Subgroups — C₃×#10614278 #14417175

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	C₃×C₅×#519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4088	C₂	1	1	yes	maximal, characteristic
3	C₃×#65857	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#3967	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65319	C₂	1	2	yes	maximal, complemented
6	C₃×C₄×#689	C₂	1	2	yes	maximal, complemented
7	C₃×#65315	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×#688	C₂	1	2	yes	maximal, complemented
9	C₃×#65291	C₂	1	1	yes	maximal, characteristic
10	C₃×#65286	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65284	C₂	1	1	yes	maximal, characteristic, complemented
12	#10614278	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×#709	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×Q₈	—	2	1	no	—
16	C₃×C₄×C₅×Q₈	—	2	1	no	—
17	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
18	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
19	C₃×C₅×#117	—	2	2	no	—
20	C₃×C₅×#117	C₂²	1	1	yes	characteristic
21	C₃×C₅×#117	C₂²	1	1	yes	characteristic
22	C₂×C₃×#689	C₂²	1	2	yes	—
23	C₃×#4088	C₄	1	8	yes	complemented
24	C₂×C₃×#688	C₂²	1	2	yes	—
25	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×#681	C₂²	1	1	yes	characteristic
27	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
28	C₃×#4038	—	2	1	no	—
29	C₃×D₅×C₄⋊C₄	—	2	1	no	—
30	C₃×#4027	—	2	2	no	—
31	C₃×C₄×D₂₀	C₂²	1	2	yes	—
32	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
33	C₃×#3967	C₂²	1	2	yes	—
34	C₃×#3967	C₂²	1	2	yes	—
35	C₃×#3942	C₂²	1	1	yes	characteristic
36	C₃×#3942	C₂²	1	1	yes	characteristic
37	C₃×#3941	C₂²	1	1	yes	characteristic
38	C₃×#3941	C₂²	1	1	yes	characteristic
39	C₃×#3940	C₂²	1	2	yes	—
40	C₃×#3939	C₂²	1	2	yes	—
41	C₃×#3935	C₂²	1	2	yes	—
42	C₃×C₄×#168	C₂²	1	2	yes	—
43	C₃×#2947	—	5	1	no	maximal, Hall
44	C₅×#519	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×#4088	C₂×C₃	1	1	yes	characteristic
46	#65857	C₂×C₃	1	1	yes	characteristic
47	C₂×#3967	C₂×C₃	1	1	yes	characteristic, complemented
48	#65319	C₂×C₃	1	2	yes	complemented
49	C₄×#689	C₂×C₃	1	2	yes	complemented
50	#65315	C₂×C₃	1	2	yes	complemented
51	C₄×#688	C₂×C₃	1	2	yes	complemented
52	#65291	C₂×C₃	1	1	yes	characteristic
53	#65286	C₂×C₃	1	1	yes	characteristic, complemented
54	#65284	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×C₃×C₅×Q₈	—	2	1	no	—
56	C₂×C₃×C₅×Q₈	—	2	2	no	—
57	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
58	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
59	C₂²×C₃×C₄×C₅	—	2	1	no	—
60	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
62	C₂²×C₃×Dic₅	—	2	1	no	—
63	C₃×#709	—	2	2	no	—
64	C₃×#709	C₂×C₄	1	4	yes	—
65	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₄×D₅	—	2	1	no	—
67	C₂×C₃×C₄×D₅	—	2	2	no	—
68	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
69	C₃×C₅×C₄⋊C₄	—	2	2	no	—
70	C₃×C₅×C₄⋊C₄	—	2	2	no	—
71	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
72	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
73	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
76	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
77	C₃×C₄²×C₅	—	2	2	no	—
78	C₃×C₄²×C₅	—	2	2	no	—
79	C₃×C₄²×C₅	—	2	1	no	—
80	C₃×C₄²×C₅	C₂³	1	2	yes	—
