Subgroups — C₃×#10610646 #14417328

Order 1920.

1056 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66132	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#686	C₂	1	1	yes	maximal, characteristic
3	C₃×#65855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#418	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65420	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65411	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65287	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65074	C₂	1	4	yes	maximal, complemented
9	C₃×#65045	C₂	1	4	yes	maximal, complemented
10	#10610646	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₃×C₅×#117	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₂²⋊Dic₅	—	2	2	no	—
16	C₃×D₄×Dic₅	—	2	2	no	—
17	C₃×D₄×Dic₅	C₂²	1	4	yes	complemented
18	C₂×C₃×#686	C₄	1	8	yes	complemented
19	C₂×C₃×#686	C₂²	1	2	yes	—
20	C₂×C₃×#686	C₂²	1	2	yes	—
21	C₃×#4072	C₂²	1	1	yes	characteristic
22	C₃×#4072	C₂²	1	1	yes	characteristic
23	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
24	C₃×#4039	C₂²	1	4	yes	complemented
25	C₃×D₅×C₂²⋊C₄	—	2	2	no	—
26	C₃×C₄×D₂₀	—	2	2	no	—
27	C₃×C₅×#102	C₂²	1	4	yes	complemented
28	C₃×#3953	C₂²	1	4	yes	complemented
29	C₃×#3947	C₂²	1	2	yes	complemented
30	C₃×C₈×Dic₅	C₂²	1	2	yes	complemented
31	C₃×#3940	C₂²	1	2	yes	complemented
32	C₃×#3939	C₂²	1	2	yes	complemented
33	C₃×#2948	—	5	1	no	maximal, Hall
34	#66132	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂²×#686	C₂×C₃	1	1	yes	characteristic
36	#65855	C₂×C₃	1	1	yes	characteristic, complemented
37	C₅×#418	C₂×C₃	1	1	yes	characteristic, complemented
38	#65420	C₂×C₃	1	1	yes	characteristic, complemented
39	#65411	C₂×C₃	1	1	yes	characteristic, complemented
40	#65287	C₂×C₃	1	1	yes	characteristic, complemented
41	#65074	C₂×C₃	1	4	yes	complemented
42	#65045	C₂×C₃	1	4	yes	complemented
43	C₂⁴×C₃×C₅	—	2	1	no	—
44	C₂³×C₃×D₅	—	2	1	no	—
45	C₂×C₃×C₅×D₄	—	2	1	no	—
46	C₂×C₃×C₅×D₄	—	2	2	no	—
47	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
48	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×Dic₅	—	2	4	no	—
51	C₂×C₃×D₂₀	—	2	1	no	—
52	C₂×C₃×D₂₀	—	2	2	no	—
53	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	complemented
54	C₂×C₃×D₂₀	C₂³	1	2	yes	—
55	C₂×C₃×C₄×D₅	—	2	4	no	—
56	C₃×C₅×M₁₆	—	2	2	no	—
57	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
58	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
59	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
60	C₃×C₄²×C₅	—	2	1	no	—
61	C₃×C₂²⋊Dic₅	—	2	1	no	—
62	C₃×C₂²⋊Dic₅	—	2	4	no	—
63	C₃×C₂²⋊Dic₅	D₄	1	2	yes	—
64	C₃×#686	C₂×C₄	1	8	yes	complemented
65	C₃×#686	C₂×C₄	1	8	yes	complemented
66	C₃×#685	—	2	4	no	—
67	C₃×C₄⋊Dic₅	D₄	1	2	yes	—
