Subgroups — C₃×#10615635 #14439073

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66166	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#4096	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#4050	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65479	C₂	1	2	yes	maximal, complemented
6	C₃×#65465	C₂	1	2	yes	maximal, complemented
7	C₃×#65456	C₂	1	2	yes	maximal, complemented
8	C₃×#65443	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×#3947	C₂	1	1	yes	maximal, characteristic, complemented
10	#10615635	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
12	C₂×C₃×#709	C₂²	1	2	yes	—
13	C₃×C₅×#135	—	2	4	no	—
14	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
16	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₃×#4096	—	2	8	no	—
19	C₃×#4093	C₂²	1	2	yes	—
20	C₃×#4090	C₂²	1	2	yes	—
21	C₂×C₃×#689	C₂²	1	2	yes	—
22	C₂×C₃×#688	C₂²	1	2	yes	—
23	C₃×#4086	C₂²	1	2	yes	—
24	C₃×#4085	—	2	4	no	—
25	C₃×#4082	C₂²	1	2	yes	—
26	C₂×C₃×#687	C₂²	1	2	yes	—
27	C₂×C₃×#686	C₂²	1	2	yes	—
28	C₃×C₄×C₂²⋊D₅	—	2	4	no	—
29	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
30	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
31	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic
32	C₃×#4050	—	2	4	no	—
33	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
34	C₂×C₃×#677	C₂²	1	2	yes	—
35	C₃×#3947	C₂²	1	2	yes	—
36	C₃×#3947	C₂²	1	2	yes	—
37	C₃×#3150	—	5	1	no	maximal, Hall
38	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic, complemented
39	#66166	C₂×C₃	1	2	yes	complemented
40	C₂×#4096	C₂×C₃	1	2	yes	complemented
41	C₂×#4050	C₂×C₃	1	1	yes	characteristic, complemented
42	#65479	C₂×C₃	1	2	yes	complemented
43	#65465	C₂×C₃	1	2	yes	complemented
44	#65456	C₂×C₃	1	2	yes	complemented
45	#65443	C₂×C₃	1	2	yes	complemented
46	C₂×#3947	C₂×C₃	1	1	yes	characteristic, complemented
47	C₃×C₅×#41	—	2	4	no	—
48	C₃×C₅×#41	—	2	4	no	—
49	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
50	C₂×C₃×C₅×D₄	—	2	2	no	—
51	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	—	2	2	no	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
55	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
56	C₂²×C₃×Dic₅	D₄	1	2	yes	—
57	C₃×#709	—	2	4	no	—
58	C₃×#709	—	2	4	no	—
59	C₂×C₃×D₂₀	C₂³	1	2	yes	—
60	C₂×C₃×C₄×D₅	—	2	2	no	—
61	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
62	C₃×C₅×Q₁₆	—	2	2	no	—
63	C₃×C₅×SD₁₆	—	2	4	no	—
64	C₃×C₅×D₈	—	2	2	no	—
65	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₃×C₂²⋊Dic₅	—	2	4	no	—
69	C₃×#689	—	2	4	no	—
70	C₃×#688	—	2	4	no	—
71	C₃×#687	—	2	4	no	—
72	C₃×#686	—	2	4	no	—
73	C₃×#685	—	2	4	no	—
74	C₃×#683	—	2	4	no	—
75	C₃×C₄×Dic₅	D₄	1	2	yes	—
76	C₃×C₄×Dic₅	C₂³	1	2	yes	—
77	C₂×C₃×#168	D₄	1	4	yes	complemented
78	C₂×C₃×#168	C₂³	1	2	yes	—
79	C₃×Dic₂₀	—	2	2	no	—
80	C₃×D₄₀	—	2	2	no	—
81	C₃×#677	—	2	4	no	—
82	C₂×C₃×#135	—	5	2	no	—
83	C₂×C₃×#135	—	5	1	no	—
84	C₂×C₃×#135	D₅	1	1	yes	characteristic, complemented
85	C₃×#532	—	5	2	no	—
86	C₃×#497	—	5	2	no	—
87	C₃×#497	—	5	2	no	—
88	C₃×#496	—	5	2	no	—
89	C₃×#496	—	5	2	no	—
90	C₂×C₃×#97	—	5	1	no	—
91	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
92	C₂×#709	C₂²×C₃	1	2	yes	—
93	C₅×#135	—	2	4	no	—
