Subgroups — C₃×#10610688 #14412714

Order 1920.

1452 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4147	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4053	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#419	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3967	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65422	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65291	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65093	C₂	1	2	yes	maximal, complemented
9	C₃×#65092	C₂	1	2	yes	maximal, complemented
10	C₃×#65091	C₂	1	2	yes	maximal, complemented
11	C₃×D₅×#103	C₂	1	2	yes	maximal, complemented
12	#10610688	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₃×#4147	—	2	4	no	—
15	C₃×#4147	C₄	1	8	yes	complemented
16	C₂×C₃×#713	—	2	1	no	—
17	C₂×C₃×#713	C₂²	1	2	yes	—
18	C₂×C₃×Q₈×D₅	—	2	1	no	—
19	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
20	C₂×C₃×#709	—	2	2	no	—
21	C₂×C₃×#709	C₂²	1	1	yes	characteristic
22	C₂×C₃×#709	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
24	C₃×C₅×#117	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
26	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
27	C₃×#4053	—	2	4	no	—
28	C₂×C₃×#676	C₂²	1	2	yes	—
29	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
30	C₃×#4038	C₂²	1	2	yes	—
31	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
32	C₃×#4027	—	2	2	no	—
33	C₃×C₄×D₂₀	—	2	1	no	—
34	C₃×C₄×Dic₁₀	—	2	1	no	—
35	C₃×C₅×#103	C₂²	1	2	yes	—
36	C₃×C₅×#103	C₂²	1	2	yes	—
37	C₃×#3967	C₂²	1	2	yes	—
38	C₃×#3967	C₂²	1	2	yes	—
39	C₃×#3953	C₂²	1	2	yes	—
40	C₃×#3948	C₂²	1	2	yes	—
41	C₃×#3942	C₂²	1	1	yes	characteristic
42	C₃×#3942	C₂²	1	1	yes	characteristic
43	C₃×#3941	C₂²	1	1	yes	characteristic
44	C₃×#3941	C₂²	1	1	yes	characteristic
45	C₃×#2898	—	5	1	no	maximal, Hall
46	C₂×#4147	C₂×C₃	1	1	yes	characteristic
47	C₂×#4053	C₂×C₃	1	1	yes	characteristic, complemented
48	#65857	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#419	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂×#3967	C₂×C₃	1	1	yes	characteristic, complemented
51	#65422	C₂×C₃	1	1	yes	characteristic, complemented
52	#65291	C₂×C₃	1	1	yes	characteristic, complemented
53	#65093	C₂×C₃	1	2	yes	complemented
54	#65092	C₂×C₃	1	2	yes	complemented
55	#65091	C₂×C₃	1	2	yes	complemented
56	D₅×#103	C₂×C₃	1	2	yes	complemented
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	C₂²×C₃×C₄×C₅	—	2	1	no	—
62	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
64	C₂×C₃×C₂²⋊D₅	D₄	1	2	yes	—
65	C₂²×C₃×Dic₅	—	2	1	no	—
66	C₃×#713	—	2	8	no	—
67	C₃×#713	—	2	4	no	—
68	C₃×#713	C₂×C₄	1	8	yes	complemented
