Subgroups — C₃×#10610602 #14430682

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41×Dic₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4036	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#417	C₂	1	1	yes	maximal, characteristic
4	C₃×#65521	C₂	1	1	yes	maximal, characteristic
5	C₃×#65410	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65407	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65253	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65088	C₂	1	2	yes	maximal, complemented
9	C₃×#65085	C₂	1	2	yes	maximal, complemented
10	C₃×#65055	C₂	1	2	yes	maximal, complemented
11	C₃×#65052	C₂	1	2	yes	maximal, complemented
12	#10610602	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic
17	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic
18	C₃×D₄×Dic₅	—	2	1	no	—
19	C₃×D₄×Dic₅	—	2	1	no	—
20	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
21	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
22	C₃×#4072	—	2	1	no	—
23	C₃×#4072	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄⋊Dic₅	—	2	1	no	—
25	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×#683	—	2	1	no	—
27	C₂×C₃×C₄×Dic₅	—	2	1	no	—
28	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
29	C₂×C₃×#681	C₂²	1	1	yes	characteristic
30	C₃×#4036	—	2	1	no	—
31	C₃×#4036	—	2	1	no	—
32	C₃×#4036	C₂²	1	2	yes	—
33	C₃×#4036	C₂²	1	2	yes	—
34	C₃×C₅×#103	C₂²	1	2	yes	—
35	C₃×C₅×#102	C₂²	1	2	yes	—
36	C₃×#3967	C₂²	1	2	yes	—
37	C₃×#3964	C₂²	1	2	yes	—
38	C₃×#3950	C₂²	1	2	yes	—
39	C₃×#3949	C₂²	1	2	yes	—
40	C₃×#3946	C₂²	1	2	yes	—
41	C₃×#3946	C₂²	1	2	yes	—
42	C₃×#3940	C₂²	1	2	yes	—
43	C₃×#3939	C₂²	1	2	yes	—
44	C₃×#3080	—	5	1	no	maximal, Hall
45	#41×Dic₅	C₂×C₃	1	1	yes	characteristic
46	C₂×#4036	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#417	C₂×C₃	1	1	yes	characteristic
48	#65521	C₂×C₃	1	1	yes	characteristic
49	#65410	C₂×C₃	1	1	yes	characteristic, complemented
50	#65407	C₂×C₃	1	1	yes	characteristic, complemented
51	#65253	C₂×C₃	1	1	yes	characteristic, complemented
52	#65088	C₂×C₃	1	2	yes	complemented
53	#65085	C₂×C₃	1	2	yes	complemented
54	#65055	C₂×C₃	1	2	yes	complemented
55	#65052	C₂×C₃	1	2	yes	complemented
56	C₃×C₅×#41	—	2	2	no	—
57	C₃×C₅×#41	Q₈	1	4	yes	—
58	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	—	2	1	no	—
60	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
61	C₂²×C₃×C₄×C₅	—	2	1	no	—
62	C₂²×C₃×C₄×C₅	—	2	1	no	—
63	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂²×C₃×Dic₅	—	2	1	no	—
65	C₂²×C₃×Dic₅	—	2	1	no	—
66	C₂²×C₃×Dic₅	—	2	1	no	—
67	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
68	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
69	C₃×C₅×M₁₆	—	2	2	no	—
70	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
71	C₃×C₅×C₄⋊C₄	—	2	1	no	—
72	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
73	C₃×C₂²⋊Dic₅	—	2	1	no	—
74	C₃×C₂²⋊Dic₅	—	2	1	no	—
75	C₃×C₂²⋊Dic₅	—	2	1	no	—
76	C₃×C₄⋊Dic₅	—	2	1	no	—
77	C₃×C₄⋊Dic₅	—	2	1	no	—
78	C₃×C₄⋊Dic₅	—	2	1	no	—
79	C₃×C₄⋊Dic₅	—	2	2	no	—