81	C₃×#689	C₂×C₄	1	8	yes	complemented
82	C₃×#688	C₂×C₄	1	8	yes	complemented
83	C₃×#685	—	2	2	no	—
84	C₃×C₄⋊Dic₅	—	2	1	no	—
85	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
86	C₃×#683	—	2	2	no	—
87	C₃×C₄×Dic₅	—	2	2	no	—
88	C₃×#681	C₂×C₄	1	4	yes	complemented
89	C₂×C₃×#168	—	2	2	no	—
90	C₂×C₃×#168	C₂³	1	1	yes	characteristic
91	C₂×C₃×#168	C₂³	1	1	yes	characteristic
92	C₂×C₃×#168	C₂³	1	2	yes	—
93	C₂×C₃×#137	—	5	1	no	—
94	C₃×#520	—	5	1	no	—
95	C₃×#519	D₅	1	1	yes	characteristic, complemented
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	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
105	C₂×#709	C₂²×C₃	1	1	yes	characteristic
106	C₄×C₅×Q₈	—	2	1	no	—
107	C₄×C₅×Q₈	—	2	1	no	—
108	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
109	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
110	C₅×#117	—	2	2	no	—
111	C₅×#117	C₂²×C₃	1	1	yes	characteristic
112	C₅×#117	C₂²×C₃	1	1	yes	characteristic
113	C₂×#689	C₂²×C₃	1	2	yes	—
114	#4088	C₃×C₄	1	8	yes	complemented
115	C₂×#688	C₂²×C₃	1	2	yes	—
116	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
117	C₂×#681	C₂²×C₃	1	1	yes	characteristic
118	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
119	#4038	—	2	1	no	—
120	D₅×C₄⋊C₄	—	2	1	no	—
121	#4027	—	2	2	no	—
122	C₄×D₂₀	C₂²×C₃	1	2	yes	—
123	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
124	#3967	C₂²×C₃	1	2	yes	—
125	#3967	C₂²×C₃	1	2	yes	—
126	#3942	C₂²×C₃	1	1	yes	characteristic
127	#3942	C₂²×C₃	1	1	yes	characteristic
128	#3941	C₂²×C₃	1	1	yes	characteristic
129	#3941	C₂²×C₃	1	1	yes	characteristic
130	#3940	C₂²×C₃	1	2	yes	—
131	#3939	C₂²×C₃	1	2	yes	—
132	#3935	C₂²×C₃	1	2	yes	—
133	C₄×#168	C₂²×C₃	1	2	yes	—
134	#2947	—	5	1	no	Sylow
135	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₃×D₅	—	2	1	no	—
137	C₃×C₅×Q₈	—	2	4	no	—
138	C₃×C₅×Q₈	—	2	2	no	—
139	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
140	C₂×C₃×C₄×C₅	—	2	4	no	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	—	2	1	no	—
144	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
145	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
146	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
148	C₂×C₃×C₄×C₅	#41	1	2	yes	—
149	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
150	C₃×C₂²⋊D₅	—	2	4	no	—
151	C₂×C₃×Dic₅	—	2	1	no	—
152	C₂×C₃×Dic₅	—	2	2	no	—
153	C₂×C₃×Dic₅	—	8	1	no	—
154	C₃×D₂₀	—	2	1	no	—
155	C₃×D₂₀	C₂²×C₄	1	2	yes	—
156	C₃×C₄×D₅	—	2	4	no	—
157	C₃×C₄×D₅	—	8	2	no	—
158	C₃×Dic₁₀	—	2	1	no	—
159	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
160	C₃×#168	—	2	1	no	—
161	C₃×#168	—	2	1	no	—
162	C₃×#168	C₂²×C₄	1	4	yes	—
163	C₂×C₃×#41	—	5	1	no	—
164	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
165	C₃×#137	—	5	8	no	—
166	C₂×C₃×Q₁₆	—	5	2	no	—
167	C₂×C₃×SD₁₆	—	5	2	no	—
168	C₂×C₃×M₁₆	—	5	1	no	—
169	C₂²×C₃×C₈	—	5	1	no	—
170	C₃×C₄×Q₈	—	2	1	no	—
171	C₃×C₄×Q₈	—	2	1	no	—
172	C₃×C₄×Q₈	—	5	2	no	—
173	C₃×C₄×Q₈	C₂×D₅	1	2	yes	—
174	C₃×C₄×Q₈	C₂×D₅	1	2	yes	—
175	C₃×C₄×D₄	—	5	2	no	—
176	C₃×C₄×D₄	—	10	2	no	—
177	C₃×#117	—	2	2	no	—
178	C₃×#117	—	10	1	no	—
179	C₃×#117	C₂×D₅	1	1	yes	characteristic
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	—	5	2	no	—
192	C₃×C₄×C₈	—	5	2	no	—
193	C₂×C₅×Q₈	—	2	1	no	—