69	C₃×Q₈×D₅	—	2	4	no	—
70	C₃×Q₈×D₅	—	2	8	no	—
71	C₃×Q₈×D₅	C₂×C₄	1	8	yes	complemented
72	C₃×#709	—	2	2	no	—
73	C₃×#709	—	2	16	no	—
74	C₃×#709	C₂×C₄	1	4	yes	—
75	C₃×#709	C₂×C₄	1	4	yes	complemented
76	C₃×#709	D₄	1	4	yes	—
77	C₂×C₃×D₂₀	—	2	2	no	—
78	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
79	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₄×D₅	—	2	2	no	—
81	C₂×C₃×C₄×D₅	—	2	1	no	—
82	C₂×C₃×C₄×D₅	—	2	2	no	—
83	C₂×C₃×C₄×D₅	—	2	2	no	—
84	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
85	C₂×C₃×Dic₁₀	—	2	2	no	—
86	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic
87	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
88	C₃×C₅×M₁₆	—	2	2	no	—
89	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
90	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
93	C₃×C₄²×C₅	—	2	1	no	—
94	C₃×#685	—	2	2	no	—
95	C₃×C₄⋊Dic₅	—	2	1	no	—
96	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
97	C₃×#683	—	2	2	no	—
98	C₃×C₄×Dic₅	—	2	2	no	—
99	C₂×C₃×#168	—	2	2	no	—
100	C₂×C₃×#168	C₂³	1	1	yes	characteristic
101	C₂×C₃×#168	C₂³	1	1	yes	characteristic
102	C₃×#676	—	2	4	no	—
103	C₃×C₈×D₅	—	2	4	no	—
104	C₂×C₃×2₋¹⁺⁴	—	5	1	no	—
105	C₂×C₃×#131	—	5	1	no	—
106	C₃×#520	—	5	1	no	—
107	C₃×#419	—	5	2	no	—
108	C₃×#419	D₅	1	1	yes	characteristic, complemented
109	C₃×#417	—	5	1	no	—
110	C₃×#417	—	5	2	no	—
111	C₃×#416	—	5	1	no	—
112	C₃×#416	—	5	2	no	—
113	C₂×C₃×#103	—	5	1	no	—
114	C₂×C₃×#103	—	5	2	no	—
115	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
116	#4147	—	2	4	no	—
117	#4147	C₃×C₄	1	8	yes	complemented
118	C₂×#713	—	2	1	no	—
119	C₂×#713	C₂²×C₃	1	2	yes	—
120	C₂×Q₈×D₅	—	2	1	no	—
121	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
122	C₂×#709	—	2	2	no	—
123	C₂×#709	C₂²×C₃	1	1	yes	characteristic
124	C₂×#709	C₂²×C₃	1	1	yes	characteristic
125	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
126	C₅×#117	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
128	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
129	#4053	—	2	4	no	—
130	C₂×#676	C₂²×C₃	1	2	yes	—
131	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
132	#4038	C₂²×C₃	1	2	yes	—
133	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
134	#4027	—	2	2	no	—
135	C₄×D₂₀	—	2	1	no	—
136	C₄×Dic₁₀	—	2	1	no	—
137	C₅×#103	C₂²×C₃	1	2	yes	—
138	C₅×#103	C₂²×C₃	1	2	yes	—
139	#3967	C₂²×C₃	1	2	yes	—
140	#3967	C₂²×C₃	1	2	yes	—
141	#3953	C₂²×C₃	1	2	yes	—
142	#3948	C₂²×C₃	1	2	yes	—
143	#3942	C₂²×C₃	1	1	yes	characteristic
144	#3942	C₂²×C₃	1	1	yes	characteristic
145	#3941	C₂²×C₃	1	1	yes	characteristic
146	#3941	C₂²×C₃	1	1	yes	characteristic
147	#2898	—	5	1	no	Sylow