80	C₃×C₄⋊Dic₅	—	2	2	no	—
81	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
82	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
83	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
84	C₃×#683	—	2	2	no	—
85	C₃×#683	—	2	2	no	—
86	C₃×C₄×Dic₅	—	2	1	no	—
87	C₃×C₄×Dic₅	—	2	1	no	—
88	C₃×C₄×Dic₅	—	2	1	no	—
89	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
90	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
91	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
92	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
93	C₃×#681	—	2	2	no	—
94	C₂×C₃×#168	C₂³	1	2	yes	—
95	C₂×C₃×#125	—	5	1	no	—
96	C₃×C₄×#41	—	5	1	no	—
97	C₃×#479	—	5	2	no	—
98	C₃×#479	—	5	2	no	—
99	C₃×#478	—	5	2	no	—
100	C₃×#478	—	5	2	no	—
101	C₃×#428	—	5	1	no	—
102	C₃×#428	—	5	1	no	—
103	C₃×#423	—	5	1	no	—
104	C₃×#417	—	5	1	no	—
105	C₃×#417	D₅	1	1	yes	characteristic
106	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
109	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
110	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
111	D₄×Dic₅	—	2	1	no	—
112	D₄×Dic₅	—	2	1	no	—
113	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
114	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
115	#4072	—	2	1	no	—
116	#4072	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₄⋊Dic₅	—	2	1	no	—
118	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
119	C₂×#683	—	2	1	no	—
120	C₂×C₄×Dic₅	—	2	1	no	—
121	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
122	C₂×#681	C₂²×C₃	1	1	yes	characteristic
123	#4036	—	2	1	no	—
124	#4036	—	2	1	no	—
125	#4036	C₂²×C₃	1	2	yes	—
126	#4036	C₂²×C₃	1	2	yes	—
127	C₅×#103	C₂²×C₃	1	2	yes	—
128	C₅×#102	C₂²×C₃	1	2	yes	—
129	#3967	C₂²×C₃	1	2	yes	—
130	#3964	C₂²×C₃	1	2	yes	—
131	#3950	C₂²×C₃	1	2	yes	—
132	#3949	C₂²×C₃	1	2	yes	—
133	#3946	C₂²×C₃	1	2	yes	—
134	#3946	C₂²×C₃	1	2	yes	—
135	#3940	C₂²×C₃	1	2	yes	—
136	#3939	C₂²×C₃	1	2	yes	—
137	#3080	—	5	1	no	Sylow
138	C₂³×C₃×C₅	—	2	1	no	—
139	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
140	C₃×C₅×Q₈	—	2	1	no	—
141	C₃×C₅×Q₈	C₂×Q₈	1	2	yes	—
142	C₃×C₅×D₄	—	2	4	no	—
143	C₃×C₅×D₄	—	2	1	no	—
144	C₃×C₅×D₄	C₂×Q₈	1	2	yes	—
145	C₂×C₃×C₄×C₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	4	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	4	2	no	—
149	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
150	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
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	—	4	1	no	—
157	C₂×C₃×Dic₅	—	4	1	no	—
158	C₂×C₃×Dic₅	—	4	2	no	—
159	C₂×C₃×Dic₅	—	4	2	no	—
160	C₂×C₃×Dic₅	—	4	2	no	—
161	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
162	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
163	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
164	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
165	C₃×C₅×C₈	—	2	2	no	—
166	C₃×#168	—	2	2	no	—
167	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
168	C₂×C₃×M₁₆	—	5	1	no	—
169	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
