Subgroups — C₂×C₃×#65041 #14425141

Order 1920.

1416 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4147	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4090	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4055	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₅×#101	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3957	C₂	1	2	yes	maximal, complemented
6	C₃×#65041	C₂	1	8	yes	maximal, direct product factor
7	C₂×#65041	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
9	C₃×#4147	—	2	2	no	—
10	C₃×#4147	—	2	4	no	—
11	C₃×#4147	C₂²	1	4	yes	—
12	C₂×C₃×#713	—	2	2	no	—
13	C₂×C₃×Q₈×D₅	—	2	2	no	—
14	C₂×C₃×#709	—	2	2	no	—
15	C₂×C₃×#709	C₂²	1	2	yes	—
16	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
18	C₃×#4090	—	2	2	no	—
19	C₃×#4090	C₂²	1	4	yes	complemented
20	C₂×C₃×#683	—	2	2	no	—
21	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
22	C₃×#4055	—	2	4	no	—
23	C₃×#4055	C₂²	1	8	yes	complemented
24	C₂×C₃×Dic₂₀	—	2	2	no	—
25	C₂×C₃×#677	—	2	2	no	—
26	C₃×C₅×#101	C₂²	1	4	yes	complemented
27	C₃×#3957	C₂²	1	8	yes	complemented
28	C₂×C₃×#456	—	5	1	no	maximal, Hall
29	C₂×#4147	C₂×C₃	1	1	yes	characteristic
30	C₂×#4090	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×#4055	C₂×C₃	1	2	yes	complemented
32	C₂×C₅×#101	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×#3957	C₂×C₃	1	2	yes	complemented
34	#65041	C₂×C₃	1	8	yes	direct product factor
35	C₂×C₃×C₅×Q₈	—	2	2	no	—
36	C₂×C₃×C₅×Q₈	—	2	2	no	—
37	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
38	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
39	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
42	C₂²×C₃×Dic₅	—	2	1	no	—
43	C₂²×C₃×Dic₅	—	2	1	no	—
44	C₃×#713	—	2	8	no	—
45	C₃×#713	—	2	8	no	—
46	C₃×Q₈×D₅	—	2	8	no	—
47	C₃×Q₈×D₅	—	2	8	no	—
48	C₃×#709	—	2	8	no	—
49	C₃×#709	—	2	8	no	—
50	C₃×#709	—	2	2	no	—
51	C₃×#709	—	2	2	no	—
52	C₃×#709	D₄	1	4	yes	—
53	C₃×#709	C₂³	1	4	yes	—
54	C₂×C₃×D₂₀	—	2	2	no	—
55	C₂×C₃×D₂₀	D₄	1	2	yes	—
56	C₂×C₃×C₄×D₅	—	2	4	no	—
57	C₂×C₃×C₄×D₅	—	2	2	no	—
58	C₂×C₃×Dic₁₀	—	2	2	no	—
59	C₂×C₃×Dic₁₀	—	2	2	no	—
60	C₂×C₃×Dic₁₀	—	2	2	no	—
61	C₂×C₃×Dic₁₀	—	2	1	no	—
62	C₂×C₃×Dic₁₀	D₄	1	2	yes	—
63	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
64	C₃×C₅×M₁₆	—	2	2	no	—
65	C₃×C₅×M₁₆	C₂³	1	4	yes	—
66	C₂×C₃×C₅×C₈	—	2	2	no	—
67	C₃×#683	—	2	8	no	—
68	C₃×C₄×Dic₅	—	2	1	no	—
69	C₃×C₄×Dic₅	C₂³	1	2	yes	—
70	C₃×Dic₂₀	—	2	8	no	—
71	C₃×#677	—	2	8	no	—
