Subgroups — C₃×#10612445 #14427796

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4058	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65940	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#466	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65446	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65405	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65330	C₂	1	2	yes	maximal, complemented
8	C₃×#65176	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65169	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65067	C₂	1	2	yes	maximal, complemented
11	C₃×#65061	C₂	1	2	yes	maximal, complemented
12	#10612445	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#711	C₂²	1	2	yes	—
14	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×#121	C₂²	1	2	yes	—
18	C₃×#4084	C₂²	1	2	yes	—
19	C₃×#4083	—	2	2	no	—
20	C₃×D₄×Dic₅	—	2	2	no	—
21	C₂×C₃×#687	C₂²	1	2	yes	complemented
22	C₃×#4070	C₂²	1	2	yes	—
23	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
24	C₃×#4058	—	2	4	no	—
25	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×C₈×D₅	—	2	4	no	—
27	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
31	C₃×#4043	C₂²	1	2	yes	—
32	C₃×#4038	C₂²	1	2	yes	—
33	C₃×#4029	—	2	2	no	—
34	C₃×#4027	—	2	2	no	—
35	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₅×#102	C₂²	1	2	yes	complemented
37	C₃×#3964	C₂²	1	2	yes	complemented
38	C₃×#3950	C₂²	1	1	yes	characteristic, complemented
39	C₃×#3948	C₂²	1	2	yes	complemented
40	C₃×#3942	C₂²	1	2	yes	complemented
41	C₃×#3940	C₂²	1	2	yes	complemented
42	C₃×#3050	—	5	1	no	maximal, Hall
43	C₂×#4058	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂²×C₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
45	#65940	C₂×C₃	1	2	yes	complemented
46	C₅×#466	C₂×C₃	1	1	yes	characteristic, complemented
47	#65446	C₂×C₃	1	1	yes	characteristic, complemented
48	#65405	C₂×C₃	1	1	yes	characteristic, complemented
49	#65330	C₂×C₃	1	2	yes	complemented
50	#65176	C₂×C₃	1	1	yes	characteristic, complemented
51	#65169	C₂×C₃	1	1	yes	characteristic, complemented
52	#65067	C₂×C₃	1	2	yes	complemented
53	#65061	C₂×C₃	1	2	yes	complemented
54	C₂³×C₃×D₅	D₄	1	1	yes	characteristic
55	C₂×C₃×C₅×D₄	—	2	2	no	—
56	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
59	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
60	C₂²×C₃×Dic₅	—	2	2	no	—
61	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
62	C₃×#711	—	2	4	no	—
63	C₃×#711	—	2	4	no	—
64	C₂×C₃×C₄×D₅	—	2	2	no	—
65	C₂×C₃×C₄×D₅	—	2	2	no	—
66	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
67	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
68	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
70	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
71	C₃×C₅×D₈	—	2	2	no	—
72	C₂×C₃×C₅×C₈	—	2	2	no	—
73	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
