Subgroups — C₃×#10610569 #14427799

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66162	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4096	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65858	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#416	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65402	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65287	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65102	C₂	1	2	yes	maximal, complemented
9	C₃×#65096	C₂	1	2	yes	maximal, complemented
10	C₃×#65067	C₂	1	2	yes	maximal, complemented
11	C₃×#65064	C₂	1	2	yes	maximal, complemented
12	#10610569	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃×#709	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×#117	C₂²	1	1	yes	characteristic
18	C₃×#4096	—	2	4	no	—
19	C₃×#4092	C₂²	1	2	yes	—
20	C₂×C₃×#689	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃×#688	C₂²	1	1	yes	characteristic, complemented
22	C₃×#4084	C₂²	1	2	yes	—
23	C₃×#4083	—	2	1	no	—
24	C₃×#4081	—	2	1	no	—
25	C₂×C₃×#687	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×#686	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₄×C₂²⋊D₅	—	2	2	no	—
28	C₃×#4072	C₂²	1	1	yes	characteristic
29	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₈×D₅	—	2	4	no	—
31	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
32	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
33	C₃×#4043	C₂²	1	2	yes	—
34	C₃×#4041	C₂²	1	2	yes	—
35	C₃×#4032	—	2	1	no	—
36	C₃×#4028	—	2	1	no	—
37	C₃×C₄×D₂₀	—	2	2	no	—
38	C₃×C₅×#103	C₂²	1	2	yes	complemented
39	C₃×C₅×#102	C₂²	1	2	yes	complemented
40	C₃×#3953	C₂²	1	2	yes	complemented
41	C₃×#3948	C₂²	1	2	yes	complemented
42	C₃×#3940	C₂²	1	2	yes	complemented
43	C₃×#3939	C₂²	1	2	yes	complemented
44	C₃×#3050	—	5	1	no	maximal, Hall
45	#66162	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×#4096	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂²×C₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
48	#65858	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#416	C₂×C₃	1	1	yes	characteristic, complemented
50	#65402	C₂×C₃	1	1	yes	characteristic, complemented
51	#65287	C₂×C₃	1	1	yes	characteristic, complemented
52	#65102	C₂×C₃	1	2	yes	complemented
53	#65096	C₂×C₃	1	2	yes	complemented
54	#65067	C₂×C₃	1	2	yes	complemented
55	#65064	C₂×C₃	1	2	yes	complemented
56	C₂³×C₃×D₅	D₄	1	1	yes	characteristic
57	C₃×C₅×#41	—	2	2	no	—
58	C₃×C₅×#41	—	2	2	no	—
59	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₅×D₄	—	2	1	no	—
61	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
