Subgroups — C₂×#11747026 #14425839

Order 1920.

1296 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#874	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#6652	C₂	1	2	yes	maximal, complemented
4	C₂×C₄⋊(C₃⋊#168)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#90966	C₂	1	2	yes	maximal, complemented
6	#11747026	C₂	1	8	yes	maximal, direct product factor
7	C₂×#65361	—	3	1	no	maximal, Hall
8	C₂²×C₅×D₁₂	—	2	1	no	—
9	C₂²×C₅×D₁₂	—	2	1	no	—
10	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
11	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×D₅	—	2	1	no	—
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₂²×C₃⋊#168	C₂²	1	2	yes	—
15	C₅×#874	—	2	2	no	—
16	C₅×#874	C₂²	1	4	yes	complemented
17	C₂×C₃×#685	—	2	1	no	—
18	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
19	C₃×C₄×D₂₀	—	2	2	no	—
20	C₃×C₄×D₂₀	C₂²	1	4	yes	complemented
21	C₂×#6652	—	2	8	no	—
22	C₂×#6652	C₂²	1	8	yes	complemented
23	C₄⋊(C₃⋊#168)	C₂²	1	4	yes	complemented
24	#90966	C₂²	1	8	yes	complemented
25	C₂×#5015	—	5	1	no	maximal, Hall
26	C₂×C₅×#127	—	3	1	no	—
27	C₂²×#686	—	3	2	no	—
28	C₂×C₄×D₂₀	D₃	1	1	yes	characteristic, complemented
29	C₂×#3964	—	3	2	no	—
30	#65361	—	3	8	no	—
31	C₂×C₄⋊#168	—	3	1	no	—
32	C₂³×C₅×D₃	—	2	2	no	—
33	C₂³×C₃×D₅	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂×C₅×D₁₂	—	2	4	no	—
38	C₂×C₅×D₁₂	—	2	4	no	—
39	C₂×C₅×D₁₂	—	2	2	no	—
40	C₂×C₅×D₁₂	—	2	4	no	—
41	C₂×C₅×D₁₂	—	2	4	no	—
42	C₂×C₅×D₁₂	—	4	4	no	—
43	C₂×C₅×D₁₂	—	4	4	no	—
44	C₂×C₅×D₁₂	C₂³	1	4	yes	—
45	C₂²×C₃×Dic₅	—	2	1	no	—
46	C₂×C₃×D₂₀	—	2	1	no	—
47	C₂×C₃×D₂₀	—	2	2	no	—
48	C₂×C₃×D₂₀	D₄	1	4	yes	complemented
49	C₂×C₃×D₂₀	C₂³	1	2	yes	—
50	C₂×C₃×C₄×D₅	—	2	4	no	—
51	C₂×C₃×C₄×D₅	—	4	4	no	—
52	C₃×C₄²×C₅	D₄	1	2	yes	—
53	C₃×C₄²×C₅	C₂³	1	2	yes	—
54	C₂×C₃⋊#168	—	2	4	no	—
55	C₂×C₃⋊#168	C₂³	1	4	yes	—
56	C₃×#685	—	2	4	no	—
57	C₃×C₄⋊Dic₅	—	2	1	no	—
58	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
59	#6652	—	2	16	no	—
60	C₂×C₃×C₄×D₄	—	5	1	no	—
61	C₂²×#213	—	5	2	no	—
62	C₂×#874	D₅	1	1	yes	characteristic, complemented
63	#5015	—	5	8	no	—
64	C₂×#809	—	5	2	no	—
65	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
66	C₂²×C₅×D₄	—	3	2	no	—
67	C₂²×C₅×D₄	—	6	1	no	—
68	C₂²×C₅×D₄	—	6	1	no	—
69	C₂²×D₂₀	C₂×D₃	1	1	yes	characteristic
70	C₂²×C₄×D₅	—	2	1	no	—