148	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₃×D₅	—	2	1	no	—
150	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
151	C₃×C₅×Q₈	—	2	4	no	—
152	C₃×C₅×Q₈	—	2	2	no	—
153	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
154	C₂×C₃×C₄×C₅	—	2	4	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	2	1	no	—
157	C₂×C₃×C₄×C₅	—	2	1	no	—
158	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
159	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
161	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
162	C₃×C₂²⋊D₅	—	2	4	no	—
163	C₃×C₂²⋊D₅	C₂²⋊C₄	1	8	yes	—
164	C₂×C₃×Dic₅	—	2	1	no	—
165	C₂×C₃×Dic₅	—	2	2	no	—
166	C₂×C₃×Dic₅	—	8	1	no	—
167	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
168	C₃×D₂₀	—	2	8	no	—
169	C₃×D₂₀	—	2	1	no	—
170	C₃×D₂₀	C₂²⋊C₄	1	4	yes	—
171	C₃×D₂₀	C₂²×C₄	1	2	yes	—
172	C₃×C₄×D₅	—	2	8	no	—
173	C₃×C₄×D₅	—	2	4	no	—
174	C₃×C₄×D₅	—	2	8	no	—
175	C₃×C₄×D₅	—	8	2	no	—
176	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
177	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
178	C₃×Dic₁₀	—	2	1	no	—
179	C₃×Dic₁₀	—	2	8	no	—
180	C₃×Dic₁₀	C₂²⋊C₄	1	4	yes	—
181	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
182	C₃×C₅×C₈	—	2	2	no	—
183	C₃×#168	—	2	1	no	—
184	C₃×#168	—	2	1	no	—
185	C₃×2₋¹⁺⁴	—	5	8	no	—
186	C₃×2₋¹⁺⁴	—	10	4	no	—
187	C₂×C₃×#41	—	5	1	no	—
188	C₂×C₃×#41	—	5	2	no	—
189	C₂×C₃×#41	—	5	1	no	—
190	C₂×C₃×#41	—	10	2	no	—
191	C₂×C₃×#41	—	10	1	no	—
192	C₂²×C₃×Q₈	—	5	2	no	—
193	C₂²×C₃×Q₈	—	10	1	no	—
194	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
195	C₃×#131	—	10	4	no	—
196	C₂×C₃×M₁₆	—	5	2	no	—
197	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
198	C₂²×C₃×C₈	—	5	1	no	—
199	C₂²×C₃×C₈	—	5	2	no	—
200	C₃×C₄×Q₈	—	10	1	no	—
201	C₃×C₄×D₄	—	10	1	no	—
202	C₃×C₄×D₄	—	10	2	no	—
203	C₃×#117	—	5	2	no	—
204	C₃×#117	C₂×D₅	1	1	yes	characteristic
205	C₂×C₃×C₄⋊C₄	—	5	1	no	—
206	C₂×C₃×C₄⋊C₄	—	5	2	no	—
207	C₃×#103	—	5	2	no	—
208	C₃×#103	—	5	2	no	—
209	C₃×#103	—	5	2	no	—
210	C₃×#103	—	5	1	no	—
211	C₃×#103	—	5	1	no	—
212	C₃×#103	C₂×D₅	1	2	yes	—
213	C₃×#103	C₂×D₅	1	2	yes	—
214	C₃×#102	—	5	2	no	—
215	C₃×#102	—	5	1	no	—
216	C₃×#102	—	5	1	no	—
217	C₂×C₅×Q₈	—	2	1	no	—
218	C₂×C₅×Q₈	—	2	2	no	—
219	C₂×C₅×Q₈	C₂×C₃×C₄	1	4	yes	complemented
220	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
221	C₂²×C₄×C₅	—	2	1	no	—
222	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
223	C₂×C₂²⋊D₅	—	2	1	no	—
224	C₂×C₂²⋊D₅	C₃×D₄	1	2	yes	—
225	C₂²×Dic₅	—	2	1	no	—
226	#713	—	2	8	no	—
227	#713	—	2	4	no	—
228	#713	C₂×C₃×C₄	1	8	yes	complemented
229	Q₈×D₅	—	2	4	no	—
230	Q₈×D₅	—	2	8	no	—
231	Q₈×D₅	C₂×C₃×C₄	1	8	yes	complemented
