Subgroups — C₃×#10611174 #14460112

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65897	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#65885	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65403	C₂	1	2	yes	maximal, complemented
5	C₃×#65402	C₂	1	2	yes	maximal, complemented
6	C₃×#65131	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65130	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65023	C₂	1	2	yes	maximal, complemented
9	C₃×#65012	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64970	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611174	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#709	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
15	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₃×#4084	—	2	1	no	—
17	C₃×#4084	—	2	1	no	—
18	C₃×#4076	C₂²	1	2	yes	—
19	C₃×#4072	C₂²	1	2	yes	—
20	C₃×#4070	C₂²	1	2	yes	—
21	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
22	C₂×C₃×#677	C₂²	1	2	yes	—
23	C₃×#4038	—	2	1	no	—
24	C₃×D₅×C₄⋊C₄	—	2	1	no	—
25	C₃×#4031	—	2	2	no	—
26	C₃×#4029	—	2	2	no	—
27	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
28	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
29	C₃×#4015	C₂²	1	1	yes	characteristic
30	C₃×#4015	C₂²	1	1	yes	characteristic
31	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
33	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
34	C₃×#3953	C₂²	1	2	yes	—
35	C₃×#3953	C₂²	1	1	yes	characteristic
36	C₃×#3953	C₂²	1	1	yes	characteristic
37	C₃×#3950	C₂²	1	1	yes	characteristic
38	C₃×#3949	C₂²	1	2	yes	—
39	C₃×#3948	C₂²	1	2	yes	—
40	C₃×#3948	C₂²	1	2	yes	—
41	C₃×#3948	C₂²	1	2	yes	—
42	C₃×#3303	—	5	1	no	maximal, Hall
43	#65897	C₂×C₃	1	1	yes	characteristic, complemented
44	#65885	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×C₈×D₄	C₂×C₃	1	1	yes	characteristic, complemented
46	#65403	C₂×C₃	1	2	yes	complemented
47	#65402	C₂×C₃	1	2	yes	complemented
48	#65131	C₂×C₃	1	1	yes	characteristic, complemented
49	#65130	C₂×C₃	1	1	yes	characteristic, complemented
50	#65023	C₂×C₃	1	2	yes	complemented
51	#65012	C₂×C₃	1	2	yes	complemented
52	C₄×D₄₀	C₂×C₃	1	1	yes	characteristic, complemented
53	#64970	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
57	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
58	C₃×#709	—	2	4	no	—
59	C₃×#709	—	4	2	no	—
60	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
61	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₄×D₅	—	2	1	no	—
63	C₂×C₃×C₄×D₅	—	2	1	no	—
64	C₂×C₃×C₄×D₅	—	2	2	no	—
65	C₂×C₃×Dic₁₀	—	2	1	no	—
66	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
67	C₂×C₃×C₅×C₈	—	4	2	no	—
68	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
71	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
72	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
73	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₃×C₂²⋊Dic₅	—	2	2	no	—
75	C₃×C₂²⋊Dic₅	—	2	2	no	—
