Subgroups — C₃×#10610752 #14426233

Order 1920.

992 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4050	C₂	1	2	yes	maximal, complemented
2	C₃×#65811	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×#709	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65402	C₂	1	2	yes	maximal, complemented
6	C₃×#65138	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65137	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65134	C₂	1	2	yes	maximal, complemented
9	C₃×#65133	C₂	1	2	yes	maximal, complemented
10	C₃×#65132	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65130	C₂	1	1	yes	maximal, characteristic, complemented
12	#10610752	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#709	C₂²	1	2	yes	—
14	C₂×C₃×#709	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₃×#4076	—	2	1	no	—
18	C₃×#4076	—	2	1	no	—
19	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
20	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
21	C₃×#4072	C₂²	1	1	yes	characteristic
22	C₂×C₃×Dic₂₀	C₂²	1	2	yes	—
23	C₃×#4050	—	2	8	no	—
24	C₂×C₃×D₄₀	C₂²	1	2	yes	—
25	C₂×C₃×#677	C₂²	1	2	yes	—
26	C₂×C₃×#677	C₂²	1	2	yes	—
27	C₃×#4021	C₂²	1	2	yes	—
28	C₃×#4020	C₂²	1	1	yes	characteristic
29	C₃×C₄×D₂₀	—	2	1	no	—
30	C₃×C₄×D₂₀	—	2	1	no	—
31	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
32	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
33	C₃×#4018	—	2	1	no	—
34	C₃×C₄²×D₅	—	2	1	no	—
35	C₃×#4015	C₂²	1	1	yes	characteristic
36	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
37	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
38	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
41	C₃×#3953	C₂²	1	2	yes	—
42	C₃×#3953	C₂²	1	2	yes	—
43	C₃×#3948	C₂²	1	2	yes	—
44	C₃×#3948	C₂²	1	2	yes	—
45	C₃×#3035	—	5	1	no	maximal, Hall
46	C₂×#4050	C₂×C₃	1	2	yes	complemented
47	#65811	C₂×C₃	1	1	yes	characteristic, complemented
48	C₄×#709	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
50	#65402	C₂×C₃	1	2	yes	complemented
51	#65138	C₂×C₃	1	1	yes	characteristic, complemented
52	#65137	C₂×C₃	1	1	yes	characteristic, complemented
53	#65134	C₂×C₃	1	2	yes	complemented
54	#65133	C₂×C₃	1	2	yes	complemented
55	#65132	C₂×C₃	1	1	yes	characteristic, complemented
56	#65130	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
59	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
61	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
62	C₃×#709	—	2	2	no	—
63	C₃×#709	—	2	4	no	—
64	C₃×#709	—	2	4	no	—
65	C₃×#709	D₄	1	4	yes	complemented
66	C₂×C₃×D₂₀	—	2	1	no	—
67	C₂×C₃×D₂₀	—	2	1	no	—
68	C₂×C₃×D₂₀	C₂³	1	2	yes	—
69	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₄×D₅	—	2	1	no	—
71	C₂×C₃×C₄×D₅	—	2	2	no	—
72	C₂×C₃×C₄×D₅	—	2	1	no	—
73	C₂×C₃×C₄×D₅	—	2	1	no	—
74	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
75	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
76	C₂×C₃×C₅×C₈	—	2	4	no	—
77	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
