Subgroups — #14295656

Order 1920.

640 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#805	C₂	1	1	yes	maximal, characteristic
3	C₃×#65221	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#90979	C₂	1	1	yes	maximal, characteristic
5	Dic₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
6	#11746344	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745978	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601147	—	3	1	no	maximal, Hall
9	C₂×C₅×#235	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
11	#91815	C₂²	1	1	yes	characteristic
12	C₂×#6710	C₂²	1	1	yes	characteristic
13	C₂×C₅×#208	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
16	Dic₅×#67	—	2	2	no	—
17	Dic₅×D₁₂	C₄	1	2	yes	complemented
18	C₄×D₃×Dic₅	—	2	1	no	—
19	#91371	—	2	1	no	—
20	Dic₅×Dic₆	C₄	1	2	yes	complemented
21	C₅×#805	C₄	1	4	yes	complemented
22	C₃×#3963	—	2	2	no	—
23	#90979	C₄	1	4	yes	complemented
24	#90952	—	2	1	no	—
25	Dic₅×C₃⋊C₈	—	2	1	no	—
26	#69430	—	5	1	no	maximal, Hall
27	#41×Dic₅	—	3	1	no	—
28	C₂×C₅×#104	—	3	1	no	—
29	C₂×#3969	—	3	1	no	—
30	M₁₆×Dic₅	—	3	1	no	—
31	#65221	D₃	1	1	yes	characteristic, complemented
32	#64775	—	3	1	no	—
33	#64743	—	3	1	no	—
34	C₂²×C₃×C₄×C₅	—	2	1	no	—
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂×C₅×#67	—	2	1	no	—
37	C₅×#235	—	2	1	no	—
38	C₅×#235	—	2	1	no	—
39	C₅×#235	C₂×C₄	1	2	yes	—
40	C₅×#235	C₂×C₄	1	2	yes	—
41	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×C₅×D₃	—	2	1	no	—
43	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₃×Dic₅	—	2	1	no	—
45	C₂²×C₃×Dic₅	D₄	1	2	yes	—
46	C₂×D₃×Dic₅	—	2	2	no	—
47	C₃×C₄²×C₅	—	2	1	no	—
48	C₃×C₄²×C₅	C₂×C₄	1	2	yes	complemented
49	#6719	—	2	1	no	—
50	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	—
51	C₄×Dic₁₅	—	2	1	no	—
52	#6710	—	2	1	no	—
53	#6710	C₂×C₄	1	2	yes	complemented
54	C₂×C₃⋊#168	—	2	1	no	—
55	C₅×#208	—	2	1	no	—
56	C₅×#208	C₂×C₄	1	2	yes	complemented
57	C₂×C₅×C₃⋊C₈	—	2	1	no	—
58	C₃×C₄×Dic₅	—	2	1	no	—
59	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
60	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	complemented
61	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
62	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
63	Dic₃⋊Dic₅	—	2	2	no	—
64	(C₂×D₃)⋊Dic₅	—	2	2	no	—
65	Dic₃×Dic₅	—	2	2	no	—
66	C₄×#235	—	5	1	no	—
67	C₃×#376	—	5	1	no	—
68	C₂×#805	—	5	1	no	—
69	C₂×#805	D₅	1	1	yes	characteristic
70	C₄×#208	—	5	1	no	—
71	#4523	—	5	1	no	—
72	#4523	—	5	1	no	—
73	C₂×C₅×#41	—	3	1	no	—
74	C₂×C₅×M₁₆	—	3	1	no	—
75	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
76	Q₈×Dic₅	—	3	2	no	—
77	D₄×Dic₅	—	3	2	no	—
78	D₄×Dic₅	—	6	2	no	—
79	#4072	—	3	1	no	—
80	#4072	—	6	1	no	—