62	C₂²×C₃×C₄×C₅	—	2	1	no	—
63	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
65	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
66	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
67	C₃×#709	—	2	2	no	—
68	C₃×#709	—	2	2	no	—
69	C₂×C₃×D₂₀	—	2	2	no	—
70	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₄×D₅	—	2	2	no	—
72	C₂×C₃×C₄×D₅	—	2	2	no	—
73	C₂×C₃×C₄×D₅	—	2	1	no	—
74	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
75	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
76	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₅×C₈	—	2	2	no	—
78	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
79	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
80	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
81	C₃×C₄²×C₅	—	2	1	no	—
82	C₃×C₂²⋊Dic₅	—	2	1	no	—
83	C₃×C₂²⋊Dic₅	—	2	2	no	—
84	C₃×#689	—	2	2	no	—
85	C₃×#688	—	2	2	no	—
86	C₃×#687	—	2	2	no	—
87	C₃×#686	—	2	2	no	—
88	C₃×#685	—	2	2	no	—
89	C₃×#685	—	2	2	no	—
90	C₃×#685	—	2	2	no	—
91	C₃×C₄⋊Dic₅	—	2	2	no	—
92	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
93	C₃×#683	—	2	2	no	—
94	C₃×C₄×Dic₅	—	2	1	no	—
95	C₂×C₃×#168	D₄	1	4	yes	complemented
96	C₂×C₃×#168	C₂³	1	1	yes	characteristic
97	C₂×C₃×#168	C₂³	1	1	yes	characteristic
98	C₃×C₈×D₅	—	2	4	no	—
99	C₃×C₈×D₅	—	2	4	no	—
100	C₂×C₃×#135	—	5	1	no	—
101	C₂³×C₃×C₈	—	5	1	no	—
102	C₃×#525	—	5	1	no	—
103	C₃×#525	—	5	1	no	—
104	C₃×#467	—	5	2	no	—
105	C₃×#466	—	5	2	no	—
106	C₃×#465	—	5	2	no	—
107	C₃×#465	—	5	2	no	—
108	C₃×#427	—	5	1	no	—
109	C₃×#416	—	5	1	no	—
110	C₃×#416	D₅	1	1	yes	characteristic, complemented
111	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
112	C₂×#709	C₂²×C₃	1	1	yes	characteristic
113	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
114	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
115	C₅×#117	C₂²×C₃	1	1	yes	characteristic
116	#4096	—	2	4	no	—
117	#4092	C₂²×C₃	1	2	yes	—
118	C₂×#689	C₂²×C₃	1	1	yes	characteristic, complemented
119	C₂×#688	C₂²×C₃	1	1	yes	characteristic, complemented
120	#4084	C₂²×C₃	1	2	yes	—
121	#4083	—	2	1	no	—
122	#4081	—	2	1	no	—
123	C₂×#687	C₂²×C₃	1	1	yes	characteristic, complemented
124	C₂×#686	C₂²×C₃	1	1	yes	characteristic, complemented
125	C₄×C₂²⋊D₅	—	2	2	no	—
126	#4072	C₂²×C₃	1	1	yes	characteristic
127	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₈×D₅	—	2	4	no	—
129	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
130	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
131	#4043	C₂²×C₃	1	2	yes	—
132	#4041	C₂²×C₃	1	2	yes	—
133	#4032	—	2	1	no	—
