Subgroups — #540×D₁₁₃ #28403928

Order 14464.

1260 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	#20299204	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299203	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299202	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299201	C₂	1	2	yes	maximal, complemented
5	#20299200	C₂	1	4	yes	maximal, complemented
6	#20299199	C₂	1	2	yes	maximal, complemented
7	#20299198	C₂	1	4	yes	maximal, complemented
8	#127×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#125×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#123×D₁₁₃	C₂	1	4	yes	maximal, complemented
11	#121×D₁₁₃	C₂	1	4	yes	maximal, complemented
12	#121×D₁₁₃	C₂	1	2	yes	maximal, complemented
13	C₄×D₄×D₁₁₃	C₂	1	2	yes	maximal, complemented
14	#117×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#540×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×D₁₁₃	C₂²	1	2	yes	—
17	C₂×D₄×D₁₁₃	C₂²	1	4	yes	—
18	C₂×D₄×D₁₁₃	C₂²	1	4	yes	—
19	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄×D₁₁₃	C₂²	1	4	yes	—
21	#16813619	C₂²	1	1	yes	characteristic, complemented
22	#16813618	C₂²	1	4	yes	complemented
23	#16813618	C₂²	1	2	yes	complemented
24	#16813614	C₂²	1	1	yes	characteristic, complemented
25	#16813613	C₂²	1	2	yes	complemented
26	#16813612	C₂²	1	4	yes	complemented
27	#16813607	C₂²	1	4	yes	complemented
28	#16813607	C₂²	1	4	yes	complemented
29	#16813606	C₂²	1	4	yes	complemented
30	#16813605	C₂²	1	4	yes	complemented
31	#16813604	C₂²	1	4	yes	complemented
32	#16813604	C₂²	1	4	yes	complemented
33	#16813603	C₂²	1	4	yes	complemented
34	#16813597	C₂²	1	2	yes	complemented
35	#16813597	C₂²	1	4	yes	complemented
36	#16813596	C₂²	1	4	yes	complemented
37	#16813596	C₂²	1	2	yes	complemented
38	#16813595	C₂²	1	4	yes	complemented
39	#16813595	C₂²	1	4	yes	complemented
40	#16813595	C₂²	1	4	yes	complemented
41	#16813594	C₂²	1	4	yes	complemented
42	#16813594	C₂²	1	4	yes	complemented
43	#16813594	C₂²	1	4	yes	complemented
44	#16813593	C₂²	1	4	yes	complemented
45	#16813593	C₂²	1	2	yes	complemented
46	C₄×D₄₅₂	C₂²	1	2	yes	complemented
47	D₄×Dic₁₁₃	C₂²	1	2	yes	complemented
48	#16813584	C₂²	1	2	yes	complemented
49	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
50	#16813582	C₂²	1	4	yes	complemented
51	#16813581	C₂²	1	1	yes	characteristic, complemented
52	#16813580	C₂²	1	2	yes	complemented
53	#16813579	C₂²	1	1	yes	characteristic, complemented
54	#16813579	C₂²	1	1	yes	characteristic, complemented
55	#16813578	C₂²	1	2	yes	complemented
56	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
57	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
58	C₄⋊C₄×D₁₁₃	C₂²	1	4	yes	—
59	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	—
60	C₂²⋊C₄×D₁₁₃	C₂²	1	4	yes	—
61	C₂²⋊C₄×D₁₁₃	C₂²	1	4	yes	—
62	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
63	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
64	#127×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
65	#125×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
66	#123×C₁₁₃	C₂²	1	4	yes	complemented
67	#121×C₁₁₃	C₂²	1	4	yes	complemented
68	#121×C₁₁₃	C₂²	1	2	yes	complemented
69	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
70	#117×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
71	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
72	C₂³×D₁₁₃	C₂³	1	4	yes	—