232	#709	—	2	2	no	—
233	#709	—	2	16	no	—
234	#709	C₂×C₃×C₄	1	4	yes	—
235	#709	C₂×C₃×C₄	1	4	yes	complemented
236	#709	C₃×D₄	1	4	yes	—
237	C₂×D₂₀	—	2	2	no	—
238	C₂×D₂₀	C₃×D₄	1	1	yes	characteristic
239	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
240	C₂×C₄×D₅	—	2	2	no	—
241	C₂×C₄×D₅	—	2	1	no	—
242	C₂×C₄×D₅	—	2	2	no	—
243	C₂×C₄×D₅	—	2	2	no	—
244	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
245	C₂×Dic₁₀	—	2	2	no	—
246	C₂×Dic₁₀	C₃×D₄	1	1	yes	characteristic
247	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
248	C₅×M₁₆	—	2	2	no	—
249	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
250	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
251	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
252	C₅×C₂²⋊C₄	—	2	1	no	—
253	C₄²×C₅	—	2	1	no	—
254	#685	—	2	2	no	—
255	C₄⋊Dic₅	—	2	1	no	—
256	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
257	#683	—	2	2	no	—
258	C₄×Dic₅	—	2	2	no	—
259	C₂×#168	—	2	2	no	—
260	C₂×#168	C₂³×C₃	1	1	yes	characteristic
261	C₂×#168	C₂³×C₃	1	1	yes	characteristic
262	#676	—	2	4	no	—
263	C₈×D₅	—	2	4	no	—
264	C₂×2₋¹⁺⁴	—	5	1	no	—
265	C₂×#131	—	5	1	no	—
266	#520	—	5	1	no	—
267	#419	—	5	2	no	—
268	#419	C₃×D₅	1	1	yes	characteristic, complemented
269	#417	—	5	1	no	—
270	#417	—	5	2	no	—
271	#416	—	5	1	no	—
272	#416	—	5	2	no	—
273	C₂×#103	—	5	1	no	—
274	C₂×#103	—	5	2	no	—
275	C₂²×C₃×C₅	—	2	1	no	—
276	C₂²×C₃×C₅	—	2	1	no	—
277	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
278	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₃×D₅	—	2	2	no	—
280	C₂×C₃×D₅	—	2	2	no	—
281	C₂×C₃×D₅	—	2	2	no	—
282	C₂×C₃×D₅	—	4	1	no	—
283	C₂×C₃×D₅	—	4	1	no	—
284	C₂×C₃×D₅	C₂×C₂²⋊C₄	1	4	yes	—
285	C₃×C₄×C₅	—	2	4	no	—
286	C₃×C₄×C₅	—	4	1	no	—
287	C₃×C₄×C₅	—	4	1	no	—
288	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
289	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
290	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
291	C₃×Dic₅	—	2	2	no	—
292	C₃×Dic₅	—	4	2	no	—
293	C₃×Dic₅	C₂×C₂²⋊C₄	1	4	yes	—
294	C₃×#41	—	5	4	no	—
295	C₃×#41	—	5	4	no	—
296	C₃×#41	—	5	8	no	—
297	C₃×#41	—	5	4	no	—
298	C₃×#41	—	10	16	no	—
299	C₃×#41	—	10	4	no	—
300	C₃×#41	—	10	8	no	—
301	C₃×#41	—	10	2	no	—
302	C₂×C₃×Q₈	—	2	1	no	—
303	C₂×C₃×Q₈	—	2	2	no	—
304	C₂×C₃×Q₈	—	5	1	no	—
305	C₂×C₃×Q₈	—	5	8	no	—
306	C₂×C₃×Q₈	—	5	1	no	—
307	C₂×C₃×Q₈	—	10	2	no	—
308	C₂×C₃×Q₈	—	10	4	no	—
309	C₂×C₃×Q₈	—	10	8	no	—
310	C₂×C₃×Q₈	C₄×D₅	1	4	yes	complemented
311	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
312	C₂×C₃×D₄	—	5	2	no	—
313	C₂×C₃×D₄	—	5	1	no	—
314	C₂×C₃×D₄	—	5	1	no	—
315	C₂×C₃×D₄	—	10	2	no	—