81	C₂×C₄×Dic₅	—	6	1	no	—
82	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
83	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
84	C₂×#681	—	3	1	no	—
85	C₅×#104	—	3	4	no	—
86	#3969	—	3	4	no	—
87	#3963	—	2	2	no	—
88	#3947	—	6	1	no	—
89	C₈×Dic₅	—	6	1	no	—
90	#1759	—	15	1	no	Sylow
91	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₅×D₃	—	2	1	no	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	—	4	2	no	—
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
101	C₂×Dic₁₅	—	2	2	no	—
102	C₅×#67	—	2	2	no	—
103	C₅×#67	—	2	2	no	—
104	C₂×C₅×Dic₃	—	2	1	no	—
105	C₅×D₁₂	—	2	1	no	—
106	C₅×D₁₂	C₄²	1	2	yes	—
107	C₄×C₅×D₃	—	2	2	no	—
108	C₄×C₅×D₃	—	2	2	no	—
109	C₅×Dic₆	—	2	1	no	—
110	C₅×Dic₆	C₄²	1	2	yes	—
111	C₂×C₃×Dic₅	—	2	2	no	—
112	C₂×C₃×Dic₅	—	4	2	no	—
113	C₂×C₃×Dic₅	—	4	2	no	—
114	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
115	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
116	D₃×Dic₅	—	4	4	no	—
117	C₃⋊#168	—	2	2	no	—
118	C₅×C₃⋊C₈	—	2	2	no	—
119	C₂×#235	C₂×D₅	1	1	yes	characteristic
120	C₂×C₃×C₄²	—	5	1	no	—
121	C₂×C₃×C₄²	—	5	1	no	—
122	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
123	C₄×#67	—	10	2	no	—
124	#926	—	5	1	no	—
125	C₂×#208	—	5	1	no	—
126	C₂×#208	C₂×D₅	1	1	yes	characteristic
127	C₄×D₁₂	—	5	2	no	—
128	#872	—	10	1	no	—
129	C₄²×D₃	—	10	1	no	—
130	C₄×Dic₆	—	5	2	no	—
131	C₃×#95	—	10	2	no	—
132	#805	—	5	4	no	—
133	#805	Dic₅	1	4	yes	complemented
134	#803	—	10	1	no	—
135	C₄×C₃⋊C₈	—	10	1	no	—
136	C₅×#41	—	3	2	no	—
137	C₅×#41	—	3	2	no	—
138	C₅×#41	—	6	1	no	—
139	C₅×#41	—	6	1	no	—
140	C₂×C₅×Q₈	—	3	1	no	—
141	C₂×C₅×D₄	—	3	1	no	—
142	C₂×C₅×D₄	—	6	1	no	—
143	C₂²×C₄×C₅	—	2	1	no	—
144	C₂²×C₄×C₅	—	6	1	no	—
145	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
146	C₂²×Dic₅	—	2	1	no	—
147	C₂²×Dic₅	—	6	2	no	—
148	C₂²×Dic₅	#67	1	2	yes	—
149	C₅×M₁₆	—	3	2	no	—
150	C₅×M₁₆	—	6	1	no	—
151	C₂×C₅×C₈	—	6	1	no	—
152	C₄²×C₅	—	2	1	no	—
153	C₄²×C₅	C₄×D₃	1	2	yes	complemented
154	C₂²⋊Dic₅	—	6	1	no	—
155	C₂²⋊Dic₅	—	6	2	no	—
156	C₄⋊Dic₅	—	3	2	no	—
157	C₄⋊Dic₅	—	6	2	no	—
158	C₄×Dic₅	—	2	1	no	—
159	C₄×Dic₅	—	6	1	no	—
160	C₄×Dic₅	—	6	2	no	—
161	C₄×Dic₅	C₄×D₃	1	2	yes	—
162	C₄×Dic₅	C₄×D₃	1	2	yes	complemented
163	C₄×Dic₅	D₁₂	1	1	yes	characteristic
164	C₄×Dic₅	D₁₂	1	1	yes	characteristic
165	#681	—	3	2	no	—
166	#681	—	6	1	no	—
167	C₂×#168	—	6	1	no	—
168	C₄×#41	—	15	1	no	—
169	C₂×#104	—	3	1	no	—
170	C₂×#104	—	15	1	no	—
171	C₄×M₁₆	—	15	1	no	—
172	#376	—	5	1	no	—
173	#339	—	15	1	no	—
174	#339	—	15	1	no	—
175	C₂²×C₃×C₅	—	2	2	no	—
176	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
178	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
179	C₂×C₅×D₃	—	2	2	no	—