76	C₃×#685	—	2	1	no	—
77	C₃×#685	—	2	1	no	—
78	C₃×#685	—	2	2	no	—
79	C₃×C₄⋊Dic₅	—	2	1	no	—
80	C₃×C₄⋊Dic₅	—	2	1	no	—
81	C₃×C₄⋊Dic₅	—	2	1	no	—
82	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
83	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
84	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
85	C₃×#683	—	2	2	no	—
86	C₃×C₄×Dic₅	—	2	2	no	—
87	C₃×D₄₀	—	2	2	no	—
88	C₃×#677	—	4	2	no	—
89	C₃×#555	—	5	1	no	—
90	C₃×#547	—	5	1	no	—
91	C₃×#487	—	5	1	no	—
92	C₃×#485	—	5	2	no	—
93	C₃×#476	—	5	1	no	—
94	C₃×#465	—	5	2	no	—
95	C₃×#461	—	5	1	no	—
96	C₃×#449	—	5	2	no	—
97	C₃×C₄×D₈	—	5	1	no	—
98	C₃×C₈×D₄	D₅	1	1	yes	characteristic, complemented
99	C₃×#416	—	5	2	no	—
100	C₂×#709	C₂²×C₃	1	2	yes	—
101	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
102	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
103	#4084	—	2	1	no	—
104	#4084	—	2	1	no	—
105	#4076	C₂²×C₃	1	2	yes	—
106	#4072	C₂²×C₃	1	2	yes	—
107	#4070	C₂²×C₃	1	2	yes	—
108	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic
109	C₂×#677	C₂²×C₃	1	2	yes	—
110	#4038	—	2	1	no	—
111	D₅×C₄⋊C₄	—	2	1	no	—
112	#4031	—	2	2	no	—
113	#4029	—	2	2	no	—
114	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
115	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
116	#4015	C₂²×C₃	1	1	yes	characteristic
117	#4015	C₂²×C₃	1	1	yes	characteristic
118	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
119	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
120	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
121	#3953	C₂²×C₃	1	2	yes	—
122	#3953	C₂²×C₃	1	1	yes	characteristic
123	#3953	C₂²×C₃	1	1	yes	characteristic
124	#3950	C₂²×C₃	1	1	yes	characteristic
125	#3949	C₂²×C₃	1	2	yes	—
126	#3948	C₂²×C₃	1	2	yes	—
127	#3948	C₂²×C₃	1	2	yes	—
128	#3948	C₂²×C₃	1	2	yes	—
129	#3303	—	5	1	no	Sylow
130	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
131	C₂²×C₃×D₅	—	2	1	no	—
132	C₂²×C₃×D₅	—	2	1	no	—
133	C₃×C₅×D₄	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
137	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₃×C₂²⋊D₅	—	4	4	no	—
141	C₃×C₂²⋊D₅	—	8	2	no	—
142	C₂×C₃×Dic₅	—	2	1	no	—
143	C₂×C₃×Dic₅	—	2	2	no	—
144	C₂×C₃×Dic₅	—	2	1	no	—
145	C₂×C₃×Dic₅	—	2	2	no	—
146	C₃×D₂₀	—	2	1	no	—
147	C₃×D₂₀	—	2	1	no	—
148	C₃×D₂₀	—	2	1	no	—
149	C₃×D₂₀	#41	1	2	yes	—
150	C₃×C₄×D₅	—	4	4	no	—
151	C₃×C₄×D₅	—	4	2	no	—
152	C₃×C₄×D₅	—	4	2	no	—
153	C₃×Dic₁₀	—	2	2	no	—
154	C₃×Dic₁₀	—	2	2	no	—
155	C₃×Dic₁₀	—	8	1	no	—
156	C₃×C₅×C₈	—	2	1	no	—
157	C₃×C₅×C₈	—	2	2	no	—
158	C₃×C₅×C₈	—	2	1	no	—
159	C₂×C₃×#41	—	5	2	no	—
160	C₂×C₃×SD₁₆	—	5	2	no	—
161	C₂×C₃×D₈	—	5	1	no	—
162	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
163	C₃×C₄⋊Q₈	—	5	1	no	—
164	C₃×C₄⋊Q₈	—	5	1	no	—
165	C₃×#124	—	10	2	no	—
166	C₃×#123	—	10	2	no	—
167	C₃×C₂²⋊Q₈	—	5	2	no	—
168	C₃×#121	—	5	2	no	—
169	C₃×#121	—	10	1	no	—
170	C₃×#121	—	10	1	no	—
171	C₃×C₄×D₄	—	5	1	no	—
172	C₃×C₄×D₄	—	5	1	no	—