94	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
96	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
97	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
98	#4096	—	2	8	no	—
99	#4093	C₂²×C₃	1	2	yes	—
100	#4090	C₂²×C₃	1	2	yes	—
101	C₂×#689	C₂²×C₃	1	2	yes	—
102	C₂×#688	C₂²×C₃	1	2	yes	—
103	#4086	C₂²×C₃	1	2	yes	—
104	#4085	—	2	4	no	—
105	#4082	C₂²×C₃	1	2	yes	—
106	C₂×#687	C₂²×C₃	1	2	yes	—
107	C₂×#686	C₂²×C₃	1	2	yes	—
108	C₄×C₂²⋊D₅	—	2	4	no	—
109	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
110	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
111	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic
112	#4050	—	2	4	no	—
113	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic
114	C₂×#677	C₂²×C₃	1	2	yes	—
115	#3947	C₂²×C₃	1	2	yes	—
116	#3947	C₂²×C₃	1	2	yes	—
117	#3150	—	5	1	no	Sylow
118	C₂³×C₃×C₅	—	2	2	no	—
119	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₃×D₅	—	2	2	no	—
121	C₃×C₅×Q₈	—	2	2	no	—
122	C₃×C₅×Q₈	—	2	2	no	—
123	C₃×C₅×D₄	—	2	2	no	—
124	C₃×C₅×D₄	—	2	2	no	—
125	C₃×C₅×D₄	—	4	4	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	4	4	no	—
128	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
132	C₃×C₂²⋊D₅	—	4	8	no	—
133	C₃×C₂²⋊D₅	—	4	4	no	—
134	C₂×C₃×Dic₅	—	2	2	no	—
135	C₂×C₃×Dic₅	—	4	2	no	—
136	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
137	C₃×D₂₀	—	2	2	no	—
138	C₃×D₂₀	—	2	2	no	—
139	C₃×C₄×D₅	—	4	4	no	—
140	C₃×Dic₁₀	—	2	2	no	—
141	C₃×Dic₁₀	—	2	2	no	—
142	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
143	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
144	C₃×#168	C₂×D₄	1	4	yes	—
145	C₂×C₃×#41	—	5	2	no	—
146	C₂×C₃×#41	C₂×D₅	1	2	yes	—
147	C₃×#135	—	2	4	no	—
148	C₃×#135	—	10	8	no	—
149	C₃×#135	—	10	4	no	—
150	C₂×C₃×Q₁₆	—	5	2	no	—
151	C₂×C₃×Q₁₆	—	5	1	no	—
152	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
153	C₂×C₃×SD₁₆	—	5	2	no	—
154	C₂×C₃×SD₁₆	—	5	2	no	—
155	C₂×C₃×SD₁₆	—	5	2	no	—
156	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	—
157	C₂×C₃×D₈	—	5	2	no	—
158	C₂×C₃×D₈	—	5	1	no	—
159	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic
160	C₂²×C₃×C₈	—	5	1	no	—
161	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
162	C₃×C₄⋊Q₈	—	5	2	no	—
163	C₃×#127	—	5	2	no	—
164	C₃×#124	—	5	2	no	—
165	C₃×#124	—	5	2	no	—
166	C₃×#121	—	10	4	no	—
167	C₃×C₄×D₄	—	10	4	no	—
168	C₂×C₃×C₄²	—	5	1	no	—
169	C₃×#97	—	5	2	no	—
170	C₃×#97	—	5	2	no	—
171	C₅×#41	—	2	4	no	—
172	C₅×#41	—	2	4	no	—
173	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
174	C₂×C₅×D₄	—	2	2	no	—
175	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
176	C₂²×C₄×C₅	—	2	2	no	—
177	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
178	C₂×C₂²⋊D₅	—	2	2	no	—
179	C₂×C₂²⋊D₅	—	2	4	no	—
180	C₂²×Dic₅	C₃×D₄	1	2	yes	—
181	#709	—	2	4	no	—
182	#709	—	2	4	no	—
183	C₂×D₂₀	C₂³×C₃	1	2	yes	—
184	C₂×C₄×D₅	—	2	2	no	—
185	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
186	C₅×Q₁₆	—	2	2	no	—
187	C₅×SD₁₆	—	2	4	no	—
188	C₅×D₈	—	2	2	no	—
189	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
190	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
191	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
192	C₂²⋊Dic₅	—	2	4	no	—
