Subgroups — C₁₁₃×#9141 #43277161

Order 28928.

752 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#423×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁₃×#2856	C₂	1	1	yes	maximal, characteristic
3	C₁₁₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#331×C₁₁₃	C₂	1	2	yes	maximal, complemented
5	C₁₁₃×#1296	C₂	1	2	yes	maximal, complemented
6	C₂²×M₁₆×C₁₁₃	—	2	1	no	—
7	C₂×#127×C₁₁₃	C₂²	1	1	yes	characteristic
8	C₂×#121×C₁₁₃	—	2	1	no	—
9	C₂×#121×C₁₁₃	—	2	1	no	—
10	C₂×#121×C₁₁₃	C₄	1	2	yes	—
11	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
12	#423×C₁₁₃	—	2	4	no	—
13	C₂×C₄⋊C₈×C₁₁₃	—	2	1	no	—
14	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
15	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₈×C₁₁₃	—	2	1	no	—
17	#390×C₁₁₃	—	2	1	no	—
18	#390×C₁₁₃	—	2	1	no	—
19	#390×C₁₁₃	C₄	1	2	yes	—
20	#384×C₁₁₃	C₂²	1	1	yes	characteristic
21	#336×C₁₁₃	—	2	1	no	—
22	#331×C₁₁₃	—	2	4	no	—
23	C₂²×D₄×C₁₁₃	—	2	2	no	—
24	C₂²×D₄×C₁₁₃	—	2	1	no	—
25	C₂²×D₄×C₁₁₃	—	2	1	no	—
26	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
27	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
30	C₂×M₁₆×C₁₁₃	—	2	4	no	—
31	C₂×M₁₆×C₁₁₃	—	4	2	no	—
32	C₂×M₁₆×C₁₁₃	—	4	2	no	—
33	C₂²×C₈×C₁₁₃	—	2	2	no	—
34	C₂²×C₈×C₁₁₃	—	2	2	no	—
35	#127×C₁₁₃	—	2	2	no	—
36	#127×C₁₁₃	—	2	2	no	—
37	#121×C₁₁₃	—	4	4	no	—
38	#121×C₁₁₃	—	4	2	no	—
39	#121×C₁₁₃	—	4	2	no	—
40	#121×C₁₁₃	—	4	4	no	—
41	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
42	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
43	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
44	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
45	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
46	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
47	C₂×C₄²×C₁₁₃	—	2	2	no	—
48	C₂×C₄²×C₁₁₃	—	2	2	no	—
49	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₁₃	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₁₃	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
53	C₄⋊C₈×C₁₁₃	—	2	4	no	—
54	C₄⋊C₈×C₁₁₃	—	2	2	no	—
55	C₄⋊C₈×C₁₁₃	—	2	2	no	—
56	C₄⋊C₈×C₁₁₃	—	2	2	no	—
57	C₄⋊C₈×C₁₁₃	D₄	1	4	yes	complemented
58	C₂²⋊C₈×C₁₁₃	—	4	2	no	—
59	C₂⁴×C₁₁₃	—	2	2	no	—
60	C₂⁴×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×D₄×C₁₁₃	—	2	4	no	—
62	C₂×D₄×C₁₁₃	—	4	2	no	—
63	C₂×D₄×C₁₁₃	—	4	2	no	—
64	C₂×D₄×C₁₁₃	—	4	4	no	—
65	C₂×D₄×C₁₁₃	—	4	4	no	—
66	C₂×D₄×C₁₁₃	—	4	4	no	—
67	C₂×D₄×C₁₁₃	—	4	1	no	—
68	C₂×D₄×C₁₁₃	—	4	2	no	—
69	C₂×D₄×C₁₁₃	—	4	1	no	—
