Subgroups — C₂×C₃×#65481 #14429428

Order 1920.

896 conjugacy classes of subgroups.

The subgroup lattice has 416 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×#4088	C₂	1	2	yes	maximal
3	C₂×C₃×#4047	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#3968	C₂	1	2	yes	maximal, complemented
5	C₃×#65481	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×#3951	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#65481	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
9	C₂×C₃×#709	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×Q₁₆	—	2	1	no	—
11	C₂×C₃×C₅×Q₁₆	—	2	1	no	—
12	C₂×C₃×C₅×Q₁₆	—	2	2	no	—
13	C₂×C₃×C₅×Q₁₆	C₂²	1	4	yes	complemented
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×#689	—	2	2	no	—
16	C₃×#4088	—	2	4	no	—
17	C₃×#4088	C₂²	1	8	yes	—
18	C₂×C₃×#688	—	2	2	no	—
19	C₂×C₃×#681	C₂²	1	2	yes	—
20	C₂×C₃×#681	C₂²	1	1	yes	characteristic
21	C₃×#4047	—	2	2	no	—
22	C₃×#4047	C₂²	1	4	yes	—
23	C₂×C₃×#676	—	2	1	no	—
24	C₂×C₃×C₈×D₅	—	2	1	no	—
25	C₃×#3968	C₂²	1	8	yes	complemented
26	C₃×#3951	C₂²	1	4	yes	complemented
27	C₂×C₃×#473	—	5	1	no	maximal, Hall
28	C₂²×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂×#4088	C₂×C₃	1	2	yes	—
30	C₂×#4047	C₂×C₃	1	1	yes	characteristic
31	C₂×#3968	C₂×C₃	1	2	yes	complemented
32	#65481	C₂×C₃	1	8	yes	direct product factor
33	C₂×#3951	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×C₃×C₅×Q₈	—	2	2	no	—
35	C₂×C₃×C₅×Q₈	—	2	2	no	—
36	C₂×C₃×C₅×Q₈	—	2	2	no	—
37	C₂×C₃×C₅×Q₈	—	2	2	no	—
38	C₂×C₃×C₅×Q₈	—	2	2	no	—
39	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
40	C₂²×C₃×C₄×C₅	—	2	2	no	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
43	C₃×#709	—	2	1	no	—
44	C₃×#709	—	2	1	no	—
45	C₃×#709	D₄	1	2	yes	—
46	C₃×#709	C₂³	1	2	yes	—
47	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
48	C₂×C₃×C₄×D₅	—	2	1	no	—
49	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic
50	C₃×C₅×Q₁₆	—	2	4	no	—
51	C₃×C₅×Q₁₆	—	2	4	no	—
52	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
53	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
54	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
55	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
56	C₃×#689	—	2	8	no	—
57	C₃×#688	—	2	8	no	—
58	C₃×#681	—	2	2	no	—
59	C₃×#681	—	2	1	no	—
60	C₃×#681	C₂³	1	4	yes	—
61	C₃×#681	C₂³	1	2	yes	—
62	C₂×C₃×#168	—	2	2	no	—
63	C₂×C₃×#168	—	2	1	no	—
64	C₃×#676	—	2	4	no	—
65	C₃×C₈×D₅	—	2	4	no	—
66	C₂×C₃×#137	—	5	2	no	—
67	C₂²×C₃×Q₁₆	D₅	1	1	yes	characteristic, complemented
68	C₂×C₃×#131	—	5	1	no	—
69	C₃×#473	—	5	8	no	—
70	C₂×C₃×#108	—	5	1	no	—
71	C₂×C₃×#101	—	5	2	no	—
72	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
73	C₂×#709	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₅×Q₁₆	—	2	1	no	—
75	C₂×C₅×Q₁₆	—	2	1	no	—
76	C₂×C₅×Q₁₆	—	2	2	no	—
77	C₂×C₅×Q₁₆	C₂²×C₃	1	4	yes	complemented