78	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
79	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
80	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
81	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
83	C₃×C₂²⋊Dic₅	—	2	1	no	—
84	C₃×#685	—	2	1	no	—
85	C₃×#685	—	2	1	no	—
86	C₃×#685	—	2	2	no	—
87	C₃×#685	—	2	2	no	—
88	C₃×C₄⋊Dic₅	—	2	1	no	—
89	C₃×C₄⋊Dic₅	—	2	1	no	—
90	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
91	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
92	C₃×#683	—	2	1	no	—
93	C₃×#683	—	2	1	no	—
94	C₃×C₄×Dic₅	—	2	1	no	—
95	C₃×C₄×Dic₅	—	2	1	no	—
96	C₃×C₄×Dic₅	—	2	1	no	—
97	C₃×Dic₂₀	—	2	4	no	—
98	C₃×D₄₀	—	2	4	no	—
99	C₃×#677	—	2	4	no	—
100	C₃×#677	—	2	4	no	—
101	C₂×C₃×#135	—	5	2	no	—
102	C₃×#532	—	5	1	no	—
103	C₃×C₄×#41	—	5	1	no	—
104	C₃×#464	—	5	2	no	—
105	C₃×#463	—	5	2	no	—
106	C₃×#462	—	5	1	no	—
107	C₃×#461	—	5	1	no	—
108	C₃×#460	—	5	1	no	—
109	C₃×#459	—	5	1	no	—
110	C₂×C₃×C₄⋊C₈	D₅	1	1	yes	characteristic, complemented
111	C₃×#416	—	5	2	no	—
112	C₂×#709	C₂²×C₃	1	2	yes	—
113	C₂×#709	C₂²×C₃	1	1	yes	characteristic
114	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
115	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
116	#4076	—	2	1	no	—
117	#4076	—	2	1	no	—
118	C₄×C₂²⋊D₅	—	2	1	no	—
119	C₄×C₂²⋊D₅	—	2	1	no	—
120	#4072	C₂²×C₃	1	1	yes	characteristic
121	C₂×Dic₂₀	C₂²×C₃	1	2	yes	—
122	#4050	—	2	8	no	—
123	C₂×D₄₀	C₂²×C₃	1	2	yes	—
124	C₂×#677	C₂²×C₃	1	2	yes	—
125	C₂×#677	C₂²×C₃	1	2	yes	—
126	#4021	C₂²×C₃	1	2	yes	—
127	#4020	C₂²×C₃	1	1	yes	characteristic
128	C₄×D₂₀	—	2	1	no	—
129	C₄×D₂₀	—	2	1	no	—
130	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
131	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
132	#4018	—	2	1	no	—
133	C₄²×D₅	—	2	1	no	—
134	#4015	C₂²×C₃	1	1	yes	characteristic
135	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
136	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
137	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
138	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
139	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
140	#3953	C₂²×C₃	1	2	yes	—
141	#3953	C₂²×C₃	1	2	yes	—
142	#3948	C₂²×C₃	1	2	yes	—
143	#3948	C₂²×C₃	1	2	yes	—
144	#3035	—	5	1	no	Sylow
145	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₃×D₅	—	2	1	no	—
147	C₂²×C₃×D₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	4	1	no	—
150	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
154	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
155	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
156	C₂×C₃×C₄×C₅	#41	1	2	yes	—
157	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
158	C₃×C₂²⋊D₅	—	2	4	no	—
159	C₃×C₂²⋊D₅	—	4	4	no	—
160	C₂×C₃×Dic₅	—	2	1	no	—
161	C₂×C₃×Dic₅	—	2	1	no	—
162	C₂×C₃×Dic₅	—	2	1	no	—
163	C₂×C₃×Dic₅	—	2	2	no	—
164	C₃×D₂₀	—	2	2	no	—
165	C₃×D₂₀	—	2	1	no	—
166	C₃×D₂₀	—	2	2	no	—
