Subgroups — C₃×#10610821 #14430784

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65855	C₂	1	1	yes	maximal, characteristic
2	C₃×#65853	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#424	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65420	C₂	1	1	yes	maximal, characteristic
5	C₃×#65410	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#3953	C₂	1	1	yes	maximal, characteristic
7	C₃×#65395	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65136	C₂	1	2	yes	maximal, complemented
9	C₃×#65136	C₂	1	2	yes	maximal, complemented
10	C₃×#65135	C₂	1	2	yes	maximal, complemented
11	C₃×#65131	C₂	1	2	yes	maximal, complemented
12	#10610821	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×#117	C₂²	1	1	yes	characteristic
17	C₃×#4072	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×#4039	—	2	1	no	—
21	C₃×#4039	—	2	1	no	—
22	C₃×#4036	—	2	1	no	—
23	C₃×#4034	—	2	1	no	—
24	C₃×D₅×C₂²⋊C₄	—	2	2	no	—
25	C₃×#4024	—	2	2	no	—
26	C₃×C₄×D₂₀	C₂²	1	2	yes	—
27	C₃×C₄×D₂₀	C₂²	1	2	yes	—
28	C₃×#4016	C₂²	1	2	yes	complemented
29	C₃×#4015	C₂²	1	2	yes	complemented
30	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
31	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
32	C₃×#3953	C₂²	1	2	yes	—
33	C₃×#3953	C₂²	1	2	yes	—
34	C₃×#3953	C₂²	1	2	yes	—
35	C₃×#3953	C₂²	1	2	yes	—
36	C₃×#3950	C₂²	1	1	yes	characteristic, complemented
37	C₃×#3950	C₂²	1	2	yes	complemented
38	C₃×#3950	C₂²	1	1	yes	characteristic, complemented
39	C₃×#3949	C₂²	1	1	yes	characteristic, complemented
40	C₃×#3949	C₂²	1	2	yes	complemented
41	C₃×#3949	C₂²	1	1	yes	characteristic, complemented
42	C₃×#3081	—	5	1	no	maximal, Hall
43	#65855	C₂×C₃	1	1	yes	characteristic
44	#65853	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#424	C₂×C₃	1	1	yes	characteristic, complemented
46	#65420	C₂×C₃	1	1	yes	characteristic
47	#65410	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂×#3953	C₂×C₃	1	1	yes	characteristic
49	#65395	C₂×C₃	1	1	yes	characteristic, complemented
50	#65136	C₂×C₃	1	2	yes	complemented
51	#65136	C₂×C₃	1	2	yes	complemented
52	#65135	C₂×C₃	1	2	yes	complemented
53	#65131	C₂×C₃	1	2	yes	complemented
54	C₂³×C₃×D₅	—	2	1	no	—
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×C₃×Dic₅	—	2	1	no	—
57	C₂×C₃×D₂₀	—	2	1	no	—
58	C₂×C₃×D₂₀	—	2	2	no	—
59	C₂×C₃×D₂₀	Q₈	1	4	yes	complemented
60	C₂×C₃×D₂₀	C₂³	1	2	yes	—
61	C₂×C₃×C₄×D₅	—	2	2	no	—
62	C₂×C₃×C₄×D₅	—	2	2	no	—
63	C₂×C₃×Dic₁₀	—	2	2	no	—
64	C₃×C₅×M₁₆	—	2	2	no	—
65	C₂×C₃×C₅×C₈	—	2	2	no	—
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
68	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
70	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
71	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
72	C₃×C₄²×C₅	C₂³	1	2	yes	—
73	C₃×C₂²⋊Dic₅	—	2	1	no	—
74	C₃×C₂²⋊Dic₅	—	2	1	no	—
75	C₃×#685	—	2	2	no	—
76	C₃×#685	—	2	2	no	—
77	C₃×C₄⋊Dic₅	—	2	2	no	—
78	C₃×C₄⋊Dic₅	—	2	1	no	—
79	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
80	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
