Subgroups — C₁₁₃×#25568 #43293588

Order 28928.

1190 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#555×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#487×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#461×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#2542	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁₃×#2000	C₂	1	4	yes	maximal, complemented
6	C₁₁₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁₃×#1873	C₂	1	4	yes	maximal, complemented
9	C₄×#102×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₁₁₃	C₂²	1	2	yes	—
11	#555×C₁₁₃	—	2	4	no	—
12	#555×C₁₁₃	—	2	4	no	—
13	C₂×C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
15	C₂×#124×C₁₁₃	—	2	2	no	—
16	C₂×C₂²⋊Q₈×C₁₁₃	C₂²	1	4	yes	—
17	C₂×#121×C₁₁₃	—	2	1	no	—
18	C₂×#121×C₁₁₃	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
21	C₂×#117×C₁₁₃	—	2	1	no	—
22	C₂×#117×C₁₁₃	C₂²	1	2	yes	—
23	#487×C₁₁₃	—	2	4	no	—
24	#461×C₁₁₃	—	2	4	no	—
25	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	1	yes	characteristic
26	C₂×#103×C₁₁₃	C₂²	1	4	yes	—
27	C₂×#103×C₁₁₃	C₂²	1	2	yes	—
28	C₂×#102×C₁₁₃	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₈×C₁₁₃	C₂²	1	4	yes	—
30	C₂×C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
31	#399×C₁₁₃	—	2	2	no	—
32	#390×C₁₁₃	—	2	1	no	—
33	#384×C₁₁₃	—	2	1	no	—
34	C₄×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
35	#340×C₁₁₃	C₂²	1	2	yes	—
36	#340×C₁₁₃	C₂²	1	4	yes	—
37	C₂²×Q₈×C₁₁₃	—	2	1	no	—
38	C₂²×Q₈×C₁₁₃	C₂³	1	2	yes	—
39	C₂²×D₄×C₁₁₃	—	2	2	no	—
40	C₂²×D₄×C₁₁₃	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₁₃	—	2	1	no	—
43	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
44	C₂×SD₁₆×C₁₁₃	—	2	4	no	—
45	C₂×SD₁₆×C₁₁₃	—	4	4	no	—
46	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
48	C₄⋊Q₈×C₁₁₃	—	2	2	no	—
49	C₄⋊Q₈×C₁₁₃	—	2	2	no	—
50	C₄⋊Q₈×C₁₁₃	—	2	2	no	—
51	C₄⋊Q₈×C₁₁₃	D₄	1	4	yes	—
52	#124×C₁₁₃	—	2	16	no	—
53	C₂²⋊Q₈×C₁₁₃	—	2	8	no	—
54	C₂²⋊Q₈×C₁₁₃	—	4	4	no	—
55	#121×C₁₁₃	—	2	8	no	—
56	#121×C₁₁₃	—	2	4	no	—
57	#121×C₁₁₃	—	2	4	no	—
58	C₄×D₄×C₁₁₃	—	2	2	no	—
59	C₄×D₄×C₁₁₃	—	2	2	no	—
60	C₄×D₄×C₁₁₃	—	2	2	no	—
61	C₄×D₄×C₁₁₃	D₄	1	4	yes	—
62	#117×C₁₁₃	—	2	8	no	—
63	#117×C₁₁₃	—	2	4	no	—
64	#117×C₁₁₃	—	2	4	no	—
65	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
67	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₁₃	D₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
73	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
77	C₂×C₂²⋊C₄×C₁₁₃	D₄	1	2	yes	—
78	C₂×C₄²×C₁₁₃	—	2	2	no	—
79	C₂×C₄²×C₁₁₃	—	2	1	no	—
80	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₁₁₃	—	2	2	no	—