167	C₃×D₂₀	—	4	2	no	—
168	C₃×D₂₀	—	4	2	no	—
169	C₃×D₂₀	C₂×D₄	1	2	yes	—
170	C₃×C₄×D₅	—	2	4	no	—
171	C₃×C₄×D₅	—	4	2	no	—
172	C₃×C₄×D₅	—	4	4	no	—
173	C₃×C₄×D₅	—	4	2	no	—
174	C₃×Dic₁₀	—	2	1	no	—
175	C₃×Dic₁₀	—	2	2	no	—
176	C₃×Dic₁₀	—	2	2	no	—
177	C₃×Dic₁₀	C₂×D₄	1	2	yes	—
178	C₃×C₅×C₈	—	2	2	no	—
179	C₃×C₅×C₈	—	2	2	no	—
180	C₂×C₃×#41	—	5	1	no	—
181	C₂×C₃×#41	—	5	2	no	—
182	C₃×#135	—	10	8	no	—
183	C₂×C₃×Q₁₆	—	5	2	no	—
184	C₂×C₃×SD₁₆	—	5	2	no	—
185	C₂×C₃×SD₁₆	—	5	2	no	—
186	C₂×C₃×D₈	—	5	2	no	—
187	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
188	C₃×C₄⋊Q₈	—	5	1	no	—
189	C₃×#127	—	5	1	no	—
190	C₃×#124	—	5	2	no	—
191	C₃×#121	—	10	1	no	—
192	C₃×#121	—	10	1	no	—
193	C₃×C₄×Q₈	—	5	1	no	—
194	C₃×C₄×Q₈	—	5	1	no	—
195	C₃×C₄×D₄	—	5	1	no	—
196	C₃×C₄×D₄	—	5	1	no	—
197	C₃×C₄×D₄	—	10	1	no	—
198	C₃×C₄×D₄	—	10	1	no	—
199	C₃×C₄×D₄	—	10	1	no	—
200	C₃×C₄×D₄	—	10	1	no	—
201	C₃×#117	—	5	1	no	—
202	C₃×#117	—	10	1	no	—
203	C₂×C₃×C₄²	—	10	1	no	—
204	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
205	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
206	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
207	C₃×C₄⋊C₈	C₂×D₅	1	2	yes	—
208	C₃×#103	—	5	2	no	—
209	C₃×#103	—	5	2	no	—
210	C₃×#102	—	5	2	no	—
211	C₃×#102	—	5	2	no	—
212	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
215	C₂×C₂²⋊D₅	—	2	1	no	—
216	C₂×C₂²⋊D₅	—	2	2	no	—
217	#709	—	2	2	no	—
218	#709	—	2	4	no	—
219	#709	—	2	4	no	—
220	#709	C₃×D₄	1	4	yes	complemented
221	C₂×D₂₀	—	2	1	no	—
222	C₂×D₂₀	—	2	1	no	—
223	C₂×D₂₀	C₂³×C₃	1	2	yes	—
224	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
225	C₂×C₄×D₅	—	2	1	no	—
226	C₂×C₄×D₅	—	2	2	no	—
227	C₂×C₄×D₅	—	2	1	no	—
228	C₂×C₄×D₅	—	2	1	no	—
229	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
230	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
231	C₂×C₅×C₈	—	2	4	no	—
232	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
233	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
234	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
235	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
236	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
237	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
238	C₂²⋊Dic₅	—	2	1	no	—
239	#685	—	2	1	no	—
240	#685	—	2	1	no	—
241	#685	—	2	2	no	—
242	#685	—	2	2	no	—
243	C₄⋊Dic₅	—	2	1	no	—
244	C₄⋊Dic₅	—	2	1	no	—
245	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
246	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
247	#683	—	2	1	no	—
248	#683	—	2	1	no	—
249	C₄×Dic₅	—	2	1	no	—
250	C₄×Dic₅	—	2	1	no	—
251	C₄×Dic₅	—	2	1	no	—
252	Dic₂₀	—	2	4	no	—
253	D₄₀	—	2	4	no	—
254	#677	—	2	4	no	—
255	#677	—	2	4	no	—
256	C₂×#135	—	5	2	no	—
257	#532	—	5	1	no	—
258	C₄×#41	—	5	1	no	—
259	#464	—	5	2	no	—
260	#463	—	5	2	no	—
261	#462	—	5	1	no	—
262	#461	—	5	1	no	—
263	#460	—	5	1	no	—
264	#459	—	5	1	no	—
265	C₂×C₄⋊C₈	C₃×D₅	1	1	yes	characteristic, complemented
