Subgroups — C₁₁₃×#24189 #43292209

Order 28928.

1082 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#556×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#462×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×SD₁₆×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₁₁₃×#2582	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁₃×#2042	C₂	1	2	yes	maximal
6	C₁₁₃×#2015	C₂	1	2	yes	maximal
7	C₁₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁₃×#1956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁₃×#1878	C₂	1	2	yes	maximal, complemented
10	C₁₁₃×#1865	C₂	1	2	yes	maximal, complemented
11	C₁₁₃×#1802	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₁₁₃	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
14	#556×C₁₁₃	—	2	4	no	—
15	#556×C₁₁₃	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
17	C₂×#126×C₁₁₃	—	2	2	no	—
18	C₂×#124×C₁₁₃	C₂²	1	2	yes	—
19	C₂×C₂²⋊Q₈×C₁₁₃	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₁₃	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
24	C₂×#117×C₁₁₃	—	2	1	no	—
25	#462×C₁₁₃	—	2	4	no	—
26	C₄×SD₁₆×C₁₁₃	—	2	4	no	—
27	C₂×#106×C₁₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	1	yes	characteristic
29	C₂×#103×C₁₁₃	C₂²	1	2	yes	—
30	C₂×#103×C₁₁₃	C₂²	1	2	yes	—
31	C₂×#103×C₁₁₃	C₂²	1	1	yes	characteristic
32	C₂×#103×C₁₁₃	C₂²	1	2	yes	—
33	C₂×#102×C₁₁₃	C₂²	1	1	yes	characteristic
34	C₂×#102×C₁₁₃	C₂²	1	2	yes	—
35	C₂×C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
36	#398×C₁₁₃	—	2	2	no	—
37	#391×C₁₁₃	—	2	1	no	—
38	#391×C₁₁₃	C₂²	1	2	yes	—
39	#389×C₁₁₃	—	2	1	no	—
40	#389×C₁₁₃	C₂²	1	2	yes	—
41	#384×C₁₁₃	C₂²	1	1	yes	characteristic
42	#340×C₁₁₃	C₂²	1	2	yes	—
43	#336×C₁₁₃	C₂²	1	2	yes	—
44	#336×C₁₁₃	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₁₃	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₁₃	C₂³	1	2	yes	—
47	C₂²×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₁₃	—	2	1	no	—
50	C₂×Q₁₆×C₁₁₃	—	2	4	no	—
51	C₂×Q₁₆×C₁₁₃	—	2	4	no	—
52	C₂×Q₁₆×C₁₁₃	—	4	2	no	—
53	C₂×SD₁₆×C₁₁₃	—	2	2	no	—
54	C₂×SD₁₆×C₁₁₃	—	2	2	no	—
55	C₂×SD₁₆×C₁₁₃	—	2	2	no	—
56	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
59	C₄⋊Q₈×C₁₁₃	—	2	2	no	—
60	C₄⋊Q₈×C₁₁₃	D₄	1	4	yes	—
61	#126×C₁₁₃	—	2	16	no	—
62	#124×C₁₁₃	—	2	4	no	—
63	#124×C₁₁₃	—	2	4	no	—
64	C₂²⋊Q₈×C₁₁₃	—	2	8	no	—
65	C₄×Q₈×C₁₁₃	—	2	4	no	—
66	C₄×Q₈×C₁₁₃	—	2	4	no	—
67	C₄×Q₈×C₁₁₃	—	2	2	no	—
68	C₄×Q₈×C₁₁₃	—	2	2	no	—
69	C₄×Q₈×C₁₁₃	—	2	2	no	—
70	C₄×Q₈×C₁₁₃	—	2	2	no	—
71	C₄×D₄×C₁₁₃	—	2	2	no	—
72	C₄×D₄×C₁₁₃	D₄	1	4	yes	—
73	#117×C₁₁₃	—	2	8	no	—