72	C₂×C₃×2₋¹⁺⁴	—	5	1	no	—
73	C₂×C₃×#137	—	5	2	no	—
74	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
75	C₃×#456	—	5	8	no	—
76	C₂×C₃×#104	—	5	2	no	—
77	C₂×C₃×#101	D₅	1	1	yes	characteristic, complemented
78	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
79	#4147	—	2	2	no	—
80	#4147	—	2	4	no	—
81	#4147	C₂²×C₃	1	4	yes	—
82	C₂×#713	—	2	2	no	—
83	C₂×Q₈×D₅	—	2	2	no	—
84	C₂×#709	—	2	2	no	—
85	C₂×#709	C₂²×C₃	1	2	yes	—
86	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
88	#4090	—	2	2	no	—
89	#4090	C₂²×C₃	1	4	yes	complemented
90	C₂×#683	—	2	2	no	—
91	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
92	#4055	—	2	4	no	—
93	#4055	C₂²×C₃	1	8	yes	complemented
94	C₂×Dic₂₀	—	2	2	no	—
95	C₂×#677	—	2	2	no	—
96	C₅×#101	C₂²×C₃	1	4	yes	complemented
97	#3957	C₂²×C₃	1	8	yes	complemented
98	C₂×#456	—	5	1	no	Sylow
99	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₃×D₅	—	2	2	no	—
101	C₃×C₅×Q₈	—	2	4	no	—
102	C₃×C₅×Q₈	—	2	4	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
109	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
110	C₃×C₂²⋊D₅	—	2	4	no	—
111	C₃×C₂²⋊D₅	—	2	4	no	—
112	C₂×C₃×Dic₅	—	2	4	no	—
113	C₂×C₃×Dic₅	—	2	2	no	—
114	C₂×C₃×Dic₅	—	2	2	no	—
115	C₂×C₃×Dic₅	—	2	2	no	—
116	C₂×C₃×Dic₅	—	4	1	no	—
117	C₂×C₃×Dic₅	—	4	1	no	—
118	C₃×D₂₀	—	2	8	no	—
119	C₃×D₂₀	—	2	2	no	—
120	C₃×D₂₀	C₂×D₄	1	4	yes	—
121	C₃×C₄×D₅	—	2	16	no	—
122	C₃×C₄×D₅	—	2	4	no	—
123	C₃×C₄×D₅	—	2	4	no	—
124	C₃×Dic₁₀	—	2	8	no	—
125	C₃×Dic₁₀	—	2	2	no	—
126	C₃×Dic₁₀	—	2	4	no	—
127	C₃×Dic₁₀	—	4	2	no	—
128	C₃×Dic₁₀	C₂×D₄	1	4	yes	—
129	C₃×C₅×C₈	—	2	4	no	—
130	C₃×2₋¹⁺⁴	—	5	4	no	—
131	C₃×2₋¹⁺⁴	—	10	4	no	—
132	C₃×2₋¹⁺⁴	—	10	2	no	—
133	C₂×C₃×#41	—	5	2	no	—
134	C₂×C₃×#41	—	10	2	no	—
135	C₂×C₃×#41	—	10	2	no	—
136	C₂²×C₃×Q₈	—	5	1	no	—
137	C₂²×C₃×Q₈	—	10	2	no	—
138	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
139	C₃×#137	—	5	8	no	—
140	C₃×#137	—	10	4	no	—
141	C₂×C₃×Q₁₆	—	10	2	no	—
142	C₂×C₃×SD₁₆	—	10	2	no	—
143	C₂×C₃×M₁₆	C₂×D₅	1	2	yes	—
144	C₃×C₄⋊Q₈	—	5	4	no	—
145	C₃×C₄⋊Q₈	—	10	2	no	—
146	C₂×C₃×C₄⋊C₄	—	10	2	no	—
147	C₂×C₃×C₄²	—	5	1	no	—
148	C₃×#104	—	5	8	no	—
149	C₃×#101	C₂×D₅	1	4	yes	complemented
150	C₂×C₅×Q₈	—	2	2	no	—
151	C₂×C₅×Q₈	—	2	2	no	—
152	C₂×C₅×Q₈	C₃×D₄	1	2	yes	—
153	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
154	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
155	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
156	C₂×C₂²⋊D₅	—	2	2	no	—
157	C₂²×Dic₅	—	2	1	no	—