170	C₃×#125	—	5	2	no	—
171	C₃×#125	—	5	2	no	—
172	C₃×#125	—	10	1	no	—
173	C₃×#125	—	10	1	no	—
174	C₃×C₄×Q₈	—	5	1	no	—
175	C₃×C₄×Q₈	—	5	1	no	—
176	C₃×C₄×D₄	—	5	1	no	—
177	C₃×C₄×D₄	—	5	1	no	—
178	C₃×C₄×D₄	—	10	1	no	—
179	C₃×C₄×D₄	—	10	1	no	—
180	C₃×#117	—	5	1	no	—
181	C₃×#117	—	10	1	no	—
182	C₂×C₃×C₄⋊C₄	—	5	1	no	—
183	C₂×C₃×C₄⋊C₄	—	10	1	no	—
184	C₂×C₃×C₄⋊C₄	—	10	1	no	—
185	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
186	C₂×C₃×C₄²	—	5	1	no	—
187	C₂×C₃×C₄²	—	10	1	no	—
188	C₃×#107	—	5	2	no	—
189	C₃×#107	—	5	2	no	—
190	C₃×#106	—	5	2	no	—
191	C₃×#106	—	5	2	no	—
192	C₃×C₄⋊C₈	—	5	2	no	—
193	C₃×C₄⋊C₈	—	5	2	no	—
194	C₃×#103	—	5	2	no	—
195	C₃×#103	C₂×D₅	1	2	yes	—
196	C₃×#102	—	5	2	no	—
197	C₃×#102	C₂×D₅	1	2	yes	—
198	C₅×#41	—	2	2	no	—
199	C₅×#41	C₃×Q₈	1	4	yes	—
200	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
201	C₂×C₅×D₄	—	2	1	no	—
202	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
203	C₂²×C₄×C₅	—	2	1	no	—
204	C₂²×C₄×C₅	—	2	1	no	—
205	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
206	C₂²×Dic₅	—	2	1	no	—
207	C₂²×Dic₅	—	2	1	no	—
208	C₂²×Dic₅	—	2	1	no	—
209	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
210	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
211	C₅×M₁₆	—	2	2	no	—
212	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
213	C₅×C₄⋊C₄	—	2	1	no	—
214	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
215	C₂²⋊Dic₅	—	2	1	no	—
216	C₂²⋊Dic₅	—	2	1	no	—
217	C₂²⋊Dic₅	—	2	1	no	—
218	C₄⋊Dic₅	—	2	1	no	—
219	C₄⋊Dic₅	—	2	2	no	—
220	C₄⋊Dic₅	—	2	2	no	—
221	C₄⋊Dic₅	—	2	1	no	—
222	C₄⋊Dic₅	—	2	1	no	—
223	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
224	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
225	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
226	#683	—	2	2	no	—
227	#683	—	2	2	no	—
228	C₄×Dic₅	—	2	1	no	—
229	C₄×Dic₅	—	2	1	no	—
230	C₄×Dic₅	—	2	1	no	—
231	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
232	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
233	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
234	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
235	#681	—	2	2	no	—
236	C₂×#168	C₂³×C₃	1	2	yes	—
237	C₂×#125	—	5	1	no	—
238	C₄×#41	—	5	1	no	—
239	#479	—	5	2	no	—
240	#479	—	5	2	no	—
241	#478	—	5	2	no	—
242	#478	—	5	2	no	—
243	#428	—	5	1	no	—
244	#428	—	5	1	no	—
245	#423	—	5	1	no	—
246	#417	—	5	1	no	—
247	#417	C₃×D₅	1	1	yes	characteristic
248	C₂²×C₃×C₅	—	2	1	no	—
249	C₂²×C₃×C₅	—	2	1	no	—
250	C₂²×C₃×C₅	—	2	2	no	—
251	C₂²×C₃×C₅	—	4	1	no	—
252	C₂²×C₃×C₅	—	4	1	no	—
253	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
254	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
255	C₃×C₄×C₅	—	2	2	no	—
256	C₃×C₄×C₅	—	4	2	no	—
257	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
258	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
259	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
260	C₃×Dic₅	—	2	1	no	—
261	C₃×Dic₅	—	2	1	no	—
262	C₃×Dic₅	—	2	1	no	—
263	C₃×Dic₅	—	2	1	no	—
264	C₃×Dic₅	—	4	1	no	—
265	C₃×Dic₅	—	4	1	no	—