76	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
77	C₃×C₂²⋊Dic₅	—	2	2	no	—
78	C₃×C₂²⋊Dic₅	—	2	2	no	—
79	C₃×#687	—	2	4	no	—
80	C₃×#685	—	2	2	no	—
81	C₃×#685	—	2	2	no	—
82	C₃×C₄⋊Dic₅	—	2	2	no	—
83	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
84	C₃×#683	—	2	2	no	—
85	C₃×C₄×Dic₅	—	2	2	no	—
86	C₂×C₃×#168	—	2	2	no	—
87	C₂×C₃×#168	C₂³	1	1	yes	characteristic
88	C₂×C₃×#168	C₂³	1	1	yes	characteristic
89	C₃×Dic₂₀	—	2	2	no	—
90	C₃×C₈×D₅	—	2	2	no	—
91	C₃×C₈×D₅	—	2	2	no	—
92	C₃×C₈×D₅	—	2	2	no	—
93	C₃×C₈×D₅	D₄	1	4	yes	complemented
94	C₂×C₃×#135	—	5	1	no	—
95	C₂³×C₃×C₈	—	5	1	no	—
96	C₃×#525	—	5	2	no	—
97	C₃×#467	—	5	1	no	—
98	C₃×#467	—	5	1	no	—
99	C₃×#466	—	5	1	no	—
100	C₃×#466	D₅	1	1	yes	characteristic, complemented
101	C₃×#465	—	5	2	no	—
102	C₃×#465	—	5	2	no	—
103	C₃×#427	—	5	1	no	—
104	C₃×#416	—	5	2	no	—
105	C₂×#711	C₂²×C₃	1	2	yes	—
106	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
108	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
109	C₅×#121	C₂²×C₃	1	2	yes	—
110	#4084	C₂²×C₃	1	2	yes	—
111	#4083	—	2	2	no	—
112	D₄×Dic₅	—	2	2	no	—
113	C₂×#687	C₂²×C₃	1	2	yes	complemented
114	#4070	C₂²×C₃	1	2	yes	—
115	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
116	#4058	—	2	4	no	—
117	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
118	C₂×C₈×D₅	—	2	4	no	—
119	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
123	#4043	C₂²×C₃	1	2	yes	—
124	#4038	C₂²×C₃	1	2	yes	—
125	#4029	—	2	2	no	—
126	#4027	—	2	2	no	—
127	C₅×#107	C₂²×C₃	1	1	yes	characteristic, complemented
128	C₅×#102	C₂²×C₃	1	2	yes	complemented
129	#3964	C₂²×C₃	1	2	yes	complemented
130	#3950	C₂²×C₃	1	1	yes	characteristic, complemented
131	#3948	C₂²×C₃	1	2	yes	complemented
132	#3942	C₂²×C₃	1	2	yes	complemented
133	#3940	C₂²×C₃	1	2	yes	complemented
134	#3050	—	5	1	no	Sylow
135	C₂³×C₃×C₅	—	2	2	no	—
136	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₃×D₅	—	2	2	no	—
138	C₂²×C₃×D₅	—	2	2	no	—
139	C₂²×C₃×D₅	—	2	2	no	—
140	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
142	C₃×C₅×D₄	—	2	2	no	—
143	C₃×C₅×D₄	—	2	2	no	—
144	C₃×C₅×D₄	—	4	4	no	—
145	C₂×C₃×C₄×C₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	1	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
149	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
150	C₃×C₂²⋊D₅	—	4	4	no	—
151	C₃×C₂²⋊D₅	—	4	4	no	—
152	C₂×C₃×Dic₅	—	2	2	no	—
153	C₂×C₃×Dic₅	—	2	2	no	—
154	C₂×C₃×Dic₅	—	2	2	no	—
155	C₂×C₃×Dic₅	—	4	4	no	—
156	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
157	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
158	C₃×C₄×D₅	—	2	2	no	—
159	C₃×C₄×D₅	—	2	1	no	—
160	C₃×C₄×D₅	—	2	1	no	—
161	C₃×C₄×D₅	—	2	2	no	—
162	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
163	C₃×C₄×D₅	#41	1	2	yes	—
164	C₃×Dic₁₀	—	2	2	no	—
165	C₃×Dic₁₀	—	2	2	no	—
166	C₃×C₅×C₈	—	2	1	no	—
167	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
168	C₃×#168	—	2	1	no	—