74	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₁₃	D₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₁₃	D₄	1	2	yes	—
83	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
89	C₂×C₄²×C₁₁₃	—	2	2	no	—
90	C₂×C₄²×C₁₁₃	—	2	1	no	—
91	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
92	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
93	#106×C₁₁₃	—	2	2	no	—
94	C₄⋊C₈×C₁₁₃	—	2	2	no	—
95	#103×C₁₁₃	—	2	4	no	—
96	#103×C₁₁₃	—	2	4	no	—
97	#103×C₁₁₃	—	2	2	no	—
98	#103×C₁₁₃	—	4	2	no	—
99	#102×C₁₁₃	—	2	2	no	—
100	#102×C₁₁₃	—	4	2	no	—
101	C₄×C₈×C₁₁₃	—	2	2	no	—
102	#95×C₁₁₃	—	2	2	no	—
103	#95×C₁₁₃	—	2	2	no	—
104	#95×C₁₁₃	—	2	2	no	—
105	C₂⁴×C₁₁₃	—	2	1	no	—
106	C₂×Q₈×C₁₁₃	—	2	2	no	—
107	C₂×Q₈×C₁₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₁₃	—	2	2	no	—
110	C₂×Q₈×C₁₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₁₃	—	2	1	no	—
112	C₂×Q₈×C₁₁₃	—	2	1	no	—
113	C₂×Q₈×C₁₁₃	—	2	2	no	—
114	C₂×Q₈×C₁₁₃	—	2	1	no	—
115	C₂×Q₈×C₁₁₃	—	2	2	no	—
116	C₂×Q₈×C₁₁₃	—	2	2	no	—
117	C₂×Q₈×C₁₁₃	—	2	1	no	—
118	C₂×Q₈×C₁₁₃	—	2	2	no	—
119	C₂×Q₈×C₁₁₃	C₂×D₄	1	4	yes	—
120	C₂×Q₈×C₁₁₃	#41	1	2	yes	—
121	C₂×D₄×C₁₁₃	—	2	1	no	—
122	C₂×D₄×C₁₁₃	—	2	1	no	—
123	C₂×D₄×C₁₁₃	—	2	1	no	—
124	C₂×D₄×C₁₁₃	—	2	1	no	—
125	C₂×D₄×C₁₁₃	—	2	1	no	—
126	C₂×D₄×C₁₁₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₁₃	—	4	2	no	—
134	C₂²×C₄×C₁₁₃	—	4	2	no	—
135	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
140	Q₁₆×C₁₁₃	—	4	8	no	—
141	SD₁₆×C₁₁₃	—	2	8	no	—
142	C₂×C₈×C₁₁₃	—	2	1	no	—
143	C₂×C₈×C₁₁₃	—	2	1	no	—
144	C₂×C₈×C₁₁₃	—	2	1	no	—
145	C₂×C₈×C₁₁₃	—	2	2	no	—
146	C₂×C₈×C₁₁₃	—	2	2	no	—
147	C₂×C₈×C₁₁₃	—	2	2	no	—
148	C₂×C₈×C₁₁₃	—	2	1	no	—
149	C₂×C₈×C₁₁₃	—	2	1	no	—
150	C₂×C₈×C₁₁₃	#41	1	2	yes	—
151	C₄⋊C₄×C₁₁₃	—	2	8	no	—
152	C₄⋊C₄×C₁₁₃	—	2	4	no	—
153	C₄⋊C₄×C₁₁₃	—	2	4	no	—
154	C₄⋊C₄×C₁₁₃	—	2	2	no	—
155	C₄⋊C₄×C₁₁₃	—	2	4	no	—
156	C₄⋊C₄×C₁₁₃	—	2	1	no	—
157	C₄⋊C₄×C₁₁₃	—	2	1	no	—
158	C₄⋊C₄×C₁₁₃	—	2	1	no	—
159	C₄⋊C₄×C₁₁₃	—	2	2	no	—
160	C₄⋊C₄×C₁₁₃	—	2	2	no	—
161	C₄⋊C₄×C₁₁₃	—	4	2	no	—
162	C₄⋊C₄×C₁₁₃	—	4	2	no	—
163	C₄⋊C₄×C₁₁₃	—	8	1	no	—
164	C₄⋊C₄×C₁₁₃	—	8	2	no	—
165	C₄⋊C₄×C₁₁₃	C₂×D₄	1	2	yes	—
166	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
167	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
168	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
169	C₄²×C₁₁₃	—	2	8	no	—
170	C₄²×C₁₁₃	—	2	2	no	—
171	C₄²×C₁₁₃	—	2	2	no	—
172	C₄²×C₁₁₃	—	4	2	no	—
173	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
174	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
175	C₂³×C₁₁₃	—	2	2	no	—
176	C₂³×C₁₁₃	—	4	1	no	—