78	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
79	C₂×#689	—	2	2	no	—
80	#4088	—	2	4	no	—
81	#4088	C₂²×C₃	1	8	yes	—
82	C₂×#688	—	2	2	no	—
83	C₂×#681	C₂²×C₃	1	1	yes	characteristic
84	C₂×#681	C₂²×C₃	1	2	yes	—
85	#4047	—	2	2	no	—
86	#4047	C₂²×C₃	1	4	yes	—
87	C₂×#676	—	2	1	no	—
88	C₂×C₈×D₅	—	2	1	no	—
89	#3968	C₂²×C₃	1	8	yes	complemented
90	#3951	C₂²×C₃	1	4	yes	complemented
91	C₂×#473	—	5	1	no	Sylow
92	C₂³×C₃×C₅	#41	1	1	yes	characteristic
93	C₂²×C₃×D₅	—	2	1	no	—
94	C₃×C₅×Q₈	—	2	4	no	—
95	C₃×C₅×Q₈	—	2	4	no	—
96	C₃×C₅×Q₈	—	4	2	no	—
97	C₃×C₅×Q₈	—	4	2	no	—
98	C₂×C₃×C₄×C₅	—	2	4	no	—
99	C₂×C₃×C₄×C₅	—	4	2	no	—
100	C₂×C₃×C₄×C₅	—	4	2	no	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
107	C₃×C₂²⋊D₅	—	2	2	no	—
108	C₃×C₂²⋊D₅	—	2	2	no	—
109	C₂×C₃×Dic₅	—	2	1	no	—
110	C₃×D₂₀	—	2	1	no	—
111	C₃×D₂₀	C₂×D₄	1	2	yes	—
112	C₃×C₄×D₅	—	2	2	no	—
113	C₃×C₄×D₅	—	2	2	no	—
114	C₃×Dic₁₀	—	2	1	no	—
115	C₃×Dic₁₀	C₂×D₄	1	2	yes	—
116	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
117	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
118	C₃×#168	—	2	2	no	—
119	C₃×#168	—	2	4	no	—
120	C₂×C₃×#41	—	5	1	no	—
121	C₂²×C₃×Q₈	C₂×D₅	1	2	yes	—
122	C₃×#137	—	5	8	no	—
123	C₃×#137	—	10	4	no	—
124	C₂×C₃×Q₁₆	—	2	1	no	—
125	C₂×C₃×Q₁₆	—	2	1	no	—
126	C₂×C₃×Q₁₆	—	2	2	no	—
127	C₂×C₃×Q₁₆	—	10	2	no	—
128	C₂×C₃×Q₁₆	C₂×D₅	1	4	yes	complemented
129	C₂×C₃×SD₁₆	—	10	2	no	—
130	C₃×#131	—	5	4	no	—
131	C₃×#131	—	10	2	no	—
132	C₂×C₃×M₁₆	—	5	1	no	—
133	C₂×C₃×M₁₆	—	5	2	no	—
134	C₂×C₃×M₁₆	—	10	1	no	—
135	C₂²×C₃×C₈	—	10	1	no	—
136	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
137	C₃×#108	—	5	4	no	—
138	C₃×#101	—	5	8	no	—
139	C₂×C₅×Q₈	—	2	2	no	—
140	C₂×C₅×Q₈	—	2	2	no	—
141	C₂×C₅×Q₈	—	2	2	no	—
142	C₂×C₅×Q₈	—	2	2	no	—
143	C₂×C₅×Q₈	—	2	2	no	—
144	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
145	C₂²×C₄×C₅	—	2	2	no	—
146	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
147	C₂×C₂²⋊D₅	—	2	1	no	—
148	#709	—	2	1	no	—
149	#709	—	2	1	no	—
150	#709	C₃×D₄	1	2	yes	—
151	#709	C₂³×C₃	1	2	yes	—
152	C₂×D₂₀	C₃×D₄	1	1	yes	characteristic
153	C₂×C₄×D₅	—	2	1	no	—
154	C₂×Dic₁₀	C₃×D₄	1	1	yes	characteristic
155	C₅×Q₁₆	—	2	4	no	—
156	C₅×Q₁₆	—	2	4	no	—
157	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
158	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
159	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
160	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
161	#689	—	2	8	no	—
162	#688	—	2	8	no	—
163	#681	—	2	1	no	—
164	#681	—	2	2	no	—
165	#681	C₂³×C₃	1	4	yes	—
166	#681	C₂³×C₃	1	2	yes	—
167	C₂×#168	—	2	1	no	—
168	C₂×#168	—	2	2	no	—
169	#676	—	2	4	no	—
170	C₈×D₅	—	2	4	no	—
171	C₂×#137	—	5	2	no	—
172	C₂²×Q₁₆	C₃×D₅	1	1	yes	characteristic, complemented
173	C₂×#131	—	5	1	no	—
174	#473	—	5	8	no	—
175	C₂×#108	—	5	1	no	—
176	C₂×#101	—	5	2	no	—
177	C₂²×C₃×C₅	—	2	2	no	—
