Subgroups — C₁₁₃×#3560 #28388356

Order 14464.

1056 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#563×C₁₁₃	C₂	1	2	yes	maximal, complemented
2	#560×C₁₁₃	C₂	1	2	yes	maximal, complemented
3	#553×C₁₁₃	C₂	1	2	yes	maximal, complemented
4	#553×C₁₁₃	C₂	1	2	yes	maximal, complemented
5	#551×C₁₁₃	C₂	1	2	yes	maximal, complemented
6	#547×C₁₁₃	C₂	1	2	yes	maximal, complemented
7	#546×C₁₁₃	C₂	1	2	yes	maximal, complemented
8	#546×C₁₁₃	C₂	1	2	yes	maximal, complemented
9	#542×C₁₁₃	C₂	1	2	yes	maximal, complemented
10	#539×C₁₁₃	C₂	1	2	yes	maximal, complemented
11	#539×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#538×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#538×C₁₁₃	C₂	1	2	yes	maximal, complemented
14	#538×C₁₁₃	C₂	1	2	yes	maximal, complemented
15	#537×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
16	#534×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#532×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#529×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#126×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#41×C₁₁₃	C₂²	1	2	yes	complemented
21	C₂×#41×C₁₁₃	C₂²	1	2	yes	complemented
22	C₂²×D₄×C₁₁₃	C₂²	1	2	yes	—
23	C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
24	C₄⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
25	#127×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
26	#126×C₁₁₃	C₂²	1	2	yes	complemented
27	#126×C₁₁₃	C₂²	1	2	yes	complemented
28	#126×C₁₁₃	C₂²	1	2	yes	complemented
29	#126×C₁₁₃	C₂²	1	2	yes	complemented
30	#126×C₁₁₃	C₂²	1	2	yes	complemented
31	#126×C₁₁₃	C₂²	1	2	yes	complemented
32	#126×C₁₁₃	C₂²	1	2	yes	complemented
33	#126×C₁₁₃	C₂²	1	2	yes	complemented
34	#126×C₁₁₃	C₂²	1	2	yes	complemented
35	#125×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
36	#125×C₁₁₃	C₂²	1	2	yes	complemented
37	#125×C₁₁₃	C₂²	1	2	yes	complemented
38	#124×C₁₁₃	C₂²	1	2	yes	—
39	#124×C₁₁₃	C₂²	1	2	yes	—
40	#124×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
41	#124×C₁₁₃	C₂²	1	2	yes	complemented
42	#124×C₁₁₃	C₂²	1	2	yes	complemented
43	#123×C₁₁₃	C₂²	1	2	yes	—
44	#123×C₁₁₃	C₂²	1	2	yes	—
45	#123×C₁₁₃	C₂²	1	2	yes	—
46	#123×C₁₁₃	C₂²	1	2	yes	—
47	#123×C₁₁₃	C₂²	1	2	yes	complemented
48	#123×C₁₁₃	C₂²	1	2	yes	complemented
49	#123×C₁₁₃	C₂²	1	2	yes	complemented
50	#123×C₁₁₃	C₂²	1	2	yes	complemented
51	#123×C₁₁₃	C₂²	1	2	yes	complemented
52	#123×C₁₁₃	C₂²	1	2	yes	complemented
53	#123×C₁₁₃	C₂²	1	2	yes	complemented
54	#123×C₁₁₃	C₂²	1	2	yes	complemented
55	C₂²⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
56	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
57	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
58	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
59	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
60	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
61	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
62	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
63	#121×C₁₁₃	C₂²	1	1	yes	characteristic
64	#121×C₁₁₃	C₂²	1	1	yes	characteristic
65	#121×C₁₁₃	C₂²	1	2	yes	—
66	#121×C₁₁₃	C₂²	1	2	yes	—
67	#121×C₁₁₃	C₂²	1	2	yes	—
68	#121×C₁₁₃	C₂²	1	2	yes	—
69	#121×C₁₁₃	C₂²	1	2	yes	—
70	#121×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
71	#121×C₁₁₃	C₂²	1	2	yes	complemented
72	#121×C₁₁₃	C₂²	1	2	yes	complemented
73	#121×C₁₁₃	C₂²	1	2	yes	complemented
74	#121×C₁₁₃	C₂²	1	2	yes	complemented
75	#121×C₁₁₃	C₂²	1	2	yes	complemented
76	#121×C₁₁₃	C₂²	1	2	yes	complemented
77	#121×C₁₁₃	C₂²	1	2	yes	complemented
78	#120×C₁₁₃	C₂²	1	2	yes	—
79	#120×C₁₁₃	C₂²	1	2	yes	—
80	#120×C₁₁₃	C₂²	1	2	yes	—
81	#120×C₁₁₃	C₂²	1	2	yes	complemented
