Subgroups — C₁₁₃×#17577 #43285597

Order 28928.

1762 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#407×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#1519	C₂	1	4	yes	maximal, complemented
5	C₁₁₃×#1510	C₂	1	4	yes	maximal, complemented
6	C₁₁₃×#1507	C₂	1	4	yes	maximal, complemented
7	C₂³×D₄×C₁₁₃	—	2	1	no	—
8	C₂³×D₄×C₁₁₃	C₄	1	1	yes	characteristic, complemented
9	C₂⁴×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₁₃	—	2	1	no	—
11	C₂×#121×C₁₁₃	—	2	1	no	—
12	C₂×#121×C₁₁₃	—	2	1	no	—
13	C₂×#121×C₁₁₃	—	2	1	no	—
14	C₂×#121×C₁₁₃	—	2	1	no	—
15	C₂×#121×C₁₁₃	—	2	1	no	—
16	C₂×#121×C₁₁₃	—	2	1	no	—
17	C₂×#121×C₁₁₃	C₄	1	2	yes	complemented
18	C₂×#121×C₁₁₃	C₄	1	2	yes	complemented
19	C₂×#121×C₁₁₃	C₄	1	2	yes	complemented
20	C₂×#121×C₁₁₃	C₂²	1	2	yes	—
21	C₂×#121×C₁₁₃	C₂²	1	2	yes	—
22	C₂×#121×C₁₁₃	C₂²	1	2	yes	—
23	C₂×#117×C₁₁₃	—	2	1	no	—
24	C₂²×C₄⋊C₄×C₁₁₃	C₄	1	1	yes	characteristic, complemented
25	C₂²×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
26	#407×C₁₁₃	—	2	1	no	—
27	#407×C₁₁₃	—	2	1	no	—
28	#407×C₁₁₃	C₂²	1	2	yes	complemented
29	#407×C₁₁₃	C₂²	1	2	yes	complemented
30	C₂×C₂²⋊C₈×C₁₁₃	—	2	1	no	—
31	C₂×C₂²⋊C₈×C₁₁₃	C₂²	1	2	yes	complemented
32	#381×C₁₁₃	C₂²	1	2	yes	complemented
33	#380×C₁₁₃	—	2	1	no	—
34	#380×C₁₁₃	C₂²	1	2	yes	complemented
35	#379×C₁₁₃	—	2	1	no	—
36	C₄×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
37	C₄×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	complemented
38	#327×C₁₁₃	C₂²	1	16	yes	complemented
39	C₂⁵×C₁₁₃	—	2	1	no	—
40	C₂⁵×C₁₁₃	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₁₁₃	—	2	2	no	—
42	C₂²×D₄×C₁₁₃	—	2	2	no	—
43	C₂²×D₄×C₁₁₃	—	2	2	no	—
44	C₂²×D₄×C₁₁₃	—	2	2	no	—
45	C₂²×D₄×C₁₁₃	—	2	2	no	—
46	C₂²×D₄×C₁₁₃	—	2	2	no	—
47	C₂²×D₄×C₁₁₃	—	2	1	no	—
48	C₂²×D₄×C₁₁₃	—	2	1	no	—
49	C₂²×D₄×C₁₁₃	—	2	1	no	—
50	C₂²×D₄×C₁₁₃	—	4	4	no	—
51	C₂²×D₄×C₁₁₃	—	4	8	no	—
52	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
53	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
54	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
55	C₂³×C₄×C₁₁₃	—	2	1	no	—
56	C₂³×C₄×C₁₁₃	—	4	4	no	—
57	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
67	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
68	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
71	C₂×M₁₆×C₁₁₃	—	2	2	no	—
72	C₂×M₁₆×C₁₁₃	—	2	2	no	—
73	C₂×M₁₆×C₁₁₃	—	4	4	no	—
74	C₂²×C₈×C₁₁₃	—	2	2	no	—
75	#121×C₁₁₃	—	2	2	no	—
76	#121×C₁₁₃	—	2	2	no	—
77	#121×C₁₁₃	—	2	2	no	—
78	#121×C₁₁₃	—	2	2	no	—
79	#121×C₁₁₃	—	2	2	no	—
80	#121×C₁₁₃	—	2	2	no	—
81	#121×C₁₁₃	—	2	2	no	—
82	#121×C₁₁₃	—	2	2	no	—
83	#121×C₁₁₃	—	2	2	no	—
84	#121×C₁₁₃	—	2	2	no	—
85	#121×C₁₁₃	—	2	2	no	—
86	#121×C₁₁₃	—	2	2	no	—
87	#121×C₁₁₃	C₂×C₄	1	4	yes	—
88	#121×C₁₁₃	C₂×C₄	1	4	yes	—
89	#121×C₁₁₃	C₂×C₄	1	4	yes	—
90	#121×C₁₁₃	C₂³	1	4	yes	—
91	#117×C₁₁₃	—	4	4	no	—
