Subgroups — C₃×#10612711 #14458285

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66060	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#474	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65377	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×#686	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65172	C₂	1	2	yes	maximal, complemented
7	C₃×#65171	C₂	1	2	yes	maximal, complemented
8	C₃×#65132	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65123	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65062	C₂	1	2	yes	maximal, complemented
11	C₃×D₅×#102	C₂	1	2	yes	maximal, complemented
12	#10612711	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#713	—	2	1	no	—
14	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
15	C₂²×C₃×D₂₀	—	2	1	no	—
16	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₃×#4092	—	2	1	no	—
19	C₂×C₃×#686	C₂²	1	1	yes	characteristic
20	C₃×#4076	—	2	1	no	—
21	C₂×C₃×D₄₀	C₂²	1	2	yes	complemented
22	C₂×C₃×C₈×D₅	C₂²	1	2	yes	complemented
23	C₃×#4041	C₂²	1	2	yes	—
24	C₃×#4041	C₂²	1	2	yes	complemented
25	C₃×#4040	—	2	2	no	—
26	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
27	C₃×#4028	—	2	2	no	—
28	C₃×#4020	C₂²	1	1	yes	characteristic
29	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
30	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×#107	C₂²	1	2	yes	complemented
32	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×#102	C₂²	1	2	yes	—
34	C₃×#3964	C₂²	1	1	yes	characteristic
35	C₃×#3953	C₂²	1	2	yes	complemented
36	C₃×#3952	C₂²	1	2	yes	complemented
37	C₃×#3941	C₂²	1	1	yes	characteristic, complemented
38	C₃×#3941	C₂²	1	2	yes	complemented
39	C₃×#3941	C₂²	1	2	yes	complemented
40	C₃×#3939	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₄×#168	C₂²	1	1	yes	characteristic, complemented
42	C₃×#3294	—	5	1	no	maximal, Hall
43	#66060	C₂×C₃	1	1	yes	characteristic, complemented
44	D₄×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#474	C₂×C₃	1	1	yes	characteristic, complemented
46	#65377	C₂×C₃	1	1	yes	characteristic, complemented
47	C₄×#686	C₂×C₃	1	1	yes	characteristic, complemented
48	#65172	C₂×C₃	1	2	yes	complemented
49	#65171	C₂×C₃	1	2	yes	complemented
50	#65132	C₂×C₃	1	1	yes	characteristic, complemented
51	#65123	C₂×C₃	1	1	yes	characteristic, complemented
52	#65062	C₂×C₃	1	2	yes	complemented
53	D₅×#102	C₂×C₃	1	2	yes	complemented
54	C₂³×C₃×D₅	—	2	2	no	—
55	C₂×C₃×C₅×Q₈	—	2	1	no	—
56	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	—	2	1	no	—
