Subgroups — C₃×#10615634 #14438884

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 504 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×#65480	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65470	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65464	C₂	1	2	yes	maximal, complemented
8	C₃×#65457	C₂	1	2	yes	maximal, complemented
9	C₃×#65444	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65440	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×C₈×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
12	#10615634	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
14	C₂×C₃×#709	C₂²	1	2	yes	—
15	C₃×C₅×#135	—	2	4	no	—
16	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
18	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
20	C₃×#4096	—	2	8	no	—
21	C₃×#4093	C₂²	1	2	yes	—
22	C₃×#4090	C₂²	1	2	yes	—
23	C₂×C₃×#689	C₂²	1	2	yes	—
24	C₂×C₃×#688	C₂²	1	2	yes	—
25	C₃×#4086	C₂²	1	2	yes	—
26	C₃×#4085	—	2	4	no	—
27	C₃×#4082	C₂²	1	2	yes	—
28	C₂×C₃×#687	C₂²	1	2	yes	—
29	C₂×C₃×#686	C₂²	1	2	yes	—
30	C₃×C₄×C₂²⋊D₅	—	2	4	no	—
31	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
32	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
33	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic
34	C₃×#4050	—	2	4	no	—
35	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
36	C₂×C₃×#677	C₂²	1	2	yes	—
37	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
38	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
39	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
40	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
41	C₃×#3147	—	5	1	no	maximal, Hall
42	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic, complemented
43	#66166	C₂×C₃	1	2	yes	complemented
44	C₂×#4096	C₂×C₃	1	2	yes	complemented
45	C₂×#4050	C₂×C₃	1	1	yes	characteristic, complemented
46	#65480	C₂×C₃	1	1	yes	characteristic, complemented
47	#65470	C₂×C₃	1	1	yes	characteristic, complemented
48	#65464	C₂×C₃	1	2	yes	complemented
49	#65457	C₂×C₃	1	2	yes	complemented
50	#65444	C₂×C₃	1	1	yes	characteristic, complemented
51	#65440	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂×C₈×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
53	C₃×C₅×#41	—	2	4	no	—
54	C₃×C₅×#41	—	2	4	no	—
55	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
56	C₂×C₃×C₅×D₄	—	2	2	no	—
57	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
58	C₂²×C₃×C₄×C₅	—	2	2	no	—
59	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
61	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
62	C₂²×C₃×Dic₅	D₄	1	2	yes	—
63	C₃×#709	—	2	4	no	—
64	C₃×#709	—	2	4	no	—
65	C₂×C₃×D₂₀	C₂³	1	2	yes	—
66	C₂×C₃×C₄×D₅	—	2	2	no	—
67	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
68	C₃×C₅×Q₁₆	—	2	2	no	—
69	C₃×C₅×SD₁₆	—	2	4	no	—
70	C₃×C₅×D₈	—	2	2	no	—
71	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
72	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₃×C₂²⋊Dic₅	—	2	4	no	—