177	C₂³×C₁₁₃	—	4	1	no	—
178	C₂³×C₁₁₃	—	4	1	no	—
179	C₂³×C₁₁₃	—	4	1	no	—
180	C₂³×C₁₁₃	—	4	1	no	—
181	C₂³×C₁₁₃	—	4	1	no	—
182	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
183	Q₈×C₁₁₃	—	2	2	no	—
184	Q₈×C₁₁₃	—	2	2	no	—
185	Q₈×C₁₁₃	—	2	4	no	—
186	Q₈×C₁₁₃	—	2	4	no	—
187	Q₈×C₁₁₃	—	4	2	no	—
188	Q₈×C₁₁₃	—	4	2	no	—
189	Q₈×C₁₁₃	—	4	1	no	—
190	Q₈×C₁₁₃	—	4	1	no	—
191	Q₈×C₁₁₃	—	4	4	no	—
192	D₄×C₁₁₃	—	2	2	no	—
193	D₄×C₁₁₃	—	2	2	no	—
194	D₄×C₁₁₃	—	4	1	no	—
195	D₄×C₁₁₃	—	4	1	no	—
196	C₂×C₄×C₁₁₃	—	2	1	no	—
197	C₂×C₄×C₁₁₃	—	2	1	no	—
198	C₂×C₄×C₁₁₃	—	2	2	no	—
199	C₂×C₄×C₁₁₃	—	2	2	no	—
200	C₂×C₄×C₁₁₃	—	2	4	no	—
201	C₂×C₄×C₁₁₃	—	2	2	no	—
202	C₂×C₄×C₁₁₃	—	2	2	no	—
203	C₂×C₄×C₁₁₃	—	2	2	no	—
204	C₂×C₄×C₁₁₃	—	2	2	no	—
205	C₂×C₄×C₁₁₃	—	2	2	no	—
206	C₂×C₄×C₁₁₃	—	2	2	no	—
207	C₂×C₄×C₁₁₃	—	4	1	no	—
208	C₂×C₄×C₁₁₃	—	4	2	no	—
209	C₂×C₄×C₁₁₃	—	4	1	no	—
210	C₂×C₄×C₁₁₃	—	4	2	no	—
211	C₂×C₄×C₁₁₃	—	4	1	no	—
212	C₂×C₄×C₁₁₃	—	4	1	no	—
213	C₂×C₄×C₁₁₃	—	4	8	no	—
214	C₂×C₄×C₁₁₃	—	4	1	no	—
215	C₂×C₄×C₁₁₃	—	4	2	no	—
216	C₂×C₄×C₁₁₃	—	4	2	no	—
217	C₂×C₄×C₁₁₃	—	4	2	no	—
218	C₂×C₄×C₁₁₃	—	4	1	no	—
219	C₂×C₄×C₁₁₃	—	4	1	no	—
220	C₂×C₄×C₁₁₃	#120	1	2	yes	—
221	C₂×C₄×C₁₁₃	#120	1	2	yes	—
222	C₂×C₄×C₁₁₃	#135	1	2	yes	—
223	C₂×C₄×C₁₁₃	#137	1	2	yes	—
224	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₁₁₃	H(5,𝔽₂)	1	1	yes	characteristic
229	C₂×C₄×C₁₁₃	2₋¹⁺⁴	1	1	yes	characteristic
230	C₈×C₁₁₃	—	2	2	no	—
231	C₈×C₁₁₃	—	4	1	no	—
232	C₈×C₁₁₃	—	4	2	no	—
233	C₂²×C₁₁₃	—	4	2	no	—
234	C₂²×C₁₁₃	—	4	2	no	—
235	C₂²×C₁₁₃	—	4	2	no	—
236	C₂²×C₁₁₃	—	8	1	no	—
237	C₂²×C₁₁₃	—	8	1	no	—
238	C₂²×C₁₁₃	—	8	1	no	—
239	C₂²×C₁₁₃	—	8	1	no	—
240	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
241	C₂²×C₁₁₃	#548	1	1	yes	characteristic
242	C₂²×C₁₁₃	#550	1	1	yes	characteristic
243	C₂²×C₁₁₃	C₂×#135	1	1	yes	characteristic
244	C₂²×C₁₁₃	C₂×#137	1	1	yes	characteristic
245	C₂²×C₁₁₃	#577	1	1	yes	characteristic
246	C₂²×C₁₁₃	#578	1	1	yes	characteristic
247	C₄×C₁₁₃	—	2	2	no	—
248	C₄×C₁₁₃	—	4	4	no	—
249	C₄×C₁₁₃	—	4	2	no	—
250	C₄×C₁₁₃	—	4	2	no	—
251	C₄×C₁₁₃	—	4	2	no	—
252	C₄×C₁₁₃	—	4	2	no	—
253	C₄×C₁₁₃	—	8	2	no	—
254	C₄×C₁₁₃	—	8	1	no	—
255	C₄×C₁₁₃	#452	1	4	yes	—
256	C₄×C₁₁₃	#525	1	1	yes	characteristic
257	C₄×C₁₁₃	#537	1	1	yes	characteristic
258	C₄×C₁₁₃	#546	1	1	yes	characteristic
259	C₄×C₁₁₃	#547	1	1	yes	characteristic
260	#24189	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
261	C₂×C₁₁₃	—	8	2	no	—
262	C₂×C₁₁₃	#2407	1	1	yes	characteristic
263	C₂×C₁₁₃	C₂×#452	1	1	yes	characteristic
264	C₂×C₁₁₃	#3013	1	1	yes	characteristic