82	#120×C₁₁₃	C₂²	1	2	yes	complemented
83	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
84	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
85	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
86	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
87	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
88	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
89	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
90	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
91	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
92	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
93	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
94	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
95	#117×C₁₁₃	C₂²	1	2	yes	complemented
96	#117×C₁₁₃	C₂²	1	2	yes	complemented
97	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
98	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
99	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	complemented
101	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	complemented
105	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	complemented
106	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
107	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
108	C₂⁴×C₁₁₃	C₂³	1	2	yes	—
109	#41×C₁₁₃	—	4	4	no	—
110	#41×C₁₁₃	—	4	4	no	—
111	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
112	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
113	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
114	C₂×D₄×C₁₁₃	—	4	4	no	—
115	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
116	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
117	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
118	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
119	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
120	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
121	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
122	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
123	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
124	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
125	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
127	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
128	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
129	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
130	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
137	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
138	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
139	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
140	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
141	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
142	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
143	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
144	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
145	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
146	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
147	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
148	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
149	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
150	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
151	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
152	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
153	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
154	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
155	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
156	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
157	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
158	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
159	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
160	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
161	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
162	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
163	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
164	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
165	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
166	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
167	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
169	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
170	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
171	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
172	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
174	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
175	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
176	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
177	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
178	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
179	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
180	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
181	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
182	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
183	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
184	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
185	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
186	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
187	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
188	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
189	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
190	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
191	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
192	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
193	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
194	C₄²×C₁₁₃	C₂³	1	2	yes	—
195	C₄²×C₁₁₃	C₂³	1	2	yes	—
196	C₄²×C₁₁₃	C₂³	1	2	yes	—
197	C₂³×C₁₁₃	—	2	2	no	—
198	C₂³×C₁₁₃	—	4	2	no	—
199	C₂³×C₁₁₃	—	4	1	no	—
200	C₂³×C₁₁₃	—	4	1	no	—
201	C₂³×C₁₁₃	—	4	2	no	—
202	C₂³×C₁₁₃	—	4	2	no	—
203	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
204	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
205	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
206	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
207	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
208	Q₈×C₁₁₃	—	4	1	no	—
209	Q₈×C₁₁₃	—	4	2	no	—
210	Q₈×C₁₁₃	—	4	2	no	—
211	D₄×C₁₁₃	—	2	4	no	—
212	D₄×C₁₁₃	—	2	4	no	—
213	D₄×C₁₁₃	—	2	4	no	—
214	D₄×C₁₁₃	—	4	2	no	—
215	D₄×C₁₁₃	—	4	2	no	—
216	D₄×C₁₁₃	—	4	2	no	—
217	D₄×C₁₁₃	—	4	2	no	—
218	D₄×C₁₁₃	—	4	2	no	—
219	D₄×C₁₁₃	—	4	2	no	—
220	D₄×C₁₁₃	—	4	1	no	—
221	D₄×C₁₁₃	—	4	1	no	—
222	D₄×C₁₁₃	—	4	2	no	—
223	D₄×C₁₁₃	—	4	1	no	—
224	D₄×C₁₁₃	—	4	2	no	—
225	D₄×C₁₁₃	—	4	2	no	—
226	C₂×C₄×C₁₁₃	—	2	2	no	—
227	C₂×C₄×C₁₁₃	—	2	2	no	—
228	C₂×C₄×C₁₁₃	—	4	2	no	—
229	C₂×C₄×C₁₁₃	—	4	1	no	—
230	C₂×C₄×C₁₁₃	—	4	1	no	—
231	C₂×C₄×C₁₁₃	—	4	1	no	—
232	C₂×C₄×C₁₁₃	—	4	2	no	—
233	C₂×C₄×C₁₁₃	—	4	2	no	—
234	C₂×C₄×C₁₁₃	—	4	1	no	—
235	C₂×C₄×C₁₁₃	—	4	2	no	—
236	C₂×C₄×C₁₁₃	—	4	2	no	—
237	C₂×C₄×C₁₁₃	—	4	2	no	—
238	C₂×C₄×C₁₁₃	—	4	2	no	—
239	C₂×C₄×C₁₁₃	—	4	2	no	—
240	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
243	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
248	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