71	C₅×#127	—	3	4	no	—
72	C₅×#127	—	6	2	no	—
73	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
74	C₂×#686	—	3	8	no	—
75	C₂×#686	—	6	8	no	—
76	C₂×#685	—	2	1	no	—
77	C₂×C₄⋊Dic₅	C₂×D₃	1	1	yes	characteristic
78	C₂²×#168	—	3	2	no	—
79	C₄×D₂₀	—	2	2	no	—
80	C₄×D₂₀	C₂×D₃	1	4	yes	complemented
81	#3964	—	3	8	no	—
82	C₄⋊#168	—	3	4	no	—
83	C₂×#459	—	15	1	no	Sylow
84	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₅×D₃	—	2	4	no	—
86	C₂²×C₅×D₃	—	4	4	no	—
87	C₂²×C₅×D₃	—	4	4	no	—
88	C₂²×C₅×D₃	—	4	4	no	—
89	C₂²×C₃×D₅	—	2	4	no	—
90	C₂²×C₃×D₅	—	2	2	no	—
91	C₂²×C₃×D₅	—	4	2	no	—
92	C₂²×C₃×D₅	—	4	2	no	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	D₈	1	4	yes	complemented
95	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	#41	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
101	C₅×D₁₂	—	2	4	no	—
102	C₅×D₁₂	—	2	4	no	—
103	C₅×D₁₂	—	4	8	no	—
104	C₅×D₁₂	—	4	4	no	—
105	C₅×D₁₂	—	4	8	no	—
106	C₂×C₃×Dic₅	—	2	2	no	—
107	C₂×C₃×Dic₅	—	4	2	no	—
108	C₃×D₂₀	—	2	4	no	—
109	C₃×D₂₀	—	2	2	no	—
110	C₃×D₂₀	C₂×D₄	1	4	yes	complemented
111	C₃×C₄×D₅	—	4	8	no	—
112	C₃⋊#168	—	2	4	no	—
113	C₂²×C₃×D₄	—	5	1	no	—
114	C₂³×C₃×C₄	—	10	1	no	—
115	C₂²×D₁₂	—	2	1	no	—
116	C₂²×D₁₂	—	2	1	no	—
117	C₂²×D₁₂	C₂×D₅	1	2	yes	—
118	C₃×C₄×D₄	—	5	4	no	—
119	C₃×C₄×D₄	—	10	2	no	—
120	C₂×C₃×C₄⋊C₄	—	5	1	no	—
121	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
122	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
123	C₂×#213	—	5	8	no	—
124	C₂×#213	—	10	8	no	—
125	C₂²×C₃⋊C₈	—	5	2	no	—
126	#874	—	2	2	no	—
127	#874	C₂×D₅	1	4	yes	complemented
128	#809	—	5	8	no	—
129	C₄⋊(C₃⋊C₈)	—	5	4	no	—
130	C₂⁴×C₅	—	6	2	no	—
131	C₂³×D₅	—	2	1	no	—
132	C₂×C₅×D₄	—	3	4	no	—
133	C₂×C₅×D₄	—	6	4	no	—
134	C₂×C₅×D₄	—	6	4	no	—
135	C₂×C₅×D₄	—	6	4	no	—
136	C₂×C₅×D₄	—	6	4	no	—
137	C₂×C₅×D₄	—	6	2	no	—
138	C₂×C₅×D₄	—	12	4	no	—
139	C₂×C₅×D₄	—	12	4	no	—
140	C₂²×C₄×C₅	#67	1	1	yes	characteristic
141	C₂²×C₄×C₅	#67	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
143	C₂²×Dic₅	—	2	1	no	—
144	C₂×D₂₀	—	2	2	no	—
145	C₂×D₂₀	—	2	1	no	—
146	C₂×D₂₀	D₁₂	1	4	yes	complemented
147	C₂×D₂₀	C₂²×D₃	1	2	yes	—
148	C₂×C₄×D₅	—	2	4	no	—
149	C₂×C₄×D₅	—	4	4	no	—
150	C₄²×C₅	#67	1	2	yes	—
151	C₄²×C₅	C₂²×D₃	1	2	yes	—
152	#686	—	6	16	no	—
153	#685	—	2	4	no	—
154	C₄⋊Dic₅	—	2	1	no	—
155	C₄⋊Dic₅	C₂²×D₃	1	2	yes	—