58	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
59	C₃×#713	—	4	4	no	—
60	C₃×D₄×D₅	—	2	4	no	—
61	C₃×D₄×D₅	—	4	2	no	—
62	C₂×C₃×D₂₀	—	2	2	no	—
63	C₂×C₃×D₂₀	—	2	2	no	—
64	C₂×C₃×D₂₀	—	2	1	no	—
65	C₂×C₃×D₂₀	—	2	1	no	—
66	C₂×C₃×D₂₀	—	4	4	no	—
67	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
68	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
69	C₂×C₃×D₂₀	C₂³	1	2	yes	—
70	C₂×C₃×C₄×D₅	—	2	2	no	—
71	C₂×C₃×C₄×D₅	—	2	1	no	—
72	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
73	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
74	C₃×C₅×C₄⋊C₄	—	2	1	no	—
75	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
77	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
78	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₃×#686	—	2	2	no	—
80	C₃×#685	—	2	1	no	—
81	C₃×#685	—	2	2	no	—
82	C₃×#685	—	2	2	no	—
83	C₃×#685	D₄	1	2	yes	—
84	C₃×C₄⋊Dic₅	D₄	1	1	yes	characteristic
85	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
86	C₃×#683	—	2	2	no	—
87	C₂×C₃×#168	C₂³	1	1	yes	characteristic
88	C₂×C₃×#168	C₂³	1	1	yes	characteristic
89	C₃×D₄₀	—	4	2	no	—
90	C₃×C₈×D₅	—	4	2	no	—
91	C₃×#547	—	5	1	no	—
92	C₃×D₄²	—	5	1	no	—
93	C₃×#486	—	5	1	no	—
94	C₃×#480	—	5	2	no	—
95	C₃×#474	D₅	1	1	yes	characteristic, complemented
96	C₃×#466	—	5	2	no	—
97	C₃×#459	—	5	1	no	—
98	C₃×#447	—	5	2	no	—
99	C₃×C₄×D₈	—	5	1	no	—
100	C₃×C₈×D₄	—	5	1	no	—
101	C₂×C₃×#102	—	5	2	no	—
102	C₂×#713	—	2	1	no	—
103	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
104	C₂²×D₂₀	—	2	1	no	—
105	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
106	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
107	#4092	—	2	1	no	—
108	C₂×#686	C₂²×C₃	1	1	yes	characteristic
109	#4076	—	2	1	no	—
110	C₂×D₄₀	C₂²×C₃	1	2	yes	complemented
111	C₂×C₈×D₅	C₂²×C₃	1	2	yes	complemented
112	#4041	C₂²×C₃	1	2	yes	—
113	#4041	C₂²×C₃	1	2	yes	complemented
114	#4040	—	2	2	no	—
115	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
116	#4028	—	2	2	no	—
117	#4020	C₂²×C₃	1	1	yes	characteristic
118	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
119	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
120	C₅×#107	C₂²×C₃	1	2	yes	complemented
121	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
122	C₅×#102	C₂²×C₃	1	2	yes	—
123	#3964	C₂²×C₃	1	1	yes	characteristic
124	#3953	C₂²×C₃	1	2	yes	complemented
125	#3952	C₂²×C₃	1	2	yes	complemented
126	#3941	C₂²×C₃	1	1	yes	characteristic, complemented
127	#3941	C₂²×C₃	1	2	yes	complemented
128	#3941	C₂²×C₃	1	2	yes	complemented