75	C₃×#689	—	2	4	no	—
76	C₃×#688	—	2	4	no	—
77	C₃×#687	—	2	4	no	—
78	C₃×#686	—	2	4	no	—
79	C₃×#685	—	2	4	no	—
80	C₃×#683	—	2	4	no	—
81	C₃×C₄×Dic₅	D₄	1	2	yes	—
82	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
83	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
84	C₂×C₃×#168	D₄	1	4	yes	complemented
85	C₂×C₃×#168	C₂³	1	1	yes	characteristic
86	C₂×C₃×#168	C₂³	1	1	yes	characteristic
87	C₃×Dic₂₀	—	2	2	no	—
88	C₃×D₄₀	—	2	2	no	—
89	C₃×#677	—	2	4	no	—
90	C₂×C₃×#135	—	5	2	no	—
91	C₂×C₃×#135	—	5	1	no	—
92	C₂×C₃×#135	D₅	1	1	yes	characteristic, complemented
93	C₃×#532	—	5	2	no	—
94	C₃×#495	—	5	1	no	—
95	C₃×#495	—	5	2	no	—
96	C₃×#495	—	5	1	no	—
97	C₃×#494	—	5	1	no	—
98	C₃×#493	—	5	1	no	—
99	C₃×#492	—	5	2	no	—
100	C₂×C₃×C₄×C₈	—	5	1	no	—
101	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
102	C₂×#709	C₂²×C₃	1	2	yes	—
103	C₅×#135	—	2	4	no	—
104	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
106	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
107	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
108	#4096	—	2	8	no	—
109	#4093	C₂²×C₃	1	2	yes	—
110	#4090	C₂²×C₃	1	2	yes	—
111	C₂×#689	C₂²×C₃	1	2	yes	—
112	C₂×#688	C₂²×C₃	1	2	yes	—
113	#4086	C₂²×C₃	1	2	yes	—
114	#4085	—	2	4	no	—
115	#4082	C₂²×C₃	1	2	yes	—
116	C₂×#687	C₂²×C₃	1	2	yes	—
117	C₂×#686	C₂²×C₃	1	2	yes	—
118	C₄×C₂²⋊D₅	—	2	4	no	—
119	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
120	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
121	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic
122	#4050	—	2	4	no	—
123	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic
124	C₂×#677	C₂²×C₃	1	2	yes	—
125	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
126	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
127	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
128	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
129	#3147	—	5	1	no	Sylow
130	C₂³×C₃×C₅	—	2	2	no	—
131	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₃×D₅	—	2	2	no	—
133	C₃×C₅×Q₈	—	2	2	no	—
134	C₃×C₅×Q₈	—	2	2	no	—
135	C₃×C₅×D₄	—	2	2	no	—
136	C₃×C₅×D₄	—	2	2	no	—
137	C₃×C₅×D₄	—	4	4	no	—
138	C₂×C₃×C₄×C₅	—	2	2	no	—
139	C₂×C₃×C₄×C₅	—	4	4	no	—
140	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
143	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
144	C₃×C₂²⋊D₅	—	4	4	no	—
145	C₃×C₂²⋊D₅	—	4	8	no	—
146	C₂×C₃×Dic₅	—	2	4	no	—
147	C₂×C₃×Dic₅	—	2	2	no	—
148	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
149	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
150	C₃×D₂₀	—	2	2	no	—
151	C₃×D₂₀	—	2	2	no	—
152	C₃×C₄×D₅	—	4	4	no	—
153	C₃×Dic₁₀	—	2	2	no	—
154	C₃×Dic₁₀	—	2	2	no	—
155	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
156	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
157	C₃×#168	C₂×D₄	1	2	yes	—
158	C₃×#168	C₂×D₄	1	2	yes	—
159	C₂×C₃×#41	—	5	2	no	—
160	C₂×C₃×#41	C₂×D₅	1	2	yes	—