92	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
95	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
96	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
97	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
98	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
99	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
100	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
103	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
104	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
105	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
106	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
107	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
108	C₂×C₄²×C₁₁₃	—	2	2	no	—
109	C₂²⋊C₈×C₁₁₃	—	2	2	no	—
110	C₂²⋊C₈×C₁₁₃	—	2	2	no	—
111	C₂²⋊C₈×C₁₁₃	—	2	2	no	—
112	C₂²⋊C₈×C₁₁₃	C₂³	1	4	yes	complemented
113	#95×C₁₁₃	—	2	2	no	—
114	#95×C₁₁₃	C₂³	1	4	yes	complemented
115	C₂⁴×C₁₁₃	—	2	4	no	—
116	C₂⁴×C₁₁₃	—	2	2	no	—
117	C₂⁴×C₁₁₃	—	2	2	no	—
118	C₂⁴×C₁₁₃	—	2	2	no	—
119	C₂⁴×C₁₁₃	—	4	2	no	—
120	C₂⁴×C₁₁₃	—	4	2	no	—
121	C₂⁴×C₁₁₃	—	4	4	no	—
122	C₂⁴×C₁₁₃	—	4	4	no	—
123	C₂⁴×C₁₁₃	—	4	4	no	—
124	C₂⁴×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₂⁴×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
126	C₂⁴×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
127	C₂⁴×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
128	C₂⁴×C₁₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂⁴×C₁₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂⁴×C₁₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂×D₄×C₁₁₃	—	2	4	no	—
132	C₂×D₄×C₁₁₃	—	2	4	no	—
133	C₂×D₄×C₁₁₃	—	2	4	no	—
134	C₂×D₄×C₁₁₃	—	2	4	no	—
135	C₂×D₄×C₁₁₃	—	2	2	no	—
136	C₂×D₄×C₁₁₃	—	2	2	no	—
137	C₂×D₄×C₁₁₃	—	2	2	no	—
138	C₂×D₄×C₁₁₃	—	4	4	no	—
139	C₂×D₄×C₁₁₃	—	4	4	no	—
140	C₂×D₄×C₁₁₃	—	4	4	no	—
141	C₂×D₄×C₁₁₃	—	4	4	no	—
142	C₂×D₄×C₁₁₃	—	4	4	no	—
143	C₂×D₄×C₁₁₃	—	4	8	no	—
144	C₂×D₄×C₁₁₃	—	4	8	no	—
145	C₂×D₄×C₁₁₃	—	4	8	no	—
146	C₂×D₄×C₁₁₃	—	4	8	no	—
147	C₂×D₄×C₁₁₃	—	4	8	no	—
148	C₂×D₄×C₁₁₃	—	4	8	no	—
149	C₂×D₄×C₁₁₃	—	4	4	no	—
150	C₂×D₄×C₁₁₃	C₂²×C₄	1	4	yes	—
151	C₂²×C₄×C₁₁₃	—	2	4	no	—
152	C₂²×C₄×C₁₁₃	—	2	4	no	—
153	C₂²×C₄×C₁₁₃	—	2	4	no	—
154	C₂²×C₄×C₁₁₃	—	2	2	no	—
155	C₂²×C₄×C₁₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₁₃	—	2	4	no	—
158	C₂²×C₄×C₁₁₃	—	4	2	no	—
159	C₂²×C₄×C₁₁₃	—	4	2	no	—
160	C₂²×C₄×C₁₁₃	—	4	2	no	—
161	C₂²×C₄×C₁₁₃	—	4	2	no	—
162	C₂²×C₄×C₁₁₃	—	4	2	no	—
163	C₂²×C₄×C₁₁₃	—	4	2	no	—
164	C₂²×C₄×C₁₁₃	—	4	2	no	—
165	C₂²×C₄×C₁₁₃	—	4	2	no	—
166	C₂²×C₄×C₁₁₃	—	4	2	no	—
167	C₂²×C₄×C₁₁₃	—	4	2	no	—
168	C₂²×C₄×C₁₁₃	—	4	2	no	—
169	C₂²×C₄×C₁₁₃	—	4	4	no	—
170	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
180	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
198	M₁₆×C₁₁₃	—	4	4	no	—
199	M₁₆×C₁₁₃	—	4	4	no	—
200	C₂×C₈×C₁₁₃	—	2	4	no	—