169	C₃×#168	C₂×D₄	1	2	yes	—
170	C₂×C₃×#41	—	5	2	no	—
171	C₂³×C₃×C₄	—	5	1	no	—
172	C₃×#135	—	10	4	no	—
173	C₂×C₃×Q₁₆	—	5	1	no	—
174	C₂×C₃×SD₁₆	—	5	2	no	—
175	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic, complemented
176	C₂²×C₃×C₈	—	5	1	no	—
177	C₂²×C₃×C₈	—	5	1	no	—
178	C₂²×C₃×C₈	—	5	1	no	—
179	C₂²×C₃×C₈	—	5	1	no	—
180	C₂²×C₃×C₈	—	5	1	no	—
181	C₂²×C₃×C₈	—	10	4	no	—
182	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
183	C₃×#123	—	10	2	no	—
184	C₃×C₂²⋊Q₈	—	5	2	no	—
185	C₃×C₂²⋊Q₈	—	5	2	no	—
186	C₃×#121	—	5	2	no	—
187	C₃×#121	C₂×D₅	1	2	yes	—
188	C₃×#120	—	10	2	no	—
189	C₃×C₄×D₄	—	10	2	no	—
190	C₃×C₄×D₄	—	10	2	no	—
191	C₃×#117	—	5	2	no	—
192	C₃×#107	—	5	1	no	—
193	C₃×#107	C₂×D₅	1	1	yes	characteristic, complemented
194	C₃×#106	—	5	2	no	—
195	C₃×#103	—	5	2	no	—
196	C₃×#103	—	5	2	no	—
197	C₃×#102	—	5	2	no	—
198	C₃×#102	C₂×D₅	1	2	yes	complemented
199	C₂³×D₅	C₃×D₄	1	1	yes	characteristic
200	C₂×C₅×D₄	—	2	2	no	—
201	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
202	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
203	C₂×C₂²⋊D₅	—	2	2	no	—
204	C₂×C₂²⋊D₅	—	2	2	no	—
205	C₂²×Dic₅	—	2	2	no	—
206	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
207	#711	—	2	4	no	—
208	#711	—	2	4	no	—
209	C₂×C₄×D₅	—	2	2	no	—
210	C₂×C₄×D₅	—	2	2	no	—
211	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
212	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
213	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
214	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
215	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
216	C₅×D₈	—	2	2	no	—
217	C₂×C₅×C₈	—	2	2	no	—
218	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
219	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
220	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
221	C₅×C₂²⋊C₄	—	2	2	no	—
222	C₂²⋊Dic₅	—	2	2	no	—
223	C₂²⋊Dic₅	—	2	2	no	—
224	#687	—	2	4	no	—
225	#685	—	2	2	no	—
226	#685	—	2	2	no	—
227	C₄⋊Dic₅	—	2	2	no	—
228	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
229	#683	—	2	2	no	—
230	C₄×Dic₅	—	2	2	no	—
231	C₂×#168	—	2	2	no	—
232	C₂×#168	C₂³×C₃	1	1	yes	characteristic
233	C₂×#168	C₂³×C₃	1	1	yes	characteristic
234	Dic₂₀	—	2	2	no	—
235	C₈×D₅	—	2	2	no	—
236	C₈×D₅	—	2	2	no	—
237	C₈×D₅	—	2	2	no	—
238	C₈×D₅	C₃×D₄	1	4	yes	complemented
239	C₂×#135	—	5	1	no	—
240	C₂³×C₈	—	5	1	no	—
241	#525	—	5	2	no	—
242	#467	—	5	1	no	—
243	#467	—	5	1	no	—
244	#466	—	5	1	no	—
245	#466	C₃×D₅	1	1	yes	characteristic, complemented
246	#465	—	5	2	no	—
247	#465	—	5	2	no	—
248	#427	—	5	1	no	—
249	#416	—	5	2	no	—
250	C₂²×C₃×C₅	—	2	1	no	—
251	C₂²×C₃×C₅	—	2	1	no	—
252	C₂²×C₃×C₅	—	4	2	no	—
253	C₂²×C₃×C₅	—	4	2	no	—
254	C₂²×C₃×C₅	—	4	2	no	—
255	C₂²×C₃×C₅	#135	1	2	yes	complemented
256	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₃×D₅	—	2	8	no	—
258	C₂×C₃×D₅	—	2	1	no	—
259	C₂×C₃×D₅	—	2	1	no	—