81	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
82	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
83	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
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×#544	—	5	1	no	—
89	C₃×#518	—	5	1	no	—
90	C₃×#478	—	5	2	no	—
91	C₃×#478	—	5	2	no	—
92	C₃×#476	—	5	2	no	—
93	C₃×#474	—	5	2	no	—
94	C₃×#428	—	5	1	no	—
95	C₃×#427	—	5	1	no	—
96	C₃×#424	D₅	1	1	yes	characteristic, complemented
97	C₃×#418	—	5	1	no	—
98	C₂×C₃×#102	—	5	1	no	—
99	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
101	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
102	C₅×#117	C₂²×C₃	1	1	yes	characteristic
103	#4072	C₂²×C₃	1	1	yes	characteristic
104	#4072	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
106	#4039	—	2	1	no	—
107	#4039	—	2	1	no	—
108	#4036	—	2	1	no	—
109	#4034	—	2	1	no	—
110	D₅×C₂²⋊C₄	—	2	2	no	—
111	#4024	—	2	2	no	—
112	C₄×D₂₀	C₂²×C₃	1	2	yes	—
113	C₄×D₂₀	C₂²×C₃	1	2	yes	—
114	#4016	C₂²×C₃	1	2	yes	complemented
115	#4015	C₂²×C₃	1	2	yes	complemented
116	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
117	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
118	#3953	C₂²×C₃	1	2	yes	—
119	#3953	C₂²×C₃	1	2	yes	—
120	#3953	C₂²×C₃	1	2	yes	—
121	#3953	C₂²×C₃	1	2	yes	—
122	#3950	C₂²×C₃	1	1	yes	characteristic, complemented
123	#3950	C₂²×C₃	1	2	yes	complemented
124	#3950	C₂²×C₃	1	1	yes	characteristic, complemented
125	#3949	C₂²×C₃	1	1	yes	characteristic, complemented
126	#3949	C₂²×C₃	1	2	yes	complemented
127	#3949	C₂²×C₃	1	1	yes	characteristic, complemented
128	#3081	—	5	1	no	Sylow
129	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₃×D₅	—	2	2	no	—
131	C₂²×C₃×D₅	—	2	4	no	—
132	C₂²×C₃×D₅	—	8	1	no	—
133	C₂²×C₃×D₅	—	8	1	no	—
134	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
135	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
136	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
138	C₂×C₃×C₄×C₅	#41	1	2	yes	—
139	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₂×C₃×Dic₅	—	2	1	no	—
141	C₂×C₃×Dic₅	—	2	1	no	—
142	C₂×C₃×Dic₅	—	2	1	no	—
143	C₂×C₃×Dic₅	—	2	1	no	—
144	C₂×C₃×Dic₅	—	2	2	no	—
145	C₂×C₃×Dic₅	—	8	1	no	—
146	C₃×D₂₀	—	2	4	no	—
147	C₃×D₂₀	—	2	2	no	—
148	C₃×D₂₀	C₂×Q₈	1	4	yes	—
149	C₃×C₄×D₅	—	8	2	no	—
150	C₃×C₄×D₅	—	8	2	no	—
151	C₃×Dic₁₀	—	8	2	no	—
152	C₃×C₅×C₈	—	2	1	no	—
153	C₃×C₅×C₈	—	2	1	no	—
154	C₃×C₅×C₈	—	2	2	no	—
155	C₂²×C₃×D₄	—	5	1	no	—
156	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
157	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
158	C₃×C₄⋊Q₈	—	5	2	no	—
159	C₃×C₄⋊Q₈	—	10	1	no	—
160	C₃×#125	—	5	2	no	—
161	C₃×#125	—	10	1	no	—
162	C₃×C₂²⋊Q₈	—	10	2	no	—
163	C₃×C₄×D₄	—	5	2	no	—
164	C₃×C₄×D₄	—	5	2	no	—
165	C₃×C₄×D₄	—	10	1	no	—
166	C₃×C₄×D₄	—	10	1	no	—
167	C₃×#117	—	5	1	no	—
168	C₃×#117	—	5	1	no	—
169	C₃×#117	C₂×D₅	1	1	yes	characteristic
170	C₂×C₃×C₄⋊C₄	—	5	1	no	—
171	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
172	C₃×#107	—	5	1	no	—
173	C₃×#107	—	5	1	no	—
