Subgroups — C₃×#10610302 #14417181

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×#4055	C₂	1	1	yes	maximal, characteristic
2	C₃×#65857	C₂	1	1	yes	maximal, characteristic
3	C₃×#65850	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65410	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65402	C₂	1	1	yes	maximal, characteristic
7	C₂×C₃×#3948	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65005	C₂	1	2	yes	maximal, complemented
9	C₃×#64999	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×Dic₂₀	C₂	1	2	yes	maximal, complemented
11	C₃×C₄×#677	C₂	1	2	yes	maximal, complemented
12	#10610302	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#709	C₂²	1	1	yes	characteristic
14	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×#117	C₂²	1	1	yes	characteristic
18	C₃×#4072	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
20	C₃×#4055	C₄	1	8	yes	complemented
21	C₂×C₃×Dic₂₀	C₂²	1	2	yes	—
22	C₂×C₃×#677	C₂²	1	2	yes	—
23	C₃×#4038	—	2	1	no	—
24	C₃×D₅×C₄⋊C₄	—	2	1	no	—
25	C₃×#4033	—	2	1	no	—
26	C₃×#4033	—	2	1	no	—
27	C₃×#4027	—	2	2	no	—
28	C₃×#4023	—	2	2	no	—
29	C₃×C₄×D₂₀	C₂²	1	2	yes	—
30	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
31	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
32	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
33	C₃×C₅×#97	C₂²	1	2	yes	—
34	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
35	C₃×#3953	C₂²	1	1	yes	characteristic
36	C₃×#3953	C₂²	1	1	yes	characteristic
37	C₃×#3950	C₂²	1	2	yes	—
38	C₃×#3949	C₂²	1	2	yes	—
39	C₃×#3948	C₂²	1	2	yes	—
40	C₃×#3948	C₂²	1	2	yes	—
41	C₃×#3948	C₂²	1	1	yes	characteristic
42	C₃×#3948	C₂²	1	1	yes	characteristic
43	C₃×#2947	—	5	1	no	maximal, Hall
44	C₂×#4055	C₂×C₃	1	1	yes	characteristic
45	#65857	C₂×C₃	1	1	yes	characteristic
46	#65850	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#405	C₂×C₃	1	1	yes	characteristic, complemented
48	#65410	C₂×C₃	1	1	yes	characteristic, complemented
49	#65402	C₂×C₃	1	1	yes	characteristic
50	C₂×#3948	C₂×C₃	1	1	yes	characteristic, complemented
51	#65005	C₂×C₃	1	2	yes	complemented
52	#64999	C₂×C₃	1	2	yes	complemented
53	C₄×Dic₂₀	C₂×C₃	1	2	yes	complemented
54	C₄×#677	C₂×C₃	1	2	yes	complemented
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
57	C₂²×C₃×Dic₅	—	2	1	no	—
58	C₂²×C₃×Dic₅	—	2	1	no	—
59	C₃×#709	—	2	2	no	—
60	C₃×#709	C₂×C₄	1	4	yes	—
61	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₄×D₅	—	2	1	no	—
63	C₂×C₃×C₄×D₅	—	2	2	no	—
64	C₂×C₃×Dic₁₀	—	2	1	no	—
65	C₂×C₃×Dic₁₀	—	2	2	no	—
66	C₂×C₃×Dic₁₀	C₂×C₄	1	4	yes	complemented
67	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
68	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
69	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
70	C₂×C₃×C₅×C₈	—	2	2	no	—
71	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