194	C₂×C₅×Q₈	—	2	2	no	—
195	C₂×C₅×Q₈	C₂×C₃×C₄	1	4	yes	complemented
196	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
197	C₂²×C₄×C₅	—	2	1	no	—
198	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
199	C₂×C₂²⋊D₅	—	2	1	no	—
200	C₂²×Dic₅	—	2	1	no	—
201	#709	—	2	2	no	—
202	#709	C₂×C₃×C₄	1	4	yes	—
203	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
204	C₂×C₄×D₅	—	2	1	no	—
205	C₂×C₄×D₅	—	2	2	no	—
206	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
207	C₅×C₄⋊C₄	—	2	2	no	—
208	C₅×C₄⋊C₄	—	2	2	no	—
209	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
210	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
211	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
212	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
213	C₅×C₂²⋊C₄	—	2	1	no	—
214	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
215	C₄²×C₅	—	2	2	no	—
216	C₄²×C₅	—	2	2	no	—
217	C₄²×C₅	—	2	1	no	—
218	C₄²×C₅	C₂³×C₃	1	2	yes	—
219	#689	C₂×C₃×C₄	1	8	yes	complemented
220	#688	C₂×C₃×C₄	1	8	yes	complemented
221	#685	—	2	2	no	—
222	C₄⋊Dic₅	—	2	1	no	—
223	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
224	#683	—	2	2	no	—
225	C₄×Dic₅	—	2	2	no	—
226	#681	C₂×C₃×C₄	1	4	yes	complemented
227	C₂×#168	—	2	2	no	—
228	C₂×#168	C₂³×C₃	1	1	yes	characteristic
229	C₂×#168	C₂³×C₃	1	1	yes	characteristic
230	C₂×#168	C₂³×C₃	1	2	yes	—
231	C₂×#137	—	5	1	no	—
232	#520	—	5	1	no	—
233	#519	C₃×D₅	1	1	yes	characteristic, complemented
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	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	4	no	—
250	C₃×C₄×C₅	—	2	2	no	—
251	C₃×C₄×C₅	—	2	2	no	—
252	C₃×C₄×C₅	—	4	1	no	—
253	C₃×C₄×C₅	—	4	1	no	—
254	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
255	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
256	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
257	C₃×Dic₅	—	2	2	no	—
258	C₃×Dic₅	—	4	2	no	—
259	C₃×#41	—	5	4	no	—
260	C₃×#41	—	10	2	no	—
261	C₂×C₃×Q₈	—	2	2	no	—
262	C₂×C₃×Q₈	—	2	1	no	—
263	C₂×C₃×Q₈	—	5	1	no	—
264	C₂×C₃×Q₈	C₄×D₅	1	4	yes	complemented
265	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
266	C₂×C₃×D₄	—	5	1	no	—
267	C₂×C₃×D₄	—	10	1	no	—
268	C₂²×C₃×C₄	—	2	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	—	5	4	no	—
276	C₂×C₃×C₈	—	5	2	no	—
277	C₂×C₃×C₈	—	5	1	no	—
278	C₂×C₃×C₈	—	5	1	no	—
279	C₂×C₃×C₈	—	10	2	no	—
280	C₃×C₄⋊C₄	—	2	2	no	—
281	C₃×C₄⋊C₄	—	2	2	no	—
282	C₃×C₄⋊C₄	—	5	2	no	—
283	C₃×C₄⋊C₄	—	10	2	no	—
284	C₃×C₄⋊C₄	—	10	1	no	—
285	C₃×C₄⋊C₄	C₂²⋊D₅	1	1	yes	characteristic
286	C₃×C₄⋊C₄	C₂²⋊D₅	1	1	yes	characteristic
287	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
288	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
289	C₃×C₂²⋊C₄	—	2	1	no	—
290	C₃×C₂²⋊C₄	—	10	2	no	—
291	C₃×C₂²⋊C₄	C₂²⋊D₅	1	2	yes	—
292	C₃×C₄²	—	2	2	no	—
293	C₃×C₄²	—	2	2	no	—
294	C₃×C₄²	—	2	1	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	C₅×Q₈	—	2	4	no	—
300	C₅×Q₈	—	2	2	no	—
301	C₅×Q₈	C₂²×C₃×C₄	1	4	yes	—
302	C₂×C₄×C₅	—	2	4	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
307	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
308	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
309	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
310	C₂×C₄×C₅	C₃×#41	1	2	yes	—