156	C₂×#168	—	3	4	no	—
157	C₂×#168	—	6	4	no	—
158	C₂²×D₈	—	15	2	no	—
159	C₂×#127	—	3	1	no	—
160	C₂×C₄×D₄	—	5	1	no	—
161	#459	—	15	8	no	—
162	C₂×C₄⋊C₈	—	15	1	no	—
163	C₂×#102	—	15	2	no	—
164	C₂²×C₃×C₅	#121	1	2	yes	—
165	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
166	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
167	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₅×D₃	—	4	4	no	—
169	C₂×C₅×D₃	—	4	4	no	—
170	C₂×C₅×D₃	—	4	4	no	—
171	C₂×C₅×D₃	—	8	8	no	—
172	C₂×C₃×D₅	—	2	4	no	—
173	C₂×C₃×D₅	—	4	2	no	—
174	C₂×C₃×D₅	—	4	2	no	—
175	C₂×C₃×D₅	—	4	8	no	—
176	C₃×C₄×C₅	—	2	2	no	—
177	C₃×C₄×C₅	#121	1	2	yes	—
178	C₃×C₄×C₅	C₂×D₈	1	4	yes	complemented
179	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
180	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
181	C₃×Dic₅	—	4	2	no	—
182	C₂⁴×C₃	—	10	1	no	—
183	C₂³×D₃	—	2	2	no	—
184	C₂×C₃×D₄	—	5	4	no	—
185	C₂×C₃×D₄	—	5	2	no	—
186	C₂×C₃×D₄	—	10	2	no	—
187	C₂×C₃×D₄	—	10	1	no	—
188	C₂²×C₃×C₄	—	10	1	no	—
189	C₂²×C₃×C₄	—	10	4	no	—
190	C₂²×C₃×C₄	—	20	4	no	—
191	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
192	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
193	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
194	C₂×D₁₂	—	2	4	no	—
195	C₂×D₁₂	—	2	4	no	—
196	C₂×D₁₂	—	2	2	no	—
197	C₂×D₁₂	—	2	4	no	—
198	C₂×D₁₂	—	2	4	no	—
199	C₂×D₁₂	—	4	4	no	—
200	C₂×D₁₂	—	4	4	no	—
201	C₂×D₁₂	C₂²×D₅	1	4	yes	—
202	C₃×C₄⋊C₄	—	5	2	no	—
203	C₃×C₄⋊C₄	—	10	1	no	—
204	C₃×C₂²⋊C₄	—	10	4	no	—
205	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
206	C₃×C₄²	C₂²×D₅	1	2	yes	—
207	#213	—	10	16	no	—
208	C₂×C₃⋊C₈	—	5	4	no	—
209	C₂×C₃⋊C₈	—	10	4	no	—
210	C₂³×C₅	—	6	4	no	—
211	C₂³×C₅	—	12	4	no	—
212	C₂³×C₅	—	12	4	no	—
213	C₂³×C₅	—	12	4	no	—
214	C₂³×C₅	C₂×#67	1	1	yes	characteristic
215	C₂²×D₅	—	2	4	no	—
216	C₂²×D₅	—	2	2	no	—
217	C₂²×D₅	—	4	2	no	—
218	C₂²×D₅	—	4	2	no	—
219	C₅×D₄	—	6	4	no	—
220	C₅×D₄	—	6	4	no	—
221	C₅×D₄	—	12	8	no	—
222	C₅×D₄	—	12	4	no	—
223	C₅×D₄	—	12	8	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	#213	1	4	yes	complemented
226	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
227	C₂×C₄×C₅	#235	1	2	yes	—
228	C₂×C₄×C₅	C₂×#67	1	2	yes	—
229	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×#67	1	2	yes	—
231	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