174	C₃×#107	—	5	2	no	—
175	C₃×#106	—	5	1	no	—
176	C₃×#106	—	5	1	no	—
177	C₃×#106	—	5	2	no	—
178	C₃×C₄⋊C₈	C₂×D₅	1	2	yes	complemented
179	C₃×C₄⋊C₈	C₂×D₅	1	2	yes	complemented
180	C₃×#102	—	5	2	no	—
181	C₃×#102	—	5	2	no	—
182	C₃×#102	—	5	2	no	—
183	C₃×#102	—	5	2	no	—
184	C₂³×D₅	—	2	1	no	—
185	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
186	C₂²×Dic₅	—	2	1	no	—
187	C₂×D₂₀	—	2	1	no	—
188	C₂×D₂₀	—	2	2	no	—
189	C₂×D₂₀	C₃×Q₈	1	4	yes	complemented
190	C₂×D₂₀	C₂³×C₃	1	2	yes	—
191	C₂×C₄×D₅	—	2	2	no	—
192	C₂×C₄×D₅	—	2	2	no	—
193	C₂×Dic₁₀	—	2	2	no	—
194	C₅×M₁₆	—	2	2	no	—
195	C₂×C₅×C₈	—	2	2	no	—
196	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
197	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
198	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
199	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
200	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
201	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
202	C₄²×C₅	C₂³×C₃	1	2	yes	—
203	C₂²⋊Dic₅	—	2	1	no	—
204	C₂²⋊Dic₅	—	2	1	no	—
205	#685	—	2	2	no	—
206	#685	—	2	2	no	—
207	C₄⋊Dic₅	—	2	2	no	—
208	C₄⋊Dic₅	—	2	1	no	—
209	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
210	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
211	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
212	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
213	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
214	#683	—	2	2	no	—
215	#683	—	2	2	no	—
216	C₄×Dic₅	—	2	1	no	—
217	C₄×Dic₅	—	2	1	no	—
218	#544	—	5	1	no	—
219	#518	—	5	1	no	—
220	#478	—	5	2	no	—
221	#478	—	5	2	no	—
222	#476	—	5	2	no	—
223	#474	—	5	2	no	—
224	#428	—	5	1	no	—
225	#427	—	5	1	no	—
226	#424	C₃×D₅	1	1	yes	characteristic, complemented
227	#418	—	5	1	no	—
228	C₂×#102	—	5	1	no	—
229	C₂²×C₃×C₅	—	2	1	no	—
230	C₂²×C₃×C₅	—	2	1	no	—
231	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
232	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₃×D₅	—	2	4	no	—
234	C₂×C₃×D₅	—	4	2	no	—
235	C₂×C₃×D₅	—	4	2	no	—
236	C₂×C₃×D₅	—	8	4	no	—
237	C₃×C₄×C₅	—	2	2	no	—
238	C₃×C₄×C₅	—	2	2	no	—
239	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
240	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
241	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
242	C₃×Dic₅	—	4	1	no	—
243	C₃×Dic₅	—	4	2	no	—
244	C₃×Dic₅	—	4	1	no	—
245	C₃×Dic₅	—	4	1	no	—
246	C₃×Dic₅	—	4	1	no	—
247	C₂⁴×C₃	—	10	1	no	—
248	C₂×C₃×Q₈	—	10	2	no	—
249	C₂×C₃×D₄	—	5	4	no	—
250	C₂×C₃×D₄	—	5	2	no	—
251	C₂×C₃×D₄	—	10	1	no	—
252	C₂×C₃×D₄	—	10	2	no	—
253	C₂²×C₃×C₄	—	10	1	no	—
254	C₂²×C₃×C₄	—	10	2	no	—
255	C₂²×C₃×C₄	—	10	2	no	—
256	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
257	C₃×M₁₆	—	2	2	no	—
258	C₂×C₃×C₈	—	2	2	no	—
259	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
260	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
261	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
262	C₃×C₄⋊C₄	—	5	2	no	—
263	C₃×C₄⋊C₄	—	5	1	no	—
264	C₃×C₄⋊C₄	—	5	1	no	—
265	C₃×C₄⋊C₄	—	5	1	no	—
266	C₃×C₄⋊C₄	—	5	1	no	—