74	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
75	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
76	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
77	C₃×C₄²×C₅	C₂³	1	2	yes	—
78	C₃×C₂²⋊Dic₅	—	2	1	no	—
79	C₃×#685	—	2	2	no	—
80	C₃×C₄⋊Dic₅	—	2	1	no	—
81	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
82	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
83	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
84	C₃×#683	—	2	2	no	—
85	C₃×#683	—	2	2	no	—
86	C₃×#683	—	2	2	no	—
87	C₃×C₄×Dic₅	—	2	2	no	—
88	C₃×C₄×Dic₅	—	2	2	no	—
89	C₃×C₄×Dic₅	—	2	2	no	—
90	C₃×C₄×Dic₅	—	2	1	no	—
91	C₃×Dic₂₀	C₂×C₄	1	8	yes	complemented
92	C₃×#677	C₂×C₄	1	8	yes	complemented
93	C₂×C₃×#137	—	5	1	no	—
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	D₅	1	1	yes	characteristic, complemented
104	C₂×#709	C₂²×C₃	1	1	yes	characteristic
105	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
107	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
108	C₅×#117	C₂²×C₃	1	1	yes	characteristic
109	#4072	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
111	#4055	C₃×C₄	1	8	yes	complemented
112	C₂×Dic₂₀	C₂²×C₃	1	2	yes	—
113	C₂×#677	C₂²×C₃	1	2	yes	—
114	#4038	—	2	1	no	—
115	D₅×C₄⋊C₄	—	2	1	no	—
116	#4033	—	2	1	no	—
117	#4033	—	2	1	no	—
118	#4027	—	2	2	no	—
119	#4023	—	2	2	no	—
120	C₄×D₂₀	C₂²×C₃	1	2	yes	—
121	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
122	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
123	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
124	C₅×#97	C₂²×C₃	1	2	yes	—
125	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
126	#3953	C₂²×C₃	1	1	yes	characteristic
127	#3953	C₂²×C₃	1	1	yes	characteristic
128	#3950	C₂²×C₃	1	2	yes	—
129	#3949	C₂²×C₃	1	2	yes	—
130	#3948	C₂²×C₃	1	2	yes	—
131	#3948	C₂²×C₃	1	2	yes	—
132	#3948	C₂²×C₃	1	1	yes	characteristic
133	#3948	C₂²×C₃	1	1	yes	characteristic
134	#2947	—	5	1	no	Sylow
135	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₃×D₅	—	2	1	no	—
137	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
138	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
139	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
140	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂×C₃×C₄×C₅	#41	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
143	C₃×C₂²⋊D₅	—	2	4	no	—
144	C₂×C₃×Dic₅	—	2	4	no	—
145	C₂×C₃×Dic₅	—	2	2	no	—
146	C₂×C₃×Dic₅	—	2	1	no	—
147	C₂×C₃×Dic₅	—	2	1	no	—
148	C₂×C₃×Dic₅	—	2	1	no	—
149	C₂×C₃×Dic₅	—	2	2	no	—
150	C₂×C₃×Dic₅	—	8	1	no	—
151	C₃×D₂₀	—	2	1	no	—
152	C₃×D₂₀	C₂²×C₄	1	2	yes	—
153	C₃×C₄×D₅	—	2	4	no	—
154	C₃×C₄×D₅	—	8	2	no	—
155	C₃×Dic₁₀	—	2	4	no	—
156	C₃×Dic₁₀	—	2	2	no	—
157	C₃×Dic₁₀	—	2	1	no	—
158	C₃×Dic₁₀	C₂²×C₄	1	4	yes	—
159	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
160	C₃×C₅×C₈	—	2	1	no	—
161	C₃×C₅×C₈	—	2	1	no	—
162	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