232	C₂×Dic₅	—	2	2	no	—
233	C₂×Dic₅	—	4	2	no	—
234	D₂₀	—	2	4	no	—
235	D₂₀	—	2	2	no	—
236	D₂₀	C₂×D₁₂	1	4	yes	complemented
237	C₄×D₅	—	4	8	no	—
238	#168	—	6	4	no	—
239	C₂²×D₄	—	3	2	no	—
240	C₂²×D₄	—	5	1	no	—
241	C₂²×D₄	—	6	1	no	—
242	C₂²×D₄	—	6	1	no	—
243	C₂³×C₄	—	10	1	no	—
244	C₂×D₈	—	15	8	no	—
245	C₂×D₈	—	30	8	no	—
246	C₂²×C₈	—	15	2	no	—
247	#127	—	3	4	no	—
248	#127	—	6	2	no	—
249	C₄×D₄	—	5	4	no	—
250	C₄×D₄	—	10	2	no	—
251	C₂×C₄⋊C₄	—	5	1	no	—
252	C₂×C₂²⋊C₄	—	10	1	no	—
253	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
254	C₄⋊C₈	—	15	4	no	—
255	#102	—	15	8	no	—
256	C₂×C₃×C₅	#459	1	4	yes	complemented
257	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
258	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
259	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
260	C₃×D₅	—	4	4	no	—
261	C₅×D₃	—	8	4	no	—
262	C₂³×C₃	—	10	2	no	—
263	C₂³×C₃	—	10	4	no	—
264	C₂³×C₃	—	20	2	no	—
265	C₂³×C₃	—	20	2	no	—
266	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
267	C₂²×D₃	—	2	4	no	—
268	C₂²×D₃	—	4	4	no	—
269	C₂²×D₃	—	4	4	no	—
270	C₂²×D₃	—	4	4	no	—
271	C₃×D₄	—	5	4	no	—
272	C₃×D₄	—	10	2	no	—
273	C₃×D₄	—	10	4	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	10	2	no	—
276	C₂×C₃×C₄	—	20	2	no	—
277	C₂×C₃×C₄	—	20	8	no	—
278	C₂×C₃×C₄	#686	1	4	yes	complemented
279	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
280	C₂×C₃×C₄	#711	1	2	yes	—
281	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
282	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
283	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
285	D₁₂	—	2	4	no	—
286	D₁₂	—	2	4	no	—
287	D₁₂	—	4	8	no	—
288	D₁₂	—	4	8	no	—
289	D₁₂	—	4	4	no	—
290	C₃⋊C₈	—	10	4	no	—
291	C₂²×C₅	—	12	4	no	—
292	C₂²×C₅	—	12	4	no	—
293	C₂²×C₅	—	12	4	no	—
294	C₂²×C₅	—	24	8	no	—
295	C₂²×C₅	#930	1	2	yes	—
296	C₂²×C₅	C₂×#213	1	2	yes	—
297	C₂²×C₅	#949	1	2	yes	—
298	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
299	C₂×D₅	—	2	4	no	—
300	C₂×D₅	—	4	8	no	—
301	C₂×D₅	—	4	2	no	—
302	C₂×D₅	—	4	2	no	—
303	C₄×C₅	—	2	2	no	—
304	C₄×C₅	#930	1	2	yes	—
305	C₄×C₅	C₂×#213	1	4	yes	complemented
306	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
307	C₄×C₅	C₂×#235	1	1	yes	characteristic
308	Dic₅	—	4	2	no	—
309	C₂⁴	—	6	2	no	—
310	C₂⁴	—	10	1	no	—