173	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
174	C₃×#117	—	5	2	no	—
175	C₃×#117	—	10	1	no	—
176	C₂×C₃×C₄⋊C₄	—	10	1	no	—
177	C₃×#107	—	5	1	no	—
178	C₃×#106	—	5	2	no	—
179	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
180	C₃×#103	—	5	2	no	—
181	C₃×#103	—	5	2	no	—
182	C₃×#103	—	5	2	no	—
183	C₃×#102	—	5	1	no	—
184	C₃×#102	—	5	2	no	—
185	C₃×#102	—	5	1	no	—
186	C₃×C₂²⋊C₈	C₂×D₅	1	2	yes	—
187	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
188	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
190	C₂×C₂²⋊D₅	—	2	2	no	—
191	C₂×C₂²⋊D₅	—	2	2	no	—
192	#709	—	2	4	no	—
193	#709	—	4	2	no	—
194	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
195	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
196	C₂×C₄×D₅	—	2	2	no	—
197	C₂×C₄×D₅	—	2	1	no	—
198	C₂×C₄×D₅	—	2	1	no	—
199	C₂×Dic₁₀	—	2	1	no	—
200	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
201	C₂×C₅×C₈	—	4	2	no	—
202	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
203	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
204	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
205	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
206	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
207	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
208	C₂²⋊Dic₅	—	2	2	no	—
209	C₂²⋊Dic₅	—	2	2	no	—
210	#685	—	2	1	no	—
211	#685	—	2	1	no	—
212	#685	—	2	2	no	—
213	C₄⋊Dic₅	—	2	1	no	—
214	C₄⋊Dic₅	—	2	1	no	—
215	C₄⋊Dic₅	—	2	1	no	—
216	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
217	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
218	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
219	#683	—	2	2	no	—
220	C₄×Dic₅	—	2	2	no	—
221	D₄₀	—	2	2	no	—
222	#677	—	4	2	no	—
223	#555	—	5	1	no	—
224	#547	—	5	1	no	—
225	#487	—	5	1	no	—
226	#485	—	5	2	no	—
227	#476	—	5	1	no	—
228	#465	—	5	2	no	—
229	#461	—	5	1	no	—
230	#449	—	5	2	no	—
231	C₄×D₈	—	5	1	no	—
232	C₈×D₄	C₃×D₅	1	1	yes	characteristic, complemented
233	#416	—	5	2	no	—
234	C₂²×C₃×C₅	—	2	2	no	—
235	C₂²×C₃×C₅	—	2	2	no	—
236	C₂²×C₃×C₅	—	2	2	no	—
237	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₃×D₅	—	2	2	no	—
239	C₂×C₃×D₅	—	4	1	no	—
240	C₂×C₃×D₅	—	4	1	no	—
241	C₂×C₃×D₅	—	4	1	no	—
242	C₂×C₃×D₅	—	4	1	no	—
243	C₂×C₃×D₅	—	4	1	no	—
244	C₃×C₄×C₅	—	2	2	no	—
245	C₃×C₄×C₅	—	2	1	no	—
246	C₃×C₄×C₅	#135	1	2	yes	—
247	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
248	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
249	C₃×Dic₅	—	4	2	no	—
250	C₃×Dic₅	—	4	1	no	—
251	C₃×Dic₅	—	4	1	no	—
252	C₃×Dic₅	—	4	2	no	—
253	C₃×#41	—	10	4	no	—
254	C₃×#41	—	20	2	no	—
255	C₂×C₃×Q₈	—	5	2	no	—
256	C₂×C₃×Q₈	—	10	1	no	—
257	C₂×C₃×D₄	—	5	1	no	—
258	C₂×C₃×D₄	—	5	1	no	—
259	C₂×C₃×D₄	—	10	2	no	—
260	C₂×C₃×D₄	—	10	2	no	—
261	C₂×C₃×D₄	D₂₀	1	1	yes	characteristic
262	C₂²×C₃×C₄	—	10	1	no	—
263	C₂²×C₃×C₄	—	10	2	no	—
264	C₂²×C₃×C₄	—	10	1	no	—
265	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