134	#4028	—	2	1	no	—
135	C₄×D₂₀	—	2	2	no	—
136	C₅×#103	C₂²×C₃	1	2	yes	complemented
137	C₅×#102	C₂²×C₃	1	2	yes	complemented
138	#3953	C₂²×C₃	1	2	yes	complemented
139	#3948	C₂²×C₃	1	2	yes	complemented
140	#3940	C₂²×C₃	1	2	yes	complemented
141	#3939	C₂²×C₃	1	2	yes	complemented
142	#3050	—	5	1	no	Sylow
143	C₂³×C₃×C₅	—	2	1	no	—
144	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₃×D₅	—	2	2	no	—
146	C₂²×C₃×D₅	—	2	4	no	—
147	C₂²×C₃×D₅	—	2	1	no	—
148	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
149	C₃×C₅×Q₈	—	2	1	no	—
150	C₃×C₅×Q₈	—	2	1	no	—
151	C₃×C₅×D₄	—	2	1	no	—
152	C₃×C₅×D₄	—	2	1	no	—
153	C₃×C₅×D₄	—	4	2	no	—
154	C₂×C₃×C₄×C₅	—	2	1	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	4	2	no	—
157	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
158	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
159	C₂×C₃×C₄×C₅	#41	1	2	yes	—
160	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
161	C₃×C₂²⋊D₅	—	4	2	no	—
162	C₃×C₂²⋊D₅	—	4	4	no	—
163	C₂×C₃×Dic₅	—	2	2	no	—
164	C₂×C₃×Dic₅	—	2	2	no	—
165	C₂×C₃×Dic₅	—	2	1	no	—
166	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
167	C₃×D₂₀	—	2	1	no	—
168	C₃×D₂₀	—	2	1	no	—
169	C₃×D₂₀	—	4	4	no	—
170	C₃×C₄×D₅	—	2	4	no	—
171	C₃×C₄×D₅	—	2	2	no	—
172	C₃×C₄×D₅	—	2	2	no	—
173	C₃×C₄×D₅	—	4	2	no	—
174	C₃×Dic₁₀	—	2	1	no	—
175	C₃×Dic₁₀	—	2	1	no	—
176	C₃×C₅×C₈	—	2	2	no	—
177	C₃×#168	C₂×D₄	1	2	yes	—
178	C₃×#168	C₂×D₄	1	2	yes	—
179	C₂×C₃×#41	—	5	1	no	—
180	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
181	C₂³×C₃×C₄	—	5	1	no	—
182	C₃×#135	—	10	4	no	—
183	C₂×C₃×Q₁₆	—	5	1	no	—
184	C₂×C₃×SD₁₆	—	5	1	no	—
185	C₂×C₃×SD₁₆	—	5	1	no	—
186	C₂×C₃×D₈	—	5	1	no	—
187	C₂²×C₃×C₈	—	5	1	no	—
188	C₂²×C₃×C₈	—	5	2	no	—
189	C₂²×C₃×C₈	—	5	2	no	—
190	C₂²×C₃×C₈	—	10	4	no	—
191	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
192	C₃×#123	—	10	1	no	—
193	C₃×#123	—	10	1	no	—
194	C₃×C₂²⋊Q₈	—	5	2	no	—
195	C₃×C₂²⋊Q₈	—	5	2	no	—
196	C₃×#121	—	5	2	no	—
197	C₃×#121	—	5	2	no	—
198	C₃×#120	—	10	1	no	—
199	C₃×#120	—	10	1	no	—
200	C₃×C₄×D₄	—	10	2	no	—
201	C₃×C₄×D₄	—	10	2	no	—
202	C₃×#117	—	5	1	no	—
203	C₃×#117	C₂×D₅	1	1	yes	characteristic
204	C₃×#107	—	5	2	no	—
205	C₃×#106	—	5	2	no	—
206	C₃×#103	—	5	2	no	—
207	C₃×#103	C₂×D₅	1	2	yes	complemented
208	C₃×#102	—	5	2	no	—
209	C₃×#102	C₂×D₅	1	2	yes	complemented
210	C₂³×D₅	C₃×D₄	1	1	yes	characteristic
211	C₅×#41	—	2	2	no	—
212	C₅×#41	—	2	2	no	—
213	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
214	C₂×C₅×D₄	—	2	1	no	—
215	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
216	C₂²×C₄×C₅	—	2	1	no	—