82	#103×C₁₁₃	—	2	4	no	—
83	#103×C₁₁₃	—	2	8	no	—
84	#102×C₁₁₃	—	2	4	no	—
85	C₂²⋊C₈×C₁₁₃	—	4	4	no	—
86	C₄×C₈×C₁₁₃	—	2	2	no	—
87	#95×C₁₁₃	—	2	1	no	—
88	C₂⁴×C₁₁₃	—	2	1	no	—
89	C₂⁴×C₁₁₃	C₂×D₄	1	2	yes	—
90	C₂×Q₈×C₁₁₃	—	2	4	no	—
91	C₂×Q₈×C₁₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₁₃	—	2	4	no	—
94	C₂×Q₈×C₁₁₃	—	2	4	no	—
95	C₂×Q₈×C₁₁₃	—	8	2	no	—
96	C₂×D₄×C₁₁₃	—	2	8	no	—
97	C₂×D₄×C₁₁₃	—	2	2	no	—
98	C₂×D₄×C₁₁₃	—	2	2	no	—
99	C₂×D₄×C₁₁₃	—	2	2	no	—
100	C₂×D₄×C₁₁₃	—	2	1	no	—
101	C₂×D₄×C₁₁₃	—	2	2	no	—
102	C₂×D₄×C₁₁₃	—	2	2	no	—
103	C₂×D₄×C₁₁₃	—	8	4	no	—
104	C₂×D₄×C₁₁₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₁₃	—	2	2	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	2	no	—
114	C₂²×C₄×C₁₁₃	—	4	2	no	—
115	C₂²×C₄×C₁₁₃	—	4	2	no	—
116	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
120	SD₁₆×C₁₁₃	—	4	8	no	—
121	C₂×C₈×C₁₁₃	—	2	2	no	—
122	C₂×C₈×C₁₁₃	—	2	2	no	—
123	C₂×C₈×C₁₁₃	—	2	2	no	—
124	C₂×C₈×C₁₁₃	—	2	2	no	—
125	C₂×C₈×C₁₁₃	—	2	4	no	—
126	C₄⋊C₄×C₁₁₃	—	2	4	no	—
127	C₄⋊C₄×C₁₁₃	—	2	2	no	—
128	C₄⋊C₄×C₁₁₃	—	2	1	no	—
129	C₄⋊C₄×C₁₁₃	—	2	2	no	—
130	C₄⋊C₄×C₁₁₃	—	2	2	no	—
131	C₄⋊C₄×C₁₁₃	—	4	8	no	—
132	C₄⋊C₄×C₁₁₃	—	4	2	no	—
133	C₄⋊C₄×C₁₁₃	—	4	2	no	—
134	C₄⋊C₄×C₁₁₃	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₁₁₃	C₂×D₄	1	4	yes	—
136	C₄⋊C₄×C₁₁₃	#41	1	4	yes	—
137	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
138	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
139	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
140	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
141	C₂²⋊C₄×C₁₁₃	—	4	8	no	—
142	C₄²×C₁₁₃	—	2	8	no	—
143	C₄²×C₁₁₃	—	4	2	no	—
144	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
145	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
146	C₂³×C₁₁₃	—	2	2	no	—
147	C₂³×C₁₁₃	—	2	2	no	—
148	C₂³×C₁₁₃	—	2	4	no	—
149	C₂³×C₁₁₃	—	2	2	no	—
150	C₂³×C₁₁₃	—	2	2	no	—
151	C₂³×C₁₁₃	—	2	4	no	—
152	C₂³×C₁₁₃	—	4	2	no	—
153	C₂³×C₁₁₃	—	4	1	no	—
154	C₂³×C₁₁₃	—	4	1	no	—
155	C₂³×C₁₁₃	—	4	2	no	—
156	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₁₁₃	—	4	2	no	—
158	Q₈×C₁₁₃	—	4	2	no	—
159	Q₈×C₁₁₃	—	4	4	no	—
160	Q₈×C₁₁₃	—	8	4	no	—
161	D₄×C₁₁₃	—	2	2	no	—
162	D₄×C₁₁₃	—	2	2	no	—
163	D₄×C₁₁₃	—	4	2	no	—
164	D₄×C₁₁₃	—	4	4	no	—
165	D₄×C₁₁₃	—	8	8	no	—
166	C₂×C₄×C₁₁₃	—	2	2	no	—
167	C₂×C₄×C₁₁₃	—	2	2	no	—
168	C₂×C₄×C₁₁₃	—	2	2	no	—
169	C₂×C₄×C₁₁₃	—	2	4	no	—
170	C₂×C₄×C₁₁₃	—	2	4	no	—
171	C₂×C₄×C₁₁₃	—	2	4	no	—
172	C₂×C₄×C₁₁₃	—	4	2	no	—
173	C₂×C₄×C₁₁₃	—	4	1	no	—
174	C₂×C₄×C₁₁₃	—	4	1	no	—
175	C₂×C₄×C₁₁₃	—	4	2	no	—
176	C₂×C₄×C₁₁₃	—	4	4	no	—
177	C₂×C₄×C₁₁₃	—	4	2	no	—
178	C₂×C₄×C₁₁₃	—	4	2	no	—