311	C₂×D₄	—	3	4	no	—
312	C₂×D₄	—	5	4	no	—
313	C₂×D₄	—	5	2	no	—
314	C₂×D₄	—	6	4	no	—
315	C₂×D₄	—	6	4	no	—
316	C₂×D₄	—	6	4	no	—
317	C₂×D₄	—	6	4	no	—
318	C₂×D₄	—	6	2	no	—
319	C₂×D₄	—	10	2	no	—
320	C₂×D₄	—	10	1	no	—
321	C₂×D₄	—	12	4	no	—
322	C₂×D₄	—	12	4	no	—
323	C₂²×C₄	—	10	1	no	—
324	C₂²×C₄	—	10	4	no	—
325	C₂²×C₄	—	20	4	no	—
326	C₂²×C₄	#1201	1	1	yes	characteristic
327	C₂²×C₄	#1201	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
329	D₈	—	30	16	no	—
330	C₂×C₈	—	15	4	no	—
331	C₂×C₈	—	30	4	no	—
332	C₄⋊C₄	—	5	2	no	—
333	C₄⋊C₄	—	10	1	no	—
334	C₂²⋊C₄	—	10	4	no	—
335	C₄²	#1201	1	2	yes	—
336	C₄²	C₂×D₃×D₅	1	2	yes	—
337	C₃×C₅	C₂×#459	1	1	yes	characteristic, complemented, Hall
338	C₂²×C₃	—	10	4	no	—
339	C₂²×C₃	—	20	2	no	—
340	C₂²×C₃	—	20	2	no	—
341	C₂²×C₃	—	20	8	no	—
342	C₂²×C₃	C₂×#686	1	2	yes	—
343	C₂²×C₃	#4078	1	2	yes	—
344	C₂²×C₃	#4084	1	2	yes	—
345	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
346	C₂×D₃	—	4	4	no	—
347	C₂×D₃	—	4	4	no	—
348	C₂×D₃	—	4	4	no	—
349	C₂×D₃	—	8	8	no	—
350	C₃×C₄	—	2	2	no	—
351	C₃×C₄	—	20	2	no	—
352	C₃×C₄	C₂×#686	1	4	yes	complemented
353	C₃×C₄	#4084	1	2	yes	—
354	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
355	C₃×C₄	C₂×#711	1	1	yes	characteristic
356	C₂×C₅	—	24	4	no	—
357	C₂×C₅	#5015	1	4	yes	complemented
358	C₂×C₅	C₂×#930	1	1	yes	characteristic
359	C₂×C₅	C₂²×#213	1	1	yes	characteristic
360	C₂×C₅	C₂×#949	1	1	yes	characteristic
361	D₅	—	4	4	no	—
362	C₂³	—	6	4	no	—
363	C₂³	—	10	4	no	—
364	C₂³	—	10	2	no	—
365	C₂³	—	12	4	no	—
366	C₂³	—	12	4	no	—
367	C₂³	—	12	4	no	—
368	C₂³	—	20	2	no	—
369	C₂³	—	20	2	no	—
370	C₂³	C₂×#1201	1	1	yes	characteristic
371	D₄	—	5	4	no	—
372	D₄	—	6	4	no	—
373	D₄	—	6	4	no	—
374	D₄	—	10	4	no	—
375	D₄	—	10	2	no	—
376	D₄	—	12	8	no	—
377	D₄	—	12	4	no	—
378	D₄	—	12	8	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	10	2	no	—
381	C₂×C₄	—	20	2	no	—
382	C₂×C₄	—	20	8	no	—
383	C₂×C₄	#6652	1	4	yes	complemented
384	C₂×C₄	#6772	1	2	yes	—
385	C₂×C₄	D₅×D₁₂	1	2	yes	—
386	C₂×C₄	C₂×#1201	1	2	yes	—
387	C₂×C₄	C₂×#1201	1	1	yes	characteristic
388	C₂×C₄	C₂×#1201	1	2	yes	—
389	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
390	C₈	—	30	4	no	—
391	C₂×C₃	—	20	4	no	—
392	C₂×C₃	#65361	1	4	yes	complemented
393	C₂×C₃	C₂²×#686	1	1	yes	characteristic