193	#689	—	2	4	no	—
194	#688	—	2	4	no	—
195	#687	—	2	4	no	—
196	#686	—	2	4	no	—
197	#685	—	2	4	no	—
198	#683	—	2	4	no	—
199	C₄×Dic₅	C₃×D₄	1	2	yes	—
200	C₄×Dic₅	C₂³×C₃	1	2	yes	—
201	C₂×#168	C₃×D₄	1	4	yes	complemented
202	C₂×#168	C₂³×C₃	1	2	yes	—
203	Dic₂₀	—	2	2	no	—
204	D₄₀	—	2	2	no	—
205	#677	—	2	4	no	—
206	C₂×#135	—	5	2	no	—
207	C₂×#135	—	5	1	no	—
208	C₂×#135	C₃×D₅	1	1	yes	characteristic, complemented
209	#532	—	5	2	no	—
210	#497	—	5	2	no	—
211	#497	—	5	2	no	—
212	#496	—	5	2	no	—
213	#496	—	5	2	no	—
214	C₂×#97	—	5	1	no	—
215	C₂²×C₃×C₅	—	2	2	no	—
216	C₂²×C₃×C₅	—	4	2	no	—
217	C₂²×C₃×C₅	—	4	4	no	—
218	C₂²×C₃×C₅	#127	1	2	yes	—
219	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₃×D₅	—	4	2	no	—
221	C₂×C₃×D₅	—	4	4	no	—
222	C₃×C₄×C₅	—	4	2	no	—
223	C₃×C₄×C₅	#127	1	2	yes	—
224	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
225	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
226	C₃×Dic₅	—	2	4	no	—
227	C₃×Dic₅	—	4	2	no	—
228	C₃×#41	—	2	4	no	—
229	C₃×#41	—	2	4	no	—
230	C₃×#41	—	10	4	no	—
231	C₃×#41	—	10	4	no	—
232	C₂×C₃×Q₈	—	5	2	no	—
233	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
234	C₂×C₃×D₄	—	2	2	no	—
235	C₂×C₃×D₄	—	5	2	no	—
236	C₂×C₃×D₄	—	10	4	no	—
237	C₂×C₃×D₄	—	10	2	no	—
238	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
239	C₂²×C₃×C₄	—	2	2	no	—
240	C₂²×C₃×C₄	—	5	2	no	—
241	C₂²×C₃×C₄	—	10	2	no	—
242	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
243	C₃×Q₁₆	—	2	2	no	—
244	C₃×Q₁₆	—	10	4	no	—
245	C₃×Q₁₆	—	10	2	no	—
246	C₃×SD₁₆	—	2	4	no	—
247	C₃×SD₁₆	—	10	4	no	—
248	C₃×SD₁₆	—	10	4	no	—
249	C₃×SD₁₆	—	10	4	no	—
250	C₃×D₈	—	2	2	no	—
251	C₃×D₈	—	10	4	no	—
252	C₃×D₈	—	10	2	no	—
253	C₂×C₃×C₈	—	5	4	no	—
254	C₂×C₃×C₈	—	5	2	no	—
255	C₂×C₃×C₈	C₂²⋊D₅	1	4	yes	complemented
256	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
257	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
258	C₃×C₄⋊C₄	—	10	4	no	—
259	C₃×C₂²⋊C₄	—	10	4	no	—
260	C₃×C₂²⋊C₄	—	10	4	no	—
261	C₃×C₄²	—	5	2	no	—
262	C₃×C₄²	—	5	2	no	—
263	C₂³×C₅	—	2	2	no	—
264	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
265	C₂²×D₅	—	2	2	no	—
266	C₅×Q₈	—	2	2	no	—
267	C₅×Q₈	—	2	2	no	—
268	C₅×D₄	—	2	2	no	—
269	C₅×D₄	—	2	2	no	—
270	C₅×D₄	—	4	4	no	—
271	C₂×C₄×C₅	—	2	2	no	—
272	C₂×C₄×C₅	—	4	4	no	—
273	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
274	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
275	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
276	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
277	C₂²⋊D₅	—	4	8	no	—
278	C₂²⋊D₅	—	4	4	no	—
279	C₂×Dic₅	—	2	2	no	—
280	C₂×Dic₅	—	4	2	no	—
281	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
282	D₂₀	—	2	2	no	—
283	D₂₀	—	2	2	no	—
284	C₄×D₅	—	4	4	no	—
285	Dic₁₀	—	2	2	no	—
286	Dic₁₀	—	2	2	no	—
287	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
288	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
289	#168	C₂×C₃×D₄	1	4	yes	—
290	C₂×#41	—	5	2	no	—
291	C₂×#41	C₂×C₃×D₅	1	2	yes	—
292	#135	—	2	4	no	—
293	#135	—	10	8	no	—
294	#135	—	10	4	no	—
295	C₂×Q₁₆	—	5	2	no	—
296	C₂×Q₁₆	—	5	1	no	—
297	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic
298	C₂×SD₁₆	—	5	2	no	—
299	C₂×SD₁₆	—	5	2	no	—
300	C₂×SD₁₆	—	5	2	no	—