179	C₂×C₄×C₁₁₃	—	4	4	no	—
180	C₂×C₄×C₁₁₃	—	4	8	no	—
181	C₂×C₄×C₁₁₃	—	4	2	no	—
182	C₂×C₄×C₁₁₃	—	4	4	no	—
183	C₂×C₄×C₁₁₃	#120	1	2	yes	—
184	C₂×C₄×C₁₁₃	#120	1	2	yes	—
185	C₂×C₄×C₁₁₃	#135	1	2	yes	—
186	C₂×C₄×C₁₁₃	#137	1	2	yes	—
187	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₁₃	C₂×#41	1	2	yes	—
190	C₂×C₄×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
191	C₈×C₁₁₃	—	4	2	no	—
192	C₈×C₁₁₃	—	4	2	no	—
193	C₂²×C₁₁₃	—	4	4	no	—
194	C₂²×C₁₁₃	—	4	2	no	—
195	C₂²×C₁₁₃	—	4	2	no	—
196	C₂²×C₁₁₃	—	4	2	no	—
197	C₂²×C₁₁₃	—	4	2	no	—
198	C₂²×C₁₁₃	—	4	2	no	—
199	C₂²×C₁₁₃	—	4	2	no	—
200	C₂²×C₁₁₃	—	4	4	no	—
201	C₂²×C₁₁₃	—	8	2	no	—
202	C₂²×C₁₁₃	—	8	2	no	—
203	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
204	C₂²×C₁₁₃	#546	1	2	yes	—
205	C₂²×C₁₁₃	C₂×#135	1	1	yes	characteristic
206	C₂²×C₁₁₃	C₂×#137	1	1	yes	characteristic
207	C₂²×C₁₁₃	#577	1	2	yes	—
208	C₄×C₁₁₃	—	2	2	no	—
209	C₄×C₁₁₃	—	4	2	no	—
210	C₄×C₁₁₃	—	4	2	no	—
211	C₄×C₁₁₃	—	4	4	no	—
212	C₄×C₁₁₃	—	4	4	no	—
213	C₄×C₁₁₃	—	8	2	no	—
214	C₄×C₁₁₃	#452	1	4	yes	—
215	C₄×C₁₁₃	#532	1	1	yes	characteristic
216	C₄×C₁₁₃	#535	1	1	yes	characteristic
217	C₄×C₁₁₃	#550	1	2	yes	—
218	#25568	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂×C₁₁₃	—	8	2	no	—
220	C₂×C₁₁₃	—	8	2	no	—
221	C₂×C₁₁₃	#2431	1	1	yes	characteristic
222	C₂×C₁₁₃	C₂×#452	1	1	yes	characteristic
223	C₂×C₁₁₃	#3009	1	1	yes	characteristic
224	C₂×C₁₁₃	#3303	1	2	yes	—
225	C₂×C₁₁₃	#3329	1	2	yes	—
226	C₂×#555	C₂×C₁₁₃	1	1	yes	characteristic
227	C₂×#487	C₂×C₁₁₃	1	1	yes	characteristic, complemented
228	C₂×#461	C₂×C₁₁₃	1	1	yes	characteristic, complemented
229	#2542	C₂×C₁₁₃	1	1	yes	characteristic, complemented
230	#2000	C₂×C₁₁₃	1	4	yes	complemented
231	#1987	C₂×C₁₁₃	1	1	yes	characteristic, complemented
232	#1954	C₂×C₁₁₃	1	1	yes	characteristic, complemented
233	#1873	C₂×C₁₁₃	1	4	yes	complemented
234	C₄×#102	C₂×C₁₁₃	1	1	yes	characteristic, complemented
235	C₁₁₃	#25568	1	1	yes	characteristic, direct product factor, Sylow
236	C₂²×SD₁₆	C₂²×C₁₁₃	1	2	yes	—
237	#555	—	2	4	no	—
238	#555	—	2	4	no	—
239	C₂×C₄⋊Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
240	C₂×C₄⋊Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
241	C₂×#124	—	2	2	no	—
242	C₂×C₂²⋊Q₈	C₂²×C₁₁₃	1	4	yes	—
243	C₂×#121	—	2	1	no	—
244	C₂×#121	C₂²×C₁₁₃	1	2	yes	—
245	C₂×C₄×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
246	C₂×C₄×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
247	C₂×#117	—	2	1	no	—
248	C₂×#117	C₂²×C₁₁₃	1	2	yes	—
249	#487	—	2	4	no	—
250	#461	—	2	4	no	—
251	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	1	yes	characteristic
