Subgroups — C₁₁₃×#25572 #43293592

Order 28928.

1326 conjugacy classes of subgroups.

The subgroup lattice has 486 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, complemented
2	C₂×#486×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#459×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#2541	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁₃×#1999	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×#1875	C₂	1	4	yes	maximal, complemented
9	C₄×#102×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×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×#127×C₁₁₃	—	2	1	no	—
15	C₂×#127×C₁₁₃	C₂²	1	1	yes	characteristic
16	C₂×#124×C₁₁₃	—	2	2	no	—
17	C₂×#121×C₁₁₃	—	2	1	no	—
18	C₂×#121×C₁₁₃	C₂²	1	2	yes	—
19	C₂×#121×C₁₁₃	C₂²	1	4	yes	—
20	C₂×C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
22	C₂×#117×C₁₁₃	—	2	1	no	—
23	C₂×#117×C₁₁₃	C₂²	1	2	yes	—
24	#486×C₁₁₃	—	2	4	no	—
25	#459×C₁₁₃	—	2	4	no	—
26	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	1	yes	characteristic
27	C₂×#102×C₁₁₃	C₂²	1	4	yes	—
28	C₂×#102×C₁₁₃	C₂²	1	2	yes	—
29	C₂×#102×C₁₁₃	C₂²	1	2	yes	—
30	C₂×C₂²⋊C₈×C₁₁₃	C₂²	1	4	yes	—
31	C₂×C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
32	#392×C₁₁₃	—	2	2	no	—
33	#390×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×D₄×C₁₁₃	—	2	2	no	—
39	C₂²×D₄×C₁₁₃	—	2	4	no	—
40	C₂²×D₄×C₁₁₃	—	2	1	no	—
41	C₂²×D₄×C₁₁₃	—	2	1	no	—
42	C₂²×D₄×C₁₁₃	D₄	1	1	yes	characteristic
43	C₂²×D₄×C₁₁₃	C₂³	1	2	yes	—
44	C₂²×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₁₃	—	2	1	no	—
46	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
47	C₂×D₈×C₁₁₃	—	2	4	no	—
48	C₂×D₈×C₁₁₃	—	4	4	no	—
49	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₁₁₃	—	2	2	no	—
52	C₄⋊Q₈×C₁₁₃	D₄	1	4	yes	complemented
53	#127×C₁₁₃	—	2	2	no	—
54	#127×C₁₁₃	—	2	2	no	—
55	#127×C₁₁₃	—	4	4	no	—
56	#124×C₁₁₃	—	2	16	no	—
57	#121×C₁₁₃	—	2	8	no	—
58	#121×C₁₁₃	—	2	4	no	—
59	#121×C₁₁₃	—	2	4	no	—
60	#121×C₁₁₃	—	2	8	no	—
61	#121×C₁₁₃	—	4	4	no	—
62	C₄×D₄×C₁₁₃	—	2	2	no	—
63	C₄×D₄×C₁₁₃	—	2	2	no	—
64	C₄×D₄×C₁₁₃	—	2	2	no	—
65	C₄×D₄×C₁₁₃	D₄	1	4	yes	complemented
66	#117×C₁₁₃	—	2	8	no	—
67	#117×C₁₁₃	—	2	4	no	—
68	#117×C₁₁₃	—	2	4	no	—
69	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₁₃	D₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
74	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
78	C₂×C₂²⋊C₄×C₁₁₃	D₄	1	2	yes	—
79	C₂×C₄²×C₁₁₃	—	2	2	no	—
80	C₂×C₄²×C₁₁₃	—	2	1	no	—
81	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
82	C₄⋊C₈×C₁₁₃	—	2	2	no	—
83	#102×C₁₁₃	—	2	4	no	—
84	#102×C₁₁₃	—	2	8	no	—
85	#102×C₁₁₃	—	2	4	no	—