73	C₂×D₄₅₂	C₂³	1	2	yes	—
74	C₂×D₄₅₂	C₂³	1	4	yes	—
75	C₂×D₄₅₂	C₂³	1	4	yes	—
76	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
77	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
78	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
79	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
80	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
81	D₄×D₁₁₃	—	2	8	no	—
82	D₄×D₁₁₃	—	4	8	no	—
83	D₄×D₁₁₃	—	4	8	no	—
84	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
85	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
86	C₂×C₄×D₁₁₃	—	2	4	no	—
87	C₂×C₄×D₁₁₃	—	4	8	no	—
88	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
89	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
90	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
91	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
92	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
93	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
94	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
95	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
96	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
97	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
98	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
99	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
100	#14268626	C₂³	1	2	yes	—
101	#14268626	C₂³	1	2	yes	—
102	#14268626	C₂³	1	4	yes	—
103	#14268626	C₂³	1	4	yes	—
104	#14268626	C₂³	1	4	yes	—
105	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
106	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
107	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
108	#14268624	C₂³	1	2	yes	—
109	#14268624	C₂³	1	2	yes	—
110	#14268624	C₂³	1	4	yes	—
111	#14268624	C₂³	1	4	yes	—
112	#14268624	C₂³	1	4	yes	—
113	#14268624	C₂³	1	4	yes	—
114	C₄×Dic₁₁₃	C₂³	1	2	yes	—
115	C₄×Dic₁₁₃	C₂³	1	2	yes	—
116	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
117	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
118	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
119	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
120	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
121	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₁₁₃	C₂³	1	4	yes	—
123	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
124	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
125	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
126	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
127	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
128	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
129	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
130	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
131	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
132	C₂³×C₁₁₃	C₂⁴	1	4	yes	—
133	C₂²×D₁₁₃	—	2	2	no	—
134	C₂²×D₁₁₃	—	2	8	no	—
135	C₂²×D₁₁₃	—	2	8	no	—
136	C₂²×D₁₁₃	—	2	4	no	—
137	C₂²×D₁₁₃	—	2	8	no	—
138	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
139	C₂²×D₁₁₃	C₂⁴	1	4	yes	—
140	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
141	D₄×C₁₁₃	—	2	4	no	—
142	D₄×C₁₁₃	—	4	4	no	—
143	D₄×C₁₁₃	—	4	4	no	—
144	C₂×C₄×C₁₁₃	—	2	2	no	—
145	C₂×C₄×C₁₁₃	—	4	4	no	—
146	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
147	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
148	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