178	C₂²×C₃×C₅	#121	1	1	yes	characteristic
179	C₂²×C₃×C₅	#121	1	1	yes	characteristic
180	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
181	C₂×C₃×D₅	—	2	2	no	—
182	C₂×C₃×D₅	—	4	2	no	—
183	C₃×C₄×C₅	—	4	4	no	—
184	C₃×C₄×C₅	#121	1	1	yes	characteristic
185	C₃×C₄×C₅	#121	1	1	yes	characteristic
186	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
187	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
188	C₃×Dic₅	—	2	2	no	—
189	C₃×#41	—	5	2	no	—
190	C₃×#41	—	5	2	no	—
191	C₃×#41	—	10	1	no	—
192	C₃×#41	—	10	1	no	—
193	C₂×C₃×Q₈	—	2	2	no	—
194	C₂×C₃×Q₈	—	2	2	no	—
195	C₂×C₃×Q₈	—	2	2	no	—
196	C₂×C₃×Q₈	—	2	2	no	—
197	C₂×C₃×Q₈	—	2	2	no	—
198	C₂×C₃×Q₈	—	5	1	no	—
199	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	—
200	C₂×C₃×D₄	—	5	1	no	—
201	C₂×C₃×D₄	—	10	1	no	—
202	C₂²×C₃×C₄	—	2	2	no	—
203	C₂²×C₃×C₄	—	10	1	no	—
204	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
205	C₃×Q₁₆	—	2	4	no	—
206	C₃×Q₁₆	—	2	4	no	—
207	C₃×Q₁₆	—	10	8	no	—
208	C₃×SD₁₆	—	10	8	no	—
209	C₃×M₁₆	—	5	2	no	—
210	C₃×M₁₆	—	5	4	no	—
211	C₃×M₁₆	—	10	2	no	—
212	C₃×M₁₆	—	10	1	no	—
213	C₃×M₁₆	—	10	4	no	—
214	C₂×C₃×C₈	—	10	2	no	—
215	C₂×C₃×C₈	—	10	1	no	—
216	C₂×C₃×C₈	—	10	4	no	—
217	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
218	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
219	C₂×C₃×C₈	C₂²⋊D₅	1	2	yes	—
220	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
221	C₂³×C₅	C₃×#41	1	1	yes	characteristic
222	C₂²×D₅	—	2	1	no	—
223	C₅×Q₈	—	2	4	no	—
224	C₅×Q₈	—	2	4	no	—
225	C₅×Q₈	—	4	2	no	—
226	C₅×Q₈	—	4	2	no	—
227	C₂×C₄×C₅	—	2	4	no	—
228	C₂×C₄×C₅	—	4	2	no	—
229	C₂×C₄×C₅	—	4	2	no	—
230	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
234	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
236	C₂²⋊D₅	—	2	2	no	—
237	C₂²⋊D₅	—	2	2	no	—
238	C₂×Dic₅	—	2	1	no	—
239	D₂₀	—	2	1	no	—
240	D₂₀	C₂×C₃×D₄	1	2	yes	—
241	C₄×D₅	—	2	2	no	—
242	C₄×D₅	—	2	2	no	—
243	Dic₁₀	—	2	1	no	—
244	Dic₁₀	C₂×C₃×D₄	1	2	yes	—
245	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
246	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
247	#168	—	2	2	no	—
248	#168	—	2	4	no	—
249	C₂×#41	—	5	1	no	—
250	C₂²×Q₈	C₂×C₃×D₅	1	2	yes	—
251	#137	—	5	8	no	—
252	#137	—	10	4	no	—
253	C₂×Q₁₆	—	2	1	no	—
254	C₂×Q₁₆	—	2	1	no	—
255	C₂×Q₁₆	—	2	2	no	—
256	C₂×Q₁₆	—	10	2	no	—
257	C₂×Q₁₆	C₂×C₃×D₅	1	4	yes	complemented
258	C₂×SD₁₆	—	10	2	no	—
259	#131	—	5	4	no	—
260	#131	—	10	2	no	—
261	C₂×M₁₆	—	5	1	no	—
262	C₂×M₁₆	—	5	2	no	—
263	C₂×M₁₆	—	10	1	no	—
264	C₂²×C₈	—	10	1	no	—
265	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
266	#108	—	5	4	no	—
267	#101	—	5	8	no	—
268	C₂×C₃×C₅	—	2	1	no	—
269	C₂×C₃×C₅	—	2	1	no	—
270	C₂×C₃×C₅	#473	1	2	yes	complemented
271	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
272	C₃×D₅	—	4	2	no	—
273	C₂³×C₃	—	10	1	no	—
274	C₂³×C₃	#711	1	1	yes	characteristic
275	C₃×Q₈	—	2	4	no	—