249	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
252	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
254	C₂²×C₁₁₃	—	2	1	no	—
255	C₂²×C₁₁₃	—	2	1	no	—
256	C₂²×C₁₁₃	—	2	2	no	—
257	C₂²×C₁₁₃	—	2	2	no	—
258	C₂²×C₁₁₃	—	2	2	no	—
259	C₂²×C₁₁₃	—	2	2	no	—
260	C₂²×C₁₁₃	—	2	2	no	—
261	C₂²×C₁₁₃	—	2	2	no	—
262	C₂²×C₁₁₃	—	2	2	no	—
263	C₂²×C₁₁₃	—	2	2	no	—
264	C₂²×C₁₁₃	—	2	2	no	—
265	C₂²×C₁₁₃	—	2	2	no	—
266	C₂²×C₁₁₃	—	2	2	no	—
267	C₂²×C₁₁₃	—	2	2	no	—
268	C₂²×C₁₁₃	—	8	2	no	—
269	C₂²×C₁₁₃	—	8	4	no	—
270	C₂²×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
271	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
272	C₄×C₁₁₃	—	2	1	no	—
273	C₄×C₁₁₃	—	2	2	no	—
274	C₄×C₁₁₃	—	2	1	no	—
275	C₄×C₁₁₃	—	2	2	no	—
276	C₄×C₁₁₃	—	2	2	no	—
277	C₄×C₁₁₃	—	2	2	no	—
278	C₄×C₁₁₃	—	2	1	no	—
279	C₄×C₁₁₃	—	2	2	no	—
280	C₄×C₁₁₃	—	2	2	no	—
281	C₄×C₁₁₃	—	2	2	no	—
282	C₄×C₁₁₃	—	2	1	no	—
283	C₄×C₁₁₃	—	2	1	no	—
284	C₄×C₁₁₃	—	2	2	no	—
285	C₄×C₁₁₃	—	2	1	no	—
286	C₂×C₁₁₃	—	2	2	no	—
287	C₂×C₁₁₃	—	4	2	no	—
288	C₂×C₁₁₃	—	4	2	no	—
289	C₂×C₁₁₃	—	4	2	no	—
290	C₂×C₁₁₃	—	4	2	no	—
291	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
292	C₂×C₁₁₃	#585	1	1	yes	characteristic
293	C₂×C₁₁₃	#585	1	1	yes	characteristic
294	#3560	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
295	C₁₁₃	#3560	1	1	yes	characteristic, direct product factor, Sylow
296	#563	C₂×C₁₁₃	1	2	yes	complemented
297	#560	C₂×C₁₁₃	1	2	yes	complemented
298	#553	C₂×C₁₁₃	1	2	yes	complemented
299	#553	C₂×C₁₁₃	1	2	yes	complemented
300	#551	C₂×C₁₁₃	1	2	yes	complemented
301	#547	C₂×C₁₁₃	1	2	yes	complemented
302	#546	C₂×C₁₁₃	1	2	yes	complemented
303	#546	C₂×C₁₁₃	1	2	yes	complemented
304	#542	C₂×C₁₁₃	1	2	yes	complemented
305	#539	C₂×C₁₁₃	1	2	yes	complemented
306	#539	C₂×C₁₁₃	1	1	yes	characteristic, complemented
307	#538	C₂×C₁₁₃	1	1	yes	characteristic, complemented
308	#538	C₂×C₁₁₃	1	2	yes	complemented
309	#538	C₂×C₁₁₃	1	2	yes	complemented
310	#537	C₂×C₁₁₃	1	1	yes	characteristic, complemented
311	#534	C₂×C₁₁₃	1	1	yes	characteristic, complemented
312	#532	C₂×C₁₁₃	1	1	yes	characteristic, complemented
313	#529	C₂×C₁₁₃	1	1	yes	characteristic, complemented
314	C₂×#126	C₂×C₁₁₃	1	1	yes	characteristic, complemented
315	C₂×#41	C₂²×C₁₁₃	1	2	yes	complemented
316	C₂×#41	C₂²×C₁₁₃	1	2	yes	complemented
317	C₂²×D₄	C₂²×C₁₁₃	1	2	yes	—
318	C₄⋊Q₈	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
319	C₄⋊Q₈	C₂²×C₁₁₃	1	2	yes	complemented
320	#127	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
321	#126	C₂²×C₁₁₃	1	2	yes	complemented
322	#126	C₂²×C₁₁₃	1	2	yes	complemented
323	#126	C₂²×C₁₁₃	1	2	yes	complemented
324	#126	C₂²×C₁₁₃	1	2	yes	complemented
325	#126	C₂²×C₁₁₃	1	2	yes	complemented
326	#126	C₂²×C₁₁₃	1	2	yes	complemented
327	#126	C₂²×C₁₁₃	1	2	yes	complemented
328	#126	C₂²×C₁₁₃	1	2	yes	complemented
329	#126	C₂²×C₁₁₃	1	2	yes	complemented
330	#125	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
331	#125	C₂²×C₁₁₃	1	2	yes	complemented
332	#125	C₂²×C₁₁₃	1	2	yes	complemented
333	#124	C₂²×C₁₁₃	1	2	yes	—
334	#124	C₂²×C₁₁₃	1	2	yes	—
335	#124	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
336	#124	C₂²×C₁₁₃	1	2	yes	complemented
337	#124	C₂²×C₁₁₃	1	2	yes	complemented
338	#123	C₂²×C₁₁₃	1	2	yes	—
339	#123	C₂²×C₁₁₃	1	2	yes	—
340	#123	C₂²×C₁₁₃	1	2	yes	—
341	#123	C₂²×C₁₁₃	1	2	yes	—
342	#123	C₂²×C₁₁₃	1	2	yes	complemented
343	#123	C₂²×C₁₁₃	1	2	yes	complemented
344	#123	C₂²×C₁₁₃	1	2	yes	complemented
345	#123	C₂²×C₁₁₃	1	2	yes	complemented
346	#123	C₂²×C₁₁₃	1	2	yes	complemented
347	#123	C₂²×C₁₁₃	1	2	yes	complemented
348	#123	C₂²×C₁₁₃	1	2	yes	complemented
349	#123	C₂²×C₁₁₃	1	2	yes	complemented