217	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
218	C₂×C₂²⋊D₅	—	2	1	no	—
219	C₂×C₂²⋊D₅	—	2	2	no	—
220	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
221	#709	—	2	2	no	—
222	#709	—	2	2	no	—
223	C₂×D₂₀	—	2	2	no	—
224	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
225	C₂×C₄×D₅	—	2	2	no	—
226	C₂×C₄×D₅	—	2	2	no	—
227	C₂×C₄×D₅	—	2	1	no	—
228	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
229	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
230	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
231	C₂×C₅×C₈	—	2	2	no	—
232	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
233	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
234	C₅×C₂²⋊C₄	—	2	1	no	—
235	C₄²×C₅	—	2	1	no	—
236	C₂²⋊Dic₅	—	2	1	no	—
237	C₂²⋊Dic₅	—	2	2	no	—
238	#689	—	2	2	no	—
239	#688	—	2	2	no	—
240	#687	—	2	2	no	—
241	#686	—	2	2	no	—
242	#685	—	2	2	no	—
243	#685	—	2	2	no	—
244	#685	—	2	2	no	—
245	C₄⋊Dic₅	—	2	2	no	—
246	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
247	#683	—	2	2	no	—
248	C₄×Dic₅	—	2	1	no	—
249	C₂×#168	C₃×D₄	1	4	yes	complemented
250	C₂×#168	C₂³×C₃	1	1	yes	characteristic
251	C₂×#168	C₂³×C₃	1	1	yes	characteristic
252	C₈×D₅	—	2	4	no	—
253	C₈×D₅	—	2	4	no	—
254	C₂×#135	—	5	1	no	—
255	C₂³×C₈	—	5	1	no	—
256	#525	—	5	1	no	—
257	#525	—	5	1	no	—
258	#467	—	5	2	no	—
259	#466	—	5	2	no	—
260	#465	—	5	2	no	—
261	#465	—	5	2	no	—
262	#427	—	5	1	no	—
263	#416	—	5	1	no	—
264	#416	C₃×D₅	1	1	yes	characteristic, complemented
265	C₂²×C₃×C₅	—	2	2	no	—
266	C₂²×C₃×C₅	—	4	1	no	—
267	C₂²×C₃×C₅	—	4	2	no	—
268	C₂²×C₃×C₅	#121	1	2	yes	—
269	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₃×D₅	—	2	8	no	—
271	C₂×C₃×D₅	—	2	2	no	—
272	C₂×C₃×D₅	—	2	2	no	—
273	C₂×C₃×D₅	—	4	1	no	—
274	C₂×C₃×D₅	—	4	2	no	—
275	C₂×C₃×D₅	#135	1	4	yes	complemented
276	C₃×C₄×C₅	—	4	1	no	—
277	C₃×C₄×C₅	—	4	2	no	—
278	C₃×C₄×C₅	#121	1	2	yes	—
279	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
280	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
281	C₃×Dic₅	—	2	2	no	—
282	C₃×Dic₅	—	4	1	no	—
283	C₃×Dic₅	—	4	2	no	—
284	C₂⁴×C₃	—	5	1	no	—
285	C₃×#41	—	2	2	no	—
286	C₃×#41	—	2	2	no	—
287	C₃×#41	—	10	2	no	—
288	C₃×#41	—	10	2	no	—
289	C₂×C₃×Q₈	—	5	1	no	—
290	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
291	C₂×C₃×D₄	—	2	1	no	—
292	C₂×C₃×D₄	—	5	1	no	—
293	C₂×C₃×D₄	—	10	2	no	—
294	C₂×C₃×D₄	—	10	2	no	—
295	C₂×C₃×D₄	—	10	1	no	—
296	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
297	C₂²×C₃×C₄	—	2	1	no	—
298	C₂²×C₃×C₄	—	5	1	no	—
299	C₂²×C₃×C₄	—	5	2	no	—
300	C₂²×C₃×C₄	—	5	2	no	—