260	C₂×C₃×D₅	—	2	1	no	—
261	C₂×C₃×D₅	—	2	1	no	—
262	C₂×C₃×D₅	#121	1	2	yes	—
263	C₂×C₃×D₅	#135	1	2	yes	complemented
264	C₃×C₄×C₅	—	2	1	no	—
265	C₃×C₄×C₅	—	4	2	no	—
266	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
267	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
268	C₃×Dic₅	—	2	1	no	—
269	C₃×Dic₅	—	4	2	no	—
270	C₃×Dic₅	—	4	2	no	—
271	C₃×Dic₅	#121	1	2	yes	—
272	C₂⁴×C₃	—	5	1	no	—
273	C₃×#41	—	10	4	no	—
274	C₃×#41	—	10	4	no	—
275	C₂×C₃×Q₈	—	5	2	no	—
276	C₂×C₃×D₄	—	2	2	no	—
277	C₂×C₃×D₄	—	10	2	no	—
278	C₂×C₃×D₄	—	10	2	no	—
279	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
280	C₂²×C₃×C₄	—	5	1	no	—
281	C₂²×C₃×C₄	—	5	1	no	—
282	C₂²×C₃×C₄	—	5	1	no	—
283	C₂²×C₃×C₄	—	5	1	no	—
284	C₂²×C₃×C₄	—	5	1	no	—
285	C₂²×C₃×C₄	—	10	2	no	—
286	C₂²×C₃×C₄	—	10	2	no	—
287	C₂²×C₃×C₄	—	10	2	no	—
288	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
289	C₃×Q₁₆	—	10	2	no	—
290	C₃×SD₁₆	—	10	4	no	—
291	C₃×D₈	—	2	2	no	—
292	C₂×C₃×C₈	—	2	2	no	—
293	C₂×C₃×C₈	—	5	1	no	—
294	C₂×C₃×C₈	—	5	4	no	—
295	C₂×C₃×C₈	—	5	1	no	—
296	C₂×C₃×C₈	—	10	2	no	—
297	C₂×C₃×C₈	—	10	2	no	—
298	C₂×C₃×C₈	—	10	2	no	—
299	C₂×C₃×C₈	—	10	2	no	—
300	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
301	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
302	C₃×C₄⋊C₄	—	5	2	no	—
303	C₃×C₄⋊C₄	—	10	2	no	—
304	C₃×C₄⋊C₄	—	10	2	no	—
305	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
306	C₃×C₂²⋊C₄	—	2	2	no	—
307	C₃×C₂²⋊C₄	—	10	2	no	—
308	C₃×C₂²⋊C₄	—	10	2	no	—
309	C₃×C₂²⋊C₄	—	10	2	no	—
310	C₃×C₂²⋊C₄	—	10	2	no	—
311	C₃×C₄²	—	10	2	no	—
312	C₂³×C₅	—	2	2	no	—
313	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
314	C₂²×D₅	—	2	2	no	—
315	C₂²×D₅	—	2	2	no	—
316	C₂²×D₅	—	2	2	no	—
317	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
318	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
319	C₅×D₄	—	2	2	no	—
320	C₅×D₄	—	2	2	no	—
321	C₅×D₄	—	4	4	no	—
322	C₂×C₄×C₅	—	2	1	no	—
323	C₂×C₄×C₅	—	2	1	no	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
326	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
327	C₂²⋊D₅	—	4	4	no	—
328	C₂²⋊D₅	—	4	4	no	—
329	C₂×Dic₅	—	2	2	no	—
330	C₂×Dic₅	—	2	2	no	—
331	C₂×Dic₅	—	2	2	no	—
332	C₂×Dic₅	—	4	4	no	—
333	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
334	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
335	C₄×D₅	—	2	2	no	—
336	C₄×D₅	—	2	1	no	—
337	C₄×D₅	—	2	1	no	—
338	C₄×D₅	—	2	2	no	—
339	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
340	C₄×D₅	C₃×#41	1	2	yes	—
341	Dic₁₀	—	2	2	no	—
342	Dic₁₀	—	2	2	no	—
343	C₅×C₈	—	2	1	no	—
344	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
345	#168	—	2	1	no	—
346	#168	C₂×C₃×D₄	1	2	yes	—
347	C₂×#41	—	5	2	no	—
348	C₂³×C₄	—	5	1	no	—
349	#135	—	10	4	no	—
350	C₂×Q₁₆	—	5	1	no	—
351	C₂×SD₁₆	—	5	2	no	—
352	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
353	C₂²×C₈	—	5	1	no	—
354	C₂²×C₈	—	5	1	no	—