266	C₃×Dic₅	—	4	2	no	—
267	C₃×#41	—	2	2	no	—
268	C₃×#41	Dic₁₀	1	4	yes	—
269	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
270	C₂×C₃×D₄	—	2	1	no	—
271	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
272	C₂²×C₃×C₄	—	2	1	no	—
273	C₂²×C₃×C₄	—	2	1	no	—
274	C₂²×C₃×C₄	—	5	1	no	—
275	C₂²×C₃×C₄	—	5	1	no	—
276	C₂²×C₃×C₄	—	10	1	no	—
277	C₂²×C₃×C₄	—	10	1	no	—
278	C₂²×C₃×C₄	—	10	1	no	—
279	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
280	C₃×M₁₆	—	2	2	no	—
281	C₃×M₁₆	—	10	2	no	—
282	C₂×C₃×C₈	—	5	2	no	—
283	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
284	C₃×C₄⋊C₄	—	2	1	no	—
285	C₃×C₄⋊C₄	—	5	2	no	—
286	C₃×C₄⋊C₄	—	5	1	no	—
287	C₃×C₄⋊C₄	—	5	1	no	—
288	C₃×C₄⋊C₄	—	10	2	no	—
289	C₃×C₄⋊C₄	—	10	2	no	—
290	C₃×C₄⋊C₄	—	10	2	no	—
291	C₃×C₄⋊C₄	—	10	2	no	—
292	C₃×C₄⋊C₄	—	10	1	no	—
293	C₃×C₄⋊C₄	—	10	1	no	—
294	C₃×C₄⋊C₄	—	10	1	no	—
295	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
296	C₃×C₂²⋊C₄	—	10	1	no	—
297	C₃×C₂²⋊C₄	—	10	1	no	—
298	C₃×C₂²⋊C₄	—	10	1	no	—
299	C₃×C₄²	—	5	1	no	—
300	C₃×C₄²	—	5	1	no	—
301	C₃×C₄²	—	5	1	no	—
302	C₃×C₄²	—	5	1	no	—
303	C₃×C₄²	—	10	1	no	—
304	C₃×C₄²	—	10	1	no	—
305	C₃×C₄²	—	10	1	no	—
306	C₂³×C₅	—	2	1	no	—
307	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
308	C₅×Q₈	—	2	1	no	—
309	C₅×Q₈	C₂×C₃×Q₈	1	2	yes	—
310	C₅×D₄	—	2	4	no	—
311	C₅×D₄	—	2	1	no	—
312	C₅×D₄	C₂×C₃×Q₈	1	2	yes	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	4	no	—
315	C₂×C₄×C₅	—	2	2	no	—
316	C₂×C₄×C₅	—	4	2	no	—
317	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
318	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
319	C₂×C₄×C₅	C₃×#41	1	2	yes	—
320	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
321	C₂×Dic₅	—	2	1	no	—
322	C₂×Dic₅	—	2	1	no	—
323	C₂×Dic₅	—	2	2	no	—
324	C₂×Dic₅	—	4	1	no	—
325	C₂×Dic₅	—	4	1	no	—
326	C₂×Dic₅	—	4	2	no	—
327	C₂×Dic₅	—	4	2	no	—
328	C₂×Dic₅	—	4	2	no	—
329	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
330	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
331	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
332	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
333	C₅×C₈	—	2	2	no	—
334	#168	—	2	2	no	—
335	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
336	C₂×M₁₆	—	5	1	no	—
337	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
338	#125	—	5	2	no	—
339	#125	—	5	2	no	—
340	#125	—	10	1	no	—
341	#125	—	10	1	no	—
342	C₄×Q₈	—	5	1	no	—
343	C₄×Q₈	—	5	1	no	—
344	C₄×D₄	—	5	1	no	—
345	C₄×D₄	—	5	1	no	—
346	C₄×D₄	—	10	1	no	—
347	C₄×D₄	—	10	1	no	—
348	#117	—	5	1	no	—
349	#117	—	10	1	no	—
350	C₂×C₄⋊C₄	—	5	1	no	—
351	C₂×C₄⋊C₄	—	10	1	no	—
352	C₂×C₄⋊C₄	—	10	1	no	—
353	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
354	C₂×C₄²	—	5	1	no	—
355	C₂×C₄²	—	10	1	no	—
356	#107	—	5	2	no	—
357	#107	—	5	2	no	—
358	#106	—	5	2	no	—
359	#106	—	5	2	no	—
360	C₄⋊C₈	—	5	2	no	—
361	C₄⋊C₈	—	5	2	no	—
362	#103	—	5	2	no	—
363	#103	C₂×C₃×D₅	1	2	yes	—
364	#102	—	5	2	no	—
365	#102	C₂×C₃×D₅	1	2	yes	—
366	C₂×C₃×C₅	—	2	2	no	—
367	C₂×C₃×C₅	—	4	2	no	—