301	C₂²×C₃×C₄	—	10	2	no	—
302	C₂²×C₃×C₄	—	10	2	no	—
303	C₂²×C₃×C₄	—	10	1	no	—
304	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
305	C₃×Q₁₆	—	10	2	no	—
306	C₃×SD₁₆	—	10	2	no	—
307	C₃×SD₁₆	—	10	2	no	—
308	C₃×D₈	—	10	2	no	—
309	C₂×C₃×C₈	—	2	2	no	—
310	C₂×C₃×C₈	—	5	4	no	—
311	C₂×C₃×C₈	—	5	1	no	—
312	C₂×C₃×C₈	—	5	1	no	—
313	C₂×C₃×C₈	—	10	4	no	—
314	C₂×C₃×C₈	—	10	4	no	—
315	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
316	C₃×C₄⋊C₄	—	5	2	no	—
317	C₃×C₄⋊C₄	—	10	2	no	—
318	C₃×C₄⋊C₄	—	10	2	no	—
319	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
320	C₃×C₂²⋊C₄	—	2	1	no	—
321	C₃×C₂²⋊C₄	—	10	2	no	—
322	C₃×C₂²⋊C₄	—	10	2	no	—
323	C₃×C₂²⋊C₄	—	10	2	no	—
324	C₃×C₂²⋊C₄	—	10	2	no	—
325	C₃×C₂²⋊C₄	—	10	1	no	—
326	C₃×C₄²	—	2	1	no	—
327	C₃×C₄²	—	10	1	no	—
328	C₂³×C₅	—	2	1	no	—
329	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
330	C₂²×D₅	—	2	2	no	—
331	C₂²×D₅	—	2	4	no	—
332	C₂²×D₅	—	2	1	no	—
333	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
334	C₅×Q₈	—	2	1	no	—
335	C₅×Q₈	—	2	1	no	—
336	C₅×D₄	—	2	1	no	—
337	C₅×D₄	—	2	1	no	—
338	C₅×D₄	—	4	2	no	—
339	C₂×C₄×C₅	—	2	1	no	—
340	C₂×C₄×C₅	—	2	2	no	—
341	C₂×C₄×C₅	—	4	2	no	—
342	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
343	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
344	C₂×C₄×C₅	C₃×#41	1	2	yes	—
345	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
346	C₂²⋊D₅	—	4	2	no	—
347	C₂²⋊D₅	—	4	4	no	—
348	C₂×Dic₅	—	2	2	no	—
349	C₂×Dic₅	—	2	2	no	—
350	C₂×Dic₅	—	2	1	no	—
351	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
352	D₂₀	—	2	1	no	—
353	D₂₀	—	2	1	no	—
354	D₂₀	—	4	4	no	—
355	C₄×D₅	—	2	4	no	—
356	C₄×D₅	—	2	2	no	—
357	C₄×D₅	—	2	2	no	—
358	C₄×D₅	—	4	2	no	—
359	Dic₁₀	—	2	1	no	—
360	Dic₁₀	—	2	1	no	—
361	C₅×C₈	—	2	2	no	—
362	#168	C₂×C₃×D₄	1	2	yes	—
363	#168	C₂×C₃×D₄	1	2	yes	—
364	C₂×#41	—	5	1	no	—
365	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
366	C₂³×C₄	—	5	1	no	—
367	#135	—	10	4	no	—
368	C₂×Q₁₆	—	5	1	no	—
369	C₂×SD₁₆	—	5	1	no	—
370	C₂×SD₁₆	—	5	1	no	—
371	C₂×D₈	—	5	1	no	—
372	C₂²×C₈	—	5	1	no	—
373	C₂²×C₈	—	5	2	no	—
374	C₂²×C₈	—	5	2	no	—
375	C₂²×C₈	—	10	4	no	—
376	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
377	#123	—	10	1	no	—
378	#123	—	10	1	no	—
379	C₂²⋊Q₈	—	5	2	no	—
380	C₂²⋊Q₈	—	5	2	no	—
381	#121	—	5	2	no	—
382	#121	—	5	2	no	—
383	#120	—	10	1	no	—
384	#120	—	10	1	no	—
385	C₄×D₄	—	10	2	no	—
386	C₄×D₄	—	10	2	no	—
387	#117	—	5	1	no	—
388	#117	C₂×C₃×D₅	1	1	yes	characteristic
389	#107	—	5	2	no	—
390	#106	—	5	2	no	—
391	#103	—	5	2	no	—
392	#103	C₂×C₃×D₅	1	2	yes	complemented
