Subgroups — C₁₁₃×#14807 #43282827

Order 28928.

2398 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#399×C₁₁₃	C₂	1	2	yes	maximal, complemented
3	C₂×#389×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#385×C₁₁₃	C₂	1	4	yes	maximal, complemented
5	C₁₁₃×#1444	C₂	1	2	yes	maximal, complemented
6	C₁₁₃×#1439	C₂	1	2	yes	maximal, complemented
7	C₁₁₃×#1438	C₂	1	2	yes	maximal
8	C₁₁₃×#1434	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₁₃	C₂²	1	2	yes	—
11	C₂×C₄×D₄×C₁₁₃	—	2	8	no	—
12	C₂×C₄×D₄×C₁₁₃	—	2	4	no	—
13	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	4	yes	—
18	C₂²×C₂²⋊C₄×C₁₁₃	C₂²	1	4	yes	—
19	C₂²×C₂²⋊C₄×C₁₁₃	C₂²	1	4	yes	—
20	C₂²×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
22	#399×C₁₁₃	—	2	8	no	—
23	#389×C₁₁₃	—	2	4	no	—
24	#385×C₁₁₃	—	2	16	no	—
25	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
26	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
27	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
28	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
29	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
30	C₂⁵×C₁₁₃	C₂³	1	2	yes	—
31	C₂²×D₄×C₁₁₃	—	2	4	no	—
32	C₂²×D₄×C₁₁₃	—	2	4	no	—
33	C₂²×D₄×C₁₁₃	—	2	2	no	—
34	C₂²×D₄×C₁₁₃	—	2	2	no	—
35	C₂²×D₄×C₁₁₃	Q₈	1	4	yes	—
36	C₂³×C₄×C₁₁₃	—	2	4	no	—
37	C₂³×C₄×C₁₁₃	—	2	4	no	—
38	C₂³×C₄×C₁₁₃	—	2	4	no	—
39	C₂³×C₄×C₁₁₃	—	2	8	no	—
40	C₂³×C₄×C₁₁₃	—	4	4	no	—
41	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₁₃	C₂³	1	4	yes	—
43	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
48	C₄×D₄×C₁₁₃	—	2	32	no	—
49	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
54	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
55	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
58	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
59	C₂×C₄⋊C₄×C₁₁₃	—	4	4	no	—
60	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
61	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
63	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
64	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
65	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
66	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
67	C₂×C₂²⋊C₄×C₁₁₃	—	4	4	no	—
68	C₂×C₂²⋊C₄×C₁₁₃	D₄	1	8	yes	—
69	C₂×C₄²×C₁₁₃	—	2	4	no	—
70	C₂×C₄²×C₁₁₃	D₄	1	4	yes	—
71	#95×C₁₁₃	—	2	8	no	—
72	#95×C₁₁₃	—	2	4	no	—
73	#95×C₁₁₃	—	2	4	no	—
74	#95×C₁₁₃	—	2	4	no	—
75	#95×C₁₁₃	D₄	1	8	yes	complemented
76	C₂⁴×C₁₁₃	—	2	4	no	—
77	C₂⁴×C₁₁₃	—	2	2	no	—
78	C₂⁴×C₁₁₃	—	2	2	no	—
79	C₂⁴×C₁₁₃	—	2	4	no	—
80	C₂⁴×C₁₁₃	—	2	2	no	—