180	C₂×C₅×D₃	—	4	2	no	—
181	C₃×C₄×C₅	—	4	2	no	—
182	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
183	C₃×C₄×C₅	#117	1	1	yes	characteristic
184	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
185	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
186	Dic₁₅	—	4	2	no	—
187	C₃×Dic₅	—	2	2	no	—
188	C₃×Dic₅	—	2	2	no	—
189	C₃×Dic₅	—	4	2	no	—
190	C₅×Dic₃	—	2	2	no	—
191	C₂²×C₃×C₄	—	2	1	no	—
192	C₂²×C₃×C₄	—	5	2	no	—
193	C₂²×C₃×C₄	—	10	1	no	—
194	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
195	C₂×#67	—	2	1	no	—
196	#235	—	2	1	no	—
197	#235	—	2	1	no	—
198	#235	C₄×D₅	1	2	yes	—
199	#235	C₂×Dic₅	1	2	yes	—
200	C₂×D₁₂	C₄×D₅	1	1	yes	characteristic
201	C₂×C₄×D₃	—	2	1	no	—
202	C₂×C₄×D₃	—	10	2	no	—
203	C₂×Dic₆	C₄×D₅	1	1	yes	characteristic
204	C₃×C₄²	—	2	1	no	—
205	C₃×C₄²	—	5	2	no	—
206	C₃×C₄²	—	5	1	no	—
207	C₃×C₄²	—	5	1	no	—
208	C₃×C₄²	—	5	2	no	—
209	C₃×C₄²	—	10	1	no	—
210	C₃×C₄²	C₂×Dic₅	1	2	yes	complemented
211	#217	—	10	1	no	—
212	(C₂×D₃)⋊C₄	—	10	2	no	—
213	C₄⋊Dic₃	—	5	2	no	—
214	Dic₃⋊C₄	—	10	2	no	—
215	C₄×Dic₃	—	10	2	no	—
216	C₄×Dic₃	—	10	1	no	—
217	#208	—	2	1	no	—
218	#208	—	5	2	no	—
219	#208	—	10	1	no	—
220	#208	C₂×Dic₅	1	2	yes	complemented
221	C₂×C₃⋊C₈	—	2	1	no	—
222	C₂×C₃⋊C₈	—	10	1	no	—
223	C₂³×C₅	—	6	1	no	—
224	C₂³×C₅	C₂×#67	1	1	yes	characteristic
225	C₅×Q₈	—	3	2	no	—
226	C₅×Q₈	—	6	1	no	—
227	C₅×D₄	—	3	2	no	—
228	C₅×D₄	—	6	2	no	—
229	C₅×D₄	—	6	2	no	—
230	C₅×D₄	—	6	1	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	4	2	no	—
233	C₂×C₄×C₅	—	6	1	no	—
234	C₂×C₄×C₅	—	6	2	no	—
235	C₂×C₄×C₅	—	6	2	no	—
236	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
240	C₂×C₄×C₅	#235	1	1	yes	characteristic
241	C₂×C₄×C₅	#235	1	1	yes	characteristic
242	C₂×Dic₅	—	2	2	no	—
243	C₂×Dic₅	—	4	2	no	—
244	C₂×Dic₅	—	4	2	no	—
245	C₂×Dic₅	—	6	2	no	—
246	C₂×Dic₅	—	12	4	no	—
247	C₂×Dic₅	(C₂×D₃)⋊C₄	1	2	yes	—
248	C₂×Dic₅	(C₂×D₃)⋊C₄	1	2	yes	—
249	C₅×C₈	—	6	2	no	—
250	#168	—	6	2	no	—
251	C₂×#41	—	3	1	no	—
252	C₂×M₁₆	—	3	1	no	—
253	C₂×M₁₆	—	15	1	no	—
254	C₄×Q₈	—	15	2	no	—
255	C₄×D₄	—	15	2	no	—
256	C₄×D₄	—	30	2	no	—
257	#117	—	15	1	no	—
258	#117	—	30	1	no	—
259	C₂×C₄²	—	5	1	no	—
260	C₂×C₄²	—	5	1	no	—
261	C₂×C₄²	—	30	1	no	—
262	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
263	#104	—	3	4	no	—
264	#104	—	15	4	no	—
265	#97	—	30	1	no	—
266	C₄×C₈	—	30	1	no	—
267	#95	—	10	2	no	—
268	C₂×C₃×C₅	—	2	1	no	—
269	C₂×C₃×C₅	—	2	1	no	—
270	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₃×C₅	#421	1	2	yes	—
272	C₅×D₃	—	4	2	no	—
273	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
274	C₂²×D₃	—	2	1	no	—
275	C₂×C₃×C₄	—	2	2	no	—
276	C₂×C₃×C₄	—	4	2	no	—
277	C₂×C₃×C₄	—	5	2	no	—
