10	2	no	—
417	C₂²×C₄	—	10	1	no	—
418	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
419	Q₁₆	C₂×C₃×Dic₅	1	8	yes	complemented
420	SD₁₆	C₂×C₃×Dic₅	1	8	yes	complemented
421	M₁₆	C₂×C₃×Dic₅	1	4	yes	complemented
422	C₂×C₈	—	5	1	no	—
423	C₂×C₈	—	5	1	no	—
424	C₂×C₈	—	10	2	no	—
425	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
426	C₄⋊C₄	—	5	1	no	—
427	C₄⋊C₄	—	5	1	no	—
428	C₄⋊C₄	—	5	1	no	—
429	C₄⋊C₄	—	5	1	no	—
430	C₄⋊C₄	—	5	2	no	—
431	C₄⋊C₄	—	10	2	no	—
432	C₄⋊C₄	—	10	2	no	—
433	C₄⋊C₄	—	10	2	no	—
434	C₄⋊C₄	—	10	1	no	—
435	C₂²⋊C₄	—	5	2	no	—
436	C₂²⋊C₄	—	10	2	no	—
437	C₂²⋊C₄	—	10	1	no	—
438	C₄²	—	5	2	no	—
439	C₄²	—	10	2	no	—
440	C₄²	—	10	2	no	—
441	C₄²	—	10	2	no	—
442	C₄²	—	10	1	no	—
443	C₃×C₅	#2947	1	1	yes	characteristic, complemented, Hall
444	C₂²×C₃	—	2	1	no	—
445	C₂²×C₃	—	2	1	no	—
446	C₂²×C₃	—	2	2	no	—
447	C₂²×C₃	—	4	1	no	—
448	C₂²×C₃	—	4	1	no	—
449	C₂²×C₃	D₄×Dic₅	1	2	yes	—
450	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
451	C₃×C₄	—	2	2	no	—
452	C₃×C₄	—	2	4	no	—
453	C₃×C₄	—	10	2	no	—
454	C₃×C₄	—	10	2	no	—
455	C₃×C₄	—	20	1	no	—
456	C₃×C₄	—	20	2	no	—
457	C₃×C₄	—	20	1	no	—
458	C₃×C₄	D₄×Dic₅	1	2	yes	—
459	C₃×C₄	C₂×#711	1	1	yes	characteristic
460	C₃×C₄	C₂³×Dic₅	1	1	yes	characteristic
461	C₂×C₅	—	2	2	no	—
462	C₂×C₅	—	4	2	no	—
463	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
464	C₂×C₅	C₃×#577	1	1	yes	characteristic
465	C₂×C₅	C₃×#578	1	1	yes	characteristic
466	C₂³	—	2	1	no	—
467	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
468	Q₈	—	2	4	no	—
469	Q₈	—	2	2	no	—
470	Q₈	—	2	1	no	—
471	Q₈	C₂²×C₃×Dic₅	1	4	yes	—
472	Q₈	C₂²×C₃×Dic₅	1	2	yes	—
473	D₄	—	2	4	no	—
474	D₄	—	2	1	no	—
475	D₄	C₂²×C₃×Dic₅	1	2	yes	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	5	2	no	—
481	C₂×C₄	—	5	2	no	—
482	C₂×C₄	—	10	1	no	—
483	C₂×C₄	—	10	1	no	—
484	C₂×C₄	—	10	2	no	—
485	C₂×C₄	—	40	2	no	—
486	C₂×C₄	—	40	1	no	—
487	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
488	C₂×C₄	C₃×#711	1	2	yes	—
489	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
490	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
491	C₈	—	10	1	no	—
492	C₈	—	10	1	no	—
493	C₈	C₂²×C₃×Dic₅	1	4	yes	—
494	C₂×C₃	—	2	2	no	—
495	C₂×C₃	—	4	2	no	—
496	C₂×C₃	#66112	1	1	yes	characteristic
497	C₂×C₃	#66113	1	1	yes	characteristic
498	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
499	C₅	C₃×#2947	1	1	yes	characteristic, complemented, Sylow