161	C₃×#135	—	2	4	no	—
162	C₃×#135	—	10	8	no	—
163	C₃×#135	—	10	4	no	—
164	C₂×C₃×Q₁₆	—	5	2	no	—
165	C₂×C₃×Q₁₆	—	5	1	no	—
166	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
167	C₂×C₃×SD₁₆	—	5	2	no	—
168	C₂×C₃×SD₁₆	—	5	2	no	—
169	C₂×C₃×SD₁₆	—	5	2	no	—
170	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	—
171	C₂×C₃×D₈	—	5	2	no	—
172	C₂×C₃×D₈	—	5	1	no	—
173	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic
174	C₂²×C₃×C₈	—	5	1	no	—
175	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
176	C₃×C₄⋊Q₈	—	5	2	no	—
177	C₃×#127	—	5	2	no	—
178	C₃×#124	—	5	2	no	—
179	C₃×#124	—	5	2	no	—
180	C₃×#121	—	10	4	no	—
181	C₃×C₄×D₄	—	10	4	no	—
182	C₂×C₃×C₄²	—	5	1	no	—
183	C₃×C₄×C₈	—	5	1	no	—
184	C₃×C₄×C₈	—	5	1	no	—
185	C₃×C₄×C₈	—	5	1	no	—
186	C₃×C₄×C₈	—	5	1	no	—
187	C₅×#41	—	2	4	no	—
188	C₅×#41	—	2	4	no	—
189	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
190	C₂×C₅×D₄	—	2	2	no	—
191	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
192	C₂²×C₄×C₅	—	2	2	no	—
193	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
194	C₂×C₂²⋊D₅	—	2	2	no	—
195	C₂×C₂²⋊D₅	—	2	4	no	—
196	C₂²×Dic₅	C₃×D₄	1	2	yes	—
197	#709	—	2	4	no	—
198	#709	—	2	4	no	—
199	C₂×D₂₀	C₂³×C₃	1	2	yes	—
200	C₂×C₄×D₅	—	2	2	no	—
201	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
202	C₅×Q₁₆	—	2	2	no	—
203	C₅×SD₁₆	—	2	4	no	—
204	C₅×D₈	—	2	2	no	—
205	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
206	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
207	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
208	C₂²⋊Dic₅	—	2	4	no	—
209	#689	—	2	4	no	—
210	#688	—	2	4	no	—
211	#687	—	2	4	no	—
212	#686	—	2	4	no	—
213	#685	—	2	4	no	—
214	#683	—	2	4	no	—
215	C₄×Dic₅	C₃×D₄	1	2	yes	—
216	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
217	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
218	C₂×#168	C₃×D₄	1	4	yes	complemented
219	C₂×#168	C₂³×C₃	1	1	yes	characteristic
220	C₂×#168	C₂³×C₃	1	1	yes	characteristic
221	Dic₂₀	—	2	2	no	—
222	D₄₀	—	2	2	no	—
223	#677	—	2	4	no	—
224	C₂×#135	—	5	2	no	—
225	C₂×#135	—	5	1	no	—
226	C₂×#135	C₃×D₅	1	1	yes	characteristic, complemented
227	#532	—	5	2	no	—
228	#495	—	5	1	no	—
229	#495	—	5	2	no	—
230	#495	—	5	1	no	—
231	#494	—	5	1	no	—
232	#493	—	5	1	no	—
233	#492	—	5	2	no	—
234	C₂×C₄×C₈	—	5	1	no	—
235	C₂²×C₃×C₅	—	2	2	no	—
236	C₂²×C₃×C₅	—	4	2	no	—
237	C₂²×C₃×C₅	—	4	4	no	—
238	C₂²×C₃×C₅	#127	1	2	yes	—
239	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₃×D₅	—	4	2	no	—
241	C₂×C₃×D₅	—	4	4	no	—
242	C₃×C₄×C₅	—	4	2	no	—
243	C₃×C₄×C₅	#127	1	2	yes	—
244	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
245	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
246	C₃×Dic₅	—	2	2	no	—
247	C₃×Dic₅	—	4	2	no	—
248	C₃×Dic₅	#135	1	4	yes	complemented
249	C₃×#41	—	2	4	no	—
250	C₃×#41	—	2	4	no	—
251	C₃×#41	—	10	4	no	—
252	C₃×#41	—	10	4	no	—
253	C₂×C₃×Q₈	—	5	2	no	—