70	C₂×D₄×C₁₁₃	—	4	1	no	—
71	C₂×D₄×C₁₁₃	—	4	1	no	—
72	C₂×D₄×C₁₁₃	—	4	2	no	—
73	C₂×D₄×C₁₁₃	—	4	1	no	—
74	C₂×D₄×C₁₁₃	—	4	1	no	—
75	C₂×D₄×C₁₁₃	—	4	1	no	—
76	C₂×D₄×C₁₁₃	—	4	1	no	—
77	C₂²×C₄×C₁₁₃	—	2	1	no	—
78	C₂²×C₄×C₁₁₃	—	2	1	no	—
79	C₂²×C₄×C₁₁₃	—	2	1	no	—
80	C₂²×C₄×C₁₁₃	—	2	1	no	—
81	C₂²×C₄×C₁₁₃	—	2	2	no	—
82	C₂²×C₄×C₁₁₃	—	2	2	no	—
83	C₂²×C₄×C₁₁₃	—	2	2	no	—
84	C₂²×C₄×C₁₁₃	—	2	1	no	—
85	C₂²×C₄×C₁₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₁₃	—	2	1	no	—
87	C₂²×C₄×C₁₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₁₃	—	4	1	no	—
89	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₁₃	D₈	1	2	yes	—
93	C₂²×C₄×C₁₁₃	SD₁₆	1	2	yes	—
94	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
97	M₁₆×C₁₁₃	—	4	8	no	—
98	C₂×C₈×C₁₁₃	—	2	4	no	—
99	C₂×C₈×C₁₁₃	—	4	2	no	—
100	C₂×C₈×C₁₁₃	—	4	2	no	—
101	C₂×C₈×C₁₁₃	—	4	2	no	—
102	C₂×C₈×C₁₁₃	—	4	2	no	—
103	C₂×C₈×C₁₁₃	—	4	2	no	—
104	C₄⋊C₄×C₁₁₃	—	4	2	no	—
105	C₄⋊C₄×C₁₁₃	—	4	1	no	—
106	C₄⋊C₄×C₁₁₃	—	4	1	no	—
107	C₄⋊C₄×C₁₁₃	—	4	2	no	—
108	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
109	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
110	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
111	C₄²×C₁₁₃	—	2	2	no	—
112	C₄²×C₁₁₃	—	2	1	no	—
113	C₄²×C₁₁₃	—	2	2	no	—
114	C₄²×C₁₁₃	—	2	1	no	—
115	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
116	C₄²×C₁₁₃	#41	1	2	yes	—
117	C₂³×C₁₁₃	—	2	1	no	—
118	C₂³×C₁₁₃	—	2	1	no	—
119	C₂³×C₁₁₃	—	2	1	no	—
120	C₂³×C₁₁₃	—	2	1	no	—
121	C₂³×C₁₁₃	—	2	1	no	—
122	C₂³×C₁₁₃	—	2	1	no	—
123	C₂³×C₁₁₃	—	4	2	no	—
124	C₂³×C₁₁₃	—	4	2	no	—
125	C₂³×C₁₁₃	—	4	2	no	—
126	C₂³×C₁₁₃	—	4	2	no	—
127	C₂³×C₁₁₃	—	4	2	no	—
128	C₂³×C₁₁₃	—	4	2	no	—
129	C₂³×C₁₁₃	—	4	2	no	—
130	C₂³×C₁₁₃	#102	1	2	yes	—
131	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	D₄×C₁₁₃	—	8	4	no	—
133	D₄×C₁₁₃	—	8	8	no	—
134	D₄×C₁₁₃	—	8	1	no	—
135	D₄×C₁₁₃	—	8	1	no	—
136	D₄×C₁₁₃	—	8	2	no	—
137	D₄×C₁₁₃	—	8	2	no	—
138	D₄×C₁₁₃	—	8	1	no	—
139	D₄×C₁₁₃	—	8	1	no	—
140	C₂×C₄×C₁₁₃	—	2	1	no	—
141	C₂×C₄×C₁₁₃	—	2	1	no	—
142	C₂×C₄×C₁₁₃	—	2	1	no	—
143	C₂×C₄×C₁₁₃	—	2	1	no	—
144	C₂×C₄×C₁₁₃	—	2	1	no	—
145	C₂×C₄×C₁₁₃	—	2	1	no	—
146	C₂×C₄×C₁₁₃	—	2	2	no	—
147	C₂×C₄×C₁₁₃	—	2	2	no	—
148	C₂×C₄×C₁₁₃	—	2	2	no	—
149	C₂×C₄×C₁₁₃	—	2	2	no	—
150	C₂×C₄×C₁₁₃	—	2	1	no	—
151	C₂×C₄×C₁₁₃	—	2	1	no	—
152	C₂×C₄×C₁₁₃	—	2	1	no	—
153	C₂×C₄×C₁₁₃	—	4	4	no	—
154	C₂×C₄×C₁₁₃	—	4	2	no	—
155	C₂×C₄×C₁₁₃	—	4	2	no	—
156	C₂×C₄×C₁₁₃	—	4	2	no	—
157	C₂×C₄×C₁₁₃	—	4	2	no	—
158	C₂×C₄×C₁₁₃	—	4	2	no	—