393	#102	—	5	2	no	—
394	#102	C₂×C₃×D₅	1	2	yes	complemented
395	C₂×C₃×C₅	—	2	2	no	—
396	C₂×C₃×C₅	—	8	1	no	—
397	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
398	C₂×C₃×C₅	C₂×#135	1	2	yes	—
399	C₃×D₅	—	2	4	no	—
400	C₃×D₅	—	8	1	no	—
401	C₂³×C₃	—	2	1	no	—
402	C₂³×C₃	—	5	2	no	—
403	C₂³×C₃	—	10	4	no	—
404	C₂³×C₃	—	10	2	no	—
405	C₂³×C₃	—	10	1	no	—
406	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
407	C₃×Q₈	—	2	1	no	—
408	C₃×Q₈	—	2	1	no	—
409	C₃×Q₈	—	10	1	no	—
410	C₃×Q₈	—	10	1	no	—
411	C₃×D₄	—	2	1	no	—
412	C₃×D₄	—	2	1	no	—
413	C₃×D₄	—	4	2	no	—
414	C₃×D₄	—	10	1	no	—
415	C₃×D₄	—	10	1	no	—
416	C₃×D₄	—	20	4	no	—
417	C₃×D₄	—	20	4	no	—
418	C₃×D₄	—	20	2	no	—
419	C₂×C₃×C₄	—	2	2	no	—
420	C₂×C₃×C₄	—	2	1	no	—
421	C₂×C₃×C₄	—	4	2	no	—
422	C₂×C₃×C₄	—	5	2	no	—
423	C₂×C₃×C₄	—	10	2	no	—
424	C₂×C₃×C₄	—	10	2	no	—
425	C₂×C₃×C₄	—	10	2	no	—
426	C₂×C₃×C₄	—	10	4	no	—
427	C₂×C₃×C₄	—	10	2	no	—
428	C₂×C₃×C₄	—	10	1	no	—
429	C₂×C₃×C₄	—	20	2	no	—
430	C₂×C₃×C₄	#709	1	2	yes	—
431	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
432	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
433	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
434	C₃×C₈	—	2	2	no	—
435	C₃×C₈	—	5	2	no	—
436	C₃×C₈	—	5	2	no	—
437	C₂²×C₅	—	2	2	no	—
438	C₂²×C₅	—	4	2	no	—
439	C₂²×C₅	—	4	1	no	—
440	C₂²×C₅	C₃×#121	1	2	yes	—
441	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
442	C₂×D₅	—	2	8	no	—
443	C₂×D₅	—	2	2	no	—
444	C₂×D₅	—	2	2	no	—
445	C₂×D₅	—	4	2	no	—
446	C₂×D₅	—	4	1	no	—
447	C₂×D₅	C₃×#135	1	4	yes	complemented
448	C₄×C₅	—	4	2	no	—
449	C₄×C₅	—	4	1	no	—
450	C₄×C₅	C₃×#121	1	2	yes	—
451	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
452	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
453	Dic₅	—	2	2	no	—
454	Dic₅	—	4	2	no	—
455	Dic₅	—	4	1	no	—
456	C₂⁴	—	5	1	no	—
457	#41	—	2	2	no	—
458	#41	—	2	2	no	—
459	#41	—	10	2	no	—
460	#41	—	10	2	no	—
461	C₂×Q₈	—	5	1	no	—
462	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	5	1	no	—
465	C₂×D₄	—	10	2	no	—
466	C₂×D₄	—	10	2	no	—
467	C₂×D₄	—	10	1	no	—
468	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	5	1	no	—
471	C₂²×C₄	—	5	2	no	—
472	C₂²×C₄	—	5	2	no	—
473	C₂²×C₄	—	10	2	no	—
474	C₂²×C₄	—	10	2	no	—
475	C₂²×C₄	—	10	1	no	—
476	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
477	Q₁₆	—	10	2	no	—
478	SD₁₆	—	10	2	no	—
479	SD₁₆	—	10	2	no	—
480	D₈	—	10	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	5	4	no	—
483	C₂×C₈	—	5	1	no	—
484	C₂×C₈	—	5	1	no	—
485	C₂×C₈	—	10	4	no	—
486	C₂×C₈	—	10	4	no	—
487	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