350	C₂²⋊Q₈	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
351	C₂²⋊Q₈	C₂²×C₁₁₃	1	2	yes	complemented
352	C₂²⋊Q₈	C₂²×C₁₁₃	1	2	yes	complemented
353	C₂²⋊Q₈	C₂²×C₁₁₃	1	2	yes	complemented
354	C₂²⋊Q₈	C₂²×C₁₁₃	1	2	yes	complemented
355	C₂²⋊Q₈	C₂²×C₁₁₃	1	2	yes	complemented
356	C₂²⋊Q₈	C₂²×C₁₁₃	1	2	yes	complemented
357	C₂²⋊Q₈	C₂²×C₁₁₃	1	2	yes	complemented
358	#121	C₂²×C₁₁₃	1	1	yes	characteristic
359	#121	C₂²×C₁₁₃	1	1	yes	characteristic
360	#121	C₂²×C₁₁₃	1	2	yes	—
361	#121	C₂²×C₁₁₃	1	2	yes	—
362	#121	C₂²×C₁₁₃	1	2	yes	—
363	#121	C₂²×C₁₁₃	1	2	yes	—
364	#121	C₂²×C₁₁₃	1	2	yes	—
365	#121	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
366	#121	C₂²×C₁₁₃	1	2	yes	complemented
367	#121	C₂²×C₁₁₃	1	2	yes	complemented
368	#121	C₂²×C₁₁₃	1	2	yes	complemented
369	#121	C₂²×C₁₁₃	1	2	yes	complemented
370	#121	C₂²×C₁₁₃	1	2	yes	complemented
371	#121	C₂²×C₁₁₃	1	2	yes	complemented
372	#121	C₂²×C₁₁₃	1	2	yes	complemented
373	#120	C₂²×C₁₁₃	1	2	yes	—
374	#120	C₂²×C₁₁₃	1	2	yes	—
375	#120	C₂²×C₁₁₃	1	2	yes	—
376	#120	C₂²×C₁₁₃	1	2	yes	complemented
377	#120	C₂²×C₁₁₃	1	2	yes	complemented
378	C₄×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
379	C₄×D₄	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
380	C₄×D₄	C₂²×C₁₁₃	1	2	yes	complemented
381	C₄×D₄	C₂²×C₁₁₃	1	2	yes	complemented
382	C₄×D₄	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
383	C₄×D₄	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
384	C₄×D₄	C₂²×C₁₁₃	1	2	yes	complemented
385	C₄×D₄	C₂²×C₁₁₃	1	2	yes	complemented
386	C₄×D₄	C₂²×C₁₁₃	1	2	yes	complemented
387	C₄×D₄	C₂²×C₁₁₃	1	2	yes	complemented
388	C₄×D₄	C₂²×C₁₁₃	1	2	yes	complemented
389	C₄×D₄	C₂²×C₁₁₃	1	2	yes	complemented
390	#117	C₂²×C₁₁₃	1	2	yes	complemented
391	#117	C₂²×C₁₁₃	1	2	yes	complemented
392	C₂×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
393	C₂×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
394	C₂×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
395	C₂×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	complemented
396	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
397	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
398	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
399	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	complemented
400	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	complemented
401	C₂×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
402	C₂⁴	C₂³×C₁₁₃	1	1	yes	characteristic
403	C₂⁴	C₂³×C₁₁₃	1	2	yes	—
404	#41	—	4	4	no	—
405	#41	—	4	4	no	—
406	C₂×Q₈	C₂³×C₁₁₃	1	1	yes	characteristic
407	C₂×Q₈	C₂³×C₁₁₃	1	2	yes	—
408	C₂×Q₈	C₂³×C₁₁₃	1	2	yes	—
409	C₂×D₄	—	4	4	no	—
410	C₂×D₄	C₂³×C₁₁₃	1	2	yes	—
411	C₂×D₄	C₂³×C₁₁₃	1	2	yes	—
412	C₂×D₄	C₂³×C₁₁₃	1	2	yes	—
413	C₂×D₄	C₂³×C₁₁₃	1	2	yes	—
414	C₂×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
415	C₂×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
416	C₂×D₄	C₂³×C₁₁₃	1	2	yes	—
417	C₂×D₄	C₂³×C₁₁₃	1	2	yes	—
418	C₂×D₄	C₂³×C₁₁₃	1	2	yes	—
419	C₂×D₄	C₂³×C₁₁₃	1	2	yes	—
420	C₂×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
421	C₂×D₄	C₂³×C₁₁₃	1	2	yes	—
422	C₂×D₄	C₂³×C₁₁₃	1	2	yes	—
423	C₂×D₄	C₂³×C₁₁₃	1	2	yes	—
424	C₂×D₄	C₂³×C₁₁₃	1	2	yes	—
425	C₂²×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
426	C₂²×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
427	C₂²×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
428	C₂²×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
430	C₂²×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂³×C₁₁₃	1	2	yes	—
432	C₂²×C₄	C₂³×C₁₁₃	1	2	yes	—
433	C₂²×C₄	C₂³×C₁₁₃	1	2	yes	—
434	C₂²×C₄	C₂³×C₁₁₃	1	2	yes	—