149	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
150	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
151	C₂²⋊D₁₁₃	—	2	8	no	—
152	C₂²⋊D₁₁₃	—	4	4	no	—
153	C₂²⋊D₁₁₃	—	4	4	no	—
154	C₂²⋊D₁₁₃	—	4	4	no	—
155	C₂²⋊D₁₁₃	—	4	4	no	—
156	C₂×Dic₁₁₃	—	2	2	no	—
157	C₂×Dic₁₁₃	—	4	4	no	—
158	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
159	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
160	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
161	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
162	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
163	D₄₅₂	—	2	4	no	—
164	D₄₅₂	—	4	4	no	—
165	D₄₅₂	—	4	4	no	—
166	C₄×D₁₁₃	—	2	2	no	—
167	C₄×D₁₁₃	—	2	4	no	—
168	C₄×D₁₁₃	—	2	8	no	—
169	C₄×D₁₁₃	—	2	4	no	—
170	C₄×D₁₁₃	—	2	2	no	—
171	C₄×D₁₁₃	—	2	2	no	—
172	C₄×D₁₁₃	—	4	4	no	—
173	C₄×D₁₁₃	—	4	4	no	—
174	C₄×D₁₁₃	#41	1	4	yes	—
175	C₂²×C₁₁₃	—	2	1	no	—
176	C₂²×C₁₁₃	—	2	4	no	—
177	C₂²×C₁₁₃	—	2	4	no	—
178	C₂²×C₁₁₃	—	2	2	no	—
179	C₂²×C₁₁₃	—	2	4	no	—
180	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
181	C₂×D₁₁₃	—	2	1	no	—
182	C₂×D₁₁₃	—	2	4	no	—
183	C₂×D₁₁₃	—	2	4	no	—
184	C₂×D₁₁₃	—	2	2	no	—
185	C₂×D₁₁₃	—	2	4	no	—
186	C₂×D₁₁₃	—	4	4	no	—
187	C₂×D₁₁₃	—	4	16	no	—
188	C₂×D₁₁₃	C₂×#41	1	2	yes	—
189	C₂×D₁₁₃	H(5,𝔽₂)	1	4	yes	—
190	C₄×C₁₁₃	—	2	1	no	—
191	C₄×C₁₁₃	—	2	2	no	—
192	C₄×C₁₁₃	—	2	4	no	—
193	C₄×C₁₁₃	—	2	2	no	—
194	C₄×C₁₁₃	C₂×#41	1	2	yes	—
195	Dic₁₁₃	—	2	1	no	—
196	Dic₁₁₃	—	2	2	no	—
197	Dic₁₁₃	—	2	4	no	—
198	Dic₁₁₃	—	2	2	no	—
199	Dic₁₁₃	C₂×#41	1	2	yes	—
200	C₂×C₁₁₃	—	4	1	no	—
201	C₂×C₁₁₃	—	4	4	no	—
202	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
203	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
204	D₁₁₃	—	4	1	no	—
205	D₁₁₃	—	4	4	no	—
206	D₁₁₃	#540	1	4	yes	direct product factor
207	C₂×#540	—	113	1	no	maximal, Sylow
208	C₁₁₃	C₂×#540	1	1	yes	characteristic, complemented, Sylow
209	#540	—	113	1	no	—
210	#540	—	113	1	no	—
211	#540	—	113	4	no	—
212	#540	—	113	4	no	—
213	#540	—	113	2	no	—
214	#540	—	113	2	no	—
215	#540	—	113	1	no	—
216	#540	D₁₁₃	1	1	yes	characteristic, direct product factor
217	C₂×#127	—	113	1	no	—
218	C₂×#125	—	113	1	no	—
219	C₂×#123	—	113	4	no	—
220	C₂×#121	—	113	4	no	—
221	C₂×#121	—	113	2	no	—
222	C₂×C₄×D₄	—	113	2	no	—
223	C₂×#117	—	113	1	no	—
224	C₂²×D₄	—	113	4	no	—
225	C₂²×D₄	—	113	4	no	—
226	C₂²×D₄	—	113	2	no	—
227	C₂³×C₄	—	113	4	no	—
228	C₂³×C₄	—	113	1	no	—
229	#127	—	113	2	no	—
230	#127	—	113	4	no	—
231	#127	—	113	1	no	—
232	#127	C₂×D₁₁₃	1	1	yes	characteristic, complemented
233	#125	—	113	4	no	—
234	#125	—	113	2	no	—
235	#125	—	113	1	no	—
236	#125	C₂×D₁₁₃	1	1	yes	characteristic, complemented
237	#123	—	113	4	no	—
238	#123	—	113	4	no	—
239	#123	—	113	4	no	—
240	#123	—	113	4	no	—
241	#123	—	113	4	no	—
242	#123	—	113	4	no	—
243	#123	—	113	4	no	—
244	#123	C₂×D₁₁₃	1	4	yes	complemented
245	#121	—	113	4	no	—
246	#121	—	113	2	no	—
247	#121	—	113	4	no	—
248	#121	—	113	4	no	—
249	#121	—	113	4	no	—
250	#121	—	113	4	no	—
251	#121	—	113	2	no	—
252	#121	—	113	4	no	—
253	#121	—	113	2	no	—
254	#121	—	113	4	no	—
255	#121	—	113	4	no	—
256	#121	—	113	4	no	—
257	#121	C₂×D₁₁₃	1	4	yes	complemented
258	#121	C₂×D₁₁₃	1	2	yes	complemented
259	C₄×D₄	—	113	2	no	—
260	C₄×D₄	—	113	4	no	—
261	C₄×D₄	—	113	2	no	—
262	C₄×D₄	—	113	4	no	—
263	C₄×D₄	—	113	2	no	—