254	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
255	C₂×C₃×D₄	—	2	2	no	—
256	C₂×C₃×D₄	—	5	2	no	—
257	C₂×C₃×D₄	—	10	4	no	—
258	C₂×C₃×D₄	—	10	2	no	—
259	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
260	C₂²×C₃×C₄	—	2	2	no	—
261	C₂²×C₃×C₄	—	5	2	no	—
262	C₂²×C₃×C₄	—	10	2	no	—
263	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
264	C₃×Q₁₆	—	2	2	no	—
265	C₃×Q₁₆	—	10	4	no	—
266	C₃×Q₁₆	—	10	2	no	—
267	C₃×SD₁₆	—	2	4	no	—
268	C₃×SD₁₆	—	10	4	no	—
269	C₃×SD₁₆	—	10	4	no	—
270	C₃×SD₁₆	—	10	4	no	—
271	C₃×D₈	—	2	2	no	—
272	C₃×D₈	—	10	4	no	—
273	C₃×D₈	—	10	2	no	—
274	C₂×C₃×C₈	—	5	4	no	—
275	C₂×C₃×C₈	—	5	1	no	—
276	C₂×C₃×C₈	—	5	1	no	—
277	C₂×C₃×C₈	C₂²⋊D₅	1	4	yes	complemented
278	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
279	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
280	C₃×C₄⋊C₄	—	10	4	no	—
281	C₃×C₂²⋊C₄	—	10	4	no	—
282	C₃×C₂²⋊C₄	—	10	4	no	—
283	C₃×C₄²	—	5	2	no	—
284	C₃×C₄²	—	5	1	no	—
285	C₃×C₄²	—	5	1	no	—
286	C₂³×C₅	—	2	2	no	—
287	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
288	C₂²×D₅	—	2	2	no	—
289	C₅×Q₈	—	2	2	no	—
290	C₅×Q₈	—	2	2	no	—
291	C₅×D₄	—	2	2	no	—
292	C₅×D₄	—	2	2	no	—
293	C₅×D₄	—	4	4	no	—
294	C₂×C₄×C₅	—	2	2	no	—
295	C₂×C₄×C₅	—	4	4	no	—
296	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
297	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
298	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
299	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
300	C₂²⋊D₅	—	4	4	no	—
301	C₂²⋊D₅	—	4	8	no	—
302	C₂×Dic₅	—	2	4	no	—
303	C₂×Dic₅	—	2	2	no	—
304	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
305	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
306	D₂₀	—	2	2	no	—
307	D₂₀	—	2	2	no	—
308	C₄×D₅	—	4	4	no	—
309	Dic₁₀	—	2	2	no	—
310	Dic₁₀	—	2	2	no	—
311	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
312	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
313	#168	C₂×C₃×D₄	1	2	yes	—
314	#168	C₂×C₃×D₄	1	2	yes	—
315	C₂×#41	—	5	2	no	—
316	C₂×#41	C₂×C₃×D₅	1	2	yes	—
317	#135	—	2	4	no	—
318	#135	—	10	8	no	—
319	#135	—	10	4	no	—
320	C₂×Q₁₆	—	5	2	no	—
321	C₂×Q₁₆	—	5	1	no	—
322	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic
323	C₂×SD₁₆	—	5	2	no	—
324	C₂×SD₁₆	—	5	2	no	—
325	C₂×SD₁₆	—	5	2	no	—
326	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	—
327	C₂×D₈	—	5	2	no	—
328	C₂×D₈	—	5	1	no	—
329	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic
330	C₂²×C₈	—	5	1	no	—
331	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
332	C₄⋊Q₈	—	5	2	no	—
333	#127	—	5	2	no	—
334	#124	—	5	2	no	—
335	#124	—	5	2	no	—
336	#121	—	10	4	no	—
337	C₄×D₄	—	10	4	no	—
338	C₂×C₄²	—	5	1	no	—
339	C₄×C₈	—	5	1	no	—
340	C₄×C₈	—	5	1	no	—
341	C₄×C₈	—	5	1	no	—
342	C₄×C₈	—	5	1	no	—
343	C₂×C₃×C₅	—	2	2	no	—
344	C₂×C₃×C₅	—	8	2	no	—
345	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
346	C₂×C₃×C₅	C₂×#135	1	2	yes	—
347	C₃×D₅	—	8	2	no	—
348	C₂³×C₃	—	2	2	no	—