159	C₂×C₄×C₁₁₃	#100	1	2	yes	—
160	C₂×C₄×C₁₁₃	#102	1	2	yes	—
161	C₂×C₄×C₁₁₃	C₄×D₄	1	2	yes	—
162	C₂×C₄×C₁₁₃	#120	1	1	yes	characteristic
163	C₂×C₄×C₁₁₃	#121	1	2	yes	—
164	C₂×C₄×C₁₁₃	#123	1	1	yes	characteristic
165	C₂×C₄×C₁₁₃	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₁₁₃	C₂×SD₁₆	1	1	yes	characteristic
167	C₂×C₄×C₁₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
168	C₂×C₄×C₁₁₃	AGL(1,ℤ/8)	1	2	yes	—
169	C₂×C₄×C₁₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
170	C₂×C₄×C₁₁₃	#137	1	1	yes	characteristic
171	C₂×C₄×C₁₁₃	#137	1	1	yes	characteristic
172	C₈×C₁₁₃	—	4	4	no	—
173	C₈×C₁₁₃	—	8	2	no	—
174	C₂²×C₁₁₃	—	2	2	no	—
175	C₂²×C₁₁₃	—	2	2	no	—
176	C₂²×C₁₁₃	—	2	2	no	—
177	C₂²×C₁₁₃	—	4	1	no	—
178	C₂²×C₁₁₃	—	4	1	no	—
179	C₂²×C₁₁₃	—	4	1	no	—
180	C₂²×C₁₁₃	—	4	1	no	—
181	C₂²×C₁₁₃	—	8	2	no	—
182	C₂²×C₁₁₃	—	8	2	no	—
183	C₂²×C₁₁₃	—	8	2	no	—
184	C₂²×C₁₁₃	—	8	2	no	—
185	C₂²×C₁₁₃	—	8	2	no	—
186	C₂²×C₁₁₃	—	8	2	no	—
187	C₂²×C₁₁₃	—	8	2	no	—
188	C₂²×C₁₁₃	#386	1	1	yes	characteristic
189	C₂²×C₁₁₃	C₂×#100	1	1	yes	characteristic
190	C₂²×C₁₁₃	#413	1	1	yes	characteristic
191	C₂²×C₁₁₃	C₂×#102	1	1	yes	characteristic
192	C₂²×C₁₁₃	#417	1	1	yes	characteristic
193	C₂²×C₁₁₃	#417	1	1	yes	characteristic
194	C₂²×C₁₁₃	#418	1	1	yes	characteristic
195	C₄×C₁₁₃	—	2	2	no	—
196	C₄×C₁₁₃	—	2	2	no	—
197	C₄×C₁₁₃	—	2	2	no	—
198	C₄×C₁₁₃	—	4	1	no	—
199	C₄×C₁₁₃	—	8	2	no	—
200	C₄×C₁₁₃	#447	1	1	yes	characteristic
201	C₄×C₁₁₃	#448	1	1	yes	characteristic
202	C₄×C₁₁₃	#468	1	2	yes	—
203	C₄×C₁₁₃	#469	1	2	yes	—
204	C₄×C₁₁₃	#480	1	1	yes	characteristic
205	C₄×C₁₁₃	#481	1	1	yes	characteristic
206	#9141	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂×C₁₁₃	—	4	2	no	—
208	C₂×C₁₁₃	—	16	2	no	—
209	C₂×C₁₁₃	#1545	1	1	yes	characteristic
210	C₂×C₁₁₃	#1547	1	1	yes	characteristic
211	C₂×C₁₁₃	#1557	1	1	yes	characteristic
212	C₂×C₁₁₃	#1560	1	1	yes	characteristic
213	C₂×C₁₁₃	#1874	1	1	yes	characteristic
214	C₂×C₁₁₃	#1895	1	1	yes	characteristic
215	C₂×C₁₁₃	#1900	1	1	yes	characteristic
216	C₂×#423	C₂×C₁₁₃	1	1	yes	characteristic, complemented
217	#2856	C₂×C₁₁₃	1	1	yes	characteristic
218	#1797	C₂×C₁₁₃	1	1	yes	characteristic, complemented
219	C₂×#331	C₂×C₁₁₃	1	2	yes	complemented
220	#1296	C₂×C₁₁₃	1	2	yes	complemented
221	C₁₁₃	#9141	1	1	yes	characteristic, direct product factor, Sylow
222	C₂²×M₁₆	—	2	1	no	—
223	C₂×#127	C₂²×C₁₁₃	1	1	yes	characteristic
224	C₂×#121	—	2	1	no	—
225	C₂×#121	—	2	1	no	—
226	C₂×#121	C₄×C₁₁₃	1	2	yes	—