68	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
69	C₃×C₄×Dic₅	—	2	1	no	—
70	C₃×C₄×Dic₅	C₂³	1	2	yes	—
71	C₂×C₃×#168	C₂×C₄	1	4	yes	complemented
72	C₂×C₃×#168	C₂³	1	1	yes	characteristic
73	C₂×C₃×#168	C₂³	1	1	yes	characteristic
74	C₂²×C₃×D₈	—	5	1	no	—
75	C₃×#518	—	5	1	no	—
76	C₃×#518	—	5	1	no	—
77	C₃×#442	—	5	4	no	—
78	C₃×C₄×D₈	—	5	4	no	—
79	C₃×#427	—	5	1	no	—
80	C₃×#418	—	5	1	no	—
81	C₃×#418	D₅	1	1	yes	characteristic, complemented
82	C₃×#405	—	5	1	no	—
83	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
84	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
86	C₅×#117	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₂²⋊Dic₅	—	2	2	no	—
88	D₄×Dic₅	—	2	2	no	—
89	D₄×Dic₅	C₂²×C₃	1	4	yes	complemented
90	C₂×#686	C₃×C₄	1	8	yes	complemented
91	C₂×#686	C₂²×C₃	1	2	yes	—
92	C₂×#686	C₂²×C₃	1	2	yes	—
93	#4072	C₂²×C₃	1	1	yes	characteristic
94	#4072	C₂²×C₃	1	1	yes	characteristic
95	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
96	#4039	C₂²×C₃	1	4	yes	complemented
97	D₅×C₂²⋊C₄	—	2	2	no	—
98	C₄×D₂₀	—	2	2	no	—
99	C₅×#102	C₂²×C₃	1	4	yes	complemented
100	#3953	C₂²×C₃	1	4	yes	complemented
101	#3947	C₂²×C₃	1	2	yes	complemented
102	C₈×Dic₅	C₂²×C₃	1	2	yes	complemented
103	#3940	C₂²×C₃	1	2	yes	complemented
104	#3939	C₂²×C₃	1	2	yes	complemented
105	#2948	—	5	1	no	Sylow
106	C₂³×C₃×C₅	—	2	2	no	—
107	C₂³×C₃×C₅	—	2	4	no	—
108	C₂³×C₃×C₅	—	8	2	no	—
109	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₃×D₅	—	2	2	no	—
111	C₂²×C₃×D₅	—	2	4	no	—
112	C₂²×C₃×D₅	—	8	2	no	—
113	C₃×C₅×D₄	—	2	4	no	—
114	C₃×C₅×D₄	—	2	2	no	—
115	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	#41	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
121	C₂×C₃×Dic₅	—	2	2	no	—
122	C₂×C₃×Dic₅	—	8	4	no	—
123	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
124	C₃×D₂₀	—	2	4	no	—
125	C₃×D₂₀	—	2	2	no	—
126	C₃×D₂₀	C₂²×C₄	1	4	yes	—
127	C₃×C₄×D₅	—	8	4	no	—
128	C₃×C₅×C₈	—	2	2	no	—
129	C₃×#168	C₂²×C₄	1	2	yes	—
130	C₃×#168	C₂²×C₄	1	2	yes	—
131	C₂²×C₃×D₄	—	5	1	no	—
132	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
133	C₂×C₃×D₈	—	5	8	no	—
134	C₂×C₃×D₈	—	5	2	no	—
135	C₂×C₃×D₈	—	5	2	no	—
136	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
137	C₂²×C₃×C₈	—	5	1	no	—
138	C₃×C₄×D₄	—	5	4	no	—
139	C₃×C₄×D₄	—	5	4	no	—
140	C₃×C₄×D₄	—	10	2	no	—
141	C₃×C₄×D₄	—	10	2	no	—
142	C₃×#117	—	5	1	no	—
143	C₃×#117	—	5	1	no	—
144	C₃×#117	C₂×D₅	1	1	yes	characteristic
145	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
146	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
147	C₃×#107	—	5	2	no	—
148	C₃×#106	—	5	2	no	—
149	C₃×#102	—	5	4	no	—
150	C₃×#102	C₂×D₅	1	4	yes	complemented
151	C₃×#97	—	5	2	no	—
152	C₃×C₄×C₈	—	5	2	no	—