158	C₂²×Dic₅	—	2	1	no	—
159	#713	—	2	8	no	—
160	#713	—	2	8	no	—
161	Q₈×D₅	—	2	8	no	—
162	Q₈×D₅	—	2	8	no	—
163	#709	—	2	8	no	—
164	#709	—	2	8	no	—
165	#709	—	2	2	no	—
166	#709	—	2	2	no	—
167	#709	C₃×D₄	1	4	yes	—
168	#709	C₂³×C₃	1	4	yes	—
169	C₂×D₂₀	—	2	2	no	—
170	C₂×D₂₀	C₃×D₄	1	2	yes	—
171	C₂×C₄×D₅	—	2	4	no	—
172	C₂×C₄×D₅	—	2	2	no	—
173	C₂×Dic₁₀	—	2	2	no	—
174	C₂×Dic₁₀	—	2	2	no	—
175	C₂×Dic₁₀	—	2	2	no	—
176	C₂×Dic₁₀	—	2	1	no	—
177	C₂×Dic₁₀	C₃×D₄	1	2	yes	—
178	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
179	C₅×M₁₆	—	2	2	no	—
180	C₅×M₁₆	C₂³×C₃	1	4	yes	—
181	C₂×C₅×C₈	—	2	2	no	—
182	#683	—	2	8	no	—
183	C₄×Dic₅	—	2	1	no	—
184	C₄×Dic₅	C₂³×C₃	1	2	yes	—
185	Dic₂₀	—	2	8	no	—
186	#677	—	2	8	no	—
187	C₂×2₋¹⁺⁴	—	5	1	no	—
188	C₂×#137	—	5	2	no	—
189	C₂×C₄⋊Q₈	—	5	1	no	—
190	#456	—	5	8	no	—
191	C₂×#104	—	5	2	no	—
192	C₂×#101	C₃×D₅	1	1	yes	characteristic, complemented
193	C₂²×C₃×C₅	—	2	2	no	—
194	C₂²×C₃×C₅	#120	1	1	yes	characteristic
195	C₂²×C₃×C₅	#120	1	1	yes	characteristic
196	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₃×D₅	—	2	4	no	—
198	C₂×C₃×D₅	—	4	4	no	—
199	C₃×C₄×C₅	—	2	4	no	—
200	C₃×C₄×C₅	#120	1	2	yes	—
201	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
202	C₃×Dic₅	—	2	4	no	—
203	C₃×Dic₅	—	2	4	no	—
204	C₃×Dic₅	—	4	2	no	—
205	C₃×#41	—	5	4	no	—
206	C₃×#41	—	5	4	no	—
207	C₃×#41	—	10	8	no	—
208	C₃×#41	—	10	8	no	—
209	C₃×#41	—	10	8	no	—
210	C₃×#41	—	10	2	no	—
211	C₃×#41	—	10	8	no	—
212	C₃×#41	—	10	2	no	—
213	C₂×C₃×Q₈	—	2	2	no	—
214	C₂×C₃×Q₈	—	2	2	no	—
215	C₂×C₃×Q₈	—	5	2	no	—
216	C₂×C₃×Q₈	—	5	2	no	—
217	C₂×C₃×Q₈	—	10	2	no	—
218	C₂×C₃×Q₈	—	10	8	no	—
219	C₂×C₃×Q₈	—	10	8	no	—
220	C₂×C₃×Q₈	—	10	1	no	—
221	C₂×C₃×Q₈	—	10	2	no	—
222	C₂×C₃×Q₈	—	10	2	no	—
223	C₂×C₃×Q₈	D₂₀	1	2	yes	—
224	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
225	C₂×C₃×D₄	—	5	2	no	—
226	C₂×C₃×D₄	—	10	2	no	—
227	C₂×C₃×D₄	—	10	2	no	—
228	C₂²×C₃×C₄	—	10	4	no	—
229	C₂²×C₃×C₄	—	10	1	no	—
230	C₂²×C₃×C₄	—	10	2	no	—
231	C₂²×C₃×C₄	—	10	1	no	—
232	C₂²×C₃×C₄	D₂₀	1	2	yes	—
233	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
234	C₃×Q₁₆	—	10	8	no	—
235	C₃×SD₁₆	—	10	8	no	—
236	C₃×M₁₆	—	2	2	no	—
237	C₃×M₁₆	C₂²×D₅	1	4	yes	—
238	C₂×C₃×C₈	—	2	2	no	—
239	C₃×C₄⋊C₄	—	10	8	no	—
240	C₃×C₄²	—	5	2	no	—
241	C₃×C₄²	—	10	1	no	—
242	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
243	C₂²×D₅	—	2	2	no	—
244	C₅×Q₈	—	2	4	no	—
245	C₅×Q₈	—	2	4	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