266	C₃×SD₁₆	—	20	2	no	—
267	C₃×D₈	—	10	2	no	—
268	C₂×C₃×C₈	—	4	2	no	—
269	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
270	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
271	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
272	C₃×C₄⋊C₄	—	5	2	no	—
273	C₃×C₄⋊C₄	—	5	1	no	—
274	C₃×C₄⋊C₄	—	5	1	no	—
275	C₃×C₄⋊C₄	—	10	2	no	—
276	C₃×C₄⋊C₄	—	10	1	no	—
277	C₃×C₄⋊C₄	—	10	1	no	—
278	C₃×C₄⋊C₄	—	10	1	no	—
279	C₃×C₄⋊C₄	D₂₀	1	1	yes	characteristic
280	C₃×C₂²⋊C₄	—	10	2	no	—
281	C₃×C₂²⋊C₄	—	10	2	no	—
282	C₃×C₂²⋊C₄	—	10	2	no	—
283	C₃×C₂²⋊C₄	—	10	1	no	—
284	C₃×C₂²⋊C₄	—	10	1	no	—
285	C₃×C₂²⋊C₄	D₂₀	1	2	yes	—
286	C₃×C₄²	—	10	2	no	—
287	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
288	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
289	C₂²×D₅	—	2	1	no	—
290	C₂²×D₅	—	2	1	no	—
291	C₅×D₄	—	2	2	no	—
292	C₂×C₄×C₅	—	2	2	no	—
293	C₂×C₄×C₅	—	2	2	no	—
294	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
295	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
297	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
298	C₂²⋊D₅	—	4	4	no	—
299	C₂²⋊D₅	—	8	2	no	—
300	C₂×Dic₅	—	2	1	no	—
301	C₂×Dic₅	—	2	2	no	—
302	C₂×Dic₅	—	2	1	no	—
303	C₂×Dic₅	—	2	2	no	—
304	D₂₀	—	2	1	no	—
305	D₂₀	—	2	1	no	—
306	D₂₀	—	2	1	no	—
307	D₂₀	C₃×#41	1	2	yes	—
308	C₄×D₅	—	4	4	no	—
309	C₄×D₅	—	4	2	no	—
310	C₄×D₅	—	4	2	no	—
311	Dic₁₀	—	2	2	no	—
312	Dic₁₀	—	2	2	no	—
313	Dic₁₀	—	8	1	no	—
314	C₅×C₈	—	2	1	no	—
315	C₅×C₈	—	2	2	no	—
316	C₅×C₈	—	2	1	no	—
317	C₂×#41	—	5	2	no	—
318	C₂×SD₁₆	—	5	2	no	—
319	C₂×D₈	—	5	1	no	—
320	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
321	C₄⋊Q₈	—	5	1	no	—
322	C₄⋊Q₈	—	5	1	no	—
323	#124	—	10	2	no	—
324	#123	—	10	2	no	—
325	C₂²⋊Q₈	—	5	2	no	—
326	#121	—	5	2	no	—
327	#121	—	10	1	no	—
328	#121	—	10	1	no	—
329	C₄×D₄	—	5	1	no	—
330	C₄×D₄	—	5	1	no	—
331	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
332	#117	—	5	2	no	—
333	#117	—	10	1	no	—
334	C₂×C₄⋊C₄	—	10	1	no	—
335	#107	—	5	1	no	—
336	#106	—	5	2	no	—
337	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
338	#103	—	5	2	no	—
339	#103	—	5	2	no	—
340	#103	—	5	2	no	—
341	#102	—	5	1	no	—
342	#102	—	5	2	no	—
343	#102	—	5	1	no	—
344	C₂²⋊C₈	C₂×C₃×D₅	1	2	yes	—
345	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
346	C₂×C₃×C₅	—	4	2	no	—
347	C₂×C₃×C₅	#546	1	1	yes	characteristic
348	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
349	C₂×C₃×C₅	#577	1	1	yes	characteristic
350	C₃×D₅	—	4	2	no	—
351	C₃×D₅	—	8	1	no	—
352	C₂³×C₃	—	10	1	no	—
353	C₂³×C₃	—	10	1	no	—
354	C₂³×C₃	C₂×D₂₀	1	2	yes	—
355	C₃×Q₈	—	10	2	no	—
356	C₃×Q₈	—	10	2	no	—
357	C₃×Q₈	—	40	1	no	—
358	C₃×D₄	—	2	2	no	—
359	C₃×D₄	—	5	2	no	—
360	C₃×D₄	—	10	1	no	—
361	C₃×D₄	—	10	1	no	—
362	C₃×D₄	—	10	1	no	—
363	C₃×D₄	—	20	4	no	—
364	C₃×D₄	—	40	2	no	—
365	C₂×C₃×C₄	—	2	2	no	—
366	C₂×C₃×C₄	—	2	2	no	—
367	C₂×C₃×C₄	—	10	1	no	—
368	C₂×C₃×C₄	—	10	2	no	—
369	C₂×C₃×C₄	—	10	1	no	—