129	#3939	C₂²×C₃	1	1	yes	characteristic, complemented
130	C₄×#168	C₂²×C₃	1	1	yes	characteristic, complemented
131	#3294	—	5	1	no	Sylow
132	C₂³×C₃×C₅	—	2	1	no	—
133	C₂²×C₃×D₅	—	2	1	no	—
134	C₂²×C₃×D₅	—	2	2	no	—
135	C₂²×C₃×D₅	—	4	4	no	—
136	C₂²×C₃×D₅	—	4	4	no	—
137	C₂²×C₃×D₅	—	8	2	no	—
138	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
139	C₃×C₅×Q₈	—	4	2	no	—
140	C₃×C₅×D₄	—	2	1	no	—
141	C₃×C₅×D₄	#41	1	2	yes	complemented
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	1	no	—
144	C₂×C₃×C₄×C₅	—	4	2	no	—
145	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
147	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
148	C₃×C₂²⋊D₅	—	4	4	no	—
149	C₂×C₃×Dic₅	—	2	1	no	—
150	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
151	C₃×D₂₀	—	2	1	no	—
152	C₃×D₂₀	—	2	2	no	—
153	C₃×D₂₀	—	2	1	no	—
154	C₃×D₂₀	—	2	2	no	—
155	C₃×D₂₀	—	4	4	no	—
156	C₃×D₂₀	—	4	4	no	—
157	C₃×D₂₀	—	4	2	no	—
158	C₃×D₂₀	—	8	1	no	—
159	C₃×D₂₀	D₈	1	4	yes	complemented
160	C₃×C₄×D₅	—	2	2	no	—
161	C₃×C₄×D₅	—	2	2	no	—
162	C₃×C₄×D₅	—	4	4	no	—
163	C₃×C₄×D₅	—	4	2	no	—
164	C₃×C₅×C₈	—	2	2	no	—
165	C₃×#168	—	2	1	no	—
166	C₃×#168	—	2	1	no	—
167	C₂×C₃×#41	—	10	1	no	—
168	C₂²×C₃×D₄	—	5	2	no	—
169	C₂²×C₃×D₄	—	10	1	no	—
170	C₂×C₃×D₈	—	5	1	no	—
171	C₂×C₃×D₈	—	5	2	no	—
172	C₂²×C₃×C₈	—	5	2	no	—
173	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
174	C₃×#127	—	5	1	no	—
175	C₃×#123	—	10	2	no	—
176	C₃×C₂²⋊Q₈	—	10	1	no	—
177	C₃×#121	—	5	2	no	—
178	C₃×#121	—	5	2	no	—
179	C₃×#121	—	10	1	no	—
180	C₃×#120	—	10	2	no	—
181	C₃×C₄×D₄	—	5	1	no	—
182	C₃×C₄×D₄	—	5	1	no	—
183	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
184	C₂×C₃×C₄⋊C₄	—	5	2	no	—
185	C₃×#107	—	5	1	no	—
186	C₃×#107	C₂×D₅	1	2	yes	complemented
187	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
188	C₃×#102	—	5	1	no	—
189	C₃×#102	—	5	2	no	—
190	C₃×#102	—	5	2	no	—
191	C₃×#102	—	5	1	no	—
192	C₃×#102	—	5	2	no	—
193	C₃×#102	C₂×D₅	1	2	yes	—
194	C₃×C₂²⋊C₈	—	5	2	no	—
195	C₃×C₄×C₈	—	5	1	no	—
196	C₂³×D₅	—	2	2	no	—
197	C₂×C₅×Q₈	—	2	1	no	—
198	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
199	C₂²×C₄×C₅	—	2	1	no	—
200	C₂×C₂²⋊D₅	—	2	2	no	—
201	#713	—	4	4	no	—
202	D₄×D₅	—	2	4	no	—
203	D₄×D₅	—	4	2	no	—
204	C₂×D₂₀	—	2	2	no	—
205	C₂×D₂₀	—	2	2	no	—
206	C₂×D₂₀	—	2	1	no	—
207	C₂×D₂₀	—	2	1	no	—
208	C₂×D₂₀	—	4	4	no	—
209	C₂×D₂₀	C₃×D₄	1	1	yes	characteristic
210	C₂×D₂₀	C₂³×C₃	1	2	yes	—
211	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
212	C₂×C₄×D₅	—	2	2	no	—
213	C₂×C₄×D₅	—	2	1	no	—
214	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