311	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
312	C₂²⋊D₅	—	2	4	no	—
313	C₂×Dic₅	—	2	1	no	—
314	C₂×Dic₅	—	2	2	no	—
315	C₂×Dic₅	—	8	1	no	—
316	D₂₀	—	2	1	no	—
317	D₂₀	C₂²×C₃×C₄	1	2	yes	—
318	C₄×D₅	—	2	4	no	—
319	C₄×D₅	—	8	2	no	—
320	Dic₁₀	—	2	1	no	—
321	Dic₁₀	C₂²×C₃×C₄	1	2	yes	—
322	#168	—	2	1	no	—
323	#168	—	2	1	no	—
324	#168	C₂²×C₃×C₄	1	4	yes	—
325	C₂×#41	—	5	1	no	—
326	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
327	#137	—	5	8	no	—
328	C₂×Q₁₆	—	5	2	no	—
329	C₂×SD₁₆	—	5	2	no	—
330	C₂×M₁₆	—	5	1	no	—
331	C₂²×C₈	—	5	1	no	—
332	C₄×Q₈	—	2	1	no	—
333	C₄×Q₈	—	2	1	no	—
334	C₄×Q₈	—	5	2	no	—
335	C₄×Q₈	C₂×C₃×D₅	1	2	yes	—
336	C₄×Q₈	C₂×C₃×D₅	1	2	yes	—
337	C₄×D₄	—	5	2	no	—
338	C₄×D₄	—	10	2	no	—
339	#117	—	2	2	no	—
340	#117	—	10	1	no	—
341	#117	C₂×C₃×D₅	1	1	yes	characteristic
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	—	5	2	no	—
354	C₄×C₈	—	5	2	no	—
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×C₂²⋊D₅	1	1	yes	characteristic
362	C₃×Q₈	—	2	2	no	—
363	C₃×Q₈	—	2	4	no	—
364	C₃×Q₈	—	5	2	no	—
365	C₃×Q₈	—	10	1	no	—
366	C₃×Q₈	C₂×C₄×D₅	1	4	yes	—
367	C₃×D₄	—	5	2	no	—
368	C₃×D₄	—	10	4	no	—
369	C₃×D₄	—	10	1	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	2	4	no	—
372	C₂×C₃×C₄	—	2	1	no	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	—	10	1	no	—
375	C₂×C₃×C₄	—	10	4	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	#709	1	2	yes	—
381	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
382	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
383	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
384	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
385	C₃×C₈	—	5	4	no	—
386	C₃×C₈	—	10	1	no	—
387	C₃×C₈	—	10	1	no	—
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	—	2	4	no	—
398	C₄×C₅	—	4	1	no	—
399	C₄×C₅	—	4	1	no	—
400	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
401	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
402	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
403	Dic₅	—	2	2	no	—
404	Dic₅	—	4	2	no	—
405	#41	—	5	4	no	—
406	#41	—	10	2	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	—	5	1	no	—
410	C₂×Q₈	C₃×C₄×D₅	1	4	yes	complemented
411	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
412	C₂×D₄	—	5	1	no	—
413	C₂×D₄	—	10	1	no	—
414	C₂²×C₄	—	2	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	—	5	4	no	—
422	C₂×C₈	—	5	2	no	—
423	C₂×C₈	—	5	1	no	—
424	C₂×C₈	—	5	1	no	—
425	C₂×C₈	—	10	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	5	2	no	—
429	C₄⋊C₄	—	10	1	no	—
430	C₄⋊C₄	—	10	2	no	—
431	C₄⋊C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
432	C₄⋊C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
433	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
434	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	—	10	2	no	—
437	C₂²⋊C₄	C₃×C₂²⋊D₅	1	2	yes	—
438	C₄²	—	2	2	no	—
439	C₄²	—	2	2	no	—
440	C₄²	—	2	1	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×C₂²⋊D₅	1	2	yes	—
450	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
451	C₃×C₄	—	2	4	no	—
452	C₃×C₄	—	2	2	no	—
453	C₃×C₄	—	2	2	no	—
454	C₃×C₄	—	4	1	no	—
455	C₃×C₄	—	4	1	no	—
456	C₃×C₄	—	10	2	no	—
457	C₃×C₄	—	20	2	no	—