201	C₂×C₈×C₁₁₃	—	4	4	no	—
202	C₄⋊C₄×C₁₁₃	—	2	2	no	—
203	C₄⋊C₄×C₁₁₃	—	2	2	no	—
204	C₄⋊C₄×C₁₁₃	—	2	2	no	—
205	C₄⋊C₄×C₁₁₃	—	4	4	no	—
206	C₄⋊C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
207	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
208	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
209	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
210	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
211	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
212	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
213	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
214	C₄²×C₁₁₃	—	4	4	no	—
215	C₂³×C₁₁₃	—	2	2	no	—
216	C₂³×C₁₁₃	—	2	2	no	—
217	C₂³×C₁₁₃	—	2	2	no	—
218	C₂³×C₁₁₃	—	2	2	no	—
219	C₂³×C₁₁₃	—	2	2	no	—
220	C₂³×C₁₁₃	—	2	2	no	—
221	C₂³×C₁₁₃	—	2	2	no	—
222	C₂³×C₁₁₃	—	2	2	no	—
223	C₂³×C₁₁₃	—	2	2	no	—
224	C₂³×C₁₁₃	—	2	2	no	—
225	C₂³×C₁₁₃	—	2	2	no	—
226	C₂³×C₁₁₃	—	2	2	no	—
227	C₂³×C₁₁₃	—	2	4	no	—
228	C₂³×C₁₁₃	—	4	1	no	—
229	C₂³×C₁₁₃	—	4	1	no	—
230	C₂³×C₁₁₃	—	4	1	no	—
231	C₂³×C₁₁₃	—	4	1	no	—
232	C₂³×C₁₁₃	—	4	1	no	—
233	C₂³×C₁₁₃	—	4	1	no	—
234	C₂³×C₁₁₃	—	4	1	no	—
235	C₂³×C₁₁₃	—	4	1	no	—
236	C₂³×C₁₁₃	—	4	16	no	—
237	C₂³×C₁₁₃	—	4	4	no	—
238	C₂³×C₁₁₃	—	4	4	no	—
239	C₂³×C₁₁₃	—	4	4	no	—
240	C₂³×C₁₁₃	—	4	4	no	—
241	C₂³×C₁₁₃	—	4	4	no	—
242	C₂³×C₁₁₃	—	4	4	no	—
243	C₂³×C₁₁₃	—	4	4	no	—
244	C₂³×C₁₁₃	—	4	4	no	—
245	C₂³×C₁₁₃	—	4	4	no	—
246	C₂³×C₁₁₃	—	8	16	no	—
247	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂³×C₁₁₃	AGL(1,ℤ/8)	1	4	yes	—
254	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
255	D₄×C₁₁₃	—	4	4	no	—
256	D₄×C₁₁₃	—	4	4	no	—
257	D₄×C₁₁₃	—	4	8	no	—
258	D₄×C₁₁₃	—	4	8	no	—
259	D₄×C₁₁₃	—	4	8	no	—
260	D₄×C₁₁₃	—	4	8	no	—
261	D₄×C₁₁₃	—	4	4	no	—
262	D₄×C₁₁₃	—	4	4	no	—
263	C₂×C₄×C₁₁₃	—	2	2	no	—
264	C₂×C₄×C₁₁₃	—	2	2	no	—
265	C₂×C₄×C₁₁₃	—	2	2	no	—
266	C₂×C₄×C₁₁₃	—	2	2	no	—
267	C₂×C₄×C₁₁₃	—	2	2	no	—
268	C₂×C₄×C₁₁₃	—	2	2	no	—
269	C₂×C₄×C₁₁₃	—	2	2	no	—
270	C₂×C₄×C₁₁₃	—	2	2	no	—
271	C₂×C₄×C₁₁₃	—	2	2	no	—
272	C₂×C₄×C₁₁₃	—	2	2	no	—
273	C₂×C₄×C₁₁₃	—	2	2	no	—
274	C₂×C₄×C₁₁₃	—	2	2	no	—
275	C₂×C₄×C₁₁₃	—	2	2	no	—
276	C₂×C₄×C₁₁₃	—	2	2	no	—
277	C₂×C₄×C₁₁₃	—	2	2	no	—
278	C₂×C₄×C₁₁₃	—	2	4	no	—
279	C₂×C₄×C₁₁₃	—	4	1	no	—
280	C₂×C₄×C₁₁₃	—	4	1	no	—
281	C₂×C₄×C₁₁₃	—	4	1	no	—
282	C₂×C₄×C₁₁₃	—	4	1	no	—
283	C₂×C₄×C₁₁₃	—	4	1	no	—
284	C₂×C₄×C₁₁₃	—	4	1	no	—
285	C₂×C₄×C₁₁₃	—	4	1	no	—
286	C₂×C₄×C₁₁₃	—	4	1	no	—
287	C₂×C₄×C₁₁₃	—	4	1	no	—
288	C₂×C₄×C₁₁₃	—	4	1	no	—
289	C₂×C₄×C₁₁₃	—	4	1	no	—
290	C₂×C₄×C₁₁₃	—	4	1	no	—
291	C₂×C₄×C₁₁₃	—	4	4	no	—
292	C₂×C₄×C₁₁₃	—	4	4	no	—
293	C₂×C₄×C₁₁₃	—	4	4	no	—
294	C₂×C₄×C₁₁₃	—	4	4	no	—
295	C₂×C₄×C₁₁₃	—	4	4	no	—
296	C₂×C₄×C₁₁₃	—	4	4	no	—
297	C₂×C₄×C₁₁₃	#99	1	4	yes	—
298	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
299	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