264	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
265	#117	—	113	1	no	—
266	#117	—	113	2	no	—
267	#117	—	113	2	no	—
268	#117	—	113	1	no	—
269	#117	—	113	1	no	—
270	#117	C₂×D₁₁₃	1	1	yes	characteristic, complemented
271	C₂×C₄⋊C₄	—	113	2	no	—
272	C₂×C₄⋊C₄	—	113	2	no	—
273	C₂×C₄⋊C₄	—	113	4	no	—
274	C₂×C₂²⋊C₄	—	113	2	no	—
275	C₂×C₂²⋊C₄	—	113	4	no	—
276	C₂×C₂²⋊C₄	—	113	4	no	—
277	C₂×C₄²	—	113	1	no	—
278	C₂×C₄²	—	113	1	no	—
279	C₂⁴	—	113	4	no	—
280	C₂⁴	—	113	1	no	—
281	C₂×D₄	—	113	4	no	—
282	C₂×D₄	—	113	4	no	—
283	C₂×D₄	—	113	4	no	—
284	C₂×D₄	—	113	4	no	—
285	C₂×D₄	—	113	4	no	—
286	C₂×D₄	—	113	4	no	—
287	C₂×D₄	—	113	4	no	—
288	C₂×D₄	—	113	2	no	—
289	C₂×D₄	—	452	8	no	—
290	C₂×D₄	—	452	8	no	—
291	C₂×D₄	—	226	8	no	—
292	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
293	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
294	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
295	C₂²×C₄	—	113	1	no	—
296	C₂²×C₄	—	113	4	no	—
297	C₂²×C₄	—	113	1	no	—
298	C₂²×C₄	—	113	4	no	—
299	C₂²×C₄	—	113	4	no	—
300	C₂²×C₄	—	113	2	no	—
301	C₂²×C₄	—	113	2	no	—
302	C₂²×C₄	—	113	1	no	—
303	C₂²×C₄	—	113	4	no	—
304	C₂²×C₄	—	113	1	no	—
305	C₂²×C₄	—	113	1	no	—
306	C₂²×C₄	—	452	8	no	—
307	C₂²×C₄	—	226	4	no	—
308	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
309	C₂²×C₄	C₂²×D₁₁₃	1	4	yes	—
310	C₄⋊C₄	—	113	2	no	—
311	C₄⋊C₄	—	113	2	no	—
312	C₄⋊C₄	—	113	2	no	—
313	C₄⋊C₄	—	113	4	no	—
314	C₄⋊C₄	—	113	2	no	—
315	C₄⋊C₄	—	113	4	no	—
316	C₄⋊C₄	—	113	4	no	—
317	C₄⋊C₄	—	113	4	no	—
318	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
319	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
320	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
321	C₂²⋊C₄	—	113	2	no	—
322	C₂²⋊C₄	—	113	4	no	—
323	C₂²⋊C₄	—	113	4	no	—
324	C₂²⋊C₄	—	113	2	no	—
325	C₂²⋊C₄	—	113	2	no	—
326	C₂²⋊C₄	—	113	4	no	—
327	C₂²⋊C₄	—	113	4	no	—
328	C₂²⋊C₄	—	113	4	no	—
329	C₂²⋊C₄	—	113	4	no	—
330	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
331	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
332	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
333	C₄²	—	113	2	no	—
334	C₄²	—	113	1	no	—
335	C₄²	—	113	2	no	—
336	C₄²	—	113	1	no	—
337	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
338	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
339	C₂³	—	113	1	no	—
340	C₂³	—	113	1	no	—
341	C₂³	—	113	4	no	—
342	C₂³	—	226	8	no	—
343	C₂³	—	226	2	no	—
344	C₂³	—	226	8	no	—
345	C₂³	—	226	4	no	—
346	C₂³	—	226	8	no	—
347	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
348	C₂³	C₂³×D₁₁₃	1	4	yes	—
349	D₄	—	2	4	no	—
350	D₄	—	4	4	no	—
351	D₄	—	4	4	no	—
352	D₄	—	452	4	no	—
353	D₄	—	452	4	no	—
354	D₄	—	452	4	no	—
355	D₄	—	452	4	no	—
356	D₄	—	452	4	no	—
357	D₄	—	452	4	no	—
358	D₄	—	226	8	no	—
359	D₄	—	226	4	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	113	1	no	—
363	C₂×C₄	—	113	4	no	—
364	C₂×C₄	—	113	2	no	—
365	C₂×C₄	—	113	2	no	—
366	C₂×C₄	—	113	1	no	—
367	C₂×C₄	—	113	4	no	—
368	C₂×C₄	—	452	4	no	—
369	C₂×C₄	—	452	4	no	—
370	C₂×C₄	—	452	4	no	—
371	C₂×C₄	—	226	2	no	—
372	C₂×C₄	—	226	4	no	—
373	C₂×C₄	—	226	8	no	—
374	C₂×C₄	—	226	2	no	—
375	C₂×C₄	—	226	4	no	—
376	C₂×C₄	—	226	2	no	—
377	C₂×C₄	—	226	2	no	—
378	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
379	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
380	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