163	C₂×C₃×#41	—	5	1	no	—
164	C₂²×C₃×Q₈	—	5	1	no	—
165	C₃×#137	—	5	8	no	—
166	C₂×C₃×Q₁₆	—	5	2	no	—
167	C₂×C₃×SD₁₆	—	5	2	no	—
168	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
169	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
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	—	10	1	no	—
179	C₃×#117	—	10	2	no	—
180	C₃×#117	C₂×D₅	1	1	yes	characteristic
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	C₂×D₅	1	2	yes	—
192	C₃×C₄×C₈	C₂×D₅	1	2	yes	—
193	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
194	C₂×C₂²⋊D₅	—	2	1	no	—
195	C₂²×Dic₅	—	2	1	no	—
196	C₂²×Dic₅	—	2	1	no	—
197	#709	—	2	2	no	—
198	#709	C₂×C₃×C₄	1	4	yes	—
199	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
200	C₂×C₄×D₅	—	2	1	no	—
201	C₂×C₄×D₅	—	2	2	no	—
202	C₂×Dic₁₀	—	2	1	no	—
203	C₂×Dic₁₀	—	2	2	no	—
204	C₂×Dic₁₀	C₂×C₃×C₄	1	4	yes	complemented
205	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
206	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
207	C₅×M₁₆	C₂×C₃×C₄	1	4	yes	complemented
208	C₂×C₅×C₈	—	2	2	no	—
209	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
210	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
211	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
212	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
213	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
214	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
215	C₄²×C₅	C₂³×C₃	1	2	yes	—
216	C₂²⋊Dic₅	—	2	1	no	—
217	#685	—	2	2	no	—
218	C₄⋊Dic₅	—	2	1	no	—
219	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
220	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
221	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
222	#683	—	2	2	no	—
223	#683	—	2	2	no	—
224	#683	—	2	2	no	—
225	C₄×Dic₅	—	2	2	no	—
226	C₄×Dic₅	—	2	2	no	—
227	C₄×Dic₅	—	2	2	no	—
228	C₄×Dic₅	—	2	1	no	—
229	Dic₂₀	C₂×C₃×C₄	1	8	yes	complemented
230	#677	C₂×C₃×C₄	1	8	yes	complemented
231	C₂×#137	—	5	1	no	—
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	C₃×D₅	1	1	yes	characteristic, complemented
242	C₂²×C₃×C₅	—	2	1	no	—
243	C₂²×C₃×C₅	—	2	1	no	—
244	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
245	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₃×D₅	—	2	2	no	—
247	C₂×C₃×D₅	—	4	1	no	—
248	C₂×C₃×D₅	—	4	1	no	—
249	C₃×C₄×C₅	—	2	2	no	—
250	C₃×C₄×C₅	—	2	2	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	4	no	—
255	C₃×Dic₅	—	2	2	no	—
256	C₃×Dic₅	—	4	2	no	—
257	C₃×Dic₅	—	4	1	no	—
258	C₃×Dic₅	—	4	1	no	—
259	C₃×#41	—	5	4	no	—
260	C₃×#41	—	10	2	no	—
261	C₂×C₃×Q₈	—	5	4	no	—
262	C₂×C₃×Q₈	—	5	2	no	—
263	C₂×C₃×Q₈	—	5	1	no	—
264	C₂×C₃×Q₈	—	10	1	no	—
265	C₂×C₃×Q₈	—	10	2	no	—
266	C₂×C₃×D₄	—	5	1	no	—
267	C₂×C₃×D₄	—	10	1	no	—
268	C₂²×C₃×C₄	—	10	1	no	—
269	C₂²×C₃×C₄	—	10	1	no	—
270	C₂²×C₃×C₄	—	10	1	no	—
271	C₂²×C₃×C₄	—	10	2	no	—
272	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