394	C₂×C₃	C₂×#4078	1	1	yes	characteristic
395	C₂×C₃	C₂×#4084	1	1	yes	characteristic
396	D₃	—	8	4	no	—
397	C₅	C₂×#5015	1	1	yes	characteristic, complemented, Sylow
398	C₂²	—	10	4	no	—
399	C₂²	—	12	4	no	—
400	C₂²	—	12	4	no	—
401	C₂²	—	12	4	no	—
402	C₂²	—	20	2	no	—
403	C₂²	—	20	2	no	—
404	C₂²	—	20	8	no	—
405	C₂²	—	24	8	no	—
406	C₂²	C₂×#6652	1	2	yes	—
407	C₂²	#91299	1	2	yes	—
408	C₂²	#91449	1	2	yes	—
409	C₂²	C₂²×#1201	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	20	2	no	—
412	C₄	C₂×#6652	1	4	yes	complemented
413	C₄	#91449	1	2	yes	—
414	C₄	C₂×#6772	1	1	yes	characteristic
415	C₄	C₂×D₅×D₁₂	1	1	yes	characteristic
416	C₃	C₂×#65361	1	1	yes	characteristic, complemented, Sylow
417	C₂	—	20	4	no	—
418	C₂	—	24	4	no	—
419	C₂	#11747026	1	4	yes	direct product factor
420	C₂	C₂²×#6652	1	1	yes	characteristic
421	C₂	C₂×#91299	1	1	yes	characteristic
422	C₂	C₂×#91449	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#1201
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	C₂×#459
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#874	C₂	semidirect
2. C₂×C₃×C₄×D₂₀	C₂	semidirect
3. C₂²×#6652	C₂	semidirect
4. C₂×C₄⋊(C₃⋊#168)	C₂	semidirect
5. C₂×#90966	C₂	semidirect
6. #11747026	C₂	direct (N × H)
16. C₅×#874	C₂²	semidirect
20. C₃×C₄×D₂₀	C₂²	semidirect
22. C₂×#6652	C₂²	semidirect
23. C₄⋊(C₃⋊#168)	C₂²	semidirect
24. #90966	C₂²	semidirect
28. C₂×C₄×D₂₀	D₃	semidirect
48. C₂×C₃×D₂₀	D₄	semidirect
62. C₂×#874	D₅	semidirect
80. C₄×D₂₀	C₂×D₃	semidirect
94. C₂×C₃×C₄×C₅	D₈	semidirect
110. C₃×D₂₀	C₂×D₄	semidirect
127. #874	C₂×D₅	semidirect
146. C₂×D₂₀	D₁₂	semidirect
178. C₃×C₄×C₅	C₂×D₈	semidirect
225. C₂×C₄×C₅	#213	semidirect
236. D₂₀	C₂×D₁₂	semidirect
256. C₂×C₃×C₅	#459	semidirect
278. C₂×C₃×C₄	#686	semidirect
305. C₄×C₅	C₂×#213	semidirect
337. C₃×C₅	C₂×#459	semidirect
352. C₃×C₄	C₂×#686	semidirect
357. C₂×C₅	#5015	semidirect
383. C₂×C₄	#6652	semidirect
392. C₂×C₃	#65361	semidirect
397. C₅	C₂×#5015	semidirect
412. C₄	C₂×#6652	semidirect
416. C₃	C₂×#65361	semidirect
419. C₂	#11747026	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×C₅×#874	2
C₂×C₃×C₄×D₂₀	2
C₂²×#6652	2
C₂×C₄⋊(C₃⋊#168)	2
C₂×#90966	2
#11747026	2
C₂×#65361	3
C₂×#5015	5

Subgroups — C2×#11747026 #14425839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11747026 #14425839