266	#416	—	5	2	no	—
267	C₂²×C₃×C₅	—	2	1	no	—
268	C₂²×C₃×C₅	—	2	1	no	—
269	C₂²×C₃×C₅	#121	1	2	yes	—
270	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₃×D₅	—	2	2	no	—
272	C₂×C₃×D₅	—	4	1	no	—
273	C₂×C₃×D₅	—	4	1	no	—
274	C₂×C₃×D₅	—	4	2	no	—
275	C₂×C₃×D₅	—	4	2	no	—
276	C₂×C₃×D₅	—	4	2	no	—
277	C₃×C₄×C₅	—	2	1	no	—
278	C₃×C₄×C₅	—	2	1	no	—
279	C₃×C₄×C₅	—	2	1	no	—
280	C₃×C₄×C₅	#121	1	2	yes	—
281	C₃×C₄×C₅	#135	1	2	yes	complemented
282	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
283	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
284	C₃×Dic₅	—	2	2	no	—
285	C₃×Dic₅	—	4	2	no	—
286	C₃×Dic₅	—	4	1	no	—
287	C₃×Dic₅	—	4	1	no	—
288	C₃×#41	—	5	4	no	—
289	C₃×#41	—	10	2	no	—
290	C₃×#41	—	10	4	no	—
291	C₃×#41	—	10	4	no	—
292	C₂×C₃×Q₈	—	5	1	no	—
293	C₂×C₃×Q₈	—	5	2	no	—
294	C₂×C₃×D₄	—	5	1	no	—
295	C₂×C₃×D₄	—	5	2	no	—
296	C₂×C₃×D₄	—	10	1	no	—
297	C₂×C₃×D₄	—	10	2	no	—
298	C₂×C₃×D₄	—	10	1	no	—
299	C₂×C₃×D₄	—	10	1	no	—
300	C₂²×C₃×C₄	—	10	1	no	—
301	C₂²×C₃×C₄	—	10	1	no	—
302	C₂²×C₃×C₄	—	10	1	no	—
303	C₂²×C₃×C₄	—	10	2	no	—
304	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
305	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
306	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
307	C₃×Q₁₆	—	10	4	no	—
308	C₃×SD₁₆	—	10	4	no	—
309	C₃×SD₁₆	—	10	4	no	—
310	C₃×D₈	—	10	4	no	—
311	C₂×C₃×C₈	—	2	4	no	—
312	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
313	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
314	C₃×C₄⋊C₄	—	5	1	no	—
315	C₃×C₄⋊C₄	—	5	1	no	—
316	C₃×C₄⋊C₄	—	10	1	no	—
317	C₃×C₄⋊C₄	—	10	1	no	—
318	C₃×C₄⋊C₄	—	10	1	no	—
319	C₃×C₄⋊C₄	—	10	1	no	—
320	C₃×C₂²⋊C₄	—	10	1	no	—
321	C₃×C₂²⋊C₄	—	10	1	no	—
322	C₃×C₂²⋊C₄	—	10	1	no	—
323	C₃×C₂²⋊C₄	—	10	2	no	—
324	C₃×C₂²⋊C₄	—	10	2	no	—
325	C₃×C₄²	—	10	1	no	—
326	C₃×C₄²	—	10	1	no	—
327	C₃×C₄²	—	10	1	no	—
328	C₃×C₄²	D₂₀	1	1	yes	characteristic
329	C₃×C₄²	D₂₀	1	1	yes	characteristic
330	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
331	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
332	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
333	C₂²×D₅	—	2	1	no	—
334	C₂²×D₅	—	2	2	no	—
335	C₂×C₄×C₅	—	2	2	no	—
336	C₂×C₄×C₅	—	4	1	no	—
337	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
338	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
339	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
340	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
341	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
342	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
343	C₂×C₄×C₅	C₃×#41	1	2	yes	—
344	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
345	C₂²⋊D₅	—	2	4	no	—
346	C₂²⋊D₅	—	4	4	no	—
347	C₂×Dic₅	—	2	1	no	—
348	C₂×Dic₅	—	2	1	no	—
349	C₂×Dic₅	—	2	1	no	—
350	C₂×Dic₅	—	2	2	no	—
351	D₂₀	—	2	2	no	—
352	D₂₀	—	2	1	no	—
353	D₂₀	—	2	2	no	—
354	D₂₀	—	4	2	no	—
355	D₂₀	—	4	2	no	—
356	D₂₀	C₂×C₃×D₄	1	2	yes	—