273	C₃×Q₁₆	—	5	8	no	—
274	C₃×SD₁₆	—	5	8	no	—
275	C₃×M₁₆	C₄×D₅	1	4	yes	complemented
276	C₂×C₃×C₈	—	2	2	no	—
277	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
278	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
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	2	no	—
283	C₃×C₄⋊C₄	—	10	2	no	—
284	C₃×C₄⋊C₄	—	10	2	no	—
285	C₃×C₄⋊C₄	—	10	2	no	—
286	C₃×C₄⋊C₄	—	10	1	no	—
287	C₃×C₄⋊C₄	D₂₀	1	1	yes	characteristic
288	C₃×C₄⋊C₄	D₂₀	1	1	yes	characteristic
289	C₃×C₂²⋊C₄	—	10	1	no	—
290	C₃×C₂²⋊C₄	—	10	2	no	—
291	C₃×C₂²⋊C₄	D₂₀	1	2	yes	—
292	C₃×C₄²	—	10	1	no	—
293	C₃×C₄²	—	10	2	no	—
294	C₃×C₄²	—	10	2	no	—
295	C₃×C₄²	—	10	2	no	—
296	C₃×C₄²	C₂²×D₅	1	2	yes	—
297	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
298	C₂²×D₅	—	2	1	no	—
299	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
300	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
301	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
302	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
303	C₂×C₄×C₅	C₃×#41	1	2	yes	—
304	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
305	C₂²⋊D₅	—	2	4	no	—
306	C₂×Dic₅	—	2	4	no	—
307	C₂×Dic₅	—	2	2	no	—
308	C₂×Dic₅	—	2	1	no	—
309	C₂×Dic₅	—	2	1	no	—
310	C₂×Dic₅	—	2	1	no	—
311	C₂×Dic₅	—	2	2	no	—
312	C₂×Dic₅	—	8	1	no	—
313	D₂₀	—	2	1	no	—
314	D₂₀	C₂²×C₃×C₄	1	2	yes	—
315	C₄×D₅	—	2	4	no	—
316	C₄×D₅	—	8	2	no	—
317	Dic₁₀	—	2	4	no	—
318	Dic₁₀	—	2	2	no	—
319	Dic₁₀	—	2	1	no	—
320	Dic₁₀	C₂²×C₃×C₄	1	4	yes	—
321	Dic₁₀	C₂²×C₃×C₄	1	2	yes	—
322	C₅×C₈	—	2	1	no	—
323	C₅×C₈	—	2	1	no	—
324	C₅×C₈	C₂²×C₃×C₄	1	4	yes	—
325	C₂×#41	—	5	1	no	—
326	C₂²×Q₈	—	5	1	no	—
327	#137	—	5	8	no	—
328	C₂×Q₁₆	—	5	2	no	—
329	C₂×SD₁₆	—	5	2	no	—
330	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
331	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
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	—	10	1	no	—
341	#117	—	10	2	no	—
342	#117	C₂×C₃×D₅	1	1	yes	characteristic
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	C₂×C₃×D₅	1	2	yes	—
354	C₄×C₈	C₂×C₃×D₅	1	2	yes	—
355	C₂×C₃×C₅	—	2	2	no	—
356	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
357	C₂×C₃×C₅	#577	1	1	yes	characteristic
358	C₂×C₃×C₅	#578	1	1	yes	characteristic
359	C₃×D₅	—	4	2	no	—
360	C₂³×C₃	—	10	1	no	—
361	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
362	C₃×Q₈	—	5	4	no	—
363	C₃×Q₈	—	5	2	no	—
364	C₃×Q₈	—	10	2	no	—
365	C₃×Q₈	—	10	1	no	—
366	C₃×Q₈	—	10	4	no	—
367	C₃×D₄	—	5	2	no	—
368	C₃×D₄	—	10	4	no	—
369	C₃×D₄	—	10	1	no	—
370	C₂×C₃×C₄	—	10	1	no	—
371	C₂×C₃×C₄	—	10	2	no	—
372	C₂×C₃×C₄	—	10	4	no	—
373	C₂×C₃×C₄	—	10	4	no	—
374	C₂×C₃×C₄	—	10	1	no	—
375	C₂×C₃×C₄	—	10	1	no	—
376	C₂×C₃×C₄	—	10	2	no	—
377	C₂×C₃×C₄	—	40	2	no	—
378	C₂×C₃×C₄	—	40	1	no	—
379	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
380	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