276	C₃×Q₈	—	2	4	no	—
277	C₃×Q₈	—	4	2	no	—
278	C₃×Q₈	—	4	2	no	—
279	C₃×Q₈	—	5	2	no	—
280	C₃×Q₈	—	10	1	no	—
281	C₃×D₄	—	5	2	no	—
282	C₃×D₄	—	10	2	no	—
283	C₃×D₄	—	10	2	no	—
284	C₃×D₄	—	10	1	no	—
285	C₂×C₃×C₄	—	2	4	no	—
286	C₂×C₃×C₄	—	4	2	no	—
287	C₂×C₃×C₄	—	4	2	no	—
288	C₂×C₃×C₄	—	10	1	no	—
289	C₂×C₃×C₄	—	10	2	no	—
290	C₂×C₃×C₄	—	10	2	no	—
291	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
292	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
293	C₂×C₃×C₄	#711	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
297	C₃×C₈	—	10	4	no	—
298	C₃×C₈	—	10	2	no	—
299	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
300	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
301	C₂²×C₅	—	2	2	no	—
302	C₂²×C₅	C₃×#121	1	1	yes	characteristic
303	C₂²×C₅	C₃×#121	1	1	yes	characteristic
304	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
305	C₂×D₅	—	2	2	no	—
306	C₂×D₅	—	4	2	no	—
307	C₄×C₅	—	4	4	no	—
308	C₄×C₅	C₃×#121	1	1	yes	characteristic
309	C₄×C₅	C₃×#121	1	1	yes	characteristic
310	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
311	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
312	Dic₅	—	2	2	no	—
313	#41	—	5	2	no	—
314	#41	—	5	2	no	—
315	#41	—	10	1	no	—
316	#41	—	10	1	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	5	1	no	—
323	C₂×Q₈	C₂²×C₃×D₅	1	4	yes	—
324	C₂×D₄	—	5	1	no	—
325	C₂×D₄	—	10	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	10	1	no	—
328	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
329	Q₁₆	—	2	4	no	—
330	Q₁₆	—	2	4	no	—
331	Q₁₆	—	10	8	no	—
332	SD₁₆	—	10	8	no	—
333	M₁₆	—	5	2	no	—
334	M₁₆	—	5	4	no	—
335	M₁₆	—	10	2	no	—
336	M₁₆	—	10	1	no	—
337	M₁₆	—	10	4	no	—
338	C₂×C₈	—	10	2	no	—
339	C₂×C₈	—	10	1	no	—
340	C₂×C₈	—	10	4	no	—
341	C₂×C₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
342	C₂×C₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
343	C₂×C₈	C₃×C₂²⋊D₅	1	2	yes	—
344	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
345	C₃×C₅	C₂×#473	1	1	yes	characteristic, complemented, Hall
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	—	10	2	no	—
348	C₂²×C₃	—	20	2	no	—
349	C₂²×C₃	#4084	1	1	yes	characteristic
350	C₂²×C₃	#4084	1	1	yes	characteristic
351	C₂²×C₃	C₂×#711	1	1	yes	characteristic
352	C₃×C₄	—	4	4	no	—
353	C₃×C₄	—	10	2	no	—
354	C₃×C₄	#4084	1	1	yes	characteristic
355	C₃×C₄	#4084	1	1	yes	characteristic
356	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
357	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
358	C₂×C₅	—	2	1	no	—
359	C₂×C₅	—	2	1	no	—
360	C₂×C₅	C₃×#473	1	2	yes	complemented
361	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
362	D₅	—	4	2	no	—
363	C₂³	—	10	1	no	—
364	C₂³	C₃×#711	1	1	yes	characteristic
365	Q₈	—	2	4	no	—
366	Q₈	—	2	4	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	5	2	no	—
370	Q₈	—	10	1	no	—
371	D₄	—	5	2	no	—
372	D₄	—	10	2	no	—