458	C₃×C₄	C₄×C₂²⋊D₅	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×C₂²⋊D₅	1	1	yes	characteristic
468	Q₈	—	2	2	no	—
469	Q₈	—	2	4	no	—
470	Q₈	—	5	2	no	—
471	Q₈	—	10	1	no	—
472	Q₈	C₂×C₃×C₄×D₅	1	4	yes	—
473	D₄	—	5	2	no	—
474	D₄	—	10	4	no	—
475	D₄	—	10	1	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	10	1	no	—
481	C₂×C₄	—	10	4	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	C₃×#709	1	2	yes	—
487	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
488	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
489	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
490	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
491	C₈	—	5	4	no	—
492	C₈	—	10	1	no	—
493	C₈	—	10	1	no	—
494	C₂×C₃	—	2	2	no	—
495	C₂×C₃	—	20	2	no	—
496	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
497	C₂×C₃	#66171	1	1	yes	characteristic
498	C₂×C₃	#66172	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×C₂²⋊D₅	1	2	yes	—
506	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
507	C₄	—	2	4	no	—
508	C₄	—	2	2	no	—
509	C₄	—	2	2	no	—
510	C₄	—	4	1	no	—
511	C₄	—	4	1	no	—
512	C₄	—	10	2	no	—
513	C₄	—	20	2	no	—
514	C₄	C₃×C₄×C₂²⋊D₅	1	2	yes	—
515	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
516	C₄	C₂×C₃×#709	1	1	yes	characteristic
517	C₃	#10614278	1	1	yes	characteristic, direct product factor, Sylow
518	C₂	—	2	2	no	—
519	C₂	—	20	2	no	—
520	C₂	C₂×C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
521	C₂	C₃×#66171	1	1	yes	characteristic
522	C₂	C₃×#66172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×C₂²⋊D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#519	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#709	C₂²
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#519	D₅
hypocenter	C₅	C₃×#2947
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117 ◁ C₃×#519

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#519	C₂	semidirect
4. C₂×C₃×#3967	C₂	semidirect
5. C₃×#65319	C₂	semidirect
6. C₃×C₄×#689	C₂	semidirect
7. C₃×#65315	C₂	semidirect
8. C₃×C₄×#688	C₂	semidirect
10. C₃×#65286	C₂	semidirect
11. C₃×#65284	C₂	semidirect
12. #10614278	C₃	direct (N × H)
23. C₃×#4088	C₄	semidirect
44. C₅×#519	C₂×C₃	semidirect
47. C₂×#3967	C₂×C₃	semidirect
48. #65319	C₂×C₃	semidirect
49. C₄×#689	C₂×C₃	semidirect
50. #65315	C₂×C₃	semidirect
51. C₄×#688	C₂×C₃	semidirect
53. #65286	C₂×C₃	semidirect
54. #65284	C₂×C₃	semidirect
57. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
81. C₃×#689	C₂×C₄	semidirect
82. C₃×#688	C₂×C₄	semidirect
88. C₃×#681	C₂×C₄	semidirect
95. C₃×#519	D₅	semidirect
114. #4088	C₃×C₄	semidirect
195. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
219. #689	C₂×C₃×C₄	semidirect
220. #688	C₂×C₃×C₄	semidirect
226. #681	C₂×C₃×C₄	semidirect
233. #519	C₃×D₅	semidirect
264. C₂×C₃×Q₈	C₄×D₅	semidirect
410. C₂×Q₈	C₃×C₄×D₅	semidirect
443. C₃×C₅	#2947	semidirect
499. C₅	C₃×#2947	semidirect
517. C₃	#10614278	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#519	2
C₂×C₃×#4088	2
C₃×#65857	2
C₂×C₃×#3967	2
C₃×#65319	2
C₃×C₄×#689	2
C₃×#65315	2
C₃×C₄×#688	2
C₃×#65291	2
C₃×#65286	2
C₃×#65284	2
#10614278	3
C₃×#2947	5

Subgroups — C3×#10614278 #14417175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10614278 #14417175