355	C₂²×C₈	—	5	1	no	—
356	C₂²×C₈	—	5	1	no	—
357	C₂²×C₈	—	5	1	no	—
358	C₂²×C₈	—	10	4	no	—
359	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
360	#123	—	10	2	no	—
361	C₂²⋊Q₈	—	5	2	no	—
362	C₂²⋊Q₈	—	5	2	no	—
363	#121	—	5	2	no	—
364	#121	C₂×C₃×D₅	1	2	yes	—
365	#120	—	10	2	no	—
366	C₄×D₄	—	10	2	no	—
367	C₄×D₄	—	10	2	no	—
368	#117	—	5	2	no	—
369	#107	—	5	1	no	—
370	#107	C₂×C₃×D₅	1	1	yes	characteristic, complemented
371	#106	—	5	2	no	—
372	#103	—	5	2	no	—
373	#103	—	5	2	no	—
374	#102	—	5	2	no	—
375	#102	C₂×C₃×D₅	1	2	yes	complemented
376	C₂×C₃×C₅	—	2	2	no	—
377	C₂×C₃×C₅	—	8	2	no	—
378	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
379	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
380	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
381	C₃×D₅	—	2	2	no	—
382	C₃×D₅	—	2	2	no	—
383	C₂³×C₃	—	2	2	no	—
384	C₂³×C₃	—	5	1	no	—
385	C₂³×C₃	—	5	1	no	—
386	C₂³×C₃	—	10	2	no	—
387	C₂³×C₃	—	10	2	no	—
388	C₂³×C₃	—	10	2	no	—
389	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
390	C₃×Q₈	—	10	2	no	—
391	C₃×Q₈	—	10	2	no	—
392	C₃×D₄	—	2	2	no	—
393	C₃×D₄	—	2	2	no	—
394	C₃×D₄	—	4	4	no	—
395	C₃×D₄	—	20	4	no	—
396	C₃×D₄	—	20	4	no	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	2	1	no	—
399	C₂×C₃×C₄	—	2	2	no	—
400	C₂×C₃×C₄	—	5	1	no	—
401	C₂×C₃×C₄	—	5	2	no	—
402	C₂×C₃×C₄	—	5	2	no	—
403	C₂×C₃×C₄	—	5	1	no	—
404	C₂×C₃×C₄	—	10	2	no	—
405	C₂×C₃×C₄	—	10	2	no	—
406	C₂×C₃×C₄	—	10	2	no	—
407	C₂×C₃×C₄	—	10	1	no	—
408	C₂×C₃×C₄	—	10	1	no	—
409	C₂×C₃×C₄	—	10	2	no	—
410	C₂×C₃×C₄	—	10	2	no	—
411	C₂×C₃×C₄	—	20	4	no	—
412	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
413	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
414	C₃×C₈	—	2	1	no	—
415	C₃×C₈	—	5	2	no	—
416	C₃×C₈	—	10	1	no	—
417	C₃×C₈	D₄×D₅	1	2	yes	—
418	C₂²×C₅	—	2	1	no	—
419	C₂²×C₅	—	2	1	no	—
420	C₂²×C₅	—	4	2	no	—
421	C₂²×C₅	—	4	2	no	—
422	C₂²×C₅	—	4	2	no	—
423	C₂²×C₅	C₃×#135	1	2	yes	complemented
424	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
425	C₂×D₅	—	2	8	no	—
426	C₂×D₅	—	2	1	no	—
427	C₂×D₅	—	2	1	no	—
428	C₂×D₅	—	2	1	no	—
429	C₂×D₅	—	2	1	no	—
430	C₂×D₅	C₃×#121	1	2	yes	—
431	C₂×D₅	C₃×#135	1	2	yes	complemented
432	C₄×C₅	—	2	1	no	—
433	C₄×C₅	—	4	2	no	—
434	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
435	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
436	Dic₅	—	2	1	no	—
437	Dic₅	—	4	2	no	—
438	Dic₅	—	4	2	no	—
439	Dic₅	C₃×#121	1	2	yes	—
440	C₂⁴	—	5	1	no	—
441	#41	—	10	4	no	—
442	#41	—	10	4	no	—
443	C₂×Q₈	—	5	2	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	10	2	no	—
446	C₂×D₄	—	10	2	no	—
447	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
448	C₂²×C₄	—	5	1	no	—
449	C₂²×C₄	—	5	1	no	—
450	C₂²×C₄	—	5	1	no	—
451	C₂²×C₄	—	5	1	no	—
452	C₂²×C₄	—	5	1	no	—
453	C₂²×C₄	—	10	2	no	—
454	C₂²×C₄	—	10	2	no	—
455	C₂²×C₄	—	10	2	no	—
456	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
