Subgroups — C₂×C₃×#65479 #14439022

Order 1920.

1128 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	C₂²×C₃×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4093	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#4090	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×#689	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₃×#688	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₃×#677	C₂	1	1	yes	maximal, characteristic
7	C₃×#65479	C₂	1	8	yes	maximal, direct product factor
8	C₂×C₃×#3947	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65479	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
13	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×Q₁₆	—	2	4	no	—
15	C₂×C₃×C₅×Q₁₆	C₂²	1	4	yes	complemented
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₃×#4093	—	2	2	no	—
18	C₃×#4093	C₂²	1	4	yes	—
19	C₃×#4090	—	2	2	no	—
20	C₃×#4090	C₂²	1	4	yes	complemented
21	C₂×C₃×#689	—	2	4	no	—
22	C₂×C₃×#689	C₂²	1	4	yes	complemented
23	C₂×C₃×#688	—	2	4	no	—
24	C₂×C₃×#688	C₂²	1	4	yes	—
25	C₂×C₃×#685	—	2	2	no	—
26	C₂×C₃×#683	—	2	2	no	—
27	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
28	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
29	C₂×C₃×#677	—	2	4	no	—
30	C₂×C₃×#677	C₂²	1	4	yes	—
31	C₃×#3947	C₂²	1	4	yes	complemented
32	C₂×C₃×#497	—	5	1	no	maximal, Hall
33	C₂²×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×#4093	C₂×C₃	1	1	yes	characteristic
35	C₂×#4090	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂²×#689	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂²×#688	C₂×C₃	1	1	yes	characteristic
38	C₂²×#677	C₂×C₃	1	1	yes	characteristic
39	#65479	C₂×C₃	1	8	yes	direct product factor
40	C₂×#3947	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂³×C₃×D₅	—	2	1	no	—
42	C₂×C₃×C₅×Q₈	—	2	1	no	—
43	C₂×C₃×C₅×Q₈	—	2	1	no	—
44	C₂×C₃×C₅×Q₈	—	2	2	no	—
45	C₂×C₃×C₅×Q₈	—	2	2	no	—
46	C₂×C₃×C₅×Q₈	—	2	2	no	—
47	C₂×C₃×C₅×Q₈	—	2	2	no	—
48	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
49	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	—	2	1	no	—
51	C₂²×C₃×C₄×C₅	—	2	1	no	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×Dic₅	—	2	1	no	—
54	C₂²×C₃×Dic₅	D₄	1	2	yes	—
55	C₂×C₃×D₂₀	—	2	2	no	—
56	C₂×C₃×D₂₀	—	2	2	no	—
57	C₂×C₃×D₂₀	—	2	1	no	—
58	C₂×C₃×D₂₀	C₂³	1	2	yes	—
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	C₂³	1	2	yes	—
63	C₃×C₅×Q₁₆	—	2	8	no	—
64	C₂×C₃×C₅×C₈	D₄	1	4	yes	—
65	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
66	C₃×#689	—	2	8	no	—
67	C₃×#688	—	2	8	no	—
68	C₃×#685	—	2	8	no	—
69	C₃×#683	—	2	8	no	—
70	C₃×C₄×Dic₅	D₄	1	2	yes	—
71	C₃×C₄×Dic₅	C₂³	1	2	yes	—
72	C₂×C₃×#168	D₄	1	4	yes	—
73	C₂×C₃×#168	C₂³	1	2	yes	—
74	C₃×#677	—	2	8	no	—
75	C₂²×C₃×Q₁₆	—	5	1	no	—
76	C₂²×C₃×Q₁₆	D₅	1	1	yes	characteristic, complemented
77	C₂²×C₃×SD₁₆	—	5	1	no	—
78	C₂²×C₃×SD₁₆	—	5	1	no	—
79	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
80	C₂×C₃×#124	—	5	1	no	—
81	C₃×#497	—	5	8	no	—
82	C₂×C₃×#97	—	5	1	no	—
83	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
84	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