267	C₃×C₄⋊C₄	—	10	2	no	—
268	C₃×C₄⋊C₄	—	10	2	no	—
269	C₃×C₄⋊C₄	—	10	1	no	—
270	C₃×C₄⋊C₄	—	10	2	no	—
271	C₃×C₄⋊C₄	D₂₀	1	1	yes	characteristic
272	C₃×C₄⋊C₄	D₂₀	1	1	yes	characteristic
273	C₃×C₂²⋊C₄	—	10	1	no	—
274	C₃×C₂²⋊C₄	—	10	1	no	—
275	C₃×C₂²⋊C₄	—	10	2	no	—
276	C₃×C₂²⋊C₄	—	10	2	no	—
277	C₃×C₂²⋊C₄	D₂₀	1	2	yes	—
278	C₃×C₄²	—	10	1	no	—
279	C₃×C₄²	—	10	1	no	—
280	C₃×C₄²	C₂²×D₅	1	2	yes	—
281	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
282	C₂²×D₅	—	2	2	no	—
283	C₂²×D₅	—	2	4	no	—
284	C₂²×D₅	—	8	1	no	—
285	C₂²×D₅	—	8	1	no	—
286	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
287	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
288	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
289	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
290	C₂×C₄×C₅	C₃×#41	1	2	yes	—
291	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
292	C₂×Dic₅	—	2	1	no	—
293	C₂×Dic₅	—	2	1	no	—
294	C₂×Dic₅	—	2	1	no	—
295	C₂×Dic₅	—	2	1	no	—
296	C₂×Dic₅	—	2	2	no	—
297	C₂×Dic₅	—	8	1	no	—
298	D₂₀	—	2	4	no	—
299	D₂₀	—	2	2	no	—
300	D₂₀	C₂×C₃×Q₈	1	4	yes	—
301	C₄×D₅	—	8	2	no	—
302	C₄×D₅	—	8	2	no	—
303	Dic₁₀	—	8	2	no	—
304	C₅×C₈	—	2	1	no	—
305	C₅×C₈	—	2	1	no	—
306	C₅×C₈	—	2	2	no	—
307	C₂²×D₄	—	5	1	no	—
308	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
309	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
310	C₄⋊Q₈	—	5	2	no	—
311	C₄⋊Q₈	—	10	1	no	—
312	#125	—	5	2	no	—
313	#125	—	10	1	no	—
314	C₂²⋊Q₈	—	10	2	no	—
315	C₄×D₄	—	5	2	no	—
316	C₄×D₄	—	5	2	no	—
317	C₄×D₄	—	10	1	no	—
318	C₄×D₄	—	10	1	no	—
319	#117	—	5	1	no	—
320	#117	—	5	1	no	—
321	#117	C₂×C₃×D₅	1	1	yes	characteristic
322	C₂×C₄⋊C₄	—	5	1	no	—
323	C₂×C₂²⋊C₄	—	10	2	no	—
324	#107	—	5	1	no	—
325	#107	—	5	1	no	—
326	#107	—	5	2	no	—
327	#106	—	5	1	no	—
328	#106	—	5	1	no	—
329	#106	—	5	2	no	—
330	C₄⋊C₈	C₂×C₃×D₅	1	2	yes	complemented
331	C₄⋊C₈	C₂×C₃×D₅	1	2	yes	complemented
332	#102	—	5	2	no	—
333	#102	—	5	2	no	—
334	#102	—	5	2	no	—
335	#102	—	5	2	no	—
336	C₂×C₃×C₅	—	2	2	no	—
337	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
338	C₂×C₃×C₅	#576	1	1	yes	characteristic
339	C₂×C₃×C₅	#577	1	1	yes	characteristic
340	C₃×D₅	—	4	4	no	—
341	C₂³×C₃	—	10	2	no	—
342	C₂³×C₃	—	10	4	no	—
343	C₂³×C₃	—	40	1	no	—
344	C₂³×C₃	—	40	1	no	—
345	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
346	C₃×Q₈	—	40	2	no	—
347	C₃×D₄	—	5	4	no	—
348	C₃×D₄	—	10	2	no	—
349	C₃×D₄	—	10	4	no	—
350	C₂×C₃×C₄	—	10	1	no	—
351	C₂×C₃×C₄	—	10	1	no	—
352	C₂×C₃×C₄	—	10	1	no	—
353	C₂×C₃×C₄	—	10	1	no	—
354	C₂×C₃×C₄	—	10	2	no	—
355	C₂×C₃×C₄	—	40	2	no	—
356	C₂×C₃×C₄	—	40	2	no	—
357	C₂×C₃×C₄	—	40	1	no	—
358	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
359	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
360	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
361	C₂×C₃×C₄	#711	1	2	yes	—
362	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
363	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
364	C₃×C₈	—	2	1	no	—
365	C₃×C₈	—	2	1	no	—
366	C₃×C₈	—	2	2	no	—