153	C₂⁴×C₅	—	2	1	no	—
154	C₂³×D₅	—	2	1	no	—
155	C₂×C₅×D₄	—	2	1	no	—
156	C₂×C₅×D₄	—	2	2	no	—
157	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	complemented
158	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
159	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
160	C₂²×Dic₅	—	2	4	no	—
161	C₂×D₂₀	—	2	1	no	—
162	C₂×D₂₀	—	2	2	no	—
163	C₂×D₂₀	C₂×C₃×C₄	1	4	yes	complemented
164	C₂×D₂₀	C₂³×C₃	1	2	yes	—
165	C₂×C₄×D₅	—	2	4	no	—
166	C₅×M₁₆	—	2	2	no	—
167	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
168	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
169	C₅×C₂²⋊C₄	—	2	1	no	—
170	C₄²×C₅	—	2	1	no	—
171	C₂²⋊Dic₅	—	2	1	no	—
172	C₂²⋊Dic₅	—	2	4	no	—
173	C₂²⋊Dic₅	C₃×D₄	1	2	yes	—
174	#686	C₂×C₃×C₄	1	8	yes	complemented
175	#686	C₂×C₃×C₄	1	8	yes	complemented
176	#685	—	2	4	no	—
177	C₄⋊Dic₅	C₃×D₄	1	2	yes	—
178	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
179	C₄×Dic₅	—	2	1	no	—
180	C₄×Dic₅	C₂³×C₃	1	2	yes	—
181	C₂×#168	C₂×C₃×C₄	1	4	yes	complemented
182	C₂×#168	C₂³×C₃	1	1	yes	characteristic
183	C₂×#168	C₂³×C₃	1	1	yes	characteristic
184	C₂²×D₈	—	5	1	no	—
185	#518	—	5	1	no	—
186	#518	—	5	1	no	—
187	#442	—	5	4	no	—
188	C₄×D₈	—	5	4	no	—
189	#427	—	5	1	no	—
190	#418	—	5	1	no	—
191	#418	C₃×D₅	1	1	yes	characteristic, complemented
192	#405	—	5	1	no	—
193	C₂²×C₃×C₅	—	2	2	no	—
194	C₂²×C₃×C₅	—	2	4	no	—
195	C₂²×C₃×C₅	—	4	4	no	—
196	C₂²×C₃×C₅	—	8	4	no	—
197	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
198	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₃×D₅	—	2	4	no	—
200	C₂×C₃×D₅	—	4	4	no	—
201	C₂×C₃×D₅	—	8	4	no	—
202	C₃×C₄×C₅	—	4	2	no	—
203	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
204	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
205	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
206	C₃×Dic₅	—	2	4	no	—
207	C₃×Dic₅	—	4	2	no	—
208	C₂⁴×C₃	—	2	1	no	—
209	C₂⁴×C₃	—	10	1	no	—
210	C₂×C₃×D₄	—	2	1	no	—
211	C₂×C₃×D₄	—	2	2	no	—
212	C₂×C₃×D₄	—	5	4	no	—
213	C₂×C₃×D₄	—	5	2	no	—
214	C₂×C₃×D₄	—	10	1	no	—
215	C₂×C₃×D₄	—	10	2	no	—
216	C₂×C₃×D₄	C₄×D₅	1	4	yes	complemented
217	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
218	C₂²×C₃×C₄	—	10	4	no	—
219	C₂²×C₃×C₄	—	10	4	no	—
220	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
221	C₃×D₈	—	5	8	no	—
222	C₃×D₈	—	5	8	no	—
223	C₃×M₁₆	—	2	2	no	—
224	C₂×C₃×C₈	—	5	4	no	—
225	C₂×C₃×C₈	—	5	1	no	—
226	C₂×C₃×C₈	—	5	1	no	—
227	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
228	C₃×C₄⋊C₄	—	5	2	no	—
229	C₃×C₄⋊C₄	—	5	2	no	—
230	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
231	C₃×C₂²⋊C₄	—	2	1	no	—
232	C₃×C₂²⋊C₄	—	5	2	no	—
233	C₃×C₂²⋊C₄	—	10	4	no	—
234	C₃×C₂²⋊C₄	—	10	4	no	—
235	C₃×C₂²⋊C₄	—	10	1	no	—