265	C₂×C₁₁₃	#3364	1	1	yes	characteristic
266	C₂×C₁₁₃	#3369	1	1	yes	characteristic
267	C₂×C₁₁₃	#3394	1	1	yes	characteristic
268	C₂×C₁₁₃	#3398	1	1	yes	characteristic
269	C₂×#556	C₂×C₁₁₃	1	1	yes	characteristic
270	C₂×#462	C₂×C₁₁₃	1	1	yes	characteristic, complemented
271	C₂×C₄×SD₁₆	C₂×C₁₁₃	1	1	yes	characteristic
272	#2582	C₂×C₁₁₃	1	1	yes	characteristic, complemented
273	#2042	C₂×C₁₁₃	1	2	yes	—
274	#2015	C₂×C₁₁₃	1	2	yes	—
275	#1984	C₂×C₁₁₃	1	1	yes	characteristic, complemented
276	#1956	C₂×C₁₁₃	1	1	yes	characteristic, complemented
277	#1878	C₂×C₁₁₃	1	2	yes	complemented
278	#1865	C₂×C₁₁₃	1	2	yes	complemented
279	#1802	C₂×C₁₁₃	1	1	yes	characteristic
280	C₁₁₃	#24189	1	1	yes	characteristic, direct product factor, Sylow
281	C₂²×Q₁₆	C₂²×C₁₁₃	1	2	yes	—
282	C₂²×SD₁₆	C₂²×C₁₁₃	1	1	yes	characteristic
283	#556	—	2	4	no	—
284	#556	—	2	4	no	—
285	C₂×C₄⋊Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
286	C₂×#126	—	2	2	no	—
287	C₂×#124	C₂²×C₁₁₃	1	2	yes	—
288	C₂×C₂²⋊Q₈	—	2	1	no	—
289	C₂×C₄×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
290	C₂×C₄×Q₈	C₂²×C₁₁₃	1	2	yes	—
291	C₂×C₄×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
292	C₂×C₄×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
293	C₂×#117	—	2	1	no	—
294	#462	—	2	4	no	—
295	C₄×SD₁₆	—	2	4	no	—
296	C₂×#106	C₂²×C₁₁₃	1	1	yes	characteristic
297	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	1	yes	characteristic
298	C₂×#103	C₂²×C₁₁₃	1	2	yes	—
299	C₂×#103	C₂²×C₁₁₃	1	2	yes	—
300	C₂×#103	C₂²×C₁₁₃	1	1	yes	characteristic
301	C₂×#103	C₂²×C₁₁₃	1	2	yes	—
302	C₂×#102	C₂²×C₁₁₃	1	1	yes	characteristic
303	C₂×#102	C₂²×C₁₁₃	1	2	yes	—
304	C₂×C₄×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
305	#398	—	2	2	no	—
306	#391	—	2	1	no	—
307	#391	C₂²×C₁₁₃	1	2	yes	—
308	#389	—	2	1	no	—
309	#389	C₂²×C₁₁₃	1	2	yes	—
310	#384	C₂²×C₁₁₃	1	1	yes	characteristic
311	#340	C₂²×C₁₁₃	1	2	yes	—
312	#336	C₂²×C₁₁₃	1	2	yes	—
313	#336	C₂²×C₁₁₃	1	2	yes	—
314	C₂²×Q₈	D₄×C₁₁₃	1	1	yes	characteristic
315	C₂²×Q₈	C₂³×C₁₁₃	1	2	yes	—
316	C₂²×Q₈	C₂³×C₁₁₃	1	1	yes	characteristic
317	C₂²×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
318	C₂³×C₄	—	2	1	no	—
319	C₂×Q₁₆	—	2	4	no	—
320	C₂×Q₁₆	—	2	4	no	—
321	C₂×Q₁₆	—	4	2	no	—
322	C₂×SD₁₆	—	2	2	no	—
323	C₂×SD₁₆	—	2	2	no	—
324	C₂×SD₁₆	—	2	2	no	—
325	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
326	C₂²×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
328	C₄⋊Q₈	—	2	2	no	—
329	C₄⋊Q₈	D₄×C₁₁₃	1	4	yes	—
330	#126	—	2	16	no	—
331	#124	—	2	4	no	—
332	#124	—	2	4	no	—
333	C₂²⋊Q₈	—	2	8	no	—