215	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
216	C₅×C₄⋊C₄	—	2	1	no	—
217	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
218	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
219	C₅×C₂²⋊C₄	—	2	1	no	—
220	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
221	#686	—	2	2	no	—
222	#685	—	2	1	no	—
223	#685	—	2	2	no	—
224	#685	—	2	2	no	—
225	#685	C₃×D₄	1	2	yes	—
226	C₄⋊Dic₅	C₃×D₄	1	1	yes	characteristic
227	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
228	#683	—	2	2	no	—
229	C₂×#168	C₂³×C₃	1	1	yes	characteristic
230	C₂×#168	C₂³×C₃	1	1	yes	characteristic
231	D₄₀	—	4	2	no	—
232	C₈×D₅	—	4	2	no	—
233	#547	—	5	1	no	—
234	D₄²	—	5	1	no	—
235	#486	—	5	1	no	—
236	#480	—	5	2	no	—
237	#474	C₃×D₅	1	1	yes	characteristic, complemented
238	#466	—	5	2	no	—
239	#459	—	5	1	no	—
240	#447	—	5	2	no	—
241	C₄×D₈	—	5	1	no	—
242	C₈×D₄	—	5	1	no	—
243	C₂×#102	—	5	2	no	—
244	C₂²×C₃×C₅	—	2	2	no	—
245	C₂²×C₃×C₅	—	4	1	no	—
246	C₂²×C₃×C₅	—	4	1	no	—
247	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₃×D₅	—	2	2	no	—
249	C₂×C₃×D₅	—	2	2	no	—
250	C₂×C₃×D₅	—	4	2	no	—
251	C₂×C₃×D₅	—	4	1	no	—
252	C₂×C₃×D₅	—	4	1	no	—
253	C₂×C₃×D₅	—	4	2	no	—
254	C₂×C₃×D₅	—	4	2	no	—
255	C₂×C₃×D₅	—	4	1	no	—
256	C₂×C₃×D₅	—	8	8	no	—
257	C₂×C₃×D₅	C₂×D₈	1	4	yes	—
258	C₃×C₄×C₅	—	2	1	no	—
259	C₃×C₄×C₅	—	4	2	no	—
260	C₃×C₄×C₅	—	4	1	no	—
261	C₃×C₄×C₅	C₂×D₈	1	2	yes	—
262	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
263	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
264	C₃×Dic₅	—	2	2	no	—
265	C₃×Dic₅	—	4	1	no	—
266	C₂⁴×C₃	—	10	2	no	—
267	C₃×#41	—	20	4	no	—
268	C₂×C₃×Q₈	—	2	1	no	—
269	C₂×C₃×D₄	—	5	1	no	—
270	C₂×C₃×D₄	—	5	2	no	—
271	C₂×C₃×D₄	—	5	1	no	—
272	C₂×C₃×D₄	—	10	2	no	—
273	C₂×C₃×D₄	—	10	2	no	—
274	C₂×C₃×D₄	—	10	2	no	—
275	C₂×C₃×D₄	—	10	4	no	—
276	C₂×C₃×D₄	—	10	1	no	—
277	C₂×C₃×D₄	—	10	1	no	—
278	C₂×C₃×D₄	—	20	4	no	—
279	C₂×C₃×D₄	—	20	2	no	—
280	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
281	C₂²×C₃×C₄	—	2	1	no	—
282	C₂²×C₃×C₄	—	5	2	no	—
283	C₂²×C₃×C₄	—	10	2	no	—
284	C₂²×C₃×C₄	—	10	1	no	—
285	C₃×D₈	—	10	2	no	—
286	C₃×D₈	—	20	2	no	—
287	C₂×C₃×C₈	—	5	1	no	—
288	C₂×C₃×C₈	—	5	1	no	—
289	C₂×C₃×C₈	—	20	2	no	—
290	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
291	C₃×C₄⋊C₄	—	2	1	no	—
292	C₃×C₄⋊C₄	—	5	1	no	—
293	C₃×C₄⋊C₄	—	5	1	no	—
294	C₃×C₄⋊C₄	—	10	2	no	—
295	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
296	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
297	C₃×C₂²⋊C₄	—	2	1	no	—