368	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
369	C₂×C₃×C₅	#575	1	1	yes	characteristic
370	C₂×C₃×C₅	#575	1	1	yes	characteristic
371	C₂³×C₃	—	2	1	no	—
372	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
373	C₃×Q₈	—	2	1	no	—
374	C₃×Q₈	C₂×Dic₁₀	1	2	yes	—
375	C₃×D₄	—	2	4	no	—
376	C₃×D₄	—	2	1	no	—
377	C₃×D₄	C₂×Dic₁₀	1	2	yes	—
378	C₂×C₃×C₄	—	2	1	no	—
379	C₂×C₃×C₄	—	2	4	no	—
380	C₂×C₃×C₄	—	2	2	no	—
381	C₂×C₃×C₄	—	4	2	no	—
382	C₂×C₃×C₄	—	5	1	no	—
383	C₂×C₃×C₄	—	5	1	no	—
384	C₂×C₃×C₄	—	5	1	no	—
385	C₂×C₃×C₄	—	5	1	no	—
386	C₂×C₃×C₄	—	10	1	no	—
387	C₂×C₃×C₄	—	10	1	no	—
388	C₂×C₃×C₄	—	10	2	no	—
389	C₂×C₃×C₄	—	20	1	no	—
390	C₂×C₃×C₄	—	20	1	no	—
391	C₂×C₃×C₄	—	20	2	no	—
392	C₂×C₃×C₄	—	20	2	no	—
393	C₂×C₃×C₄	—	20	2	no	—
394	C₂×C₃×C₄	C₂×Dic₁₀	1	2	yes	—
395	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
396	C₂×C₃×C₄	#711	1	2	yes	—
397	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
398	C₃×C₈	—	2	2	no	—
399	C₃×C₈	—	10	2	no	—
400	C₂²×C₅	—	2	1	no	—
401	C₂²×C₅	—	2	1	no	—
402	C₂²×C₅	—	2	2	no	—
403	C₂²×C₅	—	4	1	no	—
404	C₂²×C₅	—	4	1	no	—
405	C₂²×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
406	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
407	C₄×C₅	—	2	2	no	—
408	C₄×C₅	—	4	2	no	—
409	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
410	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
411	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
412	Dic₅	—	2	1	no	—
413	Dic₅	—	2	1	no	—
414	Dic₅	—	2	1	no	—
415	Dic₅	—	2	1	no	—
416	Dic₅	—	4	1	no	—
417	Dic₅	—	4	1	no	—
418	Dic₅	—	4	2	no	—
419	#41	—	2	2	no	—
420	#41	C₃×Dic₁₀	1	4	yes	—
421	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	5	1	no	—
427	C₂²×C₄	—	5	1	no	—
428	C₂²×C₄	—	10	1	no	—
429	C₂²×C₄	—	10	1	no	—
430	C₂²×C₄	—	10	1	no	—
431	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
432	M₁₆	—	2	2	no	—
433	M₁₆	—	10	2	no	—
434	C₂×C₈	—	5	2	no	—
435	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	5	2	no	—
438	C₄⋊C₄	—	5	1	no	—
439	C₄⋊C₄	—	5	1	no	—
440	C₄⋊C₄	—	10	2	no	—
441	C₄⋊C₄	—	10	2	no	—
442	C₄⋊C₄	—	10	2	no	—
443	C₄⋊C₄	—	10	2	no	—
444	C₄⋊C₄	—	10	1	no	—
445	C₄⋊C₄	—	10	1	no	—
446	C₄⋊C₄	—	10	1	no	—
447	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
448	C₂²⋊C₄	—	10	1	no	—
449	C₂²⋊C₄	—	10	1	no	—
450	C₂²⋊C₄	—	10	1	no	—
451	C₄²	—	5	1	no	—
452	C₄²	—	5	1	no	—
453	C₄²	—	5	1	no	—
454	C₄²	—	5	1	no	—
455	C₄²	—	10	1	no	—
456	C₄²	—	10	1	no	—
457	C₄²	—	10	1	no	—
458	C₃×C₅	#3080	1	1	yes	characteristic, complemented, Hall
459	C₂²×C₃	—	2	1	no	—
460	C₂²×C₃	—	2	1	no	—
461	C₂²×C₃	—	2	2	no	—
462	C₂²×C₃	—	4	1	no	—
463	C₂²×C₃	—	4	1	no	—
464	C₂²×C₃	#4024	1	2	yes	—
465	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
466	C₃×C₄	—	2	2	no	—
467	C₃×C₄	—	4	2	no	—
468	C₃×C₄	—	10	1	no	—
469	C₃×C₄	—	10	1	no	—
470	C₃×C₄	—	10	1	no	—
471	C₃×C₄	—	10	1	no	—
472	C₃×C₄	—	20	1	no	—
473	C₃×C₄	—	20	1	no	—
474	C₃×C₄	—	20	2	no	—
475	C₃×C₄	#4024	1	2	yes	—
476	C₃×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
477	C₃×C₄	C₂×#711	1	1	yes	characteristic