367	C₂²×C₅	—	2	1	no	—
368	C₂²×C₅	—	2	1	no	—
369	C₂²×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
370	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
371	C₂×D₅	—	2	4	no	—
372	C₂×D₅	—	4	2	no	—
373	C₂×D₅	—	4	2	no	—
374	C₂×D₅	—	8	4	no	—
375	C₄×C₅	—	2	2	no	—
376	C₄×C₅	—	2	2	no	—
377	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
378	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
379	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
380	Dic₅	—	4	1	no	—
381	Dic₅	—	4	2	no	—
382	Dic₅	—	4	1	no	—
383	Dic₅	—	4	1	no	—
384	Dic₅	—	4	1	no	—
385	C₂⁴	—	10	1	no	—
386	C₂×Q₈	—	10	2	no	—
387	C₂×D₄	—	5	4	no	—
388	C₂×D₄	—	5	2	no	—
389	C₂×D₄	—	10	1	no	—
390	C₂×D₄	—	10	2	no	—
391	C₂²×C₄	—	10	1	no	—
392	C₂²×C₄	—	10	2	no	—
393	C₂²×C₄	—	10	2	no	—
394	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
395	M₁₆	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
398	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
399	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
400	C₄⋊C₄	—	5	2	no	—
401	C₄⋊C₄	—	5	1	no	—
402	C₄⋊C₄	—	5	1	no	—
403	C₄⋊C₄	—	5	1	no	—
404	C₄⋊C₄	—	5	1	no	—
405	C₄⋊C₄	—	10	1	no	—
406	C₄⋊C₄	—	10	2	no	—
407	C₄⋊C₄	—	10	2	no	—
408	C₄⋊C₄	—	10	2	no	—
409	C₄⋊C₄	C₃×D₂₀	1	1	yes	characteristic
410	C₄⋊C₄	C₃×D₂₀	1	1	yes	characteristic
411	C₂²⋊C₄	—	10	1	no	—
412	C₂²⋊C₄	—	10	1	no	—
413	C₂²⋊C₄	—	10	2	no	—
414	C₂²⋊C₄	—	10	2	no	—
415	C₂²⋊C₄	C₃×D₂₀	1	2	yes	—
416	C₄²	—	10	1	no	—
417	C₄²	—	10	1	no	—
418	C₄²	C₂²×C₃×D₅	1	2	yes	—
419	C₃×C₅	#3081	1	1	yes	characteristic, complemented, Hall
420	C₂²×C₃	—	2	1	no	—
421	C₂²×C₃	—	2	1	no	—
422	C₂²×C₃	—	10	4	no	—
423	C₂²×C₃	—	20	2	no	—
424	C₂²×C₃	—	20	2	no	—
425	C₂²×C₃	—	40	4	no	—
426	C₂²×C₃	#4043	1	2	yes	—
427	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
428	C₃×C₄	—	2	2	no	—
429	C₃×C₄	—	2	2	no	—
430	C₃×C₄	—	20	1	no	—
431	C₃×C₄	—	20	1	no	—
432	C₃×C₄	—	20	1	no	—
433	C₃×C₄	—	20	2	no	—
434	C₃×C₄	—	20	1	no	—
435	C₃×C₄	#4043	1	2	yes	—
436	C₃×C₄	C₂×#711	1	1	yes	characteristic
437	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
438	C₂×C₅	—	2	2	no	—
439	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
440	C₂×C₅	C₃×#576	1	1	yes	characteristic
441	C₂×C₅	C₃×#577	1	1	yes	characteristic
442	D₅	—	4	4	no	—
443	C₂³	—	10	2	no	—
444	C₂³	—	10	4	no	—
445	C₂³	—	40	1	no	—
446	C₂³	—	40	1	no	—
447	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
448	Q₈	—	40	2	no	—
449	D₄	—	5	4	no	—
450	D₄	—	10	2	no	—
451	D₄	—	10	4	no	—
452	C₂×C₄	—	10	1	no	—
453	C₂×C₄	—	10	1	no	—
454	C₂×C₄	—	10	1	no	—
455	C₂×C₄	—	10	1	no	—
456	C₂×C₄	—	10	2	no	—
457	C₂×C₄	—	40	2	no	—
458	C₂×C₄	—	40	2	no	—
459	C₂×C₄	—	40	1	no	—
460	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
461	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
462	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
463	C₂×C₄	C₃×#711	1	2	yes	—
464	C₂×C₄	C₃×Q₈×D₅	1	2	yes	—
465	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
466	C₈	—	2	1	no	—
467	C₈	—	2	1	no	—
468	C₈	—	2	2	no	—