298	C₃×C₂²⋊C₄	—	5	2	no	—
299	C₃×C₂²⋊C₄	—	10	2	no	—
300	C₃×C₂²⋊C₄	—	10	2	no	—
301	C₃×C₂²⋊C₄	—	10	1	no	—
302	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
303	C₂³×C₅	—	2	1	no	—
304	C₂²×D₅	—	2	1	no	—
305	C₂²×D₅	—	2	2	no	—
306	C₂²×D₅	—	4	4	no	—
307	C₂²×D₅	—	4	4	no	—
308	C₂²×D₅	—	8	2	no	—
309	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
310	C₅×Q₈	—	4	2	no	—
311	C₅×D₄	—	2	1	no	—
312	C₅×D₄	C₃×#41	1	2	yes	complemented
313	C₂×C₄×C₅	—	2	2	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	4	2	no	—
316	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
317	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
318	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
319	C₂²⋊D₅	—	4	4	no	—
320	C₂×Dic₅	—	2	1	no	—
321	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
322	D₂₀	—	2	1	no	—
323	D₂₀	—	2	2	no	—
324	D₂₀	—	2	1	no	—
325	D₂₀	—	2	2	no	—
326	D₂₀	—	4	4	no	—
327	D₂₀	—	4	4	no	—
328	D₂₀	—	4	2	no	—
329	D₂₀	—	8	1	no	—
330	D₂₀	C₃×D₈	1	4	yes	complemented
331	C₄×D₅	—	2	2	no	—
332	C₄×D₅	—	2	2	no	—
333	C₄×D₅	—	4	4	no	—
334	C₄×D₅	—	4	2	no	—
335	C₅×C₈	—	2	2	no	—
336	#168	—	2	1	no	—
337	#168	—	2	1	no	—
338	C₂×#41	—	10	1	no	—
339	C₂²×D₄	—	5	2	no	—
340	C₂²×D₄	—	10	1	no	—
341	C₂×D₈	—	5	1	no	—
342	C₂×D₈	—	5	2	no	—
343	C₂²×C₈	—	5	2	no	—
344	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
345	#127	—	5	1	no	—
346	#123	—	10	2	no	—
347	C₂²⋊Q₈	—	10	1	no	—
348	#121	—	5	2	no	—
349	#121	—	5	2	no	—
350	#121	—	10	1	no	—
351	#120	—	10	2	no	—
352	C₄×D₄	—	5	1	no	—
353	C₄×D₄	—	5	1	no	—
354	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
355	C₂×C₄⋊C₄	—	5	2	no	—
356	#107	—	5	1	no	—
357	#107	C₂×C₃×D₅	1	2	yes	complemented
358	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
359	#102	—	5	1	no	—
360	#102	—	5	2	no	—
361	#102	—	5	2	no	—
362	#102	—	5	1	no	—
363	#102	—	5	2	no	—
364	#102	C₂×C₃×D₅	1	2	yes	—
365	C₂²⋊C₈	—	5	2	no	—
366	C₄×C₈	—	5	1	no	—
367	C₂×C₃×C₅	—	4	2	no	—
368	C₂×C₃×C₅	#546	1	1	yes	characteristic
369	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
370	C₂×C₃×C₅	#577	1	1	yes	characteristic
371	C₃×D₅	—	2	4	no	—
372	C₃×D₅	—	8	1	no	—
373	C₃×D₅	—	8	2	no	—
374	C₂³×C₃	—	2	1	no	—
375	C₂³×C₃	—	5	2	no	—
376	C₂³×C₃	—	10	1	no	—
377	C₂³×C₃	—	10	2	no	—
378	C₂³×C₃	—	20	4	no	—
379	C₂³×C₃	—	20	4	no	—
380	C₂³×C₃	—	40	2	no	—
381	C₃×Q₈	—	4	2	no	—
382	C₃×D₄	—	2	1	no	—
383	C₃×D₄	—	5	4	no	—
384	C₃×D₄	—	10	1	no	—
385	C₃×D₄	—	10	2	no	—
386	C₃×D₄	—	10	1	no	—
387	C₃×D₄	—	10	2	no	—
388	C₃×D₄	—	20	4	no	—
389	C₃×D₄	—	20	4	no	—
390	C₃×D₄	—	20	4	no	—