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	1	no	—
505	C₂²	C₃×D₄×Dic₅	1	2	yes	—
506	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
507	C₄	—	2	2	no	—
508	C₄	—	2	4	no	—
509	C₄	—	10	2	no	—
510	C₄	—	10	2	no	—
511	C₄	—	20	2	no	—
512	C₄	—	20	1	no	—
513	C₄	—	20	1	no	—
514	C₄	C₃×D₄×Dic₅	1	2	yes	—
515	C₄	C₂×C₃×#711	1	1	yes	characteristic
516	C₄	C₂³×C₃×Dic₅	1	1	yes	characteristic
517	C₃	#10615696	1	1	yes	characteristic, direct product factor, Sylow
518	C₂	—	2	2	no	—
519	C₂	—	4	2	no	—
520	C₂	C₃×#66112	1	1	yes	characteristic
521	C₂	C₃×#66113	1	1	yes	characteristic
522	C₂	C₂×C₃×D₄×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#137	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×C₅×#41	C₂²
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×#137	D₅
hypocenter	C₅	C₃×#2947
LCS	G ▷ 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
3. C₃×#66146	C₂	semidirect
5. C₂×C₃×#3967	C₂	semidirect
6. C₃×#65473	C₂	semidirect
7. C₃×Q₁₆×Dic₅	C₂	semidirect
8. C₃×#65453	C₂	semidirect
9. C₃×SD₁₆×Dic₅	C₂	semidirect
10. C₃×#65411	C₂	semidirect
11. C₃×#65410	C₂	semidirect
12. #10615696	C₃	direct (N × H)
15. C₃×C₅×#137	C₄	semidirect
46. #66146	C₂×C₃	semidirect
48. C₂×#3967	C₂×C₃	semidirect
49. #65473	C₂×C₃	semidirect
50. Q₁₆×Dic₅	C₂×C₃	semidirect
51. #65453	C₂×C₃	semidirect
52. SD₁₆×Dic₅	C₂×C₃	semidirect
53. #65411	C₂×C₃	semidirect
54. #65410	C₂×C₃	semidirect
59. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
69. C₃×C₅×Q₁₆	C₂×C₄	semidirect
70. C₃×C₅×SD₁₆	C₂×C₄	semidirect
71. C₃×C₅×M₁₆	C₂×C₄	semidirect
106. C₅×#137	C₃×C₄	semidirect
165. C₃×#137	Dic₅	semidirect
197. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
207. C₅×Q₁₆	C₂×C₃×C₄	semidirect
208. C₅×SD₁₆	C₂×C₃×C₄	semidirect
209. C₅×M₁₆	C₂×C₃×C₄	semidirect
263. C₂×C₃×Q₈	C₂×Dic₅	semidirect
273. C₃×Q₁₆	C₂×Dic₅	semidirect
274. C₃×SD₁₆	C₂×Dic₅	semidirect
275. C₃×M₁₆	C₂×Dic₅	semidirect
327. #137	C₃×Dic₅	semidirect
409. C₂×Q₈	C₂×C₃×Dic₅	semidirect
419. Q₁₆	C₂×C₃×Dic₅	semidirect
420. SD₁₆	C₂×C₃×Dic₅	semidirect
421. M₁₆	C₂×C₃×Dic₅	semidirect
443. C₃×C₅	#2947	semidirect
499. C₅	C₃×#2947	semidirect
517. C₃	#10615696	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×#66161	2
C₃×#66146	2
C₃×#65522	2
C₂×C₃×#3967	2
C₃×#65473	2
C₃×Q₁₆×Dic₅	2
C₃×#65453	2
C₃×SD₁₆×Dic₅	2
C₃×#65411	2
C₃×#65410	2
#10615696	3
C₃×#2947	5

Subgroups — C3×#10615696 #14417178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615696 #14417178