236	C₃×C₄²	—	2	1	no	—
237	C₃×C₄²	—	5	2	no	—
238	C₃×C₄²	—	10	1	no	—
239	C₂³×C₅	—	2	2	no	—
240	C₂³×C₅	—	2	4	no	—
241	C₂³×C₅	—	8	2	no	—
242	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
243	C₂²×D₅	—	2	2	no	—
244	C₂²×D₅	—	2	4	no	—
245	C₂²×D₅	—	8	2	no	—
246	C₅×D₄	—	2	4	no	—
247	C₅×D₄	—	2	2	no	—
248	C₅×D₄	C₂²×C₃×C₄	1	4	yes	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
251	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
252	C₂×C₄×C₅	C₃×#41	1	2	yes	—
253	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
254	C₂×Dic₅	—	2	2	no	—
255	C₂×Dic₅	—	8	4	no	—
256	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
257	D₂₀	—	2	4	no	—
258	D₂₀	—	2	2	no	—
259	D₂₀	C₂²×C₃×C₄	1	4	yes	—
260	C₄×D₅	—	8	4	no	—
261	C₅×C₈	—	2	2	no	—
262	#168	C₂²×C₃×C₄	1	2	yes	—
263	#168	C₂²×C₃×C₄	1	2	yes	—
264	C₂²×D₄	—	5	1	no	—
265	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
266	C₂×D₈	—	5	8	no	—
267	C₂×D₈	—	5	2	no	—
268	C₂×D₈	—	5	2	no	—
269	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
270	C₂²×C₈	—	5	1	no	—
271	C₄×D₄	—	5	4	no	—
272	C₄×D₄	—	5	4	no	—
273	C₄×D₄	—	10	2	no	—
274	C₄×D₄	—	10	2	no	—
275	#117	—	5	1	no	—
276	#117	—	5	1	no	—
277	#117	C₂×C₃×D₅	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	—	10	2	no	—
279	C₂×C₂²⋊C₄	—	10	2	no	—
280	#107	—	5	2	no	—
281	#106	—	5	2	no	—
282	#102	—	5	4	no	—
283	#102	C₂×C₃×D₅	1	4	yes	complemented
284	#97	—	5	2	no	—
285	C₄×C₈	—	5	2	no	—
286	C₂×C₃×C₅	—	2	2	no	—
287	C₂×C₃×C₅	—	4	4	no	—
288	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
289	C₂×C₃×C₅	#576	1	2	yes	—
290	C₃×D₅	—	4	4	no	—
291	C₂³×C₃	—	2	2	no	—
292	C₂³×C₃	—	2	4	no	—
293	C₂³×C₃	—	8	2	no	—
294	C₂³×C₃	—	10	2	no	—
295	C₂³×C₃	—	10	4	no	—
296	C₂³×C₃	—	40	2	no	—
297	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
298	C₃×D₄	—	2	2	no	—
299	C₃×D₄	—	2	4	no	—
300	C₃×D₄	—	5	4	no	—
301	C₃×D₄	—	10	2	no	—
302	C₃×D₄	—	10	4	no	—
303	C₃×D₄	C₂×C₄×D₅	1	4	yes	—
304	C₂×C₃×C₄	—	2	2	no	—
305	C₂×C₃×C₄	—	5	4	no	—
306	C₂×C₃×C₄	—	10	2	no	—
307	C₂×C₃×C₄	—	40	4	no	—
308	C₂×C₃×C₄	—	40	4	no	—
309	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
310	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
311	C₂×C₃×C₄	#711	1	2	yes	—
312	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
313	C₃×C₈	—	2	2	no	—
314	C₃×C₈	—	5	2	no	—
315	C₃×C₈	—	5	2	no	—
316	C₂²×C₅	—	2	2	no	—
317	C₂²×C₅	—	2	4	no	—
318	C₂²×C₅	—	4	4	no	—
319	C₂²×C₅	—	8	4	no	—
320	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
321	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
322	C₂×D₅	—	2	4	no	—
323	C₂×D₅	—	4	4	no	—
324	C₂×D₅	—	8	4	no	—
325	C₄×C₅	—	4	2	no	—
326	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
327	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