435	C₂²×C₄	C₂³×C₁₁₃	1	2	yes	—
436	C₂²×C₄	C₂³×C₁₁₃	1	2	yes	—
437	C₂²×C₄	C₂³×C₁₁₃	1	2	yes	—
438	C₂²×C₄	C₂³×C₁₁₃	1	2	yes	—
439	C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
440	C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
441	C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
442	C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
443	C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
444	C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
445	C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
446	C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
447	C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
448	C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
449	C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
450	C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
451	C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
452	C₄⋊C₄	C₂³×C₁₁₃	1	1	yes	characteristic
453	C₄⋊C₄	C₂³×C₁₁₃	1	1	yes	characteristic
454	C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
455	C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
456	C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
457	C₄⋊C₄	C₂³×C₁₁₃	1	1	yes	characteristic
458	C₄⋊C₄	C₂³×C₁₁₃	1	1	yes	characteristic
459	C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
460	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
461	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
462	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
463	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
464	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
465	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
466	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
467	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
468	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
469	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
470	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
471	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
472	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
473	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
474	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
475	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
476	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
477	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
478	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
479	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
480	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
481	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
482	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
483	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
484	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
485	C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
486	C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
487	C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
488	C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
489	C₄²	C₂³×C₁₁₃	1	2	yes	—
490	C₄²	C₂³×C₁₁₃	1	2	yes	—
491	C₄²	C₂³×C₁₁₃	1	2	yes	—
492	C₂³	—	2	2	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	4	1	no	—
496	C₂³	—	4	2	no	—
497	C₂³	—	4	2	no	—
498	C₂³	C₂⁴×C₁₁₃	1	2	yes	—
499	C₂³	C₂⁴×C₁₁₃	1	2	yes	—
500	C₂³	C₂⁴×C₁₁₃	1	2	yes	—
501	C₂³	C₂⁴×C₁₁₃	1	2	yes	—
502	C₂³	C₂⁴×C₁₁₃	1	1	yes	characteristic
503	Q₈	—	4	2	no	—
504	Q₈	—	4	2	no	—
505	Q₈	—	4	1	no	—
506	D₄	—	2	4	no	—
507	D₄	—	2	4	no	—
508	D₄	—	2	4	no	—
509	D₄	—	4	2	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	2	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	1	no	—