370	C₂×C₃×C₄	—	10	2	no	—
371	C₂×C₃×C₄	—	20	4	no	—
372	C₂×C₃×C₄	—	20	2	no	—
373	C₂×C₃×C₄	—	20	2	no	—
374	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
375	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
376	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
377	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
378	C₃×C₈	—	2	1	no	—
379	C₃×C₈	—	2	2	no	—
380	C₃×C₈	—	2	1	no	—
381	C₂²×C₅	—	2	2	no	—
382	C₂²×C₅	—	2	2	no	—
383	C₂²×C₅	—	2	2	no	—
384	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
385	C₂×D₅	—	2	2	no	—
386	C₂×D₅	—	4	1	no	—
387	C₂×D₅	—	4	1	no	—
388	C₂×D₅	—	4	1	no	—
389	C₂×D₅	—	4	1	no	—
390	C₂×D₅	—	4	1	no	—
391	C₄×C₅	—	2	1	no	—
392	C₄×C₅	—	2	2	no	—
393	C₄×C₅	C₃×#135	1	2	yes	—
394	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
395	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
396	Dic₅	—	4	1	no	—
397	Dic₅	—	4	1	no	—
398	Dic₅	—	4	2	no	—
399	Dic₅	—	4	2	no	—
400	#41	—	10	4	no	—
401	#41	—	20	2	no	—
402	C₂×Q₈	—	5	2	no	—
403	C₂×Q₈	—	10	1	no	—
404	C₂×D₄	—	5	1	no	—
405	C₂×D₄	—	5	1	no	—
406	C₂×D₄	—	10	2	no	—
407	C₂×D₄	—	10	2	no	—
408	C₂×D₄	C₃×D₂₀	1	1	yes	characteristic
409	C₂²×C₄	—	10	1	no	—
410	C₂²×C₄	—	10	2	no	—
411	C₂²×C₄	—	10	1	no	—
412	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
413	SD₁₆	—	20	2	no	—
414	D₈	—	10	2	no	—
415	C₂×C₈	—	4	2	no	—
416	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
417	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
418	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
419	C₄⋊C₄	—	5	2	no	—
420	C₄⋊C₄	—	5	1	no	—
421	C₄⋊C₄	—	5	1	no	—
422	C₄⋊C₄	—	10	1	no	—
423	C₄⋊C₄	—	10	2	no	—
424	C₄⋊C₄	—	10	1	no	—
425	C₄⋊C₄	—	10	1	no	—
426	C₄⋊C₄	C₃×D₂₀	1	1	yes	characteristic
427	C₂²⋊C₄	—	10	2	no	—
428	C₂²⋊C₄	—	10	2	no	—
429	C₂²⋊C₄	—	10	2	no	—
430	C₂²⋊C₄	—	10	1	no	—
431	C₂²⋊C₄	—	10	1	no	—
432	C₂²⋊C₄	C₃×D₂₀	1	2	yes	—
433	C₄²	—	10	2	no	—
434	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
435	C₃×C₅	#3303	1	1	yes	characteristic, complemented, Hall
436	C₂²×C₃	—	2	2	no	—
437	C₂²×C₃	—	2	2	no	—
438	C₂²×C₃	—	2	2	no	—
439	C₂²×C₃	—	10	2	no	—
440	C₂²×C₃	—	20	1	no	—
441	C₂²×C₃	—	20	1	no	—
442	C₂²×C₃	—	20	1	no	—
443	C₂²×C₃	—	20	1	no	—
444	C₂²×C₃	—	20	1	no	—
445	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
446	C₃×C₄	—	2	1	no	—
447	C₃×C₄	—	2	2	no	—
448	C₃×C₄	—	20	1	no	—
449	C₃×C₄	—	20	1	no	—
450	C₃×C₄	—	20	2	no	—
451	C₃×C₄	—	20	2	no	—
452	C₃×C₄	#4050	1	2	yes	—
453	C₃×C₄	#4144	1	1	yes	characteristic
454	C₃×C₄	D₅×#41	1	1	yes	characteristic
455	C₂×C₅	—	4	2	no	—
456	C₂×C₅	C₃×#546	1	1	yes	characteristic
457	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
458	C₂×C₅	C₃×#577	1	1	yes	characteristic
459	D₅	—	4	2	no	—
460	D₅	—	8	1	no	—
461	C₂³	—	10	1	no	—
462	C₂³	—	10	1	no	—
463	C₂³	C₂×C₃×D₂₀	1	2	yes	—
464	Q₈	—	10	2	no	—
465	Q₈	—	10	2	no	—
466	Q₈	—	40	1	no	—
467	D₄	—	2	2	no	—
468	D₄	—	5	2	no	—
469	D₄	—	10	1	no	—
470	D₄	—	10	1	no	—