278	C₂×C₃×C₄	—	5	2	no	—
279	C₂×C₃×C₄	—	10	2	no	—
280	C₂×C₃×C₄	—	20	2	no	—
281	C₂×C₃×C₄	—	20	2	no	—
282	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
284	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
285	C₂×C₃×C₄	#711	1	1	yes	characteristic
286	C₂×C₃×C₄	#711	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
288	#67	—	2	2	no	—
289	#67	—	2	2	no	—
290	C₂×Dic₃	—	2	1	no	—
291	C₂×Dic₃	—	10	2	no	—
292	D₁₂	—	2	1	no	—
293	D₁₂	C₄×Dic₅	1	2	yes	—
294	C₄×D₃	—	2	2	no	—
295	C₄×D₃	—	2	2	no	—
296	C₄×D₃	—	20	4	no	—
297	Dic₆	—	2	1	no	—
298	Dic₆	C₄×Dic₅	1	2	yes	—
299	C₃⋊C₈	—	2	2	no	—
300	C₃⋊C₈	—	10	2	no	—
301	C₂²×C₅	—	2	2	no	—
302	C₂²×C₅	—	6	2	no	—
303	C₂²×C₅	—	12	2	no	—
304	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
305	C₂²×C₅	C₄×#67	1	1	yes	characteristic
306	C₂²×C₅	C₄×#67	1	1	yes	characteristic
307	C₄×C₅	—	4	2	no	—
308	C₄×C₅	—	6	2	no	—
309	C₄×C₅	C₄²×D₃	1	1	yes	characteristic
310	C₄×C₅	#872	1	1	yes	characteristic
311	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
312	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
313	Dic₅	—	2	2	no	—
314	Dic₅	—	2	2	no	—
315	Dic₅	—	4	2	no	—
316	Dic₅	—	12	2	no	—
317	#41	—	3	2	no	—
318	#41	—	3	2	no	—
319	#41	—	6	1	no	—
320	#41	—	6	1	no	—
321	C₂×Q₈	—	3	1	no	—
322	C₂×D₄	—	3	1	no	—
323	C₂×D₄	—	6	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	5	2	no	—
326	C₂²×C₄	—	6	1	no	—
327	C₂²×C₄	—	10	1	no	—
328	C₂²×C₄	—	30	2	no	—
329	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
330	M₁₆	—	3	2	no	—
331	M₁₆	—	6	1	no	—
332	M₁₆	—	15	2	no	—
333	M₁₆	—	30	1	no	—
334	C₂×C₈	—	6	1	no	—
335	C₂×C₈	—	30	1	no	—
336	C₄⋊C₄	—	15	2	no	—
337	C₄⋊C₄	—	30	2	no	—
338	C₂²⋊C₄	—	30	2	no	—
339	C₂²⋊C₄	—	30	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	5	2	no	—
342	C₄²	—	5	1	no	—
343	C₄²	—	5	1	no	—
344	C₄²	—	5	2	no	—
345	C₄²	—	10	1	no	—
346	C₄²	—	30	2	no	—
347	C₄²	—	30	1	no	—
348	C₄²	D₃×Dic₅	1	2	yes	complemented
349	C₃×C₅	#1759	1	1	yes	characteristic, complemented, Hall
350	C₂²×C₃	—	2	2	no	—
351	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
352	C₂²×C₃	#4027	1	1	yes	characteristic
353	C₂²×C₃	D₄×Dic₅	1	1	yes	characteristic
354	C₂×D₃	—	2	2	no	—
355	C₂×D₃	—	4	2	no	—
356	C₃×C₄	—	4	2	no	—
357	C₃×C₄	—	10	2	no	—
358	C₃×C₄	—	10	2	no	—
359	C₃×C₄	—	20	2	no	—
360	C₃×C₄	#4023	1	1	yes	characteristic
361	C₃×C₄	#4027	1	1	yes	characteristic
362	C₃×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
363	C₃×C₄	D₄×Dic₅	1	1	yes	characteristic
364	Dic₃	—	2	2	no	—
365	Dic₃	—	20	2	no	—
366	C₂×C₅	—	2	1	no	—
367	C₂×C₅	—	2	1	no	—
368	C₂×C₅	—	12	2	no	—
369	C₂×C₅	C₄×(C₂×D₃)⋊C₄	1	1	yes	characteristic
370	C₂×C₅	#5005	1	2	yes	—
371	C₂³	—	6	1	no	—