518	D₄	—	4	1	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	1	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
536	C₂×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
537	C₂×C₄	C₂⁴×C₁₁₃	1	2	yes	—
538	C₂×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
539	C₂×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
540	C₂×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
541	C₂×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
542	C₂×C₄	C₂⁴×C₁₁₃	1	2	yes	—
543	C₂×C₄	C₂⁴×C₁₁₃	1	2	yes	—
544	C₂×C₄	C₂⁴×C₁₁₃	1	2	yes	—
545	C₂×C₄	C₂⁴×C₁₁₃	1	2	yes	—
546	C₂×C₄	C₂⁴×C₁₁₃	1	2	yes	—
547	C₂×C₄	C₂⁴×C₁₁₃	1	2	yes	—
548	C₂×C₄	C₂⁴×C₁₁₃	1	2	yes	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	8	2	no	—
564	C₂²	—	8	4	no	—
565	C₂²	H(5,𝔽₂)×C₁₁₃	1	2	yes	—
566	C₂²	C₂⁵×C₁₁₃	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	1	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	1	no	—
581	C₂	—	2	2	no	—
582	C₂	—	4	2	no	—
583	C₂	—	4	2	no	—
584	C₂	—	4	2	no	—
585	C₂	—	4	2	no	—
586	C₂	C₂×H(5,𝔽₂)×C₁₁₃	1	1	yes	characteristic
587	C₂	#585×C₁₁₃	1	1	yes	characteristic
588	C₂	#585×C₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. #563×C₁₁₃	C₂	semidirect
2. #560×C₁₁₃	C₂	semidirect
3. #553×C₁₁₃	C₂	semidirect
4. #553×C₁₁₃	C₂	semidirect
5. #551×C₁₁₃	C₂	semidirect
6. #547×C₁₁₃	C₂	semidirect
7. #546×C₁₁₃	C₂	semidirect
8. #546×C₁₁₃	C₂	semidirect
9. #542×C₁₁₃	C₂	semidirect
10. #539×C₁₁₃	C₂	semidirect
11. #539×C₁₁₃	C₂	semidirect
12. #538×C₁₁₃	C₂	semidirect
13. #538×C₁₁₃	C₂	semidirect
14. #538×C₁₁₃	C₂	semidirect
15. #537×C₁₁₃	C₂	semidirect
16. #534×C₁₁₃	C₂	semidirect
17. #532×C₁₁₃	C₂	semidirect
18. #529×C₁₁₃	C₂	semidirect
19. C₂×#126×C₁₁₃	C₂	semidirect
20. C₂×#41×C₁₁₃	C₂²	semidirect
21. C₂×#41×C₁₁₃	C₂²	semidirect
23. C₄⋊Q₈×C₁₁₃	C₂²	semidirect
24. C₄⋊Q₈×C₁₁₃	C₂²	semidirect
25. #127×C₁₁₃	C₂²	semidirect
26. #126×C₁₁₃	C₂²	semidirect
27. #126×C₁₁₃	C₂²	semidirect
28. #126×C₁₁₃	C₂²	semidirect
29. #126×C₁₁₃	C₂²	semidirect
30. #126×C₁₁₃	C₂²	semidirect
31. #126×C₁₁₃	C₂²	semidirect
32. #126×C₁₁₃	C₂²	semidirect
33. #126×C₁₁₃	C₂²	semidirect
34. #126×C₁₁₃	C₂²	semidirect
35. #125×C₁₁₃	C₂²	semidirect
36. #125×C₁₁₃	C₂²	semidirect
37. #125×C₁₁₃	C₂²	semidirect
40. #124×C₁₁₃	C₂²	semidirect
41. #124×C₁₁₃	C₂²	semidirect
42. #124×C₁₁₃	C₂²	semidirect
47. #123×C₁₁₃	C₂²	semidirect
48. #123×C₁₁₃	C₂²	semidirect
49. #123×C₁₁₃	C₂²	semidirect
50. #123×C₁₁₃	C₂²	semidirect
51. #123×C₁₁₃	C₂²	semidirect
52. #123×C₁₁₃	C₂²	semidirect
53. #123×C₁₁₃	C₂²	semidirect
54. #123×C₁₁₃	C₂²	semidirect
55. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
56. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
57. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
58. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
59. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
60. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
61. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
62. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
70. #121×C₁₁₃	C₂²	semidirect
71. #121×C₁₁₃	C₂²	semidirect
72. #121×C₁₁₃	C₂²	semidirect
73. #121×C₁₁₃	C₂²	semidirect
74. #121×C₁₁₃	C₂²	semidirect
75. #121×C₁₁₃	C₂²	semidirect
76. #121×C₁₁₃	C₂²	semidirect
77. #121×C₁₁₃	C₂²	semidirect
81. #120×C₁₁₃	C₂²	semidirect
82. #120×C₁₁₃	C₂²	semidirect
83. C₄×Q₈×C₁₁₃	C₂²	semidirect
84. C₄×D₄×C₁₁₃	C₂²	semidirect
85. C₄×D₄×C₁₁₃	C₂²	semidirect
86. C₄×D₄×C₁₁₃	C₂²	semidirect
87. C₄×D₄×C₁₁₃	C₂²	semidirect
88. C₄×D₄×C₁₁₃	C₂²	semidirect
89. C₄×D₄×C₁₁₃	C₂²	semidirect
90. C₄×D₄×C₁₁₃	C₂²	semidirect
91. C₄×D₄×C₁₁₃	C₂²	semidirect