85	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
86	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₅×Q₁₆	—	2	4	no	—
88	C₂×C₅×Q₁₆	C₂²×C₃	1	4	yes	complemented
89	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
90	#4093	—	2	2	no	—
91	#4093	C₂²×C₃	1	4	yes	—
92	#4090	—	2	2	no	—
93	#4090	C₂²×C₃	1	4	yes	complemented
94	C₂×#689	—	2	4	no	—
95	C₂×#689	C₂²×C₃	1	4	yes	complemented
96	C₂×#688	—	2	4	no	—
97	C₂×#688	C₂²×C₃	1	4	yes	—
98	C₂×#685	—	2	2	no	—
99	C₂×#683	—	2	2	no	—
100	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
101	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
102	C₂×#677	—	2	4	no	—
103	C₂×#677	C₂²×C₃	1	4	yes	—
104	#3947	C₂²×C₃	1	4	yes	complemented
105	C₂×#497	—	5	1	no	Sylow
106	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₃×D₅	—	2	2	no	—
108	C₂²×C₃×D₅	—	4	2	no	—
109	C₂²×C₃×D₅	—	4	4	no	—
110	C₃×C₅×Q₈	—	2	2	no	—
111	C₃×C₅×Q₈	—	2	2	no	—
112	C₃×C₅×Q₈	—	2	2	no	—
113	C₃×C₅×Q₈	—	2	2	no	—
114	C₃×C₅×Q₈	—	4	2	no	—
115	C₃×C₅×Q₈	—	4	2	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	4	2	no	—
119	C₂×C₃×C₄×C₅	—	4	2	no	—
120	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
122	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
123	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
124	C₂×C₃×Dic₅	—	2	4	no	—
125	C₂×C₃×Dic₅	—	2	2	no	—
126	C₂×C₃×Dic₅	—	4	2	no	—
127	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
128	C₃×D₂₀	—	2	2	no	—
129	C₃×D₂₀	—	2	2	no	—
130	C₃×D₂₀	—	4	2	no	—
131	C₃×Dic₁₀	—	2	2	no	—
132	C₃×Dic₁₀	—	2	2	no	—
133	C₃×Dic₁₀	—	4	2	no	—
134	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
135	C₃×#168	C₂×D₄	1	4	yes	—
136	C₂²×C₃×Q₈	—	5	1	no	—
137	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
138	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
139	C₂²×C₃×D₄	—	5	1	no	—
140	C₂×C₃×Q₁₆	—	2	4	no	—
141	C₂×C₃×Q₁₆	—	5	4	no	—
142	C₂×C₃×Q₁₆	—	10	4	no	—
143	C₂×C₃×Q₁₆	C₂×D₅	1	4	yes	complemented
144	C₂×C₃×SD₁₆	—	5	4	no	—
145	C₂×C₃×SD₁₆	—	5	4	no	—
146	C₂×C₃×SD₁₆	—	10	4	no	—
147	C₂×C₃×SD₁₆	—	10	4	no	—
148	C₂²×C₃×C₈	—	5	1	no	—
149	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
150	C₃×C₄⋊Q₈	—	5	4	no	—
151	C₃×C₄⋊Q₈	—	10	2	no	—
152	C₃×#124	—	5	4	no	—
153	C₃×#124	—	10	2	no	—
154	C₂×C₃×C₄⋊C₄	—	10	2	no	—
155	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
156	C₂×C₃×C₄²	—	5	1	no	—
157	C₃×#97	—	5	4	no	—
158	C₂³×D₅	—	2	1	no	—
159	C₂×C₅×Q₈	—	2	1	no	—
160	C₂×C₅×Q₈	—	2	1	no	—
161	C₂×C₅×Q₈	—	2	2	no	—
162	C₂×C₅×Q₈	—	2	2	no	—
163	C₂×C₅×Q₈	—	2	2	no	—
164	C₂×C₅×Q₈	—	2	2	no	—
165	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
166	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
167	C₂²×C₄×C₅	—	2	1	no	—
168	C₂²×C₄×C₅	—	2	1	no	—
169	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
170	C₂²×Dic₅	—	2	1	no	—
171	C₂²×Dic₅	C₃×D₄	1	2	yes	—
172	C₂×D₂₀	—	2	2	no	—
173	C₂×D₂₀	—	2	2	no	—
174	C₂×D₂₀	—	2	1	no	—
175	C₂×D₂₀	C₂³×C₃	1	2	yes	—
176	C₂×Dic₁₀	—	2	2	no	—
177	C₂×Dic₁₀	—	2	2	no	—
178	C₂×Dic₁₀	—	2	1	no	—
179	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
180	C₅×Q₁₆	—	2	8	no	—
181	C₂×C₅×C₈	C₃×D₄	1	4	yes	—