81	C₂⁴×C₁₁₃	—	2	2	no	—
82	C₂⁴×C₁₁₃	—	2	4	no	—
83	C₂⁴×C₁₁₃	—	2	4	no	—
84	C₂⁴×C₁₁₃	C₂×D₄	1	4	yes	—
85	C₂⁴×C₁₁₃	C₂×Q₈	1	4	yes	—
86	C₂⁴×C₁₁₃	#41	1	4	yes	—
87	C₂⁴×C₁₁₃	C₂⁴	1	1	yes	characteristic
88	C₂×D₄×C₁₁₃	—	2	8	no	—
89	C₂×D₄×C₁₁₃	—	2	8	no	—
90	C₂×D₄×C₁₁₃	—	2	16	no	—
91	C₂×D₄×C₁₁₃	—	2	16	no	—
92	C₂×D₄×C₁₁₃	—	2	8	no	—
93	C₂²×C₄×C₁₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₁₃	—	2	16	no	—
100	C₂²×C₄×C₁₁₃	—	2	4	no	—
101	C₂²×C₄×C₁₁₃	—	2	4	no	—
102	C₂²×C₄×C₁₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₁₃	—	2	4	no	—
104	C₂²×C₄×C₁₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₁₃	—	2	4	no	—
107	C₂²×C₄×C₁₁₃	—	2	4	no	—
108	C₂²×C₄×C₁₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₁₃	—	2	4	no	—
113	C₂²×C₄×C₁₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₁₃	—	2	4	no	—
117	C₂²×C₄×C₁₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₁₃	—	4	16	no	—
120	C₂²×C₄×C₁₁₃	—	4	16	no	—
121	C₂²×C₄×C₁₁₃	—	4	8	no	—
122	C₂²×C₄×C₁₁₃	—	4	8	no	—
123	C₂²×C₄×C₁₁₃	C₂×D₄	1	8	yes	—
124	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
125	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₁₃	C₂×Q₈	1	2	yes	—
131	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
132	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
133	C₄⋊C₄×C₁₁₃	—	2	8	no	—
134	C₄⋊C₄×C₁₁₃	—	2	8	no	—
135	C₄⋊C₄×C₁₁₃	—	4	16	no	—
136	C₄⋊C₄×C₁₁₃	—	4	4	no	—
137	C₄⋊C₄×C₁₁₃	—	4	8	no	—
138	C₂²⋊C₄×C₁₁₃	—	2	32	no	—
139	C₂²⋊C₄×C₁₁₃	—	2	16	no	—
140	C₂²⋊C₄×C₁₁₃	—	4	16	no	—
141	C₄²×C₁₁₃	—	2	8	no	—
142	C₂³×C₁₁₃	—	2	4	no	—
143	C₂³×C₁₁₃	—	2	4	no	—
144	C₂³×C₁₁₃	—	2	4	no	—
145	C₂³×C₁₁₃	—	2	8	no	—
146	C₂³×C₁₁₃	—	2	4	no	—
147	C₂³×C₁₁₃	—	2	4	no	—
148	C₂³×C₁₁₃	—	2	4	no	—
149	C₂³×C₁₁₃	—	2	8	no	—
150	C₂³×C₁₁₃	—	2	8	no	—
151	C₂³×C₁₁₃	—	2	8	no	—
152	C₂³×C₁₁₃	—	2	8	no	—
153	C₂³×C₁₁₃	—	2	8	no	—
154	C₂³×C₁₁₃	—	4	2	no	—
155	C₂³×C₁₁₃	—	4	4	no	—
156	C₂³×C₁₁₃	—	4	2	no	—
157	C₂³×C₁₁₃	—	4	2	no	—
158	C₂³×C₁₁₃	—	4	2	no	—
159	C₂³×C₁₁₃	—	4	4	no	—
160	C₂³×C₁₁₃	—	4	4	no	—
161	C₂³×C₁₁₃	—	4	4	no	—
162	C₂³×C₁₁₃	—	4	4	no	—
163	C₂³×C₁₁₃	—	4	4	no	—
164	C₂³×C₁₁₃	C₂²⋊Q₈	1	8	yes	—
165	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
166	C₂³×C₁₁₃	C₂²×D₄	1	2	yes	—
167	C₂³×C₁₁₃	C₂²×D₄	1	2	yes	—
168	C₂³×C₁₁₃	C₂²×Q₈	1	1	yes	characteristic
169	C₂³×C₁₁₃	C₂×#41	1	2	yes	—
170	C₂³×C₁₁₃	C₂×#41	1	1	yes	characteristic
171	C₂³×C₁₁₃	C₂×#41	1	2	yes	—
172	C₂³×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
173	C₂³×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
174	D₄×C₁₁₃	—	2	32	no	—
175	C₂×C₄×C₁₁₃	—	2	2	no	—