381	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
382	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
383	C₂×C₃×C₄	#709	1	2	yes	—
384	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
385	C₃×C₈	—	2	1	no	—
386	C₃×C₈	—	2	1	no	—
387	C₃×C₈	C₂×C₄×D₅	1	4	yes	—
388	C₂²×C₅	—	2	1	no	—
389	C₂²×C₅	—	2	1	no	—
390	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
391	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
392	C₂×D₅	—	2	2	no	—
393	C₂×D₅	—	4	1	no	—
394	C₂×D₅	—	4	1	no	—
395	C₄×C₅	—	2	2	no	—
396	C₄×C₅	—	2	2	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	4	no	—
401	Dic₅	—	2	2	no	—
402	Dic₅	—	4	2	no	—
403	Dic₅	—	4	1	no	—
404	Dic₅	—	4	1	no	—
405	#41	—	5	4	no	—
406	#41	—	10	2	no	—
407	C₂×Q₈	—	5	4	no	—
408	C₂×Q₈	—	5	2	no	—
409	C₂×Q₈	—	5	1	no	—
410	C₂×Q₈	—	10	1	no	—
411	C₂×Q₈	—	10	2	no	—
412	C₂×D₄	—	5	1	no	—
413	C₂×D₄	—	10	1	no	—
414	C₂²×C₄	—	10	1	no	—
415	C₂²×C₄	—	10	1	no	—
416	C₂²×C₄	—	10	1	no	—
417	C₂²×C₄	—	10	2	no	—
418	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
419	Q₁₆	—	5	8	no	—
420	SD₁₆	—	5	8	no	—
421	M₁₆	C₃×C₄×D₅	1	4	yes	complemented
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
424	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
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	2	no	—
429	C₄⋊C₄	—	10	1	no	—
430	C₄⋊C₄	—	10	2	no	—
431	C₄⋊C₄	—	10	2	no	—
432	C₄⋊C₄	—	10	2	no	—
433	C₄⋊C₄	C₃×D₂₀	1	1	yes	characteristic
434	C₄⋊C₄	C₃×D₂₀	1	1	yes	characteristic
435	C₂²⋊C₄	—	10	1	no	—
436	C₂²⋊C₄	—	10	2	no	—
437	C₂²⋊C₄	C₃×D₂₀	1	2	yes	—
438	C₄²	—	10	1	no	—
439	C₄²	—	10	2	no	—
440	C₄²	—	10	2	no	—
441	C₄²	—	10	2	no	—
442	C₄²	C₂²×C₃×D₅	1	2	yes	—
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	—	10	2	no	—
447	C₂²×C₃	—	20	1	no	—
448	C₂²×C₃	—	20	1	no	—
449	C₂²×C₃	C₄×D₂₀	1	2	yes	—
450	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
451	C₃×C₄	—	2	2	no	—
452	C₃×C₄	—	2	2	no	—
453	C₃×C₄	—	10	2	no	—
454	C₃×C₄	—	10	4	no	—
455	C₃×C₄	—	20	1	no	—
456	C₃×C₄	—	20	2	no	—
457	C₃×C₄	—	20	1	no	—
458	C₃×C₄	C₄×D₂₀	1	2	yes	—
459	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
460	C₃×C₄	C₂×#709	1	1	yes	characteristic
461	C₂×C₅	—	2	2	no	—
462	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
463	C₂×C₅	C₃×#577	1	1	yes	characteristic
464	C₂×C₅	C₃×#578	1	1	yes	characteristic
465	D₅	—	4	2	no	—
466	C₂³	—	10	1	no	—
467	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
468	Q₈	—	5	4	no	—
469	Q₈	—	5	2	no	—
470	Q₈	—	10	2	no	—
471	Q₈	—	10	1	no	—
472	Q₈	—	10	4	no	—
473	D₄	—	5	2	no	—
474	D₄	—	10	4	no	—
475	D₄	—	10	1	no	—
476	C₂×C₄	—	10	1	no	—
477	C₂×C₄	—	10	2	no	—
478	C₂×C₄	—	10	4	no	—
479	C₂×C₄	—	10	4	no	—
480	C₂×C₄	—	10	1	no	—
481	C₂×C₄	—	10	1	no	—
482	C₂×C₄	—	10	2	no	—
483	C₂×C₄	—	40	2	no	—
484	C₂×C₄	—	40	1	no	—
485	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