301	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	—
302	C₂×D₈	—	5	2	no	—
303	C₂×D₈	—	5	1	no	—
304	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic
305	C₂²×C₈	—	5	1	no	—
306	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
307	C₄⋊Q₈	—	5	2	no	—
308	#127	—	5	2	no	—
309	#124	—	5	2	no	—
310	#124	—	5	2	no	—
311	#121	—	10	4	no	—
312	C₄×D₄	—	10	4	no	—
313	C₂×C₄²	—	5	1	no	—
314	#97	—	5	2	no	—
315	#97	—	5	2	no	—
316	C₂×C₃×C₅	—	2	2	no	—
317	C₂×C₃×C₅	—	8	2	no	—
318	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
319	C₂×C₃×C₅	#575	1	2	yes	—
320	C₃×D₅	—	8	2	no	—
321	C₂³×C₃	—	2	2	no	—
322	C₂³×C₃	—	10	2	no	—
323	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
324	C₃×Q₈	—	2	2	no	—
325	C₃×Q₈	—	2	2	no	—
326	C₃×Q₈	—	10	2	no	—
327	C₃×Q₈	—	10	2	no	—
328	C₃×D₄	—	2	2	no	—
329	C₃×D₄	—	2	2	no	—
330	C₃×D₄	—	4	4	no	—
331	C₃×D₄	—	10	2	no	—
332	C₃×D₄	—	10	2	no	—
333	C₃×D₄	—	20	8	no	—
334	C₃×D₄	—	20	4	no	—
335	C₂×C₃×C₄	—	2	2	no	—
336	C₂×C₃×C₄	—	4	4	no	—
337	C₂×C₃×C₄	—	5	4	no	—
338	C₂×C₃×C₄	—	10	2	no	—
339	C₂×C₃×C₄	—	20	2	no	—
340	C₂×C₃×C₄	—	20	4	no	—
341	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
342	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
343	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
344	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
345	C₃×C₈	—	5	4	no	—
346	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
347	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
348	C₂²×C₅	—	2	2	no	—
349	C₂²×C₅	—	4	4	no	—
350	C₂²×C₅	—	4	2	no	—
351	C₂²×C₅	C₃×#127	1	2	yes	—
352	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
353	C₂×D₅	—	4	4	no	—
354	C₂×D₅	—	4	2	no	—
355	C₄×C₅	—	4	2	no	—
356	C₄×C₅	C₃×#127	1	2	yes	—
357	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
358	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
359	Dic₅	—	2	4	no	—
360	Dic₅	—	4	2	no	—
361	#41	—	2	4	no	—
362	#41	—	2	4	no	—
363	#41	—	10	4	no	—
364	#41	—	10	4	no	—
365	C₂×Q₈	—	5	2	no	—
366	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	5	2	no	—
369	C₂×D₄	—	10	4	no	—
370	C₂×D₄	—	10	2	no	—
371	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	5	2	no	—
374	C₂²×C₄	—	10	2	no	—
375	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
376	Q₁₆	—	2	2	no	—
377	Q₁₆	—	10	4	no	—
378	Q₁₆	—	10	2	no	—
379	SD₁₆	—	2	4	no	—
380	SD₁₆	—	10	4	no	—
381	SD₁₆	—	10	4	no	—
382	SD₁₆	—	10	4	no	—
383	D₈	—	2	2	no	—
384	D₈	—	10	4	no	—
385	D₈	—	10	2	no	—
386	C₂×C₈	—	5	4	no	—
387	C₂×C₈	—	5	2	no	—
388	C₂×C₈	C₃×C₂²⋊D₅	1	4	yes	complemented
389	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
390	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
391	C₄⋊C₄	—	10	4	no	—
392	C₂²⋊C₄	—	10	4	no	—
393	C₂²⋊C₄	—	10	4	no	—
394	C₄²	—	5	2	no	—
395	C₄²	—	5	2	no	—
396	C₃×C₅	#3150	1	1	yes	characteristic, complemented, Hall
397	C₂²×C₃	—	2	2	no	—
398	C₂²×C₃	—	4	4	no	—
399	C₂²×C₃	—	4	2	no	—
400	C₂²×C₃	—	20	4	no	—
401	C₂²×C₃	—	20	2	no	—
402	C₂²×C₃	#4086	1	2	yes	—
403	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
404	C₃×C₄	—	4	2	no	—
405	C₃×C₄	—	10	4	no	—
406	C₃×C₄	—	20	2	no	—
407	C₃×C₄	#4086	1	2	yes	—
408	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