300	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
301	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
302	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
303	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
304	C₂×C₄×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
305	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
306	C₈×C₁₁₃	—	4	4	no	—
307	C₂²×C₁₁₃	—	2	8	no	—
308	C₂²×C₁₁₃	—	2	1	no	—
309	C₂²×C₁₁₃	—	2	1	no	—
310	C₂²×C₁₁₃	—	2	1	no	—
311	C₂²×C₁₁₃	—	2	1	no	—
312	C₂²×C₁₁₃	—	2	1	no	—
313	C₂²×C₁₁₃	—	2	1	no	—
314	C₂²×C₁₁₃	—	2	1	no	—
315	C₂²×C₁₁₃	—	2	1	no	—
316	C₂²×C₁₁₃	—	2	1	no	—
317	C₂²×C₁₁₃	—	2	1	no	—
318	C₂²×C₁₁₃	—	2	1	no	—
319	C₂²×C₁₁₃	—	2	1	no	—
320	C₂²×C₁₁₃	—	2	1	no	—
321	C₂²×C₁₁₃	—	2	1	no	—
322	C₂²×C₁₁₃	—	2	1	no	—
323	C₂²×C₁₁₃	—	2	1	no	—
324	C₂²×C₁₁₃	—	4	4	no	—
325	C₂²×C₁₁₃	—	4	4	no	—
326	C₂²×C₁₁₃	—	4	4	no	—
327	C₂²×C₁₁₃	—	4	4	no	—
328	C₂²×C₁₁₃	—	4	4	no	—
329	C₂²×C₁₁₃	—	4	4	no	—
330	C₂²×C₁₁₃	—	4	4	no	—
331	C₂²×C₁₁₃	—	4	4	no	—
332	C₂²×C₁₁₃	—	4	4	no	—
333	C₂²×C₁₁₃	—	8	8	no	—
334	C₂²×C₁₁₃	—	8	8	no	—
335	C₂²×C₁₁₃	—	8	8	no	—
336	C₂²×C₁₁₃	C₂×#99	1	2	yes	—
337	C₂²×C₁₁₃	#418	1	2	yes	—
338	C₂²×C₁₁₃	#418	1	2	yes	—
339	C₂²×C₁₁₃	#421	1	2	yes	—
340	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
341	C₂²×C₁₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
342	C₄×C₁₁₃	—	2	1	no	—
343	C₄×C₁₁₃	—	2	1	no	—
344	C₄×C₁₁₃	—	2	1	no	—
345	C₄×C₁₁₃	—	2	1	no	—
346	C₄×C₁₁₃	—	2	1	no	—
347	C₄×C₁₁₃	—	2	1	no	—
348	C₄×C₁₁₃	—	4	4	no	—
349	C₄×C₁₁₃	—	8	4	no	—
350	C₄×C₁₁₃	C₂×#99	1	2	yes	—
351	C₄×C₁₁₃	C₂×#99	1	2	yes	—
352	#17577	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
353	C₂×C₁₁₃	—	2	2	no	—
354	C₂×C₁₁₃	—	2	2	no	—
355	C₂×C₁₁₃	—	2	2	no	—
356	C₂×C₁₁₃	—	2	2	no	—
357	C₂×C₁₁₃	—	2	2	no	—
358	C₂×C₁₁₃	—	4	1	no	—
359	C₂×C₁₁₃	—	4	1	no	—
360	C₂×C₁₁₃	—	8	4	no	—
361	C₂×C₁₁₃	C₂²×#99	1	1	yes	characteristic
362	C₂×C₁₁₃	C₂×#418	1	1	yes	characteristic
363	C₂×C₁₁₃	C₂×#421	1	1	yes	characteristic
364	C₂²×#121	C₂×C₁₁₃	1	1	yes	characteristic
365	C₂×#407	C₂×C₁₁₃	1	1	yes	characteristic, complemented
366	#2280	C₂×C₁₁₃	1	1	yes	characteristic, complemented
367	#1519	C₂×C₁₁₃	1	4	yes	complemented
368	#1510	C₂×C₁₁₃	1	4	yes	complemented
369	#1507	C₂×C₁₁₃	1	4	yes	complemented
370	C₁₁₃	#17577	1	1	yes	characteristic, direct product factor, Sylow
371	C₂³×D₄	—	2	1	no	—
372	C₂³×D₄	C₄×C₁₁₃	1	1	yes	characteristic, complemented
373	C₂⁴×C₄	C₂²×C₁₁₃	1	1	yes	characteristic
374	C₂²×M₁₆	—	2	1	no	—
375	C₂×#121	—	2	1	no	—
376	C₂×#121	—	2	1	no	—
377	C₂×#121	—	2	1	no	—
378	C₂×#121	—	2	1	no	—
379	C₂×#121	—	2	1	no	—
380	C₂×#121	—	2	1	no	—
381	C₂×#121	C₄×C₁₁₃	1	2	yes	complemented
382	C₂×#121	C₄×C₁₁₃	1	2	yes	complemented
383	C₂×#121	C₄×C₁₁₃	1	2	yes	complemented
384	C₂×#121	C₂²×C₁₁₃	1	2	yes	—
385	C₂×#121	C₂²×C₁₁₃	1	2	yes	—
386	C₂×#121	C₂²×C₁₁₃	1	2	yes	—