328	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
329	Dic₅	—	2	4	no	—
330	Dic₅	—	4	2	no	—
331	C₂⁴	—	2	1	no	—
332	C₂⁴	—	10	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	5	4	no	—
336	C₂×D₄	—	5	2	no	—
337	C₂×D₄	—	10	1	no	—
338	C₂×D₄	—	10	2	no	—
339	C₂×D₄	C₃×C₄×D₅	1	4	yes	complemented
340	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
341	C₂²×C₄	—	10	4	no	—
342	C₂²×C₄	—	10	4	no	—
343	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
344	D₈	—	5	8	no	—
345	D₈	—	5	8	no	—
346	M₁₆	—	2	2	no	—
347	C₂×C₈	—	5	4	no	—
348	C₂×C₈	—	5	1	no	—
349	C₂×C₈	—	5	1	no	—
350	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
351	C₄⋊C₄	—	5	2	no	—
352	C₄⋊C₄	—	5	2	no	—
353	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	5	2	no	—
356	C₂²⋊C₄	—	10	4	no	—
357	C₂²⋊C₄	—	10	4	no	—
358	C₂²⋊C₄	—	10	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	5	2	no	—
361	C₄²	—	10	1	no	—
362	C₃×C₅	#2948	1	1	yes	characteristic, complemented, Hall
363	C₂²×C₃	—	2	2	no	—
364	C₂²×C₃	—	2	4	no	—
365	C₂²×C₃	—	4	4	no	—
366	C₂²×C₃	—	8	4	no	—
367	C₂²×C₃	—	10	4	no	—
368	C₂²×C₃	—	20	4	no	—
369	C₂²×C₃	—	40	4	no	—
370	C₂²×C₃	#4027	1	2	yes	—
371	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
372	C₃×C₄	—	4	2	no	—
373	C₃×C₄	—	10	4	no	—
374	C₃×C₄	—	20	2	no	—
375	C₃×C₄	#4027	1	2	yes	—
376	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
377	C₃×C₄	C₂×#711	1	1	yes	characteristic
378	C₂×C₅	—	2	2	no	—
379	C₂×C₅	—	4	4	no	—
380	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
381	C₂×C₅	C₃×#576	1	2	yes	—
382	D₅	—	4	4	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	4	no	—
385	C₂³	—	8	2	no	—
386	C₂³	—	10	2	no	—
387	C₂³	—	10	4	no	—
388	C₂³	—	40	2	no	—
389	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
390	D₄	—	2	2	no	—
391	D₄	—	2	4	no	—
392	D₄	—	5	4	no	—
393	D₄	—	10	2	no	—
394	D₄	—	10	4	no	—
395	D₄	C₂×C₃×C₄×D₅	1	4	yes	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	5	4	no	—
398	C₂×C₄	—	10	2	no	—
399	C₂×C₄	—	40	4	no	—
400	C₂×C₄	—	40	4	no	—
401	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
402	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
403	C₂×C₄	C₃×#711	1	2	yes	—
404	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
405	C₈	—	2	2	no	—
406	C₈	—	5	2	no	—
407	C₈	—	5	2	no	—
408	C₂×C₃	—	2	2	no	—
409	C₂×C₃	—	4	4	no	—
410	C₂×C₃	—	20	4	no	—
411	C₂×C₃	C₂×#4027	1	1	yes	characteristic
412	C₂×C₃	#66108	1	2	yes	—
413	C₅	C₃×#2948	1	1	yes	characteristic, complemented, Sylow
414	C₂²	—	2	2	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	8	4	no	—
418	C₂²	—	10	4	no	—
419	C₂²	—	20	4	no	—
420	C₂²	—	40	4	no	—
421	C₂²	C₃×#4027	1	2	yes	—