391	C₃×D₄	—	20	2	no	—
392	C₃×D₄	—	40	1	no	—
393	C₃×D₄	#713	1	2	yes	complemented
394	C₂×C₃×C₄	—	2	1	no	—
395	C₂×C₃×C₄	—	2	2	no	—
396	C₂×C₃×C₄	—	4	2	no	—
397	C₂×C₃×C₄	—	5	2	no	—
398	C₂×C₃×C₄	—	10	2	no	—
399	C₂×C₃×C₄	—	10	2	no	—
400	C₂×C₃×C₄	—	10	1	no	—
401	C₂×C₃×C₄	—	20	4	no	—
402	C₂×C₃×C₄	—	20	2	no	—
403	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
404	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
405	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
406	C₃×C₈	—	2	2	no	—
407	C₃×C₈	—	10	1	no	—
408	C₃×C₈	—	10	1	no	—
409	C₂²×C₅	—	2	2	no	—
410	C₂²×C₅	—	4	1	no	—
411	C₂²×C₅	—	4	1	no	—
412	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
413	C₂×D₅	—	2	2	no	—
414	C₂×D₅	—	2	2	no	—
415	C₂×D₅	—	4	1	no	—
416	C₂×D₅	—	4	2	no	—
417	C₂×D₅	—	4	2	no	—
418	C₂×D₅	—	4	1	no	—
419	C₂×D₅	—	4	2	no	—
420	C₂×D₅	—	4	1	no	—
421	C₂×D₅	—	8	8	no	—
422	C₂×D₅	C₂×C₃×D₈	1	4	yes	—
423	C₄×C₅	—	2	1	no	—
424	C₄×C₅	—	4	2	no	—
425	C₄×C₅	—	4	1	no	—
426	C₄×C₅	C₂×C₃×D₈	1	2	yes	—
427	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
428	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
429	Dic₅	—	2	2	no	—
430	Dic₅	—	4	1	no	—
431	C₂⁴	—	10	2	no	—
432	#41	—	20	4	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×D₄	—	5	1	no	—
435	C₂×D₄	—	5	2	no	—
436	C₂×D₄	—	5	1	no	—
437	C₂×D₄	—	10	2	no	—
438	C₂×D₄	—	10	2	no	—
439	C₂×D₄	—	10	2	no	—
440	C₂×D₄	—	10	4	no	—
441	C₂×D₄	—	10	1	no	—
442	C₂×D₄	—	10	1	no	—
443	C₂×D₄	—	20	4	no	—
444	C₂×D₄	—	20	2	no	—
445	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	5	2	no	—
448	C₂²×C₄	—	10	2	no	—
449	C₂²×C₄	—	10	1	no	—
450	D₈	—	10	2	no	—
451	D₈	—	20	2	no	—
452	C₂×C₈	—	5	1	no	—
453	C₂×C₈	—	5	1	no	—
454	C₂×C₈	—	20	2	no	—
455	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	5	1	no	—
458	C₄⋊C₄	—	5	1	no	—
459	C₄⋊C₄	—	10	2	no	—
460	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
461	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	5	2	no	—
464	C₂²⋊C₄	—	10	2	no	—
465	C₂²⋊C₄	—	10	2	no	—
466	C₂²⋊C₄	—	10	1	no	—
467	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
468	C₃×C₅	#3294	1	1	yes	characteristic, complemented, Hall
469	C₂²×C₃	—	2	2	no	—
470	C₂²×C₃	—	4	1	no	—
471	C₂²×C₃	—	4	1	no	—
472	C₂²×C₃	—	5	4	no	—
473	C₂²×C₃	—	10	2	no	—
474	C₂²×C₃	—	10	2	no	—
475	C₂²×C₃	—	20	1	no	—
476	C₂²×C₃	—	20	2	no	—
477	C₂²×C₃	—	20	2	no	—
478	C₂²×C₃	—	20	1	no	—
479	C₂²×C₃	—	20	2	no	—
480	C₂²×C₃	—	20	1	no	—
481	C₂²×C₃	—	40	8	no	—
482	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
483	C₃×C₄	—	2	1	no	—