387	C₂×#117	—	2	1	no	—
388	C₂²×C₄⋊C₄	C₄×C₁₁₃	1	1	yes	characteristic, complemented
389	C₂²×C₂²⋊C₄	—	2	1	no	—
390	#407	—	2	1	no	—
391	#407	—	2	1	no	—
392	#407	C₂²×C₁₁₃	1	2	yes	complemented
393	#407	C₂²×C₁₁₃	1	2	yes	complemented
394	C₂×C₂²⋊C₈	—	2	1	no	—
395	C₂×C₂²⋊C₈	C₂²×C₁₁₃	1	2	yes	complemented
396	#381	C₂²×C₁₁₃	1	2	yes	complemented
397	#380	—	2	1	no	—
398	#380	C₂²×C₁₁₃	1	2	yes	complemented
399	#379	—	2	1	no	—
400	C₄×C₂²⋊C₄	—	2	1	no	—
401	C₄×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	complemented
402	#327	C₂²×C₁₁₃	1	16	yes	complemented
403	C₂⁵	—	2	1	no	—
404	C₂⁵	D₄×C₁₁₃	1	1	yes	characteristic
405	C₂²×D₄	—	2	2	no	—
406	C₂²×D₄	—	2	2	no	—
407	C₂²×D₄	—	2	2	no	—
408	C₂²×D₄	—	2	2	no	—
409	C₂²×D₄	—	2	2	no	—
410	C₂²×D₄	—	2	2	no	—
411	C₂²×D₄	—	2	1	no	—
412	C₂²×D₄	—	2	1	no	—
413	C₂²×D₄	—	2	1	no	—
414	C₂²×D₄	—	4	4	no	—
415	C₂²×D₄	—	4	8	no	—
416	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
417	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
418	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
419	C₂³×C₄	—	2	1	no	—
420	C₂³×C₄	—	4	4	no	—
421	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
422	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
423	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
424	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
425	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
426	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
427	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
428	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
429	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
430	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
431	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
432	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
433	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
435	C₂×M₁₆	—	2	2	no	—
436	C₂×M₁₆	—	2	2	no	—
437	C₂×M₁₆	—	4	4	no	—
438	C₂²×C₈	—	2	2	no	—
439	#121	—	2	2	no	—
440	#121	—	2	2	no	—
441	#121	—	2	2	no	—
442	#121	—	2	2	no	—
443	#121	—	2	2	no	—
444	#121	—	2	2	no	—
445	#121	—	2	2	no	—
446	#121	—	2	2	no	—
447	#121	—	2	2	no	—
448	#121	—	2	2	no	—
449	#121	—	2	2	no	—
450	#121	—	2	2	no	—
451	#121	C₂×C₄×C₁₁₃	1	4	yes	—
452	#121	C₂×C₄×C₁₁₃	1	4	yes	—
453	#121	C₂×C₄×C₁₁₃	1	4	yes	—
454	#121	C₂³×C₁₁₃	1	4	yes	—
455	#117	—	4	4	no	—
456	C₂×C₄⋊C₄	—	2	1	no	—
457	C₂×C₄⋊C₄	—	2	1	no	—
458	C₂×C₄⋊C₄	—	2	1	no	—
459	C₂×C₄⋊C₄	—	2	2	no	—
460	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
461	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
462	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
463	C₂×C₂²⋊C₄	—	2	2	no	—
464	C₂×C₂²⋊C₄	—	2	2	no	—
465	C₂×C₂²⋊C₄	—	2	2	no	—
466	C₂×C₂²⋊C₄	—	2	2	no	—
467	C₂×C₂²⋊C₄	—	2	2	no	—
468	C₂×C₂²⋊C₄	—	2	2	no	—
469	C₂×C₂²⋊C₄	—	2	2	no	—