422	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
423	C₄	—	4	2	no	—
424	C₄	—	10	4	no	—
425	C₄	—	20	2	no	—
426	C₄	C₃×#4027	1	2	yes	—
427	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
428	C₄	C₂×C₃×#711	1	1	yes	characteristic
429	C₃	#10610646	1	1	yes	characteristic, direct product factor, Sylow
430	C₂	—	2	2	no	—
431	C₂	—	4	4	no	—
432	C₂	—	20	4	no	—
433	C₂	C₂×C₃×#4027	1	1	yes	characteristic
434	C₂	C₃×#66108	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#418	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₃×#686	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#418	D₅
hypocenter	C₅	C₃×#2948
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#418

Complements

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

N	H ≅ G/N	type
1. C₃×#66132	C₂	semidirect
3. C₃×#65855	C₂	semidirect
4. C₃×C₅×#418	C₂	semidirect
5. C₃×#65420	C₂	semidirect
6. C₃×#65411	C₂	semidirect
7. C₃×#65287	C₂	semidirect
8. C₃×#65074	C₂	semidirect
9. C₃×#65045	C₂	semidirect
10. #10610646	C₃	direct (N × H)
17. C₃×D₄×Dic₅	C₂²	semidirect
18. C₂×C₃×#686	C₄	semidirect
24. C₃×#4039	C₂²	semidirect
27. C₃×C₅×#102	C₂²	semidirect
28. C₃×#3953	C₂²	semidirect
29. C₃×#3947	C₂²	semidirect
30. C₃×C₈×Dic₅	C₂²	semidirect
31. C₃×#3940	C₂²	semidirect
32. C₃×#3939	C₂²	semidirect
34. #66132	C₂×C₃	semidirect
36. #65855	C₂×C₃	semidirect
37. C₅×#418	C₂×C₃	semidirect
38. #65420	C₂×C₃	semidirect
39. #65411	C₂×C₃	semidirect
40. #65287	C₂×C₃	semidirect
41. #65074	C₂×C₃	semidirect
42. #65045	C₂×C₃	semidirect
47. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
53. C₂×C₃×D₂₀	C₂×C₄	semidirect
64. C₃×#686	C₂×C₄	semidirect
65. C₃×#686	C₂×C₄	semidirect
71. C₂×C₃×#168	C₂×C₄	semidirect
81. C₃×#418	D₅	semidirect
89. D₄×Dic₅	C₂²×C₃	semidirect
90. C₂×#686	C₃×C₄	semidirect
96. #4039	C₂²×C₃	semidirect
99. C₅×#102	C₂²×C₃	semidirect
100. #3953	C₂²×C₃	semidirect
101. #3947	C₂²×C₃	semidirect
102. C₈×Dic₅	C₂²×C₃	semidirect
103. #3940	C₂²×C₃	semidirect
104. #3939	C₂²×C₃	semidirect
150. C₃×#102	C₂×D₅	semidirect
157. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
163. C₂×D₂₀	C₂×C₃×C₄	semidirect
174. #686	C₂×C₃×C₄	semidirect
175. #686	C₂×C₃×C₄	semidirect
181. C₂×#168	C₂×C₃×C₄	semidirect
191. #418	C₃×D₅	semidirect
216. C₂×C₃×D₄	C₄×D₅	semidirect
283. #102	C₂×C₃×D₅	semidirect
339. C₂×D₄	C₃×C₄×D₅	semidirect
362. C₃×C₅	#2948	semidirect
413. C₅	C₃×#2948	semidirect
429. C₃	#10610646	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×#66132	2
C₂²×C₃×#686	2
C₃×#65855	2
C₃×C₅×#418	2
C₃×#65420	2
C₃×#65411	2
C₃×#65287	2
C₃×#65074	2
C₃×#65045	2
#10610646	3
C₃×#2948	5

Subgroups — C3×#10610646 #14417328

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610646 #14417328