252	C₂×#103	C₂²×C₁₁₃	1	4	yes	—
253	C₂×#103	C₂²×C₁₁₃	1	2	yes	—
254	C₂×#102	C₂²×C₁₁₃	1	2	yes	—
255	C₂×C₂²⋊C₈	C₂²×C₁₁₃	1	4	yes	—
256	C₂×C₄×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
257	#399	—	2	2	no	—
258	#390	—	2	1	no	—
259	#384	—	2	1	no	—
260	C₄×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
261	#340	C₂²×C₁₁₃	1	2	yes	—
262	#340	C₂²×C₁₁₃	1	4	yes	—
263	C₂²×Q₈	—	2	1	no	—
264	C₂²×Q₈	C₂³×C₁₁₃	1	2	yes	—
265	C₂²×D₄	—	2	2	no	—
266	C₂²×D₄	D₄×C₁₁₃	1	1	yes	characteristic
267	C₂²×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
268	C₂³×C₄	—	2	1	no	—
269	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
270	C₂×SD₁₆	—	2	4	no	—
271	C₂×SD₁₆	—	4	4	no	—
272	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
273	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
274	C₄⋊Q₈	—	2	2	no	—
275	C₄⋊Q₈	—	2	2	no	—
276	C₄⋊Q₈	—	2	2	no	—
277	C₄⋊Q₈	D₄×C₁₁₃	1	4	yes	—
278	#124	—	2	16	no	—
279	C₂²⋊Q₈	—	2	8	no	—
280	C₂²⋊Q₈	—	4	4	no	—
281	#121	—	2	8	no	—
282	#121	—	2	4	no	—
283	#121	—	2	4	no	—
284	C₄×D₄	—	2	2	no	—
285	C₄×D₄	—	2	2	no	—
286	C₄×D₄	—	2	2	no	—
287	C₄×D₄	D₄×C₁₁₃	1	4	yes	—
288	#117	—	2	8	no	—
289	#117	—	2	4	no	—
290	#117	—	2	4	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	4	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	D₄×C₁₁₃	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
298	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₂²⋊C₄	—	2	1	no	—
302	C₂×C₂²⋊C₄	—	2	4	no	—
303	C₂×C₂²⋊C₄	D₄×C₁₁₃	1	2	yes	—
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
307	C₄⋊C₈	—	2	2	no	—
308	#103	—	2	4	no	—
309	#103	—	2	8	no	—
310	#102	—	2	4	no	—
311	C₂²⋊C₈	—	4	4	no	—
312	C₄×C₈	—	2	2	no	—
313	#95	—	2	1	no	—
314	C₂⁴	—	2	1	no	—
315	C₂⁴	C₂×D₄×C₁₁₃	1	2	yes	—
316	C₂×Q₈	—	2	4	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	4	no	—
320	C₂×Q₈	—	2	4	no	—
321	C₂×Q₈	—	8	2	no	—
322	C₂×D₄	—	2	8	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	8	4	no	—
330	C₂×D₄	C₂×D₄×C₁₁₃	1	2	yes	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
343	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
345	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
346	SD₁₆	—	4	8	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	4	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	4	8	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	C₂×D₄×C₁₁₃	1	2	yes	—
361	C₄⋊C₄	C₂×D₄×C₁₁₃	1	4	yes	—
362	C₄⋊C₄	#41×C₁₁₃	1	4	yes	—
363	C₂²⋊C₄	—	2	8	no	—
364	C₂²⋊C₄	—	2	8	no	—
365	C₂²⋊C₄	—	2	4	no	—
366	C₂²⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	4	8	no	—
368	C₄²	—	2	8	no	—
369	C₄²	—	4	2	no	—