470	C₂×C₂²⋊C₄	—	2	2	no	—
471	C₂×C₂²⋊C₄	—	2	2	no	—
472	C₂×C₄²	—	2	2	no	—
473	C₂²⋊C₈	—	2	2	no	—
474	C₂²⋊C₈	—	2	2	no	—
475	C₂²⋊C₈	—	2	2	no	—
476	C₂²⋊C₈	C₂³×C₁₁₃	1	4	yes	complemented
477	#95	—	2	2	no	—
478	#95	C₂³×C₁₁₃	1	4	yes	complemented
479	C₂⁴	—	2	4	no	—
480	C₂⁴	—	2	2	no	—
481	C₂⁴	—	2	2	no	—
482	C₂⁴	—	2	2	no	—
483	C₂⁴	—	4	2	no	—
484	C₂⁴	—	4	2	no	—
485	C₂⁴	—	4	4	no	—
486	C₂⁴	—	4	4	no	—
487	C₂⁴	—	4	4	no	—
488	C₂⁴	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
489	C₂⁴	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
490	C₂⁴	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
491	C₂⁴	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
492	C₂⁴	C₂×D₄×C₁₁₃	1	1	yes	characteristic
493	C₂⁴	C₂×D₄×C₁₁₃	1	1	yes	characteristic
494	C₂⁴	C₂×D₄×C₁₁₃	1	1	yes	characteristic
495	C₂×D₄	—	2	4	no	—
496	C₂×D₄	—	2	4	no	—
497	C₂×D₄	—	2	4	no	—
498	C₂×D₄	—	2	4	no	—
499	C₂×D₄	—	2	2	no	—
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	4	4	no	—
503	C₂×D₄	—	4	4	no	—
504	C₂×D₄	—	4	4	no	—
505	C₂×D₄	—	4	4	no	—
506	C₂×D₄	—	4	4	no	—
507	C₂×D₄	—	4	8	no	—
508	C₂×D₄	—	4	8	no	—
509	C₂×D₄	—	4	8	no	—
510	C₂×D₄	—	4	8	no	—
511	C₂×D₄	—	4	8	no	—
512	C₂×D₄	—	4	8	no	—
513	C₂×D₄	—	4	4	no	—
514	C₂×D₄	C₂²×C₄×C₁₁₃	1	4	yes	—
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	2	4	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	4	2	no	—
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	—	4	2	no	—
525	C₂²×C₄	—	4	2	no	—
526	C₂²×C₄	—	4	2	no	—
527	C₂²×C₄	—	4	2	no	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	—	4	2	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	4	2	no	—
532	C₂²×C₄	—	4	2	no	—
533	C₂²×C₄	—	4	4	no	—
534	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
535	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
536	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
537	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
538	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
539	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
540	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
541	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
542	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
543	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
544	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
545	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
546	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
547	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
548	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
549	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
550	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
551	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
552	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
553	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