409	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
410	C₂×C₅	—	2	2	no	—
411	C₂×C₅	—	8	2	no	—
412	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
413	C₂×C₅	C₃×#575	1	2	yes	—
414	D₅	—	8	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	10	2	no	—
417	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
418	Q₈	—	2	2	no	—
419	Q₈	—	2	2	no	—
420	Q₈	—	10	2	no	—
421	Q₈	—	10	2	no	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	4	4	no	—
425	D₄	—	10	2	no	—
426	D₄	—	10	2	no	—
427	D₄	—	20	8	no	—
428	D₄	—	20	4	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	4	4	no	—
431	C₂×C₄	—	5	4	no	—
432	C₂×C₄	—	10	2	no	—
433	C₂×C₄	—	20	2	no	—
434	C₂×C₄	—	20	4	no	—
435	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
436	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
437	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
438	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
439	C₈	—	5	4	no	—
440	C₈	C₂×C₃×C₂²⋊D₅	1	2	yes	—
441	C₈	C₂×C₃×C₂²⋊D₅	1	2	yes	—
442	C₂×C₃	—	2	2	no	—
443	C₂×C₃	—	8	2	no	—
444	C₂×C₃	—	40	2	no	—
445	C₂×C₃	#66102	1	2	yes	—
446	C₂×C₃	C₂×#4086	1	1	yes	characteristic
447	C₅	C₃×#3150	1	1	yes	characteristic, complemented, Sylow
448	C₂²	—	2	2	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	20	4	no	—
452	C₂²	—	20	2	no	—
453	C₂²	C₃×#4086	1	2	yes	—
454	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
455	C₄	—	4	2	no	—
456	C₄	—	10	4	no	—
457	C₄	—	20	2	no	—
458	C₄	C₃×#4086	1	2	yes	—
459	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
460	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
461	C₃	#10615635	1	1	yes	characteristic, direct product factor, Sylow
462	C₂	—	2	2	no	—
463	C₂	—	8	2	no	—
464	C₂	—	40	2	no	—
465	C₂	C₃×#66102	1	2	yes	—
466	C₂	C₂×C₃×#4086	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#135	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₃×#135	D₅
hypocenter	C₅	C₃×#3150
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#135

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#135	C₂	semidirect
2. C₃×#66166	C₂	semidirect
3. C₂×C₃×#4096	C₂	semidirect
4. C₂×C₃×#4050	C₂	semidirect
5. C₃×#65479	C₂	semidirect
6. C₃×#65465	C₂	semidirect
7. C₃×#65456	C₂	semidirect
8. C₃×#65443	C₂	semidirect
9. C₂×C₃×#3947	C₂	semidirect
10. #10615635	C₃	direct (N × H)
38. C₂×C₅×#135	C₂×C₃	semidirect
39. #66166	C₂×C₃	semidirect
40. C₂×#4096	C₂×C₃	semidirect
41. C₂×#4050	C₂×C₃	semidirect
42. #65479	C₂×C₃	semidirect
43. #65465	C₂×C₃	semidirect
44. #65456	C₂×C₃	semidirect
45. #65443	C₂×C₃	semidirect
46. C₂×#3947	C₂×C₃	semidirect
65. C₂×C₃×C₅×C₈	D₄	semidirect
77. C₂×C₃×#168	D₄	semidirect
84. C₂×C₃×#135	D₅	semidirect
189. C₂×C₅×C₈	C₃×D₄	semidirect
201. C₂×#168	C₃×D₄	semidirect
208. C₂×#135	C₃×D₅	semidirect
255. C₂×C₃×C₈	C₂²⋊D₅	semidirect
388. C₂×C₈	C₃×C₂²⋊D₅	semidirect
396. C₃×C₅	#3150	semidirect
447. C₅	C₃×#3150	semidirect
461. C₃	#10615635	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×C₅×#135	2
C₃×#66166	2
C₂×C₃×#4096	2
C₂×C₃×#4050	2
C₃×#65479	2
C₃×#65465	2
C₃×#65456	2
C₃×#65443	2
C₂×C₃×#3947	2
#10615635	3
C₃×#3150	5

Subgroups — C3×#10615635 #14439073

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615635 #14439073