316	C₂×C₃×D₄	—	10	1	no	—
317	C₂²×C₃×C₄	—	2	1	no	—
318	C₂²×C₃×C₄	—	5	2	no	—
319	C₂²×C₃×C₄	—	10	2	no	—
320	C₂²×C₃×C₄	—	10	2	no	—
321	C₂²×C₃×C₄	—	10	2	no	—
322	C₂²×C₃×C₄	—	10	1	no	—
323	C₂²×C₃×C₄	—	10	1	no	—
324	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
325	C₃×M₁₆	—	2	2	no	—
326	C₃×M₁₆	—	10	4	no	—
327	C₂×C₃×C₈	—	5	1	no	—
328	C₂×C₃×C₈	—	5	1	no	—
329	C₂×C₃×C₈	—	10	4	no	—
330	C₂×C₃×C₈	—	10	2	no	—
331	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
332	C₃×C₄⋊C₄	—	5	2	no	—
333	C₃×C₄⋊C₄	—	10	2	no	—
334	C₃×C₄⋊C₄	—	10	1	no	—
335	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
336	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
337	C₃×C₂²⋊C₄	—	2	1	no	—
338	C₃×C₂²⋊C₄	—	10	2	no	—
339	C₃×C₄²	—	2	1	no	—
340	C₃×C₄²	—	10	2	no	—
341	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
342	C₂²×D₅	—	2	1	no	—
343	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
344	C₅×Q₈	—	2	4	no	—
345	C₅×Q₈	—	2	2	no	—
346	C₅×Q₈	C₂²×C₃×C₄	1	4	yes	—
347	C₂×C₄×C₅	—	2	4	no	—
348	C₂×C₄×C₅	—	2	2	no	—
349	C₂×C₄×C₅	—	2	1	no	—
350	C₂×C₄×C₅	—	2	1	no	—
351	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
352	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
353	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
354	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
355	C₂²⋊D₅	—	2	4	no	—
356	C₂²⋊D₅	C₃×C₂²⋊C₄	1	8	yes	—
357	C₂×Dic₅	—	2	1	no	—
358	C₂×Dic₅	—	2	2	no	—
359	C₂×Dic₅	—	8	1	no	—
360	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
361	D₂₀	—	2	8	no	—
362	D₂₀	—	2	1	no	—
363	D₂₀	C₃×C₂²⋊C₄	1	4	yes	—
364	D₂₀	C₂²×C₃×C₄	1	2	yes	—
365	C₄×D₅	—	2	8	no	—
366	C₄×D₅	—	2	4	no	—
367	C₄×D₅	—	2	8	no	—
368	C₄×D₅	—	8	2	no	—
369	C₄×D₅	C₂²×C₃×C₄	1	4	yes	—
370	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
371	Dic₁₀	—	2	1	no	—
372	Dic₁₀	—	2	8	no	—
373	Dic₁₀	C₃×C₂²⋊C₄	1	4	yes	—
374	Dic₁₀	C₂²×C₃×C₄	1	2	yes	—
375	C₅×C₈	—	2	2	no	—
376	#168	—	2	1	no	—
377	#168	—	2	1	no	—
378	2₋¹⁺⁴	—	5	8	no	—
379	2₋¹⁺⁴	—	10	4	no	—
380	C₂×#41	—	5	1	no	—
381	C₂×#41	—	5	2	no	—
382	C₂×#41	—	5	1	no	—
383	C₂×#41	—	10	2	no	—
384	C₂×#41	—	10	1	no	—
385	C₂²×Q₈	—	5	2	no	—
386	C₂²×Q₈	—	10	1	no	—
387	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
388	#131	—	10	4	no	—
389	C₂×M₁₆	—	5	2	no	—
390	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
391	C₂²×C₈	—	5	1	no	—
392	C₂²×C₈	—	5	2	no	—
393	C₄×Q₈	—	10	1	no	—
394	C₄×D₄	—	10	1	no	—
395	C₄×D₄	—	10	2	no	—
396	#117	—	5	2	no	—
397	#117	C₂×C₃×D₅	1	1	yes	characteristic
398	C₂×C₄⋊C₄	—	5	1	no	—
399	C₂×C₄⋊C₄	—	5	2	no	—
400	#103	—	5	2	no	—
401	#103	—	5	2	no	—
402	#103	—	5	2	no	—
403	#103	—	5	1	no	—
404	#103	—	5	1	no	—