488	C₄⋊C₄	—	5	2	no	—
489	C₄⋊C₄	—	10	2	no	—
490	C₄⋊C₄	—	10	2	no	—
491	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	10	2	no	—
494	C₂²⋊C₄	—	10	2	no	—
495	C₂²⋊C₄	—	10	2	no	—
496	C₂²⋊C₄	—	10	2	no	—
497	C₂²⋊C₄	—	10	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	10	1	no	—
500	C₃×C₅	#3050	1	1	yes	characteristic, complemented, Hall
501	C₂²×C₃	—	2	2	no	—
502	C₂²×C₃	—	4	1	no	—
503	C₂²×C₃	—	4	2	no	—
504	C₂²×C₃	—	5	4	no	—
505	C₂²×C₃	—	10	8	no	—
506	C₂²×C₃	—	10	2	no	—
507	C₂²×C₃	—	10	2	no	—
508	C₂²×C₃	—	20	1	no	—
509	C₂²×C₃	—	20	2	no	—
510	C₂²×C₃	#4030	1	2	yes	—
511	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
512	C₃×C₄	—	4	1	no	—
513	C₃×C₄	—	4	2	no	—
514	C₃×C₄	—	10	2	no	—
515	C₃×C₄	—	20	1	no	—
516	C₃×C₄	—	20	2	no	—
517	C₃×C₄	#4030	1	2	yes	—
518	C₃×C₄	C₂×#709	1	1	yes	characteristic
519	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
520	C₂×C₅	—	2	2	no	—
521	C₂×C₅	—	8	1	no	—
522	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
523	C₂×C₅	C₂×C₃×#135	1	2	yes	—
524	D₅	—	2	4	no	—
525	D₅	—	8	1	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	5	2	no	—
528	C₂³	—	10	4	no	—
529	C₂³	—	10	2	no	—
530	C₂³	—	10	1	no	—
531	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
532	Q₈	—	2	1	no	—
533	Q₈	—	2	1	no	—
534	Q₈	—	10	1	no	—
535	Q₈	—	10	1	no	—
536	D₄	—	2	1	no	—
537	D₄	—	2	1	no	—
538	D₄	—	4	2	no	—
539	D₄	—	10	1	no	—
540	D₄	—	10	1	no	—
541	D₄	—	20	4	no	—
542	D₄	—	20	4	no	—
543	D₄	—	20	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	5	2	no	—
548	C₂×C₄	—	10	2	no	—
549	C₂×C₄	—	10	2	no	—
550	C₂×C₄	—	10	2	no	—
551	C₂×C₄	—	10	4	no	—
552	C₂×C₄	—	10	2	no	—
553	C₂×C₄	—	10	1	no	—
554	C₂×C₄	—	20	2	no	—
555	C₂×C₄	C₃×#709	1	2	yes	—
556	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
557	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
558	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
559	C₈	—	2	2	no	—
560	C₈	—	5	2	no	—
561	C₈	—	5	2	no	—
562	C₂×C₃	—	2	2	no	—
563	C₂×C₃	—	8	1	no	—
564	C₂×C₃	—	10	4	no	—
565	C₂×C₃	—	40	1	no	—
566	C₂×C₃	C₂×#4030	1	1	yes	characteristic
567	C₂×C₃	D₅×#135	1	2	yes	—
568	C₅	C₃×#3050	1	1	yes	characteristic, complemented, Sylow
569	C₂²	—	2	2	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	5	4	no	—
573	C₂²	—	10	8	no	—
574	C₂²	—	10	2	no	—
575	C₂²	—	10	2	no	—
576	C₂²	—	20	2	no	—
577	C₂²	—	20	1	no	—
578	C₂²	C₃×#4030	1	2	yes	—
579	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
580	C₄	—	4	2	no	—
581	C₄	—	4	1	no	—
582	C₄	—	10	2	no	—
583	C₄	—	20	2	no	—
584	C₄	—	20	1	no	—
585	C₄	C₃×#4030	1	2	yes	—