182	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
183	#689	—	2	8	no	—
184	#688	—	2	8	no	—
185	#685	—	2	8	no	—
186	#683	—	2	8	no	—
187	C₄×Dic₅	C₃×D₄	1	2	yes	—
188	C₄×Dic₅	C₂³×C₃	1	2	yes	—
189	C₂×#168	C₃×D₄	1	4	yes	—
190	C₂×#168	C₂³×C₃	1	2	yes	—
191	#677	—	2	8	no	—
192	C₂²×Q₁₆	—	5	1	no	—
193	C₂²×Q₁₆	C₃×D₅	1	1	yes	characteristic, complemented
194	C₂²×SD₁₆	—	5	1	no	—
195	C₂²×SD₁₆	—	5	1	no	—
196	C₂×C₄⋊Q₈	—	5	1	no	—
197	C₂×#124	—	5	1	no	—
198	#497	—	5	8	no	—
199	C₂×#97	—	5	1	no	—
200	C₂²×C₃×C₅	#127	1	2	yes	—
201	C₂²×C₃×C₅	#137	1	4	yes	—
202	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₃×D₅	—	4	2	no	—
204	C₂×C₃×D₅	—	4	4	no	—
205	C₂×C₃×D₅	—	8	4	no	—
206	C₃×C₄×C₅	—	4	2	no	—
207	C₃×C₄×C₅	—	4	2	no	—
208	C₃×C₄×C₅	#127	1	2	yes	—
209	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
210	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
211	C₃×Dic₅	—	2	4	no	—
212	C₃×Dic₅	—	4	2	no	—
213	C₂⁴×C₃	—	10	1	no	—
214	C₂×C₃×Q₈	—	2	1	no	—
215	C₂×C₃×Q₈	—	2	1	no	—
216	C₂×C₃×Q₈	—	2	2	no	—
217	C₂×C₃×Q₈	—	2	2	no	—
218	C₂×C₃×Q₈	—	2	2	no	—
219	C₂×C₃×Q₈	—	2	2	no	—
220	C₂×C₃×Q₈	—	5	2	no	—
221	C₂×C₃×Q₈	—	10	1	no	—
222	C₂×C₃×Q₈	—	10	2	no	—
223	C₂×C₃×Q₈	—	10	2	no	—
224	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
225	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
226	C₂×C₃×D₄	—	5	2	no	—
227	C₂×C₃×D₄	—	10	2	no	—
228	C₂×C₃×D₄	—	10	1	no	—
229	C₂×C₃×D₄	—	10	2	no	—
230	C₂²×C₃×C₄	—	2	1	no	—
231	C₂²×C₃×C₄	—	2	1	no	—
232	C₂²×C₃×C₄	—	5	2	no	—
233	C₂²×C₃×C₄	—	10	1	no	—
234	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
235	C₃×Q₁₆	—	2	8	no	—
236	C₃×Q₁₆	—	10	8	no	—
237	C₃×SD₁₆	—	10	8	no	—
238	C₃×SD₁₆	—	10	8	no	—
239	C₂×C₃×C₈	—	5	4	no	—
240	C₂×C₃×C₈	—	5	2	no	—
241	C₂×C₃×C₈	C₂²⋊D₅	1	4	yes	—
242	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
243	C₃×C₄⋊C₄	—	10	8	no	—
244	C₃×C₂²⋊C₄	—	10	8	no	—
245	C₃×C₄²	—	5	2	no	—
246	C₃×C₄²	—	5	2	no	—
247	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
248	C₂²×D₅	—	2	2	no	—
249	C₂²×D₅	—	4	2	no	—
250	C₂²×D₅	—	4	4	no	—
251	C₅×Q₈	—	2	2	no	—
252	C₅×Q₈	—	2	2	no	—
253	C₅×Q₈	—	2	2	no	—
254	C₅×Q₈	—	2	2	no	—
255	C₅×Q₈	—	4	2	no	—
256	C₅×Q₈	—	4	2	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	4	2	no	—
260	C₂×C₄×C₅	—	4	2	no	—
261	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
263	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
264	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
265	C₂×Dic₅	—	2	4	no	—
266	C₂×Dic₅	—	2	2	no	—
267	C₂×Dic₅	—	4	2	no	—
268	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
269	D₂₀	—	2	2	no	—
270	D₂₀	—	2	2	no	—
271	D₂₀	—	4	2	no	—
272	Dic₁₀	—	2	2	no	—
273	Dic₁₀	—	2	2	no	—
274	Dic₁₀	—	4	2	no	—
275	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
276	#168	C₂×C₃×D₄	1	4	yes	—
277	C₂²×Q₈	—	5	1	no	—
278	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
279	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
280	C₂²×D₄	—	5	1	no	—
281	C₂×Q₁₆	—	2	4	no	—
282	C₂×Q₁₆	—	5	4	no	—
283	C₂×Q₁₆	—	10	4	no	—
284	C₂×Q₁₆	C₂×C₃×D₅	1	4	yes	complemented
285	C₂×SD₁₆	—	5	4	no	—
286	C₂×SD₁₆	—	5	4	no	—