405	#103	C₂×C₃×D₅	1	2	yes	—
406	#103	C₂×C₃×D₅	1	2	yes	—
407	#102	—	5	2	no	—
408	#102	—	5	1	no	—
409	#102	—	5	1	no	—
410	C₂×C₃×C₅	—	2	2	no	—
411	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
412	C₂×C₃×C₅	#577	1	1	yes	characteristic
413	C₂×C₃×C₅	#578	1	1	yes	characteristic
414	C₃×D₅	—	2	4	no	—
415	C₃×D₅	—	4	2	no	—
416	C₂³×C₃	—	5	2	no	—
417	C₂³×C₃	—	10	1	no	—
418	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
419	C₃×Q₈	—	2	2	no	—
420	C₃×Q₈	—	2	4	no	—
421	C₃×Q₈	—	5	4	no	—
422	C₃×Q₈	—	5	2	no	—
423	C₃×Q₈	—	10	8	no	—
424	C₃×Q₈	—	10	1	no	—
425	C₃×Q₈	C₂×C₄×D₅	1	4	yes	—
426	C₃×D₄	—	5	8	no	—
427	C₃×D₄	—	5	2	no	—
428	C₃×D₄	—	5	4	no	—
429	C₃×D₄	—	10	8	no	—
430	C₃×D₄	—	10	4	no	—
431	C₃×D₄	—	10	1	no	—
432	C₂×C₃×C₄	—	2	2	no	—
433	C₂×C₃×C₄	—	2	4	no	—
434	C₂×C₃×C₄	—	2	1	no	—
435	C₂×C₃×C₄	—	2	1	no	—
436	C₂×C₃×C₄	—	5	2	no	—
437	C₂×C₃×C₄	—	5	4	no	—
438	C₂×C₃×C₄	—	5	4	no	—
439	C₂×C₃×C₄	—	10	8	no	—
440	C₂×C₃×C₄	—	10	8	no	—
441	C₂×C₃×C₄	—	10	1	no	—
442	C₂×C₃×C₄	—	10	4	no	—
443	C₂×C₃×C₄	—	10	2	no	—
444	C₂×C₃×C₄	—	40	2	no	—
445	C₂×C₃×C₄	—	40	1	no	—
446	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
447	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
448	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
449	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
450	C₃×C₈	—	2	2	no	—
451	C₃×C₈	—	10	1	no	—
452	C₃×C₈	—	10	1	no	—
453	C₂²×C₅	—	2	1	no	—
454	C₂²×C₅	—	2	1	no	—
455	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
456	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
457	C₂×D₅	—	2	2	no	—
458	C₂×D₅	—	2	2	no	—
459	C₂×D₅	—	2	2	no	—
460	C₂×D₅	—	4	1	no	—
461	C₂×D₅	—	4	1	no	—
462	C₂×D₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
463	C₄×C₅	—	2	4	no	—
464	C₄×C₅	—	4	1	no	—
465	C₄×C₅	—	4	1	no	—
466	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
467	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
468	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
469	Dic₅	—	2	2	no	—
470	Dic₅	—	4	2	no	—
471	Dic₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
472	#41	—	5	4	no	—
473	#41	—	5	4	no	—
474	#41	—	5	8	no	—
475	#41	—	5	4	no	—
476	#41	—	10	16	no	—
477	#41	—	10	4	no	—
478	#41	—	10	8	no	—
479	#41	—	10	2	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	2	no	—
482	C₂×Q₈	—	5	1	no	—
483	C₂×Q₈	—	5	8	no	—
484	C₂×Q₈	—	5	1	no	—
485	C₂×Q₈	—	10	2	no	—
486	C₂×Q₈	—	10	4	no	—
487	C₂×Q₈	—	10	8	no	—
488	C₂×Q₈	C₃×C₄×D₅	1	4	yes	complemented
489	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
490	C₂×D₄	—	5	2	no	—
491	C₂×D₄	—	5	1	no	—
492	C₂×D₄	—	5	1	no	—
493	C₂×D₄	—	10	2	no	—