357	C₄×D₅	—	2	4	no	—
358	C₄×D₅	—	4	2	no	—
359	C₄×D₅	—	4	4	no	—
360	C₄×D₅	—	4	2	no	—
361	Dic₁₀	—	2	1	no	—
362	Dic₁₀	—	2	2	no	—
363	Dic₁₀	—	2	2	no	—
364	Dic₁₀	C₂×C₃×D₄	1	2	yes	—
365	C₅×C₈	—	2	2	no	—
366	C₅×C₈	—	2	2	no	—
367	C₂×#41	—	5	1	no	—
368	C₂×#41	—	5	2	no	—
369	#135	—	10	8	no	—
370	C₂×Q₁₆	—	5	2	no	—
371	C₂×SD₁₆	—	5	2	no	—
372	C₂×SD₁₆	—	5	2	no	—
373	C₂×D₈	—	5	2	no	—
374	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
375	C₄⋊Q₈	—	5	1	no	—
376	#127	—	5	1	no	—
377	#124	—	5	2	no	—
378	#121	—	10	1	no	—
379	#121	—	10	1	no	—
380	C₄×Q₈	—	5	1	no	—
381	C₄×Q₈	—	5	1	no	—
382	C₄×D₄	—	5	1	no	—
383	C₄×D₄	—	5	1	no	—
384	C₄×D₄	—	10	1	no	—
385	C₄×D₄	—	10	1	no	—
386	C₄×D₄	—	10	1	no	—
387	C₄×D₄	—	10	1	no	—
388	#117	—	5	1	no	—
389	#117	—	10	1	no	—
390	C₂×C₄²	—	10	1	no	—
391	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
392	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
393	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
394	C₄⋊C₈	C₂×C₃×D₅	1	2	yes	—
395	#103	—	5	2	no	—
396	#103	—	5	2	no	—
397	#102	—	5	2	no	—
398	#102	—	5	2	no	—
399	C₂×C₃×C₅	—	2	2	no	—
400	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
401	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
402	C₂×C₃×C₅	#575	1	1	yes	characteristic
403	C₃×D₅	—	4	2	no	—
404	C₃×D₅	—	8	2	no	—
405	C₂³×C₃	—	10	1	no	—
406	C₂³×C₃	—	10	2	no	—
407	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
408	C₃×Q₈	—	5	2	no	—
409	C₃×Q₈	—	10	1	no	—
410	C₃×Q₈	—	10	2	no	—
411	C₃×Q₈	—	10	2	no	—
412	C₃×D₄	—	5	2	no	—
413	C₃×D₄	—	10	4	no	—
414	C₃×D₄	—	10	2	no	—
415	C₃×D₄	—	10	1	no	—
416	C₃×D₄	—	10	2	no	—
417	C₃×D₄	—	20	2	no	—
418	C₃×D₄	—	20	4	no	—
419	C₃×D₄	—	20	2	no	—
420	C₂×C₃×C₄	—	2	2	no	—
421	C₂×C₃×C₄	—	4	1	no	—
422	C₂×C₃×C₄	—	10	1	no	—
423	C₂×C₃×C₄	—	10	4	no	—
424	C₂×C₃×C₄	—	10	1	no	—
425	C₂×C₃×C₄	—	10	1	no	—
426	C₂×C₃×C₄	—	10	2	no	—
427	C₂×C₃×C₄	—	20	2	no	—
428	C₂×C₃×C₄	—	20	4	no	—
429	C₂×C₃×C₄	—	20	2	no	—
430	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
431	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
432	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
433	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
434	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
435	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
436	C₂×C₃×C₄	#713	1	2	yes	—
437	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
438	C₃×C₈	—	2	2	no	—
439	C₃×C₈	—	2	2	no	—
440	C₂²×C₅	—	2	1	no	—
441	C₂²×C₅	—	2	1	no	—
442	C₂²×C₅	C₃×#121	1	2	yes	—
443	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
444	C₂×D₅	—	2	2	no	—
445	C₂×D₅	—	4	1	no	—
446	C₂×D₅	—	4	1	no	—
447	C₂×D₅	—	4	2	no	—
448	C₂×D₅	—	4	2	no	—
449	C₂×D₅	—	4	2	no	—
450	C₄×C₅	—	2	1	no	—
451	C₄×C₅	—	2	1	no	—
452	C₄×C₅	—	2	1	no	—
453	C₄×C₅	C₃×#121	1	2	yes	—
454	C₄×C₅	C₃×#135	1	2	yes	complemented
455	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
456	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