486	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
487	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
488	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
489	C₂×C₄	C₃×#709	1	2	yes	—
490	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
491	C₈	—	2	1	no	—
492	C₈	—	2	1	no	—
493	C₈	C₂×C₃×C₄×D₅	1	4	yes	—
494	C₂×C₃	—	2	2	no	—
495	C₂×C₃	—	20	2	no	—
496	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
497	C₂×C₃	#66085	1	1	yes	characteristic
498	C₂×C₃	#66087	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	—	10	2	no	—
503	C₂²	—	20	1	no	—
504	C₂²	—	20	1	no	—
505	C₂²	C₃×C₄×D₂₀	1	2	yes	—
506	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	10	2	no	—
510	C₄	—	10	4	no	—
511	C₄	—	20	2	no	—
512	C₄	—	20	1	no	—
513	C₄	—	20	1	no	—
514	C₄	C₃×C₄×D₂₀	1	2	yes	—
515	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
516	C₄	C₂×C₃×#709	1	1	yes	characteristic
517	C₃	#10610302	1	1	yes	characteristic, direct product factor, Sylow
518	C₂	—	2	2	no	—
519	C₂	—	20	2	no	—
520	C₂	C₂×C₃×C₄×D₂₀	1	1	yes	characteristic
521	C₂	C₃×#66085	1	1	yes	characteristic
522	C₂	C₃×#66087	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₂₀
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#405	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#709	C₂²
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#405	D₅
hypocenter	C₅	C₃×#2947
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117 ◁ C₃×#405

Complements

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

N	H ≅ G/N	type
3. C₃×#65850	C₂	semidirect
4. C₃×C₅×#405	C₂	semidirect
5. C₃×#65410	C₂	semidirect
7. C₂×C₃×#3948	C₂	semidirect
8. C₃×#65005	C₂	semidirect
9. C₃×#64999	C₂	semidirect
10. C₃×C₄×Dic₂₀	C₂	semidirect
11. C₃×C₄×#677	C₂	semidirect
12. #10610302	C₃	direct (N × H)
20. C₃×#4055	C₄	semidirect
46. #65850	C₂×C₃	semidirect
47. C₅×#405	C₂×C₃	semidirect
48. #65410	C₂×C₃	semidirect
50. C₂×#3948	C₂×C₃	semidirect
51. #65005	C₂×C₃	semidirect
52. #64999	C₂×C₃	semidirect
53. C₄×Dic₂₀	C₂×C₃	semidirect
54. C₄×#677	C₂×C₃	semidirect
66. C₂×C₃×Dic₁₀	C₂×C₄	semidirect
69. C₃×C₅×M₁₆	C₂×C₄	semidirect
91. C₃×Dic₂₀	C₂×C₄	semidirect
92. C₃×#677	C₂×C₄	semidirect
103. C₃×#405	D₅	semidirect
111. #4055	C₃×C₄	semidirect
204. C₂×Dic₁₀	C₂×C₃×C₄	semidirect
207. C₅×M₁₆	C₂×C₃×C₄	semidirect
229. Dic₂₀	C₂×C₃×C₄	semidirect
230. #677	C₂×C₃×C₄	semidirect
241. #405	C₃×D₅	semidirect
275. C₃×M₁₆	C₄×D₅	semidirect
421. M₁₆	C₃×C₄×D₅	semidirect
443. C₃×C₅	#2947	semidirect
499. C₅	C₃×#2947	semidirect
517. C₃	#10610302	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×#4055	2
C₃×#65857	2
C₃×#65850	2
C₃×C₅×#405	2
C₃×#65410	2
C₃×#65402	2
C₂×C₃×#3948	2
C₃×#65005	2
C₃×#64999	2
C₃×C₄×Dic₂₀	2
C₃×C₄×#677	2
#10610302	3
C₃×#2947	5

Subgroups — C3×#10610302 #14417181

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610302 #14417181