176	C₂×C₄×C₁₁₃	—	2	2	no	—
177	C₂×C₄×C₁₁₃	—	2	4	no	—
178	C₂×C₄×C₁₁₃	—	2	2	no	—
179	C₂×C₄×C₁₁₃	—	2	2	no	—
180	C₂×C₄×C₁₁₃	—	2	4	no	—
181	C₂×C₄×C₁₁₃	—	2	2	no	—
182	C₂×C₄×C₁₁₃	—	2	2	no	—
183	C₂×C₄×C₁₁₃	—	2	8	no	—
184	C₂×C₄×C₁₁₃	—	2	8	no	—
185	C₂×C₄×C₁₁₃	—	2	4	no	—
186	C₂×C₄×C₁₁₃	—	2	8	no	—
187	C₂×C₄×C₁₁₃	—	2	8	no	—
188	C₂×C₄×C₁₁₃	—	2	4	no	—
189	C₂×C₄×C₁₁₃	—	2	8	no	—
190	C₂×C₄×C₁₁₃	—	2	8	no	—
191	C₂×C₄×C₁₁₃	—	2	8	no	—
192	C₂×C₄×C₁₁₃	—	4	32	no	—
193	C₂×C₄×C₁₁₃	—	4	2	no	—
194	C₂×C₄×C₁₁₃	—	4	4	no	—
195	C₂×C₄×C₁₁₃	—	4	4	no	—
196	C₂×C₄×C₁₁₃	—	4	2	no	—
197	C₂×C₄×C₁₁₃	—	4	2	no	—
198	C₂×C₄×C₁₁₃	—	4	2	no	—
199	C₂×C₄×C₁₁₃	—	4	4	no	—
200	C₂×C₄×C₁₁₃	—	4	4	no	—
201	C₂×C₄×C₁₁₃	—	4	4	no	—
202	C₂×C₄×C₁₁₃	—	4	4	no	—
203	C₂×C₄×C₁₁₃	—	4	2	no	—
204	C₂×C₄×C₁₁₃	—	4	2	no	—
205	C₂×C₄×C₁₁₃	—	4	2	no	—
206	C₂×C₄×C₁₁₃	—	4	4	no	—
207	C₂×C₄×C₁₁₃	—	4	4	no	—
208	C₂×C₄×C₁₁₃	#120	1	4	yes	—
209	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	4	yes	—
210	C₂×C₄×C₁₁₃	#127	1	4	yes	—
211	C₂²×C₁₁₃	—	2	8	no	—
212	C₂²×C₁₁₃	—	2	16	no	—
213	C₂²×C₁₁₃	—	4	4	no	—
214	C₂²×C₁₁₃	—	4	4	no	—
215	C₂²×C₁₁₃	—	4	4	no	—
216	C₂²×C₁₁₃	—	4	4	no	—
217	C₂²×C₁₁₃	—	4	4	no	—
218	C₂²×C₁₁₃	—	4	8	no	—
219	C₂²×C₁₁₃	—	4	8	no	—
220	C₂²×C₁₁₃	—	4	8	no	—
221	C₂²×C₁₁₃	—	4	4	no	—
222	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
223	C₂²×C₁₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
224	C₂²×C₁₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
225	C₂²×C₁₁₃	#525	1	1	yes	characteristic
226	C₂²×C₁₁₃	#525	1	1	yes	characteristic
227	C₂²×C₁₁₃	#525	1	2	yes	—
228	C₂²×C₁₁₃	#525	1	4	yes	—
229	C₂²×C₁₁₃	C₂×#127	1	1	yes	characteristic
230	C₂²×C₁₁₃	#535	1	1	yes	characteristic
231	C₂²×C₁₁₃	#536	1	1	yes	characteristic
232	C₂²×C₁₁₃	#539	1	4	yes	—
233	C₂²×C₁₁₃	D₄²	1	4	yes	—
234	C₂²×C₁₁₃	#547	1	4	yes	—
235	C₂²×C₁₁₃	#547	1	2	yes	—
236	C₂²×C₁₁₃	D₄×Q₈	1	2	yes	—
237	C₂²×C₁₁₃	#554	1	2	yes	—
238	C₂²×C₁₁₃	#559	1	2	yes	—
239	C₄×C₁₁₃	—	2	4	no	—
240	C₄×C₁₁₃	—	2	4	no	—
241	C₄×C₁₁₃	—	2	4	no	—
242	C₄×C₁₁₃	—	4	4	no	—
243	C₄×C₁₁₃	—	4	4	no	—
244	C₄×C₁₁₃	—	4	8	no	—
245	C₄×C₁₁₃	—	8	2	no	—
246	#14807	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₂×C₁₁₃	—	4	8	no	—
248	C₂×C₁₁₃	#2397	1	1	yes	characteristic
249	C₂×C₁₁₃	#2406	1	1	yes	characteristic
250	C₂×C₁₁₃	#2433	1	1	yes	characteristic
251	C₂×C₁₁₃	#2449	1	4	yes	—
252	C₂×C₁₁₃	#2455	1	4	yes	—
253	C₂×C₁₁₃	#2542	1	1	yes	characteristic
254	C₂×C₁₁₃	#2580	1	1	yes	characteristic
255	C₂×C₁₁₃	#2633	1	1	yes	characteristic
256	C₂×C₁₁₃	#2848	1	1	yes	characteristic