381	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
382	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
383	C₂²	—	2	1	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	113	2	no	—
389	C₂²	—	113	4	no	—
390	C₂²	—	452	16	no	—
391	C₂²	—	452	4	no	—
392	C₂²	—	226	1	no	—
393	C₂²	—	226	4	no	—
394	C₂²	—	226	4	no	—
395	C₂²	—	226	2	no	—
396	C₂²	—	226	4	no	—
397	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	4	no	—
401	C₄	—	2	2	no	—
402	C₄	—	113	2	no	—
403	C₄	—	226	1	no	—
404	C₄	—	226	2	no	—
405	C₄	—	226	4	no	—
406	C₄	—	226	2	no	—
407	C₄	#41×D₁₁₃	1	2	yes	—
408	C₂	—	4	1	no	—
409	C₂	—	4	4	no	—
410	C₂	—	113	4	no	—
411	C₂	—	452	1	no	—
412	C₂	—	452	4	no	—
413	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
414	C₂	H(5,𝔽₂)×D₁₁₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#540×C₁₁₃	C₂
hypercenter	#540	D₁₁₃
hypocenter	C₁₁₃	C₂×#540
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #540

Complements

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

N	H ≅ G/N	type
1. #20299204	C₂	semidirect
2. #20299203	C₂	semidirect
3. #20299202	C₂	semidirect
4. #20299201	C₂	semidirect
5. #20299200	C₂	semidirect
6. #20299199	C₂	semidirect
7. #20299198	C₂	semidirect
8. #127×D₁₁₃	C₂	semidirect
9. #125×D₁₁₃	C₂	semidirect
10. #123×D₁₁₃	C₂	semidirect
11. #121×D₁₁₃	C₂	semidirect
12. #121×D₁₁₃	C₂	semidirect
13. C₄×D₄×D₁₁₃	C₂	semidirect
14. #117×D₁₁₃	C₂	semidirect
15. #540×C₁₁₃	C₂	semidirect
21. #16813619	C₂²	semidirect
22. #16813618	C₂²	semidirect
23. #16813618	C₂²	semidirect
24. #16813614	C₂²	semidirect
25. #16813613	C₂²	semidirect
26. #16813612	C₂²	semidirect
27. #16813607	C₂²	semidirect
28. #16813607	C₂²	semidirect
29. #16813606	C₂²	semidirect
30. #16813605	C₂²	semidirect
31. #16813604	C₂²	semidirect
32. #16813604	C₂²	semidirect
33. #16813603	C₂²	semidirect
34. #16813597	C₂²	semidirect
35. #16813597	C₂²	semidirect
36. #16813596	C₂²	semidirect
37. #16813596	C₂²	semidirect
38. #16813595	C₂²	semidirect
39. #16813595	C₂²	semidirect
40. #16813595	C₂²	semidirect
41. #16813594	C₂²	semidirect
42. #16813594	C₂²	semidirect
43. #16813594	C₂²	semidirect
44. #16813593	C₂²	semidirect
45. #16813593	C₂²	semidirect
46. C₄×D₄₅₂	C₂²	semidirect
47. D₄×Dic₁₁₃	C₂²	semidirect
48. #16813584	C₂²	semidirect
49. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
50. #16813582	C₂²	semidirect
51. #16813581	C₂²	semidirect
52. #16813580	C₂²	semidirect
53. #16813579	C₂²	semidirect
54. #16813579	C₂²	semidirect
55. #16813578	C₂²	semidirect
64. #127×C₁₁₃	C₂²	semidirect
65. #125×C₁₁₃	C₂²	semidirect
66. #123×C₁₁₃	C₂²	semidirect
67. #121×C₁₁₃	C₂²	semidirect
68. #121×C₁₁₃	C₂²	semidirect
69. C₄×D₄×C₁₁₃	C₂²	semidirect
70. #117×C₁₁₃	C₂²	semidirect
206. D₁₁₃	#540	direct (N × H)
208. C₁₁₃	C₂×#540	semidirect
216. #540	D₁₁₃	direct (N × H)
232. #127	C₂×D₁₁₃	semidirect
236. #125	C₂×D₁₁₃	semidirect
244. #123	C₂×D₁₁₃	semidirect
257. #121	C₂×D₁₁₃	semidirect
258. #121	C₂×D₁₁₃	semidirect
264. C₄×D₄	C₂×D₁₁₃	semidirect
270. #117	C₂×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299204	2
#20299203	2
#20299202	2
#20299201	2
#20299200	2
#20299199	2
#20299198	2
#127×D₁₁₃	2
#125×D₁₁₃	2
#123×D₁₁₃	2
#121×D₁₁₃	2
C₄×D₄×D₁₁₃	2
#117×D₁₁₃	2
#540×C₁₁₃	2
C₂×#540	113

Subgroups — #540×D113 #28403928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #540×D₁₁₃ #28403928