249	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
250	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
251	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
252	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
253	C₂²⋊D₅	—	2	4	no	—
254	C₂²⋊D₅	—	2	4	no	—
255	C₂×Dic₅	—	2	4	no	—
256	C₂×Dic₅	—	2	2	no	—
257	C₂×Dic₅	—	2	2	no	—
258	C₂×Dic₅	—	2	2	no	—
259	C₂×Dic₅	—	4	1	no	—
260	C₂×Dic₅	—	4	1	no	—
261	D₂₀	—	2	8	no	—
262	D₂₀	—	2	2	no	—
263	D₂₀	C₂×C₃×D₄	1	4	yes	—
264	C₄×D₅	—	2	16	no	—
265	C₄×D₅	—	2	4	no	—
266	C₄×D₅	—	2	4	no	—
267	Dic₁₀	—	2	8	no	—
268	Dic₁₀	—	2	2	no	—
269	Dic₁₀	—	2	4	no	—
270	Dic₁₀	—	4	2	no	—
271	Dic₁₀	C₂×C₃×D₄	1	4	yes	—
272	C₅×C₈	—	2	4	no	—
273	2₋¹⁺⁴	—	5	4	no	—
274	2₋¹⁺⁴	—	10	4	no	—
275	2₋¹⁺⁴	—	10	2	no	—
276	C₂×#41	—	5	2	no	—
277	C₂×#41	—	10	2	no	—
278	C₂×#41	—	10	2	no	—
279	C₂²×Q₈	—	5	1	no	—
280	C₂²×Q₈	—	10	2	no	—
281	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
282	#137	—	5	8	no	—
283	#137	—	10	4	no	—
284	C₂×Q₁₆	—	10	2	no	—
285	C₂×SD₁₆	—	10	2	no	—
286	C₂×M₁₆	C₂×C₃×D₅	1	2	yes	—
287	C₄⋊Q₈	—	5	4	no	—
288	C₄⋊Q₈	—	10	2	no	—
289	C₂×C₄⋊C₄	—	10	2	no	—
290	C₂×C₄²	—	5	1	no	—
291	#104	—	5	8	no	—
292	#101	C₂×C₃×D₅	1	4	yes	complemented
293	C₂×C₃×C₅	—	2	1	no	—
294	C₂×C₃×C₅	—	2	1	no	—
295	C₂×C₃×C₅	#456	1	2	yes	complemented
296	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
297	C₃×D₅	—	4	4	no	—
298	C₂³×C₃	—	10	2	no	—
299	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
300	C₃×Q₈	—	2	4	no	—
301	C₃×Q₈	—	2	4	no	—
302	C₃×Q₈	—	5	4	no	—
303	C₃×Q₈	—	10	8	no	—
304	C₃×Q₈	—	10	2	no	—
305	C₃×Q₈	—	10	4	no	—
306	C₃×Q₈	—	20	2	no	—
307	C₃×D₄	—	5	4	no	—
308	C₃×D₄	—	10	8	no	—
309	C₃×D₄	—	10	4	no	—
310	C₃×D₄	—	10	4	no	—
311	C₃×D₄	—	10	2	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	10	16	no	—
315	C₂×C₃×C₄	—	10	4	no	—
316	C₂×C₃×C₄	—	10	2	no	—
317	C₂×C₃×C₄	—	10	2	no	—
318	C₂×C₃×C₄	—	10	4	no	—
319	C₂×C₃×C₄	—	10	4	no	—
320	C₂×C₃×C₄	—	10	2	no	—
321	C₂×C₃×C₄	—	20	1	no	—
322	C₂×C₃×C₄	—	20	1	no	—
323	C₂×C₃×C₄	C₂×D₂₀	1	4	yes	—
324	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
325	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
326	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
327	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
328	C₃×C₈	—	2	4	no	—
329	C₂²×C₅	—	2	2	no	—
330	C₂²×C₅	C₃×#120	1	1	yes	characteristic
331	C₂²×C₅	C₃×#120	1	1	yes	characteristic