257	C₂²×C₄×D₄	C₂×C₁₁₃	1	1	yes	characteristic
258	C₂×#399	C₂×C₁₁₃	1	2	yes	complemented
259	C₂×#389	C₂×C₁₁₃	1	1	yes	characteristic, complemented
260	C₂×#385	C₂×C₁₁₃	1	4	yes	complemented
261	#1444	C₂×C₁₁₃	1	2	yes	complemented
262	#1439	C₂×C₁₁₃	1	2	yes	complemented
263	#1438	C₂×C₁₁₃	1	2	yes	—
264	#1434	C₂×C₁₁₃	1	1	yes	characteristic, complemented
265	C₁₁₃	#14807	1	1	yes	characteristic, direct product factor, Sylow
266	C₂³×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
267	C₂⁴×C₄	C₂²×C₁₁₃	1	2	yes	—
268	C₂×C₄×D₄	—	2	8	no	—
269	C₂×C₄×D₄	—	2	4	no	—
270	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
271	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
272	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
273	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
274	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	4	yes	—
275	C₂²×C₂²⋊C₄	C₂²×C₁₁₃	1	4	yes	—
276	C₂²×C₂²⋊C₄	C₂²×C₁₁₃	1	4	yes	—
277	C₂²×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	—
278	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
279	#399	—	2	8	no	—
280	#389	—	2	4	no	—
281	#385	—	2	16	no	—
282	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
283	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
284	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
285	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
286	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
287	C₂⁵	C₂³×C₁₁₃	1	2	yes	—
288	C₂²×D₄	—	2	4	no	—
289	C₂²×D₄	—	2	4	no	—
290	C₂²×D₄	—	2	2	no	—
291	C₂²×D₄	—	2	2	no	—
292	C₂²×D₄	Q₈×C₁₁₃	1	4	yes	—
293	C₂³×C₄	—	2	4	no	—
294	C₂³×C₄	—	2	4	no	—
295	C₂³×C₄	—	2	4	no	—
296	C₂³×C₄	—	2	8	no	—
297	C₂³×C₄	—	4	4	no	—
298	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
299	C₂³×C₄	C₂³×C₁₁₃	1	4	yes	—
300	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
301	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
302	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
303	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
304	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
305	C₄×D₄	—	2	32	no	—
306	C₂×C₄⋊C₄	—	2	4	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	4	no	—
310	C₂×C₄⋊C₄	—	2	8	no	—
311	C₂×C₄⋊C₄	—	2	8	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	4	no	—
314	C₂×C₄⋊C₄	—	2	8	no	—
315	C₂×C₄⋊C₄	—	2	4	no	—
316	C₂×C₄⋊C₄	—	4	4	no	—
317	C₂×C₂²⋊C₄	—	2	8	no	—
318	C₂×C₂²⋊C₄	—	2	4	no	—
319	C₂×C₂²⋊C₄	—	2	4	no	—
320	C₂×C₂²⋊C₄	—	2	8	no	—
321	C₂×C₂²⋊C₄	—	2	8	no	—
322	C₂×C₂²⋊C₄	—	2	8	no	—
323	C₂×C₂²⋊C₄	—	2	8	no	—