469	C₂×C₃	—	2	2	no	—
470	C₂×C₃	—	20	4	no	—
471	C₂×C₃	C₂×#4043	1	1	yes	characteristic
472	C₂×C₃	#66085	1	1	yes	characteristic
473	C₂×C₃	#66086	1	1	yes	characteristic
474	C₅	C₃×#3081	1	1	yes	characteristic, complemented, Sylow
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	10	4	no	—
478	C₂²	—	20	2	no	—
479	C₂²	—	20	2	no	—
480	C₂²	—	40	4	no	—
481	C₂²	C₃×#4043	1	2	yes	—
482	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
483	C₄	—	2	2	no	—
484	C₄	—	2	2	no	—
485	C₄	—	20	1	no	—
486	C₄	—	20	1	no	—
487	C₄	—	20	1	no	—
488	C₄	—	20	2	no	—
489	C₄	—	20	1	no	—
490	C₄	C₃×#4043	1	2	yes	—
491	C₄	C₂×C₃×#711	1	1	yes	characteristic
492	C₄	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
493	C₃	#10610821	1	1	yes	characteristic, direct product factor, Sylow
494	C₂	—	2	2	no	—
495	C₂	—	20	4	no	—
496	C₂	C₂×C₃×#4043	1	1	yes	characteristic
497	C₂	C₃×#66085	1	1	yes	characteristic
498	C₂	C₃×#66086	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₂₀
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#424	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₃×D₂₀	C₂²
hypercenter	C₃×#424	D₅
hypocenter	C₅	C₃×#3081
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117 ◁ C₃×#424

Complements

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

N	H ≅ G/N	type
2. C₃×#65853	C₂	semidirect
3. C₃×C₅×#424	C₂	semidirect
5. C₃×#65410	C₂	semidirect
7. C₃×#65395	C₂	semidirect
8. C₃×#65136	C₂	semidirect
9. C₃×#65136	C₂	semidirect
10. C₃×#65135	C₂	semidirect
11. C₃×#65131	C₂	semidirect
12. #10610821	C₃	direct (N × H)
28. C₃×#4016	C₂²	semidirect
29. C₃×#4015	C₂²	semidirect
30. C₃×C₅×C₄⋊C₈	C₂²	semidirect
31. C₃×C₅×C₄⋊C₈	C₂²	semidirect
36. C₃×#3950	C₂²	semidirect
37. C₃×#3950	C₂²	semidirect
38. C₃×#3950	C₂²	semidirect
39. C₃×#3949	C₂²	semidirect
40. C₃×#3949	C₂²	semidirect
41. C₃×#3949	C₂²	semidirect
44. #65853	C₂×C₃	semidirect
45. C₅×#424	C₂×C₃	semidirect
47. #65410	C₂×C₃	semidirect
49. #65395	C₂×C₃	semidirect
50. #65136	C₂×C₃	semidirect
51. #65136	C₂×C₃	semidirect
52. #65135	C₂×C₃	semidirect
53. #65131	C₂×C₃	semidirect
59. C₂×C₃×D₂₀	Q₈	semidirect
96. C₃×#424	D₅	semidirect
114. #4016	C₂²×C₃	semidirect
115. #4015	C₂²×C₃	semidirect
116. C₅×C₄⋊C₈	C₂²×C₃	semidirect
117. C₅×C₄⋊C₈	C₂²×C₃	semidirect
122. #3950	C₂²×C₃	semidirect
123. #3950	C₂²×C₃	semidirect
124. #3950	C₂²×C₃	semidirect
125. #3949	C₂²×C₃	semidirect
126. #3949	C₂²×C₃	semidirect
127. #3949	C₂²×C₃	semidirect
178. C₃×C₄⋊C₈	C₂×D₅	semidirect
179. C₃×C₄⋊C₈	C₂×D₅	semidirect
189. C₂×D₂₀	C₃×Q₈	semidirect
226. #424	C₃×D₅	semidirect
330. C₄⋊C₈	C₂×C₃×D₅	semidirect
331. C₄⋊C₈	C₂×C₃×D₅	semidirect
419. C₃×C₅	#3081	semidirect
474. C₅	C₃×#3081	semidirect
493. C₃	#10610821	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×#65855	2
C₃×#65853	2
C₃×C₅×#424	2
C₃×#65420	2
C₃×#65410	2
C₂×C₃×#3953	2
C₃×#65395	2
C₃×#65136	2
C₃×#65135	2
C₃×#65131	2
#10610821	3
C₃×#3081	5

Subgroups — C3×#10610821 #14430784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610821 #14430784