494	C₂×D₄	—	10	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	5	2	no	—
497	C₂²×C₄	—	10	2	no	—
498	C₂²×C₄	—	10	2	no	—
499	C₂²×C₄	—	10	2	no	—
500	C₂²×C₄	—	10	1	no	—
501	C₂²×C₄	—	10	1	no	—
502	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
503	M₁₆	—	2	2	no	—
504	M₁₆	—	10	4	no	—
505	C₂×C₈	—	5	1	no	—
506	C₂×C₈	—	5	1	no	—
507	C₂×C₈	—	10	4	no	—
508	C₂×C₈	—	10	2	no	—
509	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
510	C₄⋊C₄	—	5	2	no	—
511	C₄⋊C₄	—	10	2	no	—
512	C₄⋊C₄	—	10	1	no	—
513	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
515	C₂²⋊C₄	—	2	1	no	—
516	C₂²⋊C₄	—	10	2	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	10	2	no	—
519	C₃×C₅	#2898	1	1	yes	characteristic, complemented, Hall
520	C₂²×C₃	—	2	1	no	—
521	C₂²×C₃	—	2	1	no	—
522	C₂²×C₃	—	5	4	no	—
523	C₂²×C₃	—	10	2	no	—
524	C₂²×C₃	—	10	2	no	—
525	C₂²×C₃	—	10	2	no	—
526	C₂²×C₃	—	20	1	no	—
527	C₂²×C₃	—	20	1	no	—
528	C₂²×C₃	D₅×C₂²⋊C₄	1	2	yes	—
529	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
530	C₃×C₄	—	2	4	no	—
531	C₃×C₄	—	4	1	no	—
532	C₃×C₄	—	4	1	no	—
533	C₃×C₄	—	5	4	no	—
534	C₃×C₄	—	10	2	no	—
535	C₃×C₄	—	20	2	no	—
536	C₃×C₄	D₅×C₂²⋊C₄	1	2	yes	—
537	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
538	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
539	C₂×C₅	—	2	2	no	—
540	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
541	C₂×C₅	C₃×#577	1	1	yes	characteristic
542	C₂×C₅	C₃×#578	1	1	yes	characteristic
543	D₅	—	2	4	no	—
544	D₅	—	4	2	no	—
545	C₂³	—	5	2	no	—
546	C₂³	—	10	1	no	—
547	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
548	Q₈	—	2	2	no	—
549	Q₈	—	2	4	no	—
550	Q₈	—	5	4	no	—
551	Q₈	—	5	2	no	—
552	Q₈	—	10	8	no	—
553	Q₈	—	10	1	no	—
554	Q₈	C₂×C₃×C₄×D₅	1	4	yes	—
555	D₄	—	5	8	no	—
556	D₄	—	5	2	no	—
557	D₄	—	5	4	no	—
558	D₄	—	10	8	no	—
559	D₄	—	10	4	no	—
560	D₄	—	10	1	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	5	2	no	—
566	C₂×C₄	—	5	4	no	—
567	C₂×C₄	—	5	4	no	—
568	C₂×C₄	—	10	8	no	—
569	C₂×C₄	—	10	8	no	—
570	C₂×C₄	—	10	1	no	—
571	C₂×C₄	—	10	4	no	—
572	C₂×C₄	—	10	2	no	—
573	C₂×C₄	—	40	2	no	—
574	C₂×C₄	—	40	1	no	—
575	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
576	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
577	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
578	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
579	C₈	—	2	2	no	—
580	C₈	—	10	1	no	—
581	C₈	—	10	1	no	—
582	C₂×C₃	—	2	2	no	—
583	C₂×C₃	—	10	4	no	—
584	C₂×C₃	—	20	2	no	—
585	C₂×C₃	C₂×D₅×C₂²⋊C₄	1	1	yes	characteristic
586	C₂×C₃	#66112	1	1	yes	characteristic
587	C₂×C₃	#66113	1	1	yes	characteristic
588	C₅	C₃×#2898	1	1	yes	characteristic, complemented, Sylow