324	C₂×C₂²⋊C₄	—	4	4	no	—
325	C₂×C₂²⋊C₄	D₄×C₁₁₃	1	8	yes	—
326	C₂×C₄²	—	2	4	no	—
327	C₂×C₄²	D₄×C₁₁₃	1	4	yes	—
328	#95	—	2	8	no	—
329	#95	—	2	4	no	—
330	#95	—	2	4	no	—
331	#95	—	2	4	no	—
332	#95	D₄×C₁₁₃	1	8	yes	complemented
333	C₂⁴	—	2	4	no	—
334	C₂⁴	—	2	2	no	—
335	C₂⁴	—	2	2	no	—
336	C₂⁴	—	2	4	no	—
337	C₂⁴	—	2	2	no	—
338	C₂⁴	—	2	2	no	—
339	C₂⁴	—	2	4	no	—
340	C₂⁴	—	2	4	no	—
341	C₂⁴	C₂×D₄×C₁₁₃	1	4	yes	—
342	C₂⁴	C₂×Q₈×C₁₁₃	1	4	yes	—
343	C₂⁴	#41×C₁₁₃	1	4	yes	—
344	C₂⁴	C₂⁴×C₁₁₃	1	1	yes	characteristic
345	C₂×D₄	—	2	8	no	—
346	C₂×D₄	—	2	8	no	—
347	C₂×D₄	—	2	16	no	—
348	C₂×D₄	—	2	16	no	—
349	C₂×D₄	—	2	8	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	16	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	4	16	no	—
377	C₂²×C₄	—	4	16	no	—
378	C₂²×C₄	—	4	8	no	—
379	C₂²×C₄	—	4	8	no	—
380	C₂²×C₄	C₂×D₄×C₁₁₃	1	8	yes	—
381	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
382	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
383	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
384	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
385	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
386	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
387	C₂²×C₄	C₂×Q₈×C₁₁₃	1	2	yes	—
388	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
389	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
390	C₄⋊C₄	—	2	8	no	—
391	C₄⋊C₄	—	2	8	no	—
392	C₄⋊C₄	—	4	16	no	—
393	C₄⋊C₄	—	4	4	no	—
394	C₄⋊C₄	—	4	8	no	—
395	C₂²⋊C₄	—	2	32	no	—
396	C₂²⋊C₄	—	2	16	no	—
397	C₂²⋊C₄	—	4	16	no	—
398	C₄²	—	2	8	no	—
399	C₂³	—	2	4	no	—
400	C₂³	—	2	4	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	2	8	no	—
403	C₂³	—	2	4	no	—
404	C₂³	—	2	4	no	—
405	C₂³	—	2	4	no	—
406	C₂³	—	2	8	no	—
407	C₂³	—	2	8	no	—
408	C₂³	—	2	8	no	—
409	C₂³	—	2	8	no	—
410	C₂³	—	2	8	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	4	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	4	no	—
417	C₂³	—	4	4	no	—
418	C₂³	—	4	4	no	—
419	C₂³	—	4	4	no	—
420	C₂³	—	4	4	no	—
421	C₂³	C₂²⋊Q₈×C₁₁₃	1	8	yes	—
422	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
423	C₂³	C₂²×D₄×C₁₁₃	1	2	yes	—
424	C₂³	C₂²×D₄×C₁₁₃	1	2	yes	—
425	C₂³	C₂²×Q₈×C₁₁₃	1	1	yes	characteristic
426	C₂³	C₂×#41×C₁₁₃	1	2	yes	—
427	C₂³	C₂×#41×C₁₁₃	1	1	yes	characteristic
428	C₂³	C₂×#41×C₁₁₃	1	2	yes	—
429	C₂³	H(5,𝔽₂)×C₁₁₃	1	2	yes	—
430	C₂³	2₋¹⁺⁴×C₁₁₃	1	2	yes	—
431	D₄	—	2	32	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	8	no	—
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	8	no	—