478	C₂×C₅	—	2	2	no	—
479	C₂×C₅	—	4	2	no	—
480	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
481	C₂×C₅	C₃×#575	1	1	yes	characteristic
482	C₂×C₅	C₃×#575	1	1	yes	characteristic
483	C₂³	—	2	1	no	—
484	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
485	Q₈	—	2	1	no	—
486	Q₈	C₂×C₃×Dic₁₀	1	2	yes	—
487	D₄	—	2	4	no	—
488	D₄	—	2	1	no	—
489	D₄	C₂×C₃×Dic₁₀	1	2	yes	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	5	1	no	—
495	C₂×C₄	—	5	1	no	—
496	C₂×C₄	—	5	1	no	—
497	C₂×C₄	—	5	1	no	—
498	C₂×C₄	—	10	1	no	—
499	C₂×C₄	—	10	1	no	—
500	C₂×C₄	—	10	2	no	—
501	C₂×C₄	—	20	1	no	—
502	C₂×C₄	—	20	1	no	—
503	C₂×C₄	—	20	2	no	—
504	C₂×C₄	—	20	2	no	—
505	C₂×C₄	—	20	2	no	—
506	C₂×C₄	C₂×C₃×Dic₁₀	1	2	yes	—
507	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
508	C₂×C₄	C₃×#711	1	2	yes	—
509	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
510	C₈	—	2	2	no	—
511	C₈	—	10	2	no	—
512	C₂×C₃	—	2	2	no	—
513	C₂×C₃	—	4	2	no	—
514	C₂×C₃	C₂×#4024	1	1	yes	characteristic
515	C₂×C₃	#66107	1	1	yes	characteristic
516	C₂×C₃	#66111	1	1	yes	characteristic
517	C₅	C₃×#3080	1	1	yes	characteristic, complemented, Sylow
518	C₂²	—	2	1	no	—
519	C₂²	—	2	1	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	4	1	no	—
522	C₂²	—	4	1	no	—
523	C₂²	C₃×#4024	1	2	yes	—
524	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
525	C₄	—	2	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	10	1	no	—
528	C₄	—	10	1	no	—
529	C₄	—	10	1	no	—
530	C₄	—	10	1	no	—
531	C₄	—	20	1	no	—
532	C₄	—	20	1	no	—
533	C₄	—	20	2	no	—
534	C₄	C₃×#4024	1	2	yes	—
535	C₄	C₂²×C₃×Dic₁₀	1	1	yes	characteristic
536	C₄	C₂×C₃×#711	1	1	yes	characteristic
537	C₃	#10610602	1	1	yes	characteristic, direct product factor, Sylow
538	C₂	—	2	2	no	—
539	C₂	—	4	2	no	—
540	C₂	C₂×C₃×#4024	1	1	yes	characteristic
541	C₂	C₃×#66107	1	1	yes	characteristic
542	C₂	C₃×#66111	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	C₃×C₅×#417	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×C₅×#41	C₂²
hypercenter	C₃×#417	D₅
hypocenter	C₅	C₃×#3080
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#417

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4036	C₂	semidirect
5. C₃×#65410	C₂	semidirect
6. C₃×#65407	C₂	semidirect
7. C₃×#65253	C₂	semidirect
8. C₃×#65088	C₂	semidirect
9. C₃×#65085	C₂	semidirect
10. C₃×#65055	C₂	semidirect
11. C₃×#65052	C₂	semidirect
12. #10610602	C₃	direct (N × H)
46. C₂×#4036	C₂×C₃	semidirect
49. #65410	C₂×C₃	semidirect
50. #65407	C₂×C₃	semidirect
51. #65253	C₂×C₃	semidirect
52. #65088	C₂×C₃	semidirect
53. #65085	C₂×C₃	semidirect
54. #65055	C₂×C₃	semidirect
55. #65052	C₂×C₃	semidirect
458. C₃×C₅	#3080	semidirect
517. C₅	C₃×#3080	semidirect
537. C₃	#10610602	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×#41×Dic₅	2
C₂×C₃×#4036	2
C₃×C₅×#417	2
C₃×#65521	2
C₃×#65410	2
C₃×#65407	2
C₃×#65253	2
C₃×#65088	2
C₃×#65085	2
C₃×#65055	2
C₃×#65052	2
#10610602	3
C₃×#3080	5

Subgroups — C3×#10610602 #14430682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610602 #14430682