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	5	4	no	—
592	C₂²	—	10	2	no	—
593	C₂²	—	10	2	no	—
594	C₂²	—	10	2	no	—
595	C₂²	—	20	1	no	—
596	C₂²	—	20	1	no	—
597	C₂²	C₃×D₅×C₂²⋊C₄	1	2	yes	—
598	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
599	C₄	—	2	4	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	1	no	—
602	C₄	—	5	4	no	—
603	C₄	—	10	2	no	—
604	C₄	—	20	2	no	—
605	C₄	C₃×D₅×C₂²⋊C₄	1	2	yes	—
606	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
607	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
608	C₃	#10610688	1	1	yes	characteristic, direct product factor, Sylow
609	C₂	—	2	2	no	—
610	C₂	—	10	4	no	—
611	C₂	—	20	2	no	—
612	C₂	C₂×C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
613	C₂	C₃×#66112	1	1	yes	characteristic
614	C₂	C₃×#66113	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	C₃×C₅×#419	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#4147	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#419	D₅
hypocenter	C₅	C₃×#2898
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#419

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4053	C₂	semidirect
3. C₃×#65857	C₂	semidirect
4. C₃×C₅×#419	C₂	semidirect
5. C₂×C₃×#3967	C₂	semidirect
6. C₃×#65422	C₂	semidirect
7. C₃×#65291	C₂	semidirect
8. C₃×#65093	C₂	semidirect
9. C₃×#65092	C₂	semidirect
10. C₃×#65091	C₂	semidirect
11. C₃×D₅×#103	C₂	semidirect
12. #10610688	C₃	direct (N × H)
15. C₃×#4147	C₄	semidirect
47. C₂×#4053	C₂×C₃	semidirect
48. #65857	C₂×C₃	semidirect
49. C₅×#419	C₂×C₃	semidirect
50. C₂×#3967	C₂×C₃	semidirect
51. #65422	C₂×C₃	semidirect
52. #65291	C₂×C₃	semidirect
53. #65093	C₂×C₃	semidirect
54. #65092	C₂×C₃	semidirect
55. #65091	C₂×C₃	semidirect
56. D₅×#103	C₂×C₃	semidirect
59. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
68. C₃×#713	C₂×C₄	semidirect
71. C₃×Q₈×D₅	C₂×C₄	semidirect
75. C₃×#709	C₂×C₄	semidirect
108. C₃×#419	D₅	semidirect
117. #4147	C₃×C₄	semidirect
219. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
228. #713	C₂×C₃×C₄	semidirect
231. Q₈×D₅	C₂×C₃×C₄	semidirect
235. #709	C₂×C₃×C₄	semidirect
268. #419	C₃×D₅	semidirect
310. C₂×C₃×Q₈	C₄×D₅	semidirect
488. C₂×Q₈	C₃×C₄×D₅	semidirect
519. C₃×C₅	#2898	semidirect
588. C₅	C₃×#2898	semidirect
608. C₃	#10610688	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×#4147	2
C₂×C₃×#4053	2
C₃×#65857	2
C₃×C₅×#419	2
C₂×C₃×#3967	2
C₃×#65422	2
C₃×#65291	2
C₃×#65093	2
C₃×#65092	2
C₃×#65091	2
C₃×D₅×#103	2
#10610688	3
C₃×#2898	5

Subgroups — C3×#10610688 #14412714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610688 #14412714