457	Q₁₆	—	10	2	no	—
458	SD₁₆	—	10	4	no	—
459	D₈	—	2	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	5	1	no	—
462	C₂×C₈	—	5	4	no	—
463	C₂×C₈	—	5	1	no	—
464	C₂×C₈	—	10	2	no	—
465	C₂×C₈	—	10	2	no	—
466	C₂×C₈	—	10	2	no	—
467	C₂×C₈	—	10	2	no	—
468	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
469	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
470	C₄⋊C₄	—	5	2	no	—
471	C₄⋊C₄	—	10	2	no	—
472	C₄⋊C₄	—	10	2	no	—
473	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	10	2	no	—
476	C₂²⋊C₄	—	10	2	no	—
477	C₂²⋊C₄	—	10	2	no	—
478	C₂²⋊C₄	—	10	2	no	—
479	C₄²	—	10	2	no	—
480	C₃×C₅	#3050	1	1	yes	characteristic, complemented, Hall
481	C₂²×C₃	—	2	1	no	—
482	C₂²×C₃	—	2	1	no	—
483	C₂²×C₃	—	4	2	no	—
484	C₂²×C₃	—	4	2	no	—
485	C₂²×C₃	—	4	2	no	—
486	C₂²×C₃	—	5	2	no	—
487	C₂²×C₃	—	5	2	no	—
488	C₂²×C₃	—	10	8	no	—
489	C₂²×C₃	—	10	1	no	—
490	C₂²×C₃	—	10	1	no	—
491	C₂²×C₃	—	10	1	no	—
492	C₂²×C₃	—	10	1	no	—
493	C₂²×C₃	#4058	1	2	yes	complemented
494	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
495	C₃×C₄	—	2	1	no	—
496	C₃×C₄	—	4	2	no	—
497	C₃×C₄	—	5	2	no	—
498	C₃×C₄	—	10	1	no	—
499	C₃×C₄	—	20	2	no	—
500	C₃×C₄	—	20	2	no	—
501	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
502	C₃×C₄	D₅×#41	1	1	yes	characteristic
503	C₂×C₅	—	2	2	no	—
504	C₂×C₅	—	8	2	no	—
505	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
506	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
507	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
508	D₅	—	2	2	no	—
509	D₅	—	2	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	5	1	no	—
512	C₂³	—	5	1	no	—
513	C₂³	—	10	2	no	—
514	C₂³	—	10	2	no	—
515	C₂³	—	10	2	no	—
516	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
517	Q₈	—	10	2	no	—
518	Q₈	—	10	2	no	—
519	D₄	—	2	2	no	—
520	D₄	—	2	2	no	—
521	D₄	—	4	4	no	—
522	D₄	—	20	4	no	—
523	D₄	—	20	4	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	5	1	no	—
528	C₂×C₄	—	5	2	no	—
529	C₂×C₄	—	5	2	no	—
530	C₂×C₄	—	5	1	no	—
531	C₂×C₄	—	10	2	no	—
532	C₂×C₄	—	10	2	no	—
533	C₂×C₄	—	10	2	no	—
534	C₂×C₄	—	10	1	no	—
535	C₂×C₄	—	10	1	no	—
536	C₂×C₄	—	10	2	no	—
537	C₂×C₄	—	10	2	no	—
538	C₂×C₄	—	20	4	no	—
539	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
540	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
541	C₈	—	2	1	no	—
542	C₈	—	5	2	no	—
543	C₈	—	10	1	no	—
544	C₈	C₃×D₄×D₅	1	2	yes	—
545	C₂×C₃	—	2	2	no	—
546	C₂×C₃	—	8	2	no	—
547	C₂×C₃	—	10	2	no	—
548	C₂×C₃	—	10	2	no	—
549	C₂×C₃	D₅×#121	1	1	yes	characteristic
550	C₂×C₃	C₂×#4058	1	1	yes	characteristic
551	C₂×C₃	D₅×#135	1	1	yes	characteristic
552	C₅	C₃×#3050	1	1	yes	characteristic, complemented, Sylow
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	5	2	no	—
559	C₂²	—	5	2	no	—
560	C₂²	—	10	8	no	—
561	C₂²	—	10	1	no	—
562	C₂²	—	10	1	no	—
563	C₂²	—	10	1	no	—
564	C₂²	—	10	1	no	—
565	C₂²	C₃×#4058	1	2	yes	complemented