92. C₄×D₄×C₁₁₃	C₂²	semidirect
93. C₄×D₄×C₁₁₃	C₂²	semidirect
94. C₄×D₄×C₁₁₃	C₂²	semidirect
95. #117×C₁₁₃	C₂²	semidirect
96. #117×C₁₁₃	C₂²	semidirect
97. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
98. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
99. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
100. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
104. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
105. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
106. C₂×C₄²×C₁₁₃	C₂²	semidirect
294. #3560	C₁₁₃	direct (N × H)
295. C₁₁₃	#3560	direct (N × H)
296. #563	C₂×C₁₁₃	semidirect
297. #560	C₂×C₁₁₃	semidirect
298. #553	C₂×C₁₁₃	semidirect
299. #553	C₂×C₁₁₃	semidirect
300. #551	C₂×C₁₁₃	semidirect
301. #547	C₂×C₁₁₃	semidirect
302. #546	C₂×C₁₁₃	semidirect
303. #546	C₂×C₁₁₃	semidirect
304. #542	C₂×C₁₁₃	semidirect
305. #539	C₂×C₁₁₃	semidirect
306. #539	C₂×C₁₁₃	semidirect
307. #538	C₂×C₁₁₃	semidirect
308. #538	C₂×C₁₁₃	semidirect
309. #538	C₂×C₁₁₃	semidirect
310. #537	C₂×C₁₁₃	semidirect
311. #534	C₂×C₁₁₃	semidirect
312. #532	C₂×C₁₁₃	semidirect
313. #529	C₂×C₁₁₃	semidirect
314. C₂×#126	C₂×C₁₁₃	semidirect
315. C₂×#41	C₂²×C₁₁₃	semidirect
316. C₂×#41	C₂²×C₁₁₃	semidirect
318. C₄⋊Q₈	C₂²×C₁₁₃	semidirect
319. C₄⋊Q₈	C₂²×C₁₁₃	semidirect
320. #127	C₂²×C₁₁₃	semidirect
321. #126	C₂²×C₁₁₃	semidirect
322. #126	C₂²×C₁₁₃	semidirect
323. #126	C₂²×C₁₁₃	semidirect
324. #126	C₂²×C₁₁₃	semidirect
325. #126	C₂²×C₁₁₃	semidirect
326. #126	C₂²×C₁₁₃	semidirect
327. #126	C₂²×C₁₁₃	semidirect
328. #126	C₂²×C₁₁₃	semidirect
329. #126	C₂²×C₁₁₃	semidirect
330. #125	C₂²×C₁₁₃	semidirect
331. #125	C₂²×C₁₁₃	semidirect
332. #125	C₂²×C₁₁₃	semidirect
335. #124	C₂²×C₁₁₃	semidirect
336. #124	C₂²×C₁₁₃	semidirect
337. #124	C₂²×C₁₁₃	semidirect
342. #123	C₂²×C₁₁₃	semidirect
343. #123	C₂²×C₁₁₃	semidirect
344. #123	C₂²×C₁₁₃	semidirect
345. #123	C₂²×C₁₁₃	semidirect
346. #123	C₂²×C₁₁₃	semidirect
347. #123	C₂²×C₁₁₃	semidirect
348. #123	C₂²×C₁₁₃	semidirect
349. #123	C₂²×C₁₁₃	semidirect
350. C₂²⋊Q₈	C₂²×C₁₁₃	semidirect
351. C₂²⋊Q₈	C₂²×C₁₁₃	semidirect
352. C₂²⋊Q₈	C₂²×C₁₁₃	semidirect
353. C₂²⋊Q₈	C₂²×C₁₁₃	semidirect
354. C₂²⋊Q₈	C₂²×C₁₁₃	semidirect
355. C₂²⋊Q₈	C₂²×C₁₁₃	semidirect
356. C₂²⋊Q₈	C₂²×C₁₁₃	semidirect
357. C₂²⋊Q₈	C₂²×C₁₁₃	semidirect
365. #121	C₂²×C₁₁₃	semidirect
366. #121	C₂²×C₁₁₃	semidirect
367. #121	C₂²×C₁₁₃	semidirect
368. #121	C₂²×C₁₁₃	semidirect
369. #121	C₂²×C₁₁₃	semidirect
370. #121	C₂²×C₁₁₃	semidirect
371. #121	C₂²×C₁₁₃	semidirect
372. #121	C₂²×C₁₁₃	semidirect
376. #120	C₂²×C₁₁₃	semidirect
377. #120	C₂²×C₁₁₃	semidirect
378. C₄×Q₈	C₂²×C₁₁₃	semidirect
379. C₄×D₄	C₂²×C₁₁₃	semidirect
380. C₄×D₄	C₂²×C₁₁₃	semidirect
381. C₄×D₄	C₂²×C₁₁₃	semidirect
382. C₄×D₄	C₂²×C₁₁₃	semidirect
383. C₄×D₄	C₂²×C₁₁₃	semidirect
384. C₄×D₄	C₂²×C₁₁₃	semidirect
385. C₄×D₄	C₂²×C₁₁₃	semidirect
386. C₄×D₄	C₂²×C₁₁₃	semidirect
387. C₄×D₄	C₂²×C₁₁₃	semidirect
388. C₄×D₄	C₂²×C₁₁₃	semidirect
389. C₄×D₄	C₂²×C₁₁₃	semidirect
390. #117	C₂²×C₁₁₃	semidirect
391. #117	C₂²×C₁₁₃	semidirect
392. C₂×C₄⋊C₄	C₂²×C₁₁₃	semidirect
393. C₂×C₄⋊C₄	C₂²×C₁₁₃	semidirect
394. C₂×C₄⋊C₄	C₂²×C₁₁₃	semidirect
395. C₂×C₄⋊C₄	C₂²×C₁₁₃	semidirect
399. C₂×C₂²⋊C₄	C₂²×C₁₁₃	semidirect
400. C₂×C₂²⋊C₄	C₂²×C₁₁₃	semidirect
401. C₂×C₄²	C₂²×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#563×C₁₁₃	2
#560×C₁₁₃	2
#553×C₁₁₃	2
#551×C₁₁₃	2
#547×C₁₁₃	2
#546×C₁₁₃	2
#542×C₁₁₃	2
#539×C₁₁₃	2
#538×C₁₁₃	2
#537×C₁₁₃	2
#534×C₁₁₃	2
#532×C₁₁₃	2
#529×C₁₁₃	2
C₂×#126×C₁₁₃	2
#3560	113

Subgroups — C113×#3560 #28388356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#3560 #28388356