457	Dic₅	—	2	2	no	—
458	Dic₅	—	4	1	no	—
459	Dic₅	—	4	1	no	—
460	Dic₅	—	4	2	no	—
461	#41	—	5	4	no	—
462	#41	—	10	2	no	—
463	#41	—	10	4	no	—
464	#41	—	10	4	no	—
465	C₂×Q₈	—	5	1	no	—
466	C₂×Q₈	—	5	2	no	—
467	C₂×D₄	—	5	1	no	—
468	C₂×D₄	—	5	2	no	—
469	C₂×D₄	—	10	1	no	—
470	C₂×D₄	—	10	2	no	—
471	C₂×D₄	—	10	1	no	—
472	C₂×D₄	—	10	1	no	—
473	C₂²×C₄	—	10	1	no	—
474	C₂²×C₄	—	10	1	no	—
475	C₂²×C₄	—	10	1	no	—
476	C₂²×C₄	—	10	2	no	—
477	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
478	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
479	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
480	Q₁₆	—	10	4	no	—
481	SD₁₆	—	10	4	no	—
482	SD₁₆	—	10	4	no	—
483	D₈	—	10	4	no	—
484	C₂×C₈	—	2	4	no	—
485	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
486	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
487	C₄⋊C₄	—	5	1	no	—
488	C₄⋊C₄	—	5	1	no	—
489	C₄⋊C₄	—	10	1	no	—
490	C₄⋊C₄	—	10	1	no	—
491	C₄⋊C₄	—	10	1	no	—
492	C₄⋊C₄	—	10	1	no	—
493	C₂²⋊C₄	—	10	1	no	—
494	C₂²⋊C₄	—	10	1	no	—
495	C₂²⋊C₄	—	10	1	no	—
496	C₂²⋊C₄	—	10	2	no	—
497	C₂²⋊C₄	—	10	2	no	—
498	C₄²	—	10	1	no	—
499	C₄²	—	10	1	no	—
500	C₄²	—	10	1	no	—
501	C₄²	C₃×D₂₀	1	1	yes	characteristic
502	C₄²	C₃×D₂₀	1	1	yes	characteristic
503	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
504	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
505	C₃×C₅	#3035	1	1	yes	characteristic, complemented, Hall
506	C₂²×C₃	—	2	1	no	—
507	C₂²×C₃	—	2	1	no	—
508	C₂²×C₃	—	10	2	no	—
509	C₂²×C₃	—	20	1	no	—
510	C₂²×C₃	—	20	1	no	—
511	C₂²×C₃	—	20	2	no	—
512	C₂²×C₃	—	20	2	no	—
513	C₂²×C₃	—	20	2	no	—
514	C₂²×C₃	#4041	1	2	yes	—
515	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
516	C₃×C₄	—	2	1	no	—
517	C₃×C₄	—	2	1	no	—
518	C₃×C₄	—	2	1	no	—
519	C₃×C₄	—	10	2	no	—
520	C₃×C₄	—	20	1	no	—
521	C₃×C₄	—	20	1	no	—
522	C₃×C₄	—	20	2	no	—
523	C₃×C₄	#4041	1	2	yes	—
524	C₃×C₄	#4050	1	2	yes	complemented
525	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
526	C₃×C₄	C₂×#713	1	1	yes	characteristic
527	C₂×C₅	—	2	2	no	—
528	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
529	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
530	C₂×C₅	C₃×#575	1	1	yes	characteristic
531	D₅	—	4	2	no	—
532	D₅	—	8	2	no	—
533	C₂³	—	10	1	no	—
534	C₂³	—	10	2	no	—
535	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
536	Q₈	—	5	2	no	—
537	Q₈	—	10	1	no	—
538	Q₈	—	10	2	no	—
539	Q₈	—	10	2	no	—
540	D₄	—	5	2	no	—
541	D₄	—	10	4	no	—
542	D₄	—	10	2	no	—
543	D₄	—	10	1	no	—
544	D₄	—	10	2	no	—
545	D₄	—	20	2	no	—
546	D₄	—	20	4	no	—
547	D₄	—	20	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	10	1	no	—
551	C₂×C₄	—	10	4	no	—
552	C₂×C₄	—	10	1	no	—
553	C₂×C₄	—	10	1	no	—
554	C₂×C₄	—	10	2	no	—
555	C₂×C₄	—	20	2	no	—
556	C₂×C₄	—	20	4	no	—
557	C₂×C₄	—	20	2	no	—
558	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
559	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