227	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
228	#423	—	2	4	no	—
229	C₂×C₄⋊C₈	—	2	1	no	—
230	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
231	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
232	C₂×C₂²⋊C₈	—	2	1	no	—
233	#390	—	2	1	no	—
234	#390	—	2	1	no	—
235	#390	C₄×C₁₁₃	1	2	yes	—
236	#384	C₂²×C₁₁₃	1	1	yes	characteristic
237	#336	—	2	1	no	—
238	#331	—	2	4	no	—
239	C₂²×D₄	—	2	2	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
243	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
244	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
245	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
246	C₂×M₁₆	—	2	4	no	—
247	C₂×M₁₆	—	4	2	no	—
248	C₂×M₁₆	—	4	2	no	—
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	—	2	2	no	—
251	#127	—	2	2	no	—
252	#127	—	2	2	no	—
253	#121	—	4	4	no	—
254	#121	—	4	2	no	—
255	#121	—	4	2	no	—
256	#121	—	4	4	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
266	C₂×C₄²	D₄×C₁₁₃	1	1	yes	characteristic
267	C₂×C₄²	D₄×C₁₁₃	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
269	C₄⋊C₈	—	2	4	no	—
270	C₄⋊C₈	—	2	2	no	—
271	C₄⋊C₈	—	2	2	no	—
272	C₄⋊C₈	—	2	2	no	—
273	C₄⋊C₈	D₄×C₁₁₃	1	4	yes	complemented
274	C₂²⋊C₈	—	4	2	no	—
275	C₂⁴	—	2	2	no	—
276	C₂⁴	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	—	4	4	no	—
281	C₂×D₄	—	4	4	no	—
282	C₂×D₄	—	4	4	no	—
283	C₂×D₄	—	4	1	no	—
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	—	4	1	no	—
286	C₂×D₄	—	4	1	no	—
287	C₂×D₄	—	4	1	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
306	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
307	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
308	C₂²×C₄	D₈×C₁₁₃	1	2	yes	—
309	C₂²×C₄	SD₁₆×C₁₁₃	1	2	yes	—
310	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
313	M₁₆	—	4	8	no	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	—	4	2	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	—	4	2	no	—
318	C₂×C₈	—	4	2	no	—
319	C₂×C₈	—	4	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	4	no	—
325	C₂²⋊C₄	—	4	4	no	—
326	C₂²⋊C₄	—	4	4	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	1	no	—
331	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
332	C₄²	#41×C₁₁₃	1	2	yes	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	#102×C₁₁₃	1	2	yes	—
347	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
348	D₄	—	8	4	no	—
349	D₄	—	8	8	no	—
350	D₄	—	8	1	no	—
351	D₄	—	8	1	no	—
352	D₄	—	8	2	no	—
353	D₄	—	8	2	no	—
354	D₄	—	8	1	no	—