334	C₄×Q₈	—	2	4	no	—
335	C₄×Q₈	—	2	4	no	—
336	C₄×Q₈	—	2	2	no	—
337	C₄×Q₈	—	2	2	no	—
338	C₄×Q₈	—	2	2	no	—
339	C₄×Q₈	—	2	2	no	—
340	C₄×D₄	—	2	2	no	—
341	C₄×D₄	D₄×C₁₁₃	1	4	yes	—
342	#117	—	2	8	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	2	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	D₄×C₁₁₃	1	1	yes	characteristic
351	C₂×C₄⋊C₄	D₄×C₁₁₃	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	1	yes	characteristic
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₄²	—	2	2	no	—
359	C₂×C₄²	—	2	1	no	—
360	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
361	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
362	#106	—	2	2	no	—
363	C₄⋊C₈	—	2	2	no	—
364	#103	—	2	4	no	—
365	#103	—	2	4	no	—
366	#103	—	2	2	no	—
367	#103	—	4	2	no	—
368	#102	—	2	2	no	—
369	#102	—	4	2	no	—
370	C₄×C₈	—	2	2	no	—
371	#95	—	2	2	no	—
372	#95	—	2	2	no	—
373	#95	—	2	2	no	—
374	C₂⁴	—	2	1	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	1	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	C₂×D₄×C₁₁₃	1	4	yes	—
389	C₂×Q₈	#41×C₁₁₃	1	2	yes	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	C₂×D₄×C₁₁₃	1	2	yes	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	4	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	4	2	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
405	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
406	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
408	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
409	Q₁₆	—	4	8	no	—
410	SD₁₆	—	2	8	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	#41×C₁₁₃	1	2	yes	—
420	C₄⋊C₄	—	2	8	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	4	2	no	—
431	C₄⋊C₄	—	4	2	no	—
432	C₄⋊C₄	—	8	1	no	—
433	C₄⋊C₄	—	8	2	no	—
434	C₄⋊C₄	C₂×D₄×C₁₁₃	1	2	yes	—
435	C₂²⋊C₄	—	2	8	no	—
436	C₂²⋊C₄	—	2	8	no	—
437	C₂²⋊C₄	—	2	4	no	—
438	C₄²	—	2	8	no	—
439	C₄²	—	2	2	no	—
440	C₄²	—	2	2	no	—
441	C₄²	—	4	2	no	—
442	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
443	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
444	C₂³	—	2	2	no	—
445	C₂³	—	4	1	no	—
446	C₂³	—	4	1	no	—
447	C₂³	—	4	1	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	4	1	no	—
450	C₂³	—	4	1	no	—
451	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
452	Q₈	—	2	2	no	—
453	Q₈	—	2	2	no	—
454	Q₈	—	2	4	no	—
455	Q₈	—	2	4	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	4	2	no	—
458	Q₈	—	4	1	no	—
459	Q₈	—	4	1	no	—
460	Q₈	—	4	4	no	—
461	D₄	—	2	2	no	—
462	D₄	—	2	2	no	—
463	D₄	—	4	1	no	—