349	C₂³×C₃	—	10	2	no	—
350	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
351	C₃×Q₈	—	2	2	no	—
352	C₃×Q₈	—	2	2	no	—
353	C₃×Q₈	—	10	2	no	—
354	C₃×Q₈	—	10	2	no	—
355	C₃×D₄	—	2	2	no	—
356	C₃×D₄	—	2	2	no	—
357	C₃×D₄	—	4	4	no	—
358	C₃×D₄	—	10	2	no	—
359	C₃×D₄	—	10	2	no	—
360	C₃×D₄	—	20	8	no	—
361	C₃×D₄	—	20	4	no	—
362	C₂×C₃×C₄	—	2	2	no	—
363	C₂×C₃×C₄	—	4	4	no	—
364	C₂×C₃×C₄	—	5	2	no	—
365	C₂×C₃×C₄	—	5	2	no	—
366	C₂×C₃×C₄	—	10	4	no	—
367	C₂×C₃×C₄	—	10	2	no	—
368	C₂×C₃×C₄	—	20	4	no	—
369	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
370	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
371	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
372	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
373	C₃×C₈	—	5	2	no	—
374	C₃×C₈	—	5	2	no	—
375	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
376	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
377	C₂²×C₅	—	2	2	no	—
378	C₂²×C₅	—	4	4	no	—
379	C₂²×C₅	—	4	2	no	—
380	C₂²×C₅	C₃×#127	1	2	yes	—
381	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
382	C₂×D₅	—	4	4	no	—
383	C₂×D₅	—	4	2	no	—
384	C₄×C₅	—	4	2	no	—
385	C₄×C₅	C₃×#127	1	2	yes	—
386	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
387	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
388	Dic₅	—	2	2	no	—
389	Dic₅	—	4	2	no	—
390	Dic₅	C₃×#135	1	4	yes	complemented
391	#41	—	2	4	no	—
392	#41	—	2	4	no	—
393	#41	—	10	4	no	—
394	#41	—	10	4	no	—
395	C₂×Q₈	—	5	2	no	—
396	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	5	2	no	—
399	C₂×D₄	—	10	4	no	—
400	C₂×D₄	—	10	2	no	—
401	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	5	2	no	—
404	C₂²×C₄	—	10	2	no	—
405	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
406	Q₁₆	—	2	2	no	—
407	Q₁₆	—	10	4	no	—
408	Q₁₆	—	10	2	no	—
409	SD₁₆	—	2	4	no	—
410	SD₁₆	—	10	4	no	—
411	SD₁₆	—	10	4	no	—
412	SD₁₆	—	10	4	no	—
413	D₈	—	2	2	no	—
414	D₈	—	10	4	no	—
415	D₈	—	10	2	no	—
416	C₂×C₈	—	5	4	no	—
417	C₂×C₈	—	5	1	no	—
418	C₂×C₈	—	5	1	no	—
419	C₂×C₈	C₃×C₂²⋊D₅	1	4	yes	complemented
420	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
421	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
422	C₄⋊C₄	—	10	4	no	—
423	C₂²⋊C₄	—	10	4	no	—
424	C₂²⋊C₄	—	10	4	no	—
425	C₄²	—	5	2	no	—
426	C₄²	—	5	1	no	—
427	C₄²	—	5	1	no	—
428	C₃×C₅	#3147	1	1	yes	characteristic, complemented, Hall
429	C₂²×C₃	—	2	2	no	—
430	C₂²×C₃	—	4	4	no	—
431	C₂²×C₃	—	4	2	no	—
432	C₂²×C₃	—	20	4	no	—
433	C₂²×C₃	—	20	2	no	—
434	C₂²×C₃	#4086	1	2	yes	—
435	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
436	C₃×C₄	—	4	2	no	—
437	C₃×C₄	—	5	4	no	—
438	C₃×C₄	—	10	2	no	—
439	C₃×C₄	—	20	2	no	—
440	C₃×C₄	#4086	1	2	yes	—
441	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
442	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
443	C₂×C₅	—	2	2	no	—
444	C₂×C₅	—	8	2	no	—
445	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
446	C₂×C₅	C₂×C₃×#135	1	2	yes	—