484	C₃×C₄	—	4	1	no	—
485	C₃×C₄	—	4	2	no	—
486	C₃×C₄	—	10	2	no	—
487	C₃×C₄	—	20	1	no	—
488	C₃×C₄	D₅×D₈	1	2	yes	—
489	C₃×C₄	C₂×#713	1	1	yes	characteristic
490	C₃×C₄	#4149	1	1	yes	characteristic
491	C₂×C₅	—	4	2	no	—
492	C₂×C₅	C₃×#546	1	1	yes	characteristic
493	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
494	C₂×C₅	C₃×#577	1	1	yes	characteristic
495	D₅	—	2	4	no	—
496	D₅	—	8	2	no	—
497	D₅	—	8	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	5	2	no	—
500	C₂³	—	10	1	no	—
501	C₂³	—	10	2	no	—
502	C₂³	—	20	4	no	—
503	C₂³	—	20	4	no	—
504	C₂³	—	40	2	no	—
505	Q₈	—	4	2	no	—
506	D₄	—	2	1	no	—
507	D₄	—	5	4	no	—
508	D₄	—	10	1	no	—
509	D₄	—	10	2	no	—
510	D₄	—	10	1	no	—
511	D₄	—	10	2	no	—
512	D₄	—	20	4	no	—
513	D₄	—	20	4	no	—
514	D₄	—	20	4	no	—
515	D₄	—	20	2	no	—
516	D₄	—	40	1	no	—
517	D₄	C₃×#713	1	2	yes	complemented
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	5	2	no	—
522	C₂×C₄	—	10	2	no	—
523	C₂×C₄	—	10	2	no	—
524	C₂×C₄	—	10	1	no	—
525	C₂×C₄	—	20	4	no	—
526	C₂×C₄	—	20	2	no	—
527	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
528	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
529	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
530	C₈	—	2	2	no	—
531	C₈	—	10	1	no	—
532	C₈	—	10	1	no	—
533	C₂×C₃	—	4	2	no	—
534	C₂×C₃	—	10	4	no	—
535	C₂×C₃	—	40	2	no	—
536	C₂×C₃	—	40	1	no	—
537	C₂×C₃	#65964	1	1	yes	characteristic
538	C₂×C₃	C₂×D₅×D₈	1	1	yes	characteristic
539	C₂×C₃	#66112	1	1	yes	characteristic
540	C₅	C₃×#3294	1	1	yes	characteristic, complemented, Sylow
541	C₂²	—	2	2	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	5	4	no	—
545	C₂²	—	10	2	no	—
546	C₂²	—	10	2	no	—
547	C₂²	—	20	2	no	—
548	C₂²	—	20	1	no	—
549	C₂²	—	20	2	no	—
550	C₂²	—	20	1	no	—
551	C₂²	—	20	1	no	—
552	C₂²	—	20	2	no	—
553	C₂²	—	40	8	no	—
554	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
555	C₄	—	2	1	no	—
556	C₄	—	4	1	no	—
557	C₄	—	4	2	no	—
558	C₄	—	10	2	no	—
559	C₄	—	20	1	no	—
560	C₄	C₃×D₅×D₈	1	2	yes	—
561	C₄	C₂×C₃×#713	1	1	yes	characteristic
562	C₄	C₃×#4149	1	1	yes	characteristic
563	C₃	#10612711	1	1	yes	characteristic, direct product factor, Sylow
564	C₂	—	4	2	no	—
565	C₂	—	10	4	no	—
566	C₂	—	40	2	no	—
567	C₂	—	40	1	no	—
568	C₂	C₃×#65964	1	1	yes	characteristic
569	C₂	C₂×C₃×D₅×D₈	1	1	yes	characteristic
570	C₂	C₃×#66112	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×#474	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₃×#474	D₅
hypocenter	C₅	C₃×#3294
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#474