554	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
555	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
556	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
557	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
558	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
559	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
560	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
561	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
562	M₁₆	—	4	4	no	—
563	M₁₆	—	4	4	no	—
564	C₂×C₈	—	2	4	no	—
565	C₂×C₈	—	4	4	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	4	4	no	—
570	C₄⋊C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
571	C₂²⋊C₄	—	2	4	no	—
572	C₂²⋊C₄	—	2	4	no	—
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	4	no	—
575	C₂²⋊C₄	—	4	4	no	—
576	C₂²⋊C₄	—	4	4	no	—
577	C₂²⋊C₄	—	4	4	no	—
578	C₄²	—	4	4	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	2	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	2	2	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	4	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	1	no	—
597	C₂³	—	4	1	no	—
598	C₂³	—	4	1	no	—
599	C₂³	—	4	1	no	—
600	C₂³	—	4	16	no	—
601	C₂³	—	4	4	no	—
602	C₂³	—	4	4	no	—
603	C₂³	—	4	4	no	—
604	C₂³	—	4	4	no	—
605	C₂³	—	4	4	no	—
606	C₂³	—	4	4	no	—
607	C₂³	—	4	4	no	—
608	C₂³	—	4	4	no	—
609	C₂³	—	4	4	no	—
610	C₂³	—	8	16	no	—
611	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
612	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
613	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
614	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
615	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
616	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
617	C₂³	AGL(1,ℤ/8)×C₁₁₃	1	4	yes	—
618	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
619	D₄	—	4	4	no	—
620	D₄	—	4	4	no	—
621	D₄	—	4	8	no	—
622	D₄	—	4	8	no	—
623	D₄	—	4	8	no	—
624	D₄	—	4	8	no	—
625	D₄	—	4	4	no	—
626	D₄	—	4	4	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	4	no	—
656	C₂×C₄	—	4	4	no	—
657	C₂×C₄	—	4	4	no	—
658	C₂×C₄	—	4	4	no	—
659	C₂×C₄	—	4	4	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	#99×C₁₁₃	1	4	yes	—
662	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
663	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
664	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
665	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
666	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
667	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
668	C₂×C₄	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
669	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
670	C₈	—	4	4	no	—
671	C₂²	—	2	8	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	2	1	no	—
679	C₂²	—	2	1	no	—