447	D₅	—	8	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	10	2	no	—
450	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
451	Q₈	—	2	2	no	—
452	Q₈	—	2	2	no	—
453	Q₈	—	10	2	no	—
454	Q₈	—	10	2	no	—
455	D₄	—	2	2	no	—
456	D₄	—	2	2	no	—
457	D₄	—	4	4	no	—
458	D₄	—	10	2	no	—
459	D₄	—	10	2	no	—
460	D₄	—	20	8	no	—
461	D₄	—	20	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	5	2	no	—
465	C₂×C₄	—	5	2	no	—
466	C₂×C₄	—	10	4	no	—
467	C₂×C₄	—	10	2	no	—
468	C₂×C₄	—	20	4	no	—
469	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
470	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
471	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
472	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
473	C₈	—	5	2	no	—
474	C₈	—	5	2	no	—
475	C₈	C₂×C₃×C₂²⋊D₅	1	2	yes	—
476	C₈	C₂×C₃×C₂²⋊D₅	1	2	yes	—
477	C₂×C₃	—	2	2	no	—
478	C₂×C₃	—	8	2	no	—
479	C₂×C₃	—	40	2	no	—
480	C₂×C₃	D₅×#135	1	2	yes	—
481	C₂×C₃	C₂×#4086	1	1	yes	characteristic
482	C₅	C₃×#3147	1	1	yes	characteristic, complemented, Sylow
483	C₂²	—	2	2	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	20	4	no	—
487	C₂²	—	20	2	no	—
488	C₂²	C₃×#4086	1	2	yes	—
489	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
490	C₄	—	4	2	no	—
491	C₄	—	5	4	no	—
492	C₄	—	10	2	no	—
493	C₄	—	20	2	no	—
494	C₄	C₃×#4086	1	2	yes	—
495	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
496	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
497	C₃	#10615634	1	1	yes	characteristic, direct product factor, Sylow
498	C₂	—	2	2	no	—
499	C₂	—	8	2	no	—
500	C₂	—	40	2	no	—
501	C₂	C₃×D₅×#135	1	2	yes	—
502	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×#3147
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×#65480	C₂	semidirect
6. C₃×#65470	C₂	semidirect
7. C₃×#65464	C₂	semidirect
8. C₃×#65457	C₂	semidirect
9. C₃×#65444	C₂	semidirect
10. C₃×#65440	C₂	semidirect
11. C₂×C₃×C₈×Dic₅	C₂	semidirect
12. #10615634	C₃	direct (N × H)
42. C₂×C₅×#135	C₂×C₃	semidirect
43. #66166	C₂×C₃	semidirect
44. C₂×#4096	C₂×C₃	semidirect
45. C₂×#4050	C₂×C₃	semidirect
46. #65480	C₂×C₃	semidirect
47. #65470	C₂×C₃	semidirect
48. #65464	C₂×C₃	semidirect
49. #65457	C₂×C₃	semidirect
50. #65444	C₂×C₃	semidirect
51. #65440	C₂×C₃	semidirect
52. C₂×C₈×Dic₅	C₂×C₃	semidirect
71. C₂×C₃×C₅×C₈	D₄	semidirect
84. C₂×C₃×#168	D₄	semidirect
92. C₂×C₃×#135	D₅	semidirect
205. C₂×C₅×C₈	C₃×D₄	semidirect
218. C₂×#168	C₃×D₄	semidirect
226. C₂×#135	C₃×D₅	semidirect
248. C₃×Dic₅	#135	semidirect
277. C₂×C₃×C₈	C₂²⋊D₅	semidirect
390. Dic₅	C₃×#135	semidirect
419. C₂×C₈	C₃×C₂²⋊D₅	semidirect
428. C₃×C₅	#3147	semidirect
482. C₅	C₃×#3147	semidirect
497. C₃	#10615634	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×#65480	2
C₃×#65470	2
C₃×#65464	2
C₃×#65457	2
C₃×#65444	2
C₃×#65440	2
C₂×C₃×C₈×Dic₅	2
#10615634	3
C₃×#3147	5

Subgroups — C3×#10615634 #14438884

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615634 #14438884