372	C₂³	D₅×#67	1	1	yes	characteristic
373	Q₈	—	3	2	no	—
374	Q₈	—	6	1	no	—
375	D₄	—	3	2	no	—
376	D₄	—	6	2	no	—
377	D₄	—	6	2	no	—
378	D₄	—	6	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	5	2	no	—
382	C₂×C₄	—	5	2	no	—
383	C₂×C₄	—	6	1	no	—
384	C₂×C₄	—	6	2	no	—
385	C₂×C₄	—	6	2	no	—
386	C₂×C₄	—	10	2	no	—
387	C₂×C₄	—	20	2	no	—
388	C₂×C₄	—	20	2	no	—
389	C₂×C₄	—	30	2	no	—
390	C₂×C₄	—	60	4	no	—
391	C₂×C₄	#6772	1	1	yes	characteristic
392	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
393	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
394	C₂×C₄	D₅×D₁₂	1	1	yes	characteristic
395	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
396	C₂×C₄	#6782	1	1	yes	characteristic
397	C₈	—	6	2	no	—
398	C₈	—	30	2	no	—
399	C₂×C₃	—	2	1	no	—
400	C₂×C₃	—	2	1	no	—
401	C₂×C₃	#65110	1	2	yes	—
402	C₂×C₃	C₂²⋊C₄×Dic₅	1	1	yes	characteristic
403	D₃	—	4	2	no	—
404	C₅	#69430	1	1	yes	characteristic, complemented, Sylow
405	C₂²	—	2	2	no	—
406	C₂²	—	6	2	no	—
407	C₂²	—	12	2	no	—
408	C₂²	#91440	1	1	yes	characteristic
409	C₂²	D₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
410	C₂²	Dic₅×#67	1	1	yes	characteristic
411	C₄	—	4	2	no	—
412	C₄	—	6	2	no	—
413	C₄	—	10	2	no	—
414	C₄	—	10	2	no	—
415	C₄	—	20	2	no	—
416	C₄	—	60	2	no	—
417	C₄	C₄×D₃×Dic₅	1	1	yes	characteristic
418	C₄	#91398	1	1	yes	characteristic
419	C₄	#91405	1	1	yes	characteristic
420	C₄	Dic₅×D₁₂	1	1	yes	characteristic
421	C₃	#10601147	1	1	yes	characteristic, complemented, Sylow
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	12	2	no	—
425	C₂	#11747109	1	2	yes	—
426	C₂	Dic₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₅×D₁₂
commutator	C₃×C₄×C₅	C₂×C₄²
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₅×#235	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	#1759
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
3. C₃×#65221	C₂	semidirect
5. Dic₅×#208	C₂	semidirect
6. #11746344	C₂	semidirect
7. #11745978	C₂	semidirect
17. Dic₅×D₁₂	C₄	semidirect
20. Dic₅×Dic₆	C₄	semidirect
21. C₅×#805	C₄	semidirect
23. #90979	C₄	semidirect
31. #65221	D₃	semidirect
48. C₃×C₄²×C₅	C₂×C₄	semidirect
53. #6710	C₂×C₄	semidirect
56. C₅×#208	C₂×C₄	semidirect
60. C₃×C₄×Dic₅	C₂×C₄	semidirect
133. #805	Dic₅	semidirect
153. C₄²×C₅	C₄×D₃	semidirect
162. C₄×Dic₅	C₄×D₃	semidirect
210. C₃×C₄²	C₂×Dic₅	semidirect
220. #208	C₂×Dic₅	semidirect
348. C₄²	D₃×Dic₅	semidirect
349. C₃×C₅	#1759	semidirect
404. C₅	#69430	semidirect
421. C₃	#10601147	semidirect

Maximal subgroups

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

subgroup	index
Dic₅×#235	2
C₂×C₅×#805	2
C₃×#65221	2
C₂×#90979	2
Dic₅×#208	2
#11746344	2
#11745978	2
#10601147	3
#69430	5