680	C₂²	—	2	1	no	—
681	C₂²	—	2	1	no	—
682	C₂²	—	2	1	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	2	1	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	1	no	—
687	C₂²	—	2	1	no	—
688	C₂²	—	4	4	no	—
689	C₂²	—	4	4	no	—
690	C₂²	—	4	4	no	—
691	C₂²	—	4	4	no	—
692	C₂²	—	4	4	no	—
693	C₂²	—	4	4	no	—
694	C₂²	—	4	4	no	—
695	C₂²	—	4	4	no	—
696	C₂²	—	4	4	no	—
697	C₂²	—	8	8	no	—
698	C₂²	—	8	8	no	—
699	C₂²	—	8	8	no	—
700	C₂²	C₂×#99×C₁₁₃	1	2	yes	—
701	C₂²	#418×C₁₁₃	1	2	yes	—
702	C₂²	#418×C₁₁₃	1	2	yes	—
703	C₂²	#421×C₁₁₃	1	2	yes	—
704	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
705	C₂²	C₂×AGL(1,ℤ/8)×C₁₁₃	1	2	yes	—
706	C₄	—	2	1	no	—
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	2	1	no	—
710	C₄	—	2	1	no	—
711	C₄	—	2	1	no	—
712	C₄	—	4	4	no	—
713	C₄	—	8	4	no	—
714	C₄	C₂×#99×C₁₁₃	1	2	yes	—
715	C₄	C₂×#99×C₁₁₃	1	2	yes	—
716	C₂	—	2	2	no	—
717	C₂	—	2	2	no	—
718	C₂	—	2	2	no	—
719	C₂	—	2	2	no	—
720	C₂	—	2	2	no	—
721	C₂	—	4	1	no	—
722	C₂	—	4	1	no	—
723	C₂	—	8	4	no	—
724	C₂	C₂²×#99×C₁₁₃	1	1	yes	characteristic
725	C₂	C₂×#418×C₁₁₃	1	1	yes	characteristic
726	C₂	C₂×#421×C₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
prime radical	C₂²×#121×C₁₁₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁₃ ◁ C₂⁴×C₄×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#407×C₁₁₃	C₂	semidirect
3. C₁₁₃×#2280	C₂	semidirect
4. C₁₁₃×#1519	C₂	semidirect
5. C₁₁₃×#1510	C₂	semidirect
6. C₁₁₃×#1507	C₂	semidirect
8. C₂³×D₄×C₁₁₃	C₄	semidirect
17. C₂×#121×C₁₁₃	C₄	semidirect
18. C₂×#121×C₁₁₃	C₄	semidirect
19. C₂×#121×C₁₁₃	C₄	semidirect
24. C₂²×C₄⋊C₄×C₁₁₃	C₄	semidirect
28. #407×C₁₁₃	C₂²	semidirect
29. #407×C₁₁₃	C₂²	semidirect
31. C₂×C₂²⋊C₈×C₁₁₃	C₂²	semidirect
32. #381×C₁₁₃	C₂²	semidirect
34. #380×C₁₁₃	C₂²	semidirect
37. C₄×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
38. #327×C₁₁₃	C₂²	semidirect
112. C₂²⋊C₈×C₁₁₃	C₂³	semidirect
114. #95×C₁₁₃	C₂³	semidirect
352. #17577	C₁₁₃	direct (N × H)
365. C₂×#407	C₂×C₁₁₃	semidirect
366. #2280	C₂×C₁₁₃	semidirect
367. #1519	C₂×C₁₁₃	semidirect
368. #1510	C₂×C₁₁₃	semidirect
369. #1507	C₂×C₁₁₃	semidirect
370. C₁₁₃	#17577	direct (N × H)
372. C₂³×D₄	C₄×C₁₁₃	semidirect
381. C₂×#121	C₄×C₁₁₃	semidirect
382. C₂×#121	C₄×C₁₁₃	semidirect
383. C₂×#121	C₄×C₁₁₃	semidirect
388. C₂²×C₄⋊C₄	C₄×C₁₁₃	semidirect
392. #407	C₂²×C₁₁₃	semidirect
393. #407	C₂²×C₁₁₃	semidirect
395. C₂×C₂²⋊C₈	C₂²×C₁₁₃	semidirect
396. #381	C₂²×C₁₁₃	semidirect
398. #380	C₂²×C₁₁₃	semidirect
401. C₄×C₂²⋊C₄	C₂²×C₁₁₃	semidirect
402. #327	C₂²×C₁₁₃	semidirect
476. C₂²⋊C₈	C₂³×C₁₁₃	semidirect
478. #95	C₂³×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#121×C₁₁₃	2
C₂×#407×C₁₁₃	2
C₁₁₃×#2280	2
C₁₁₃×#1519	2
C₁₁₃×#1510	2
C₁₁₃×#1507	2
#17577	113

Subgroups — C113×#17577 #43285597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#17577 #43285597