566	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	4	2	no	—
569	C₄	—	5	2	no	—
570	C₄	—	10	1	no	—
571	C₄	—	20	2	no	—
572	C₄	—	20	2	no	—
573	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
574	C₄	C₃×D₅×#41	1	1	yes	characteristic
575	C₃	#10612445	1	1	yes	characteristic, direct product factor, Sylow
576	C₂	—	2	2	no	—
577	C₂	—	8	2	no	—
578	C₂	—	10	2	no	—
579	C₂	—	10	2	no	—
580	C₂	C₃×D₅×#121	1	1	yes	characteristic
581	C₂	C₂×C₃×#4058	1	1	yes	characteristic
582	C₂	C₃×D₅×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#466	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₃×#466	D₅
hypocenter	C₅	C₃×#3050
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#466

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4058	C₂	semidirect
2. C₂²×C₃×C₈×D₅	C₂	semidirect
3. C₃×#65940	C₂	semidirect
4. C₃×C₅×#466	C₂	semidirect
5. C₃×#65446	C₂	semidirect
6. C₃×#65405	C₂	semidirect
7. C₃×#65330	C₂	semidirect
8. C₃×#65176	C₂	semidirect
9. C₃×#65169	C₂	semidirect
10. C₃×#65067	C₂	semidirect
11. C₃×#65061	C₂	semidirect
12. #10612445	C₃	direct (N × H)
15. C₂×C₃×C₅×D₈	C₂²	semidirect
21. C₂×C₃×#687	C₂²	semidirect
25. C₂×C₃×Dic₂₀	C₂²	semidirect
35. C₃×C₅×#107	C₂²	semidirect
36. C₃×C₅×#102	C₂²	semidirect
37. C₃×#3964	C₂²	semidirect
38. C₃×#3950	C₂²	semidirect
39. C₃×#3948	C₂²	semidirect
40. C₃×#3942	C₂²	semidirect
41. C₃×#3940	C₂²	semidirect
43. C₂×#4058	C₂×C₃	semidirect
44. C₂²×C₈×D₅	C₂×C₃	semidirect
45. #65940	C₂×C₃	semidirect
46. C₅×#466	C₂×C₃	semidirect
47. #65446	C₂×C₃	semidirect
48. #65405	C₂×C₃	semidirect
49. #65330	C₂×C₃	semidirect
50. #65176	C₂×C₃	semidirect
51. #65169	C₂×C₃	semidirect
52. #65067	C₂×C₃	semidirect
53. #65061	C₂×C₃	semidirect
93. C₃×C₈×D₅	D₄	semidirect
100. C₃×#466	D₅	semidirect
107. C₂×C₅×D₈	C₂²×C₃	semidirect
113. C₂×#687	C₂²×C₃	semidirect
117. C₂×Dic₂₀	C₂²×C₃	semidirect
127. C₅×#107	C₂²×C₃	semidirect
128. C₅×#102	C₂²×C₃	semidirect
129. #3964	C₂²×C₃	semidirect
130. #3950	C₂²×C₃	semidirect
131. #3948	C₂²×C₃	semidirect
132. #3942	C₂²×C₃	semidirect
133. #3940	C₂²×C₃	semidirect
175. C₂×C₃×D₈	C₂×D₅	semidirect
193. C₃×#107	C₂×D₅	semidirect
198. C₃×#102	C₂×D₅	semidirect
238. C₈×D₅	C₃×D₄	semidirect
245. #466	C₃×D₅	semidirect
255. C₂²×C₃×C₅	#135	semidirect
263. C₂×C₃×D₅	#135	semidirect
352. C₂×D₈	C₂×C₃×D₅	semidirect
370. #107	C₂×C₃×D₅	semidirect
375. #102	C₂×C₃×D₅	semidirect
423. C₂²×C₅	C₃×#135	semidirect
431. C₂×D₅	C₃×#135	semidirect
480. C₃×C₅	#3050	semidirect
493. C₂²×C₃	#4058	semidirect
552. C₅	C₃×#3050	semidirect
565. C₂²	C₃×#4058	semidirect
575. C₃	#10612445	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×#4058	2
C₂²×C₃×C₈×D₅	2
C₃×#65940	2
C₃×C₅×#466	2
C₃×#65446	2
C₃×#65405	2
C₃×#65330	2
C₃×#65176	2
C₃×#65169	2
C₃×#65067	2
C₃×#65061	2
#10612445	3
C₃×#3050	5

Subgroups — C3×#10612445 #14427796

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10612445 #14427796