332	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
333	C₂×D₅	—	2	4	no	—
334	C₂×D₅	—	4	4	no	—
335	C₄×C₅	—	2	4	no	—
336	C₄×C₅	C₃×#120	1	2	yes	—
337	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
338	Dic₅	—	2	4	no	—
339	Dic₅	—	2	4	no	—
340	Dic₅	—	4	2	no	—
341	#41	—	5	4	no	—
342	#41	—	5	4	no	—
343	#41	—	10	8	no	—
344	#41	—	10	8	no	—
345	#41	—	10	8	no	—
346	#41	—	10	2	no	—
347	#41	—	10	8	no	—
348	#41	—	10	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	5	2	no	—
352	C₂×Q₈	—	5	2	no	—
353	C₂×Q₈	—	10	2	no	—
354	C₂×Q₈	—	10	8	no	—
355	C₂×Q₈	—	10	8	no	—
356	C₂×Q₈	—	10	1	no	—
357	C₂×Q₈	—	10	2	no	—
358	C₂×Q₈	—	10	2	no	—
359	C₂×Q₈	C₃×D₂₀	1	2	yes	—
360	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
361	C₂×D₄	—	5	2	no	—
362	C₂×D₄	—	10	2	no	—
363	C₂×D₄	—	10	2	no	—
364	C₂²×C₄	—	10	4	no	—
365	C₂²×C₄	—	10	1	no	—
366	C₂²×C₄	—	10	2	no	—
367	C₂²×C₄	—	10	1	no	—
368	C₂²×C₄	C₃×D₂₀	1	2	yes	—
369	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
370	Q₁₆	—	10	8	no	—
371	SD₁₆	—	10	8	no	—
372	M₁₆	—	2	2	no	—
373	M₁₆	C₂²×C₃×D₅	1	4	yes	—
374	C₂×C₈	—	2	2	no	—
375	C₄⋊C₄	—	10	8	no	—
376	C₄²	—	5	2	no	—
377	C₄²	—	10	1	no	—
378	C₃×C₅	C₂×#456	1	1	yes	characteristic, complemented, Hall
379	C₂²×C₃	—	2	2	no	—
380	C₂²×C₃	—	10	4	no	—
381	C₂²×C₃	—	20	4	no	—
382	C₂²×C₃	#4028	1	1	yes	characteristic
383	C₂²×C₃	#4028	1	1	yes	characteristic
384	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
385	C₃×C₄	—	2	4	no	—
386	C₃×C₄	—	10	4	no	—
387	C₃×C₄	—	10	4	no	—
388	C₃×C₄	—	20	2	no	—
389	C₃×C₄	#4028	1	2	yes	—
390	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
391	C₂×C₅	—	2	1	no	—
392	C₂×C₅	—	2	1	no	—
393	C₂×C₅	C₃×#456	1	2	yes	complemented
394	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
395	D₅	—	4	4	no	—
396	C₂³	—	10	2	no	—
397	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
398	Q₈	—	2	4	no	—
399	Q₈	—	2	4	no	—
400	Q₈	—	5	4	no	—
401	Q₈	—	10	8	no	—
402	Q₈	—	10	2	no	—
403	Q₈	—	10	4	no	—
404	Q₈	—	20	2	no	—
405	D₄	—	5	4	no	—
406	D₄	—	10	8	no	—
407	D₄	—	10	4	no	—
408	D₄	—	10	4	no	—
409	D₄	—	10	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	10	16	no	—
413	C₂×C₄	—	10	4	no	—
414	C₂×C₄	—	10	2	no	—
415	C₂×C₄	—	10	2	no	—
416	C₂×C₄	—	10	4	no	—
417	C₂×C₄	—	10	4	no	—
418	C₂×C₄	—	10	2	no	—
419	C₂×C₄	—	20	1	no	—
420	C₂×C₄	—	20	1	no	—
421	C₂×C₄	C₂×C₃×D₂₀	1	4	yes	—
422	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
423	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