373	D₄	—	10	2	no	—
374	D₄	—	10	1	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	10	1	no	—
379	C₂×C₄	—	10	2	no	—
380	C₂×C₄	—	10	2	no	—
381	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
382	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
383	C₂×C₄	C₃×#711	1	1	yes	characteristic
384	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
385	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
386	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
387	C₈	—	10	4	no	—
388	C₈	—	10	2	no	—
389	C₈	C₂×C₃×C₂²⋊D₅	1	2	yes	—
390	C₈	C₂×C₃×C₂²⋊D₅	1	2	yes	—
391	C₂×C₃	—	2	1	no	—
392	C₂×C₃	—	2	1	no	—
393	C₂×C₃	—	20	2	no	—
394	C₂×C₃	#65481	1	2	yes	direct product factor
395	C₂×C₃	C₂×#4084	1	1	yes	characteristic
396	C₅	C₂×C₃×#473	1	1	yes	characteristic, complemented, Sylow
397	C₂²	—	2	2	no	—
398	C₂²	—	10	2	no	—
399	C₂²	—	20	2	no	—
400	C₂²	C₃×#4084	1	1	yes	characteristic
401	C₂²	C₃×#4084	1	1	yes	characteristic
402	C₂²	C₂×C₃×#711	1	1	yes	characteristic
403	C₄	—	4	4	no	—
404	C₄	—	10	2	no	—
405	C₄	C₃×#4084	1	1	yes	characteristic
406	C₄	C₃×#4084	1	1	yes	characteristic
407	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
408	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
409	C₃	C₂×#65481	1	1	yes	characteristic, direct product factor, Sylow
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	20	2	no	—
413	C₂	C₃×#65481	1	2	yes	direct product factor
414	C₂	C₂×C₃×#4084	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	#4084
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂²×C₃×C₅×Q₁₆	C₂
socle	C₂²×C₃×C₅	#121
prime radical	C₂×C₃×#709	C₂²
hypercenter	C₂²×C₃×Q₁₆	D₅
hypocenter	C₅	C₂×C₃×#473
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×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
4. C₂×C₃×#3968	C₂	semidirect
5. C₃×#65481	C₂	direct (N × H)
6. C₂×C₃×#3951	C₂	semidirect
7. C₂×#65481	C₃	direct (N × H)
13. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
25. C₃×#3968	C₂²	semidirect
26. C₃×#3951	C₂²	semidirect
28. C₂²×C₅×Q₁₆	C₂×C₃	semidirect
31. C₂×#3968	C₂×C₃	semidirect
32. #65481	C₂×C₃	direct (N × H)
33. C₂×#3951	C₂×C₃	semidirect
67. C₂²×C₃×Q₁₆	D₅	semidirect
77. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
89. #3968	C₂²×C₃	semidirect
90. #3951	C₂²×C₃	semidirect
128. C₂×C₃×Q₁₆	C₂×D₅	semidirect
172. C₂²×Q₁₆	C₃×D₅	semidirect
257. C₂×Q₁₆	C₂×C₃×D₅	semidirect
270. C₂×C₃×C₅	#473	semidirect
345. C₃×C₅	C₂×#473	semidirect
360. C₂×C₅	C₃×#473	semidirect
394. C₂×C₃	#65481	direct (N × H)
396. C₅	C₂×C₃×#473	semidirect
409. C₃	C₂×#65481	direct (N × H)
413. C₂	C₃×#65481	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×#4088	2
C₂×C₃×#4047	2
C₂×C₃×#3968	2
C₃×#65481	2
C₂×C₃×#3951	2
C₂×#65481	3
C₂×C₃×#473	5

Subgroups — C2×C3×#65481 #14429428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65481 #14429428