287	C₂×SD₁₆	—	10	4	no	—
288	C₂×SD₁₆	—	10	4	no	—
289	C₂²×C₈	—	5	1	no	—
290	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
291	C₄⋊Q₈	—	5	4	no	—
292	C₄⋊Q₈	—	10	2	no	—
293	#124	—	5	4	no	—
294	#124	—	10	2	no	—
295	C₂×C₄⋊C₄	—	10	2	no	—
296	C₂×C₂²⋊C₄	—	10	2	no	—
297	C₂×C₄²	—	5	1	no	—
298	#97	—	5	4	no	—
299	C₂×C₃×C₅	#497	1	4	yes	complemented
300	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
301	C₂×C₃×C₅	C₂×#137	1	2	yes	—
302	C₃×D₅	—	8	2	no	—
303	C₂³×C₃	—	10	2	no	—
304	C₂³×C₃	—	20	4	no	—
305	C₂³×C₃	—	20	2	no	—
306	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
307	C₃×Q₈	—	2	2	no	—
308	C₃×Q₈	—	2	2	no	—
309	C₃×Q₈	—	2	2	no	—
310	C₃×Q₈	—	2	2	no	—
311	C₃×Q₈	—	4	2	no	—
312	C₃×Q₈	—	4	2	no	—
313	C₃×Q₈	—	10	2	no	—
314	C₃×Q₈	—	10	2	no	—
315	C₃×Q₈	—	20	2	no	—
316	C₃×D₄	—	10	2	no	—
317	C₃×D₄	—	10	2	no	—
318	C₃×D₄	—	20	2	no	—
319	C₂×C₃×C₄	—	2	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	4	2	no	—
322	C₂×C₃×C₄	—	4	2	no	—
323	C₂×C₃×C₄	—	5	4	no	—
324	C₂×C₃×C₄	—	10	4	no	—
325	C₂×C₃×C₄	—	10	2	no	—
326	C₂×C₃×C₄	—	20	2	no	—
327	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
328	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
329	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
330	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
331	C₃×C₈	—	5	4	no	—
332	C₃×C₈	C₂×C₂²⋊D₅	1	4	yes	—
333	C₂²×C₅	C₃×#127	1	2	yes	—
334	C₂²×C₅	C₃×#137	1	4	yes	—
335	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
336	C₂×D₅	—	4	4	no	—
337	C₂×D₅	—	4	2	no	—
338	C₂×D₅	—	8	4	no	—
339	C₄×C₅	—	4	2	no	—
340	C₄×C₅	—	4	2	no	—
341	C₄×C₅	C₃×#127	1	2	yes	—
342	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
343	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
344	Dic₅	—	2	4	no	—
345	Dic₅	—	4	2	no	—
346	C₂⁴	—	10	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	5	2	no	—
354	C₂×Q₈	—	10	1	no	—
355	C₂×Q₈	—	10	2	no	—
356	C₂×Q₈	—	10	2	no	—
357	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
358	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
359	C₂×D₄	—	5	2	no	—
360	C₂×D₄	—	10	2	no	—
361	C₂×D₄	—	10	1	no	—
362	C₂×D₄	—	10	2	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	5	2	no	—
366	C₂²×C₄	—	10	1	no	—
367	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
368	Q₁₆	—	2	8	no	—
369	Q₁₆	—	10	8	no	—
370	SD₁₆	—	10	8	no	—
371	SD₁₆	—	10	8	no	—
372	C₂×C₈	—	5	4	no	—
373	C₂×C₈	—	5	2	no	—
374	C₂×C₈	C₃×C₂²⋊D₅	1	4	yes	—
375	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
376	C₄⋊C₄	—	10	8	no	—
377	C₂²⋊C₄	—	10	8	no	—
378	C₄²	—	5	2	no	—
379	C₄²	—	5	2	no	—
380	C₃×C₅	C₂×#497	1	1	yes	characteristic, complemented, Hall
381	C₂²×C₃	—	20	4	no	—
382	C₂²×C₃	—	20	2	no	—
383	C₂²×C₃	—	40	4	no	—
384	C₂²×C₃	#4064	1	4	yes	—
385	C₂²×C₃	#4086	1	2	yes	—
386	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
387	C₃×C₄	—	4	2	no	—
388	C₃×C₄	—	4	2	no	—
389	C₃×C₄	—	10	4	no	—
390	C₃×C₄	—	20	2	no	—
391	C₃×C₄	#4086	1	2	yes	—
392	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
393	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
394	C₂×C₅	C₃×#497	1	4	yes	complemented