424	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
425	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
426	C₈	—	2	4	no	—
427	C₂×C₃	—	2	1	no	—
428	C₂×C₃	—	2	1	no	—
429	C₂×C₃	—	20	4	no	—
430	C₂×C₃	#65041	1	2	yes	direct product factor
431	C₂×C₃	C₂×#4028	1	1	yes	characteristic
432	C₅	C₂×C₃×#456	1	1	yes	characteristic, complemented, Sylow
433	C₂²	—	2	2	no	—
434	C₂²	—	10	4	no	—
435	C₂²	—	20	4	no	—
436	C₂²	C₃×#4028	1	1	yes	characteristic
437	C₂²	C₃×#4028	1	1	yes	characteristic
438	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
439	C₄	—	2	4	no	—
440	C₄	—	10	4	no	—
441	C₄	—	10	4	no	—
442	C₄	—	20	2	no	—
443	C₄	C₃×#4028	1	2	yes	—
444	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
445	C₃	C₂×#65041	1	1	yes	characteristic, direct product factor, Sylow
446	C₂	—	2	1	no	—
447	C₂	—	2	1	no	—
448	C₂	—	20	4	no	—
449	C₂	C₃×#65041	1	2	yes	direct product factor
450	C₂	C₂×C₃×#4028	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	#4028
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#101	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₂×C₃×#4147	C₂
hypercenter	C₂×C₃×#101	D₅
hypocenter	C₅	C₂×C₃×#456
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#101

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4090	C₂	semidirect
3. C₂×C₃×#4055	C₂	semidirect
4. C₂×C₃×C₅×#101	C₂	semidirect
5. C₂×C₃×#3957	C₂	semidirect
6. C₃×#65041	C₂	direct (N × H)
7. C₂×#65041	C₃	direct (N × H)
19. C₃×#4090	C₂²	semidirect
23. C₃×#4055	C₂²	semidirect
26. C₃×C₅×#101	C₂²	semidirect
27. C₃×#3957	C₂²	semidirect
30. C₂×#4090	C₂×C₃	semidirect
31. C₂×#4055	C₂×C₃	semidirect
32. C₂×C₅×#101	C₂×C₃	semidirect
33. C₂×#3957	C₂×C₃	semidirect
34. #65041	C₂×C₃	direct (N × H)
77. C₂×C₃×#101	D₅	semidirect
89. #4090	C₂²×C₃	semidirect
93. #4055	C₂²×C₃	semidirect
96. C₅×#101	C₂²×C₃	semidirect
97. #3957	C₂²×C₃	semidirect
149. C₃×#101	C₂×D₅	semidirect
192. C₂×#101	C₃×D₅	semidirect
292. #101	C₂×C₃×D₅	semidirect
295. C₂×C₃×C₅	#456	semidirect
378. C₃×C₅	C₂×#456	semidirect
393. C₂×C₅	C₃×#456	semidirect
430. C₂×C₃	#65041	direct (N × H)
432. C₅	C₂×C₃×#456	semidirect
445. C₃	C₂×#65041	direct (N × H)
449. C₂	C₃×#65041	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×#4147	2
C₂×C₃×#4090	2
C₂×C₃×#4055	2
C₂×C₃×C₅×#101	2
C₂×C₃×#3957	2
C₃×#65041	2
C₂×#65041	3
C₂×C₃×#456	5

Subgroups — C2×C3×#65041 #14425141

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65041 #14425141