370	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
371	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	4	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	2	no	—
382	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
383	Q₈	—	4	2	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	4	4	no	—
386	Q₈	—	8	4	no	—
387	D₄	—	2	2	no	—
388	D₄	—	2	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	4	no	—
391	D₄	—	8	8	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	8	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	#120×C₁₁₃	1	2	yes	—
410	C₂×C₄	#120×C₁₁₃	1	2	yes	—
411	C₂×C₄	#135×C₁₁₃	1	2	yes	—
412	C₂×C₄	#137×C₁₁₃	1	2	yes	—
413	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
414	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
415	C₂×C₄	C₂×#41×C₁₁₃	1	2	yes	—
416	C₂×C₄	H(5,𝔽₂)×C₁₁₃	1	2	yes	—
417	C₈	—	4	2	no	—
418	C₈	—	4	2	no	—
419	C₂²	—	4	4	no	—
420	C₂²	—	4	4	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
430	C₂²	#546×C₁₁₃	1	2	yes	—
431	C₂²	C₂×#135×C₁₁₃	1	1	yes	characteristic
432	C₂²	C₂×#137×C₁₁₃	1	1	yes	characteristic
433	C₂²	#577×C₁₁₃	1	2	yes	—
434	C₄	—	2	2	no	—
435	C₄	—	4	4	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	4	no	—
439	C₄	—	8	2	no	—
440	C₄	#452×C₁₁₃	1	4	yes	—
441	C₄	#532×C₁₁₃	1	1	yes	characteristic
442	C₄	#535×C₁₁₃	1	1	yes	characteristic
443	C₄	#550×C₁₁₃	1	2	yes	—
444	C₂	—	8	2	no	—
445	C₂	—	8	2	no	—
446	C₂	C₁₁₃×#2431	1	1	yes	characteristic
447	C₂	C₂×#452×C₁₁₃	1	1	yes	characteristic
448	C₂	C₁₁₃×#3009	1	1	yes	characteristic
449	C₂	C₁₁₃×#3303	1	2	yes	—
450	C₂	C₁₁₃×#3329	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
prime radical	C₂×#555×C₁₁₃	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁₃ ◁ C₂×C₄×D₄×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#487×C₁₁₃	C₂	semidirect
3. C₂×#461×C₁₁₃	C₂	semidirect
4. C₁₁₃×#2542	C₂	semidirect
5. C₁₁₃×#2000	C₂	semidirect
6. C₁₁₃×#1987	C₂	semidirect
7. C₁₁₃×#1954	C₂	semidirect
8. C₁₁₃×#1873	C₂	semidirect
9. C₄×#102×C₁₁₃	C₂	semidirect
218. #25568	C₁₁₃	direct (N × H)
227. C₂×#487	C₂×C₁₁₃	semidirect
228. C₂×#461	C₂×C₁₁₃	semidirect
229. #2542	C₂×C₁₁₃	semidirect
230. #2000	C₂×C₁₁₃	semidirect
231. #1987	C₂×C₁₁₃	semidirect
232. #1954	C₂×C₁₁₃	semidirect
233. #1873	C₂×C₁₁₃	semidirect
234. C₄×#102	C₂×C₁₁₃	semidirect
235. C₁₁₃	#25568	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×#555×C₁₁₃	2
C₂×#487×C₁₁₃	2
C₂×#461×C₁₁₃	2
C₁₁₃×#2542	2
C₁₁₃×#2000	2
C₁₁₃×#1987	2
C₁₁₃×#1954	2
C₁₁₃×#1873	2
C₄×#102×C₁₁₃	2
#25568	113

Subgroups — C113×#25568 #43293588

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#25568 #43293588