560	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
561	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
562	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
563	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
564	C₂×C₄	C₃×#713	1	2	yes	—
565	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
566	C₈	—	2	2	no	—
567	C₈	—	2	2	no	—
568	C₂×C₃	—	2	2	no	—
569	C₂×C₃	—	20	2	no	—
570	C₂×C₃	—	40	2	no	—
571	C₂×C₃	C₂×#4041	1	1	yes	characteristic
572	C₂×C₃	C₂×#4050	1	1	yes	characteristic
573	C₂×C₃	#66082	1	1	yes	characteristic
574	C₅	C₃×#3035	1	1	yes	characteristic, complemented, Sylow
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	10	2	no	—
578	C₂²	—	20	1	no	—
579	C₂²	—	20	1	no	—
580	C₂²	—	20	2	no	—
581	C₂²	—	20	2	no	—
582	C₂²	—	20	2	no	—
583	C₂²	C₃×#4041	1	2	yes	—
584	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	10	2	no	—
589	C₄	—	20	1	no	—
590	C₄	—	20	1	no	—
591	C₄	—	20	2	no	—
592	C₄	C₃×#4041	1	2	yes	—
593	C₄	C₃×#4050	1	2	yes	complemented
594	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
595	C₄	C₂×C₃×#713	1	1	yes	characteristic
596	C₃	#10610752	1	1	yes	characteristic, direct product factor, Sylow
597	C₂	—	2	2	no	—
598	C₂	—	20	2	no	—
599	C₂	—	40	2	no	—
600	C₂	C₂×C₃×#4041	1	1	yes	characteristic
601	C₂	C₂×C₃×#4050	1	1	yes	characteristic
602	C₂	C₃×#66082	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₂₀
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×C₄⋊C₈	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₃×C₄⋊C₈	D₅
hypocenter	C₅	C₃×#3035
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4050	C₂	semidirect
2. C₃×#65811	C₂	semidirect
3. C₃×C₄×#709	C₂	semidirect
4. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
5. C₃×#65402	C₂	semidirect
6. C₃×#65138	C₂	semidirect
7. C₃×#65137	C₂	semidirect
8. C₃×#65134	C₂	semidirect
9. C₃×#65133	C₂	semidirect
10. C₃×#65132	C₂	semidirect
11. C₃×#65130	C₂	semidirect
12. #10610752	C₃	direct (N × H)
46. C₂×#4050	C₂×C₃	semidirect
47. #65811	C₂×C₃	semidirect
48. C₄×#709	C₂×C₃	semidirect
49. C₂×C₅×C₄⋊C₈	C₂×C₃	semidirect
50. #65402	C₂×C₃	semidirect
51. #65138	C₂×C₃	semidirect
52. #65137	C₂×C₃	semidirect
53. #65134	C₂×C₃	semidirect
54. #65133	C₂×C₃	semidirect
55. #65132	C₂×C₃	semidirect
56. #65130	C₂×C₃	semidirect
65. C₃×#709	D₄	semidirect
110. C₂×C₃×C₄⋊C₈	D₅	semidirect
220. #709	C₃×D₄	semidirect
265. C₂×C₄⋊C₈	C₃×D₅	semidirect
281. C₃×C₄×C₅	#135	semidirect
454. C₄×C₅	C₃×#135	semidirect
505. C₃×C₅	#3035	semidirect
524. C₃×C₄	#4050	semidirect
574. C₅	C₃×#3035	semidirect
593. C₄	C₃×#4050	semidirect
596. C₃	#10610752	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×#4050	2
C₃×#65811	2
C₃×C₄×#709	2
C₂×C₃×C₅×C₄⋊C₈	2
C₃×#65402	2
C₃×#65138	2
C₃×#65137	2
C₃×#65134	2
C₃×#65133	2
C₃×#65132	2
C₃×#65130	2
#10610752	3
C₃×#3035	5

Subgroups — C3×#10610752 #14426233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610752 #14426233