444	C₂×C₄	—	2	8	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	8	no	—
447	C₂×C₄	—	2	8	no	—
448	C₂×C₄	—	2	8	no	—
449	C₂×C₄	—	4	32	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	#120×C₁₁₃	1	4	yes	—
466	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	4	yes	—
467	C₂×C₄	#127×C₁₁₃	1	4	yes	—
468	C₂²	—	2	8	no	—
469	C₂²	—	2	16	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	4	4	no	—
473	C₂²	—	4	4	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	8	no	—
477	C₂²	—	4	8	no	—
478	C₂²	—	4	8	no	—
479	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
480	C₂²	C₂×C₂²⋊Q₈×C₁₁₃	1	1	yes	characteristic
481	C₂²	C₂×C₂²⋊Q₈×C₁₁₃	1	2	yes	—
482	C₂²	#525×C₁₁₃	1	1	yes	characteristic
483	C₂²	#525×C₁₁₃	1	1	yes	characteristic
484	C₂²	#525×C₁₁₃	1	2	yes	—
485	C₂²	#525×C₁₁₃	1	4	yes	—
486	C₂²	C₂×#127×C₁₁₃	1	1	yes	characteristic
487	C₂²	#535×C₁₁₃	1	1	yes	characteristic
488	C₂²	#536×C₁₁₃	1	1	yes	characteristic
489	C₂²	#539×C₁₁₃	1	4	yes	—
490	C₂²	D₄²×C₁₁₃	1	4	yes	—
491	C₂²	#547×C₁₁₃	1	2	yes	—
492	C₂²	#547×C₁₁₃	1	4	yes	—
493	C₂²	D₄×Q₈×C₁₁₃	1	2	yes	—
494	C₂²	#554×C₁₁₃	1	2	yes	—
495	C₂²	#559×C₁₁₃	1	2	yes	—
496	C₄	—	2	4	no	—
497	C₄	—	2	4	no	—
498	C₄	—	2	4	no	—
499	C₄	—	4	4	no	—
500	C₄	—	4	4	no	—
501	C₄	—	4	8	no	—
502	C₄	—	8	2	no	—
503	C₂	—	4	8	no	—
504	C₂	C₁₁₃×#2397	1	1	yes	characteristic
505	C₂	C₁₁₃×#2406	1	1	yes	characteristic
506	C₂	C₁₁₃×#2433	1	1	yes	characteristic
507	C₂	C₁₁₃×#2449	1	4	yes	—
508	C₂	C₁₁₃×#2455	1	4	yes	—
509	C₂	C₁₁₃×#2542	1	1	yes	characteristic
510	C₂	C₁₁₃×#2580	1	1	yes	characteristic
511	C₂	C₁₁₃×#2633	1	1	yes	characteristic
512	C₂	C₁₁₃×#2848	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₁₃	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₁₃
prime radical	C₂³×D₄×C₁₁₃	C₂²
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#399×C₁₁₃	C₂	semidirect
3. C₂×#389×C₁₁₃	C₂	semidirect
4. C₂×#385×C₁₁₃	C₂	semidirect
5. C₁₁₃×#1444	C₂	semidirect
6. C₁₁₃×#1439	C₂	semidirect
8. C₁₁₃×#1434	C₂	semidirect
75. #95×C₁₁₃	D₄	semidirect
246. #14807	C₁₁₃	direct (N × H)
258. C₂×#399	C₂×C₁₁₃	semidirect
259. C₂×#389	C₂×C₁₁₃	semidirect
260. C₂×#385	C₂×C₁₁₃	semidirect
261. #1444	C₂×C₁₁₃	semidirect
262. #1439	C₂×C₁₁₃	semidirect
264. #1434	C₂×C₁₁₃	semidirect
265. C₁₁₃	#14807	direct (N × H)
332. #95	D₄×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₁₁₃	2
C₂×#399×C₁₁₃	2
C₂×#389×C₁₁₃	2
C₂×#385×C₁₁₃	2
C₁₁₃×#1444	2
C₁₁₃×#1439	2
C₁₁₃×#1438	2
C₁₁₃×#1434	2
#14807	113

Subgroups — C113×#14807 #43282827

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#14807 #43282827