395	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
396	C₂×C₅	C₂×C₃×#137	1	2	yes	—
397	D₅	—	8	2	no	—
398	C₂³	—	10	2	no	—
399	C₂³	—	20	2	no	—
400	C₂³	—	20	4	no	—
401	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
402	Q₈	—	2	2	no	—
403	Q₈	—	2	2	no	—
404	Q₈	—	2	2	no	—
405	Q₈	—	2	2	no	—
406	Q₈	—	4	2	no	—
407	Q₈	—	4	2	no	—
408	Q₈	—	10	2	no	—
409	Q₈	—	10	2	no	—
410	Q₈	—	20	2	no	—
411	D₄	—	10	2	no	—
412	D₄	—	10	2	no	—
413	D₄	—	20	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	5	4	no	—
419	C₂×C₄	—	10	4	no	—
420	C₂×C₄	—	10	2	no	—
421	C₂×C₄	—	20	2	no	—
422	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
423	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
424	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
425	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
426	C₈	—	5	4	no	—
427	C₈	C₂×C₃×C₂²⋊D₅	1	4	yes	—
428	C₂×C₃	—	40	2	no	—
429	C₂×C₃	#65479	1	4	yes	direct product factor
430	C₂×C₃	C₂×#4064	1	2	yes	—
431	C₂×C₃	C₂×#4086	1	1	yes	characteristic
432	C₅	C₂×C₃×#497	1	1	yes	characteristic, complemented, Sylow
433	C₂²	—	20	2	no	—
434	C₂²	—	20	4	no	—
435	C₂²	—	40	4	no	—
436	C₂²	C₃×#4064	1	4	yes	—
437	C₂²	C₃×#4086	1	2	yes	—
438	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	10	4	no	—
442	C₄	—	20	2	no	—
443	C₄	C₃×#4086	1	2	yes	—
444	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
445	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
446	C₃	C₂×#65479	1	1	yes	characteristic, direct product factor, Sylow
447	C₂	—	40	2	no	—
448	C₂	C₃×#65479	1	4	yes	direct product factor
449	C₂	C₂×C₃×#4064	1	2	yes	—
450	C₂	C₂×C₃×#4086	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂²×C₃×C₅×Q₁₆	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×D₂₀	C₂²
hypercenter	C₂²×C₃×Q₁₆	D₅
hypocenter	C₅	C₂×C₃×#497
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×Q₁₆	C₂	semidirect
3. C₂×C₃×#4090	C₂	semidirect
4. C₂²×C₃×#689	C₂	semidirect
7. C₃×#65479	C₂	direct (N × H)
8. C₂×C₃×#3947	C₂	semidirect
9. C₂×#65479	C₃	direct (N × H)
15. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
20. C₃×#4090	C₂²	semidirect
22. C₂×C₃×#689	C₂²	semidirect
31. C₃×#3947	C₂²	semidirect
33. C₂²×C₅×Q₁₆	C₂×C₃	semidirect
35. C₂×#4090	C₂×C₃	semidirect
36. C₂²×#689	C₂×C₃	semidirect
39. #65479	C₂×C₃	direct (N × H)
40. C₂×#3947	C₂×C₃	semidirect
76. C₂²×C₃×Q₁₆	D₅	semidirect
88. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
93. #4090	C₂²×C₃	semidirect
95. C₂×#689	C₂²×C₃	semidirect
104. #3947	C₂²×C₃	semidirect
143. C₂×C₃×Q₁₆	C₂×D₅	semidirect
193. C₂²×Q₁₆	C₃×D₅	semidirect
284. C₂×Q₁₆	C₂×C₃×D₅	semidirect
299. C₂×C₃×C₅	#497	semidirect
380. C₃×C₅	C₂×#497	semidirect
394. C₂×C₅	C₃×#497	semidirect
429. C₂×C₃	#65479	direct (N × H)
432. C₅	C₂×C₃×#497	semidirect
446. C₃	C₂×#65479	direct (N × H)
448. C₂	C₃×#65479	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₅×Q₁₆	2
C₂×C₃×#4093	2
C₂×C₃×#4090	2
C₂²×C₃×#689	2
C₂²×C₃×#688	2
C₂²×C₃×#677	2
C₃×#65479	2
C₂×C₃×#3947	2
C₂×#65479	3
C₂×C₃×#497	5

Subgroups — C2×C3×#65479 #14439022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65479 #14439022