464	D₄	—	4	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	8	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	#120×C₁₁₃	1	2	yes	—
490	C₂×C₄	#120×C₁₁₃	1	2	yes	—
491	C₂×C₄	#135×C₁₁₃	1	2	yes	—
492	C₂×C₄	#137×C₁₁₃	1	2	yes	—
493	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
494	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
495	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
496	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
497	C₂×C₄	H(5,𝔽₂)×C₁₁₃	1	1	yes	characteristic
498	C₂×C₄	2₋¹⁺⁴×C₁₁₃	1	1	yes	characteristic
499	C₈	—	2	2	no	—
500	C₈	—	4	1	no	—
501	C₈	—	4	2	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	8	1	no	—
506	C₂²	—	8	1	no	—
507	C₂²	—	8	1	no	—
508	C₂²	—	8	1	no	—
509	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
510	C₂²	#548×C₁₁₃	1	1	yes	characteristic
511	C₂²	#550×C₁₁₃	1	1	yes	characteristic
512	C₂²	C₂×#135×C₁₁₃	1	1	yes	characteristic
513	C₂²	C₂×#137×C₁₁₃	1	1	yes	characteristic
514	C₂²	#577×C₁₁₃	1	1	yes	characteristic
515	C₂²	#578×C₁₁₃	1	1	yes	characteristic
516	C₄	—	2	2	no	—
517	C₄	—	4	4	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	2	no	—
522	C₄	—	8	2	no	—
523	C₄	—	8	1	no	—
524	C₄	#452×C₁₁₃	1	4	yes	—
525	C₄	#525×C₁₁₃	1	1	yes	characteristic
526	C₄	#537×C₁₁₃	1	1	yes	characteristic
527	C₄	#546×C₁₁₃	1	1	yes	characteristic
528	C₄	#547×C₁₁₃	1	1	yes	characteristic
529	C₂	—	8	2	no	—
530	C₂	C₁₁₃×#2407	1	1	yes	characteristic
531	C₂	C₂×#452×C₁₁₃	1	1	yes	characteristic
532	C₂	C₁₁₃×#3013	1	1	yes	characteristic
533	C₂	C₁₁₃×#3364	1	1	yes	characteristic
534	C₂	C₁₁₃×#3369	1	1	yes	characteristic
535	C₂	C₁₁₃×#3394	1	1	yes	characteristic
536	C₂	C₁₁₃×#3398	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
prime radical	C₂²×D₄×C₁₁₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁₃ ◁ C₂×C₄×Q₈×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#462×C₁₁₃	C₂	semidirect
4. C₁₁₃×#2582	C₂	semidirect
7. C₁₁₃×#1984	C₂	semidirect
8. C₁₁₃×#1956	C₂	semidirect
9. C₁₁₃×#1878	C₂	semidirect
10. C₁₁₃×#1865	C₂	semidirect
260. #24189	C₁₁₃	direct (N × H)
270. C₂×#462	C₂×C₁₁₃	semidirect
272. #2582	C₂×C₁₁₃	semidirect
275. #1984	C₂×C₁₁₃	semidirect
276. #1956	C₂×C₁₁₃	semidirect
277. #1878	C₂×C₁₁₃	semidirect
278. #1865	C₂×C₁₁₃	semidirect
280. C₁₁₃	#24189	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×#556×C₁₁₃	2
C₂×#462×C₁₁₃	2
C₂×C₄×SD₁₆×C₁₁₃	2
C₁₁₃×#2582	2
C₁₁₃×#2042	2
C₁₁₃×#2015	2
C₁₁₃×#1984	2
C₁₁₃×#1956	2
C₁₁₃×#1878	2
C₁₁₃×#1865	2
C₁₁₃×#1802	2
#24189	113

Subgroups — C113×#24189 #43292209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#24189 #43292209