355	D₄	—	8	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	#100×C₁₁₃	1	2	yes	—
376	C₂×C₄	#102×C₁₁₃	1	2	yes	—
377	C₂×C₄	C₄×D₄×C₁₁₃	1	2	yes	—
378	C₂×C₄	#120×C₁₁₃	1	1	yes	characteristic
379	C₂×C₄	#121×C₁₁₃	1	2	yes	—
380	C₂×C₄	#123×C₁₁₃	1	1	yes	characteristic
381	C₂×C₄	C₂×D₈×C₁₁₃	1	1	yes	characteristic
382	C₂×C₄	C₂×SD₁₆×C₁₁₃	1	1	yes	characteristic
383	C₂×C₄	AGL(1,ℤ/8)×C₁₁₃	1	1	yes	characteristic
384	C₂×C₄	AGL(1,ℤ/8)×C₁₁₃	1	2	yes	—
385	C₂×C₄	AGL(1,ℤ/8)×C₁₁₃	1	1	yes	characteristic
386	C₂×C₄	#137×C₁₁₃	1	1	yes	characteristic
387	C₂×C₄	#137×C₁₁₃	1	1	yes	characteristic
388	C₈	—	4	4	no	—
389	C₈	—	8	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	8	2	no	—
404	C₂²	#386×C₁₁₃	1	1	yes	characteristic
405	C₂²	C₂×#100×C₁₁₃	1	1	yes	characteristic
406	C₂²	#413×C₁₁₃	1	1	yes	characteristic
407	C₂²	C₂×#102×C₁₁₃	1	1	yes	characteristic
408	C₂²	#417×C₁₁₃	1	1	yes	characteristic
409	C₂²	#417×C₁₁₃	1	1	yes	characteristic
410	C₂²	#418×C₁₁₃	1	1	yes	characteristic
411	C₄	—	2	2	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	2	no	—
414	C₄	—	4	1	no	—
415	C₄	—	8	2	no	—
416	C₄	#447×C₁₁₃	1	1	yes	characteristic
417	C₄	#448×C₁₁₃	1	1	yes	characteristic
418	C₄	#468×C₁₁₃	1	2	yes	—
419	C₄	#469×C₁₁₃	1	2	yes	—
420	C₄	#480×C₁₁₃	1	1	yes	characteristic
421	C₄	#481×C₁₁₃	1	1	yes	characteristic
422	C₂	—	4	2	no	—
423	C₂	—	16	2	no	—
424	C₂	C₁₁₃×#1545	1	1	yes	characteristic
425	C₂	C₁₁₃×#1547	1	1	yes	characteristic
426	C₂	C₁₁₃×#1557	1	1	yes	characteristic
427	C₂	C₁₁₃×#1560	1	1	yes	characteristic
428	C₂	C₁₁₃×#1874	1	1	yes	characteristic
429	C₂	C₁₁₃×#1895	1	1	yes	characteristic
430	C₂	C₁₁₃×#1900	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁₃	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁₃
prime radical	C₁₁₃×#2856	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁₃ ◁ C₂²×C₄²×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#423×C₁₁₃	C₂	semidirect
3. C₁₁₃×#1797	C₂	semidirect
4. C₂×#331×C₁₁₃	C₂	semidirect
5. C₁₁₃×#1296	C₂	semidirect
57. C₄⋊C₈×C₁₁₃	D₄	semidirect
206. #9141	C₁₁₃	direct (N × H)
216. C₂×#423	C₂×C₁₁₃	semidirect
218. #1797	C₂×C₁₁₃	semidirect
219. C₂×#331	C₂×C₁₁₃	semidirect
220. #1296	C₂×C₁₁₃	semidirect
221. C₁₁₃	#9141	direct (N × H)
273. C₄⋊C₈	D₄×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#423×C₁₁₃	2
C₁₁₃×#2856	2
C₁₁₃×#1797	2
C₂×#331×C₁₁₃	2
C₁₁₃×#1296	2
#9141	113

Subgroups — C113×#9141 #43277161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#9141 #43277161