586	C₄	C₂×C₃×#709	1	1	yes	characteristic
587	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
588	C₃	#10610569	1	1	yes	characteristic, direct product factor, Sylow
589	C₂	—	2	2	no	—
590	C₂	—	8	1	no	—
591	C₂	—	10	4	no	—
592	C₂	—	40	1	no	—
593	C₂	C₂×C₃×#4030	1	1	yes	characteristic
594	C₂	C₃×D₅×#135	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#416	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₃×#416	D₅
hypocenter	C₅	C₃×#3050
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₃×#416

Complements

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

N	H ≅ G/N	type
1. C₃×#66162	C₂	semidirect
2. C₂×C₃×#4096	C₂	semidirect
3. C₂²×C₃×C₈×D₅	C₂	semidirect
4. C₃×#65858	C₂	semidirect
5. C₃×C₅×#416	C₂	semidirect
6. C₃×#65402	C₂	semidirect
7. C₃×#65287	C₂	semidirect
8. C₃×#65102	C₂	semidirect
9. C₃×#65096	C₂	semidirect
10. C₃×#65067	C₂	semidirect
11. C₃×#65064	C₂	semidirect
12. #10610569	C₃	direct (N × H)
20. C₂×C₃×#689	C₂²	semidirect
21. C₂×C₃×#688	C₂²	semidirect
25. C₂×C₃×#687	C₂²	semidirect
26. C₂×C₃×#686	C₂²	semidirect
38. C₃×C₅×#103	C₂²	semidirect
39. C₃×C₅×#102	C₂²	semidirect
40. C₃×#3953	C₂²	semidirect
41. C₃×#3948	C₂²	semidirect
42. C₃×#3940	C₂²	semidirect
43. C₃×#3939	C₂²	semidirect
45. #66162	C₂×C₃	semidirect
46. C₂×#4096	C₂×C₃	semidirect
47. C₂²×C₈×D₅	C₂×C₃	semidirect
48. #65858	C₂×C₃	semidirect
49. C₅×#416	C₂×C₃	semidirect
50. #65402	C₂×C₃	semidirect
51. #65287	C₂×C₃	semidirect
52. #65102	C₂×C₃	semidirect
53. #65096	C₂×C₃	semidirect
54. #65067	C₂×C₃	semidirect
55. #65064	C₂×C₃	semidirect
95. C₂×C₃×#168	D₄	semidirect
110. C₃×#416	D₅	semidirect
118. C₂×#689	C₂²×C₃	semidirect
119. C₂×#688	C₂²×C₃	semidirect
123. C₂×#687	C₂²×C₃	semidirect
124. C₂×#686	C₂²×C₃	semidirect
136. C₅×#103	C₂²×C₃	semidirect
137. C₅×#102	C₂²×C₃	semidirect
138. #3953	C₂²×C₃	semidirect
139. #3948	C₂²×C₃	semidirect
140. #3940	C₂²×C₃	semidirect
141. #3939	C₂²×C₃	semidirect
207. C₃×#103	C₂×D₅	semidirect
209. C₃×#102	C₂×D₅	semidirect
249. C₂×#168	C₃×D₄	semidirect
264. #416	C₃×D₅	semidirect
275. C₂×C₃×D₅	#135	semidirect
392. #103	C₂×C₃×D₅	semidirect
394. #102	C₂×C₃×D₅	semidirect
447. C₂×D₅	C₃×#135	semidirect
500. C₃×C₅	#3050	semidirect
568. C₅	C₃×#3050	semidirect
588. C₃	#10610569	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×#66162	2
C₂×C₃×#4096	2
C₂²×C₃×C₈×D₅	2
C₃×#65858	2
C₃×C₅×#416	2
C₃×#65402	2
C₃×#65287	2
C₃×#65102	2
C₃×#65096	2
C₃×#65067	2
C₃×#65064	2
#10610569	3
C₃×#3050	5

Subgroups — C3×#10610569 #14427799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610569 #14427799