471	D₄	—	10	1	no	—
472	D₄	—	20	4	no	—
473	D₄	—	40	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	10	1	no	—
477	C₂×C₄	—	10	2	no	—
478	C₂×C₄	—	10	1	no	—
479	C₂×C₄	—	10	2	no	—
480	C₂×C₄	—	20	4	no	—
481	C₂×C₄	—	20	2	no	—
482	C₂×C₄	—	20	2	no	—
483	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
484	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
485	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
486	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
487	C₈	—	2	1	no	—
488	C₈	—	2	2	no	—
489	C₈	—	2	1	no	—
490	C₂×C₃	—	4	2	no	—
491	C₂×C₃	—	20	2	no	—
492	C₂×C₃	—	40	1	no	—
493	C₂×C₃	#65888	1	1	yes	characteristic
494	C₂×C₃	C₂×#4050	1	1	yes	characteristic
495	C₂×C₃	#66085	1	1	yes	characteristic
496	C₅	C₃×#3303	1	1	yes	characteristic, complemented, Sylow
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	10	2	no	—
501	C₂²	—	20	1	no	—
502	C₂²	—	20	1	no	—
503	C₂²	—	20	1	no	—
504	C₂²	—	20	1	no	—
505	C₂²	—	20	1	no	—
506	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
507	C₄	—	2	2	no	—
508	C₄	—	2	1	no	—
509	C₄	—	20	2	no	—
510	C₄	—	20	1	no	—
511	C₄	—	20	1	no	—
512	C₄	—	20	2	no	—
513	C₄	C₃×#4050	1	2	yes	—
514	C₄	C₃×#4144	1	1	yes	characteristic
515	C₄	C₃×D₅×#41	1	1	yes	characteristic
516	C₃	#10611174	1	1	yes	characteristic, direct product factor, Sylow
517	C₂	—	4	2	no	—
518	C₂	—	20	2	no	—
519	C₂	—	40	1	no	—
520	C₂	C₃×#65888	1	1	yes	characteristic
521	C₂	C₂×C₃×#4050	1	1	yes	characteristic
522	C₂	C₃×#66085	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₂₀
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×C₈×D₄	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₃×C₈×D₄	D₅
hypocenter	C₅	C₃×#3303
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×D₄ ◁ C₃×C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₃×#65897	C₂	semidirect
2. C₃×#65885	C₂	semidirect
3. C₃×C₅×C₈×D₄	C₂	semidirect
4. C₃×#65403	C₂	semidirect
5. C₃×#65402	C₂	semidirect
6. C₃×#65131	C₂	semidirect
7. C₃×#65130	C₂	semidirect
8. C₃×#65023	C₂	semidirect
9. C₃×#65012	C₂	semidirect
10. C₃×C₄×D₄₀	C₂	semidirect
11. C₃×#64970	C₂	semidirect
12. #10611174	C₃	direct (N × H)
43. #65897	C₂×C₃	semidirect
44. #65885	C₂×C₃	semidirect
45. C₅×C₈×D₄	C₂×C₃	semidirect
46. #65403	C₂×C₃	semidirect
47. #65402	C₂×C₃	semidirect
48. #65131	C₂×C₃	semidirect
49. #65130	C₂×C₃	semidirect
50. #65023	C₂×C₃	semidirect
51. #65012	C₂×C₃	semidirect
52. C₄×D₄₀	C₂×C₃	semidirect
53. #64970	C₂×C₃	semidirect
98. C₃×C₈×D₄	D₅	semidirect
232. C₈×D₄	C₃×D₅	semidirect
435. C₃×C₅	#3303	semidirect
496. C₅	C₃×#3303	semidirect
516. C₃	#10611174	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×#65897	2
C₃×#65885	2
C₃×C₅×C₈×D₄	2
C₃×#65403	2
C₃×#65402	2
C₃×#65131	2
C₃×#65130	2
C₃×#65023	2
C₃×#65012	2
C₃×C₄×D₄₀	2
C₃×#64970	2
#10611174	3
C₃×#3303	5

Subgroups — C3×#10611174 #14460112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611174 #14460112