Complements

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

N	H ≅ G/N	type
1. C₃×#66060	C₂	semidirect
2. C₃×D₄×D₂₀	C₂	semidirect
3. C₃×C₅×#474	C₂	semidirect
4. C₃×#65377	C₂	semidirect
5. C₃×C₄×#686	C₂	semidirect
6. C₃×#65172	C₂	semidirect
7. C₃×#65171	C₂	semidirect
8. C₃×#65132	C₂	semidirect
9. C₃×#65123	C₂	semidirect
10. C₃×#65062	C₂	semidirect
11. C₃×D₅×#102	C₂	semidirect
12. #10612711	C₃	direct (N × H)
16. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
21. C₂×C₃×D₄₀	C₂²	semidirect
22. C₂×C₃×C₈×D₅	C₂²	semidirect
24. C₃×#4041	C₂²	semidirect
26. C₃×D₅×C₄⋊C₄	C₂²	semidirect
30. C₃×C₄×D₂₀	C₂²	semidirect
31. C₃×C₅×#107	C₂²	semidirect
32. C₃×C₅×C₄⋊C₈	C₂²	semidirect
35. C₃×#3953	C₂²	semidirect
36. C₃×#3952	C₂²	semidirect
37. C₃×#3941	C₂²	semidirect
38. C₃×#3941	C₂²	semidirect
39. C₃×#3941	C₂²	semidirect
40. C₃×#3939	C₂²	semidirect
41. C₃×C₄×#168	C₂²	semidirect
43. #66060	C₂×C₃	semidirect
44. D₄×D₂₀	C₂×C₃	semidirect
45. C₅×#474	C₂×C₃	semidirect
46. #65377	C₂×C₃	semidirect
47. C₄×#686	C₂×C₃	semidirect
48. #65172	C₂×C₃	semidirect
49. #65171	C₂×C₃	semidirect
50. #65132	C₂×C₃	semidirect
51. #65123	C₂×C₃	semidirect
52. #65062	C₂×C₃	semidirect
53. D₅×#102	C₂×C₃	semidirect
95. C₃×#474	D₅	semidirect
105. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
110. C₂×D₄₀	C₂²×C₃	semidirect
111. C₂×C₈×D₅	C₂²×C₃	semidirect
113. #4041	C₂²×C₃	semidirect
115. D₅×C₄⋊C₄	C₂²×C₃	semidirect
119. C₄×D₂₀	C₂²×C₃	semidirect
120. C₅×#107	C₂²×C₃	semidirect
121. C₅×C₄⋊C₈	C₂²×C₃	semidirect
124. #3953	C₂²×C₃	semidirect
125. #3952	C₂²×C₃	semidirect
126. #3941	C₂²×C₃	semidirect
127. #3941	C₂²×C₃	semidirect
128. #3941	C₂²×C₃	semidirect
129. #3939	C₂²×C₃	semidirect
130. C₄×#168	C₂²×C₃	semidirect
141. C₃×C₅×D₄	#41	semidirect
159. C₃×D₂₀	D₈	semidirect
173. C₃×C₄⋊Q₈	C₂×D₅	semidirect
186. C₃×#107	C₂×D₅	semidirect
187. C₃×C₄⋊C₈	C₂×D₅	semidirect
237. #474	C₃×D₅	semidirect
312. C₅×D₄	C₃×#41	semidirect
330. D₂₀	C₃×D₈	semidirect
344. C₄⋊Q₈	C₂×C₃×D₅	semidirect
357. #107	C₂×C₃×D₅	semidirect
358. C₄⋊C₈	C₂×C₃×D₅	semidirect
393. C₃×D₄	#713	semidirect
468. C₃×C₅	#3294	semidirect
517. D₄	C₃×#713	semidirect
540. C₅	C₃×#3294	semidirect
563. C₃	#10612711	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×#66060	2
C₃×D₄×D₂₀	2
C₃×C₅×#474	2
C₃×#65377	2
C₃×C₄×#686	2
C₃×#65172	2
C₃×#65171	2
C₃×#65132	2
C₃×#65123	2
C₃×#65062	2
C₃×D₅×#102	2
#10612711	3
C₃×#3294	5

Subgroups — C3×#10612711 #14458285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10612711 #14458285