86	C₂²⋊C₈×C₁₁₃	—	4	4	no	—
87	C₄×C₈×C₁₁₃	—	2	2	no	—
88	#95×C₁₁₃	—	2	1	no	—
89	C₂⁴×C₁₁₃	—	2	1	no	—
90	C₂⁴×C₁₁₃	—	2	2	no	—
91	C₂⁴×C₁₁₃	C₂×D₄	1	2	yes	—
92	C₂×Q₈×C₁₁₃	—	2	4	no	—
93	C₂×Q₈×C₁₁₃	—	8	2	no	—
94	C₂×D₄×C₁₁₃	—	2	8	no	—
95	C₂×D₄×C₁₁₃	—	2	2	no	—
96	C₂×D₄×C₁₁₃	—	2	2	no	—
97	C₂×D₄×C₁₁₃	—	2	2	no	—
98	C₂×D₄×C₁₁₃	—	2	1	no	—
99	C₂×D₄×C₁₁₃	—	2	2	no	—
100	C₂×D₄×C₁₁₃	—	2	2	no	—
101	C₂×D₄×C₁₁₃	—	2	2	no	—
102	C₂×D₄×C₁₁₃	—	2	4	no	—
103	C₂×D₄×C₁₁₃	—	2	2	no	—
104	C₂×D₄×C₁₁₃	—	2	4	no	—
105	C₂×D₄×C₁₁₃	—	4	8	no	—
106	C₂×D₄×C₁₁₃	—	4	8	no	—
107	C₂×D₄×C₁₁₃	—	4	2	no	—
108	C₂×D₄×C₁₁₃	—	4	2	no	—
109	C₂×D₄×C₁₁₃	—	4	2	no	—
110	C₂×D₄×C₁₁₃	—	4	2	no	—
111	C₂×D₄×C₁₁₃	—	8	2	no	—
112	C₂×D₄×C₁₁₃	—	8	4	no	—
113	C₂×D₄×C₁₁₃	—	8	4	no	—
114	C₂×D₄×C₁₁₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₁₃	—	2	4	no	—
122	C₂²×C₄×C₁₁₃	—	2	4	no	—
123	C₂²×C₄×C₁₁₃	—	4	2	no	—
124	C₂²×C₄×C₁₁₃	—	4	2	no	—
125	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
129	D₈×C₁₁₃	—	4	8	no	—
130	C₂×C₈×C₁₁₃	—	2	2	no	—
131	C₂×C₈×C₁₁₃	—	2	2	no	—
132	C₂×C₈×C₁₁₃	—	2	2	no	—
133	C₂×C₈×C₁₁₃	—	2	2	no	—
134	C₂×C₈×C₁₁₃	—	2	4	no	—
135	C₄⋊C₄×C₁₁₃	—	2	4	no	—
136	C₄⋊C₄×C₁₁₃	—	2	2	no	—
137	C₄⋊C₄×C₁₁₃	—	2	1	no	—
138	C₄⋊C₄×C₁₁₃	—	2	2	no	—
139	C₄⋊C₄×C₁₁₃	—	2	2	no	—
140	C₄⋊C₄×C₁₁₃	C₂×D₄	1	2	yes	—
141	C₄⋊C₄×C₁₁₃	C₂×D₄	1	4	yes	—
142	C₄⋊C₄×C₁₁₃	#41	1	4	yes	—
143	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
144	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
145	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
146	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
147	C₂²⋊C₄×C₁₁₃	—	4	8	no	—
148	C₄²×C₁₁₃	—	2	8	no	—
149	C₄²×C₁₁₃	—	4	2	no	—
150	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
151	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
152	C₂³×C₁₁₃	—	2	2	no	—
153	C₂³×C₁₁₃	—	2	2	no	—
154	C₂³×C₁₁₃	—	2	4	no	—
155	C₂³×C₁₁₃	—	2	2	no	—
156	C₂³×C₁₁₃	—	2	2	no	—
157	C₂³×C₁₁₃	—	2	4	no	—
158	C₂³×C₁₁₃	—	4	2	no	—
159	C₂³×C₁₁₃	—	4	1	no	—
160	C₂³×C₁₁₃	—	4	1	no	—
161	C₂³×C₁₁₃	—	4	2	no	—
162	C₂³×C₁₁₃	—	4	2	no	—
163	C₂³×C₁₁₃	—	4	4	no	—
164	C₂³×C₁₁₃	—	4	2	no	—
165	C₂³×C₁₁₃	—	4	2	no	—
166	C₂³×C₁₁₃	—	4	4	no	—
167	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
168	Q₈×C₁₁₃	—	8	4	no	—
169	D₄×C₁₁₃	—	2	2	no	—
170	D₄×C₁₁₃	—	2	2	no	—
171	D₄×C₁₁₃	—	4	2	no	—
172	D₄×C₁₁₃	—	4	2	no	—
173	D₄×C₁₁₃	—	4	2	no	—
174	D₄×C₁₁₃	—	4	4	no	—
175	D₄×C₁₁₃	—	4	4	no	—
176	D₄×C₁₁₃	—	8	4	no	—
177	D₄×C₁₁₃	—	8	8	no	—
178	D₄×C₁₁₃	—	8	16	no	—
179	D₄×C₁₁₃	—	8	4	no	—
180	C₂×C₄×C₁₁₃	—	2	2	no	—
181	C₂×C₄×C₁₁₃	—	2	2	no	—
182	C₂×C₄×C₁₁₃	—	2	2	no	—
183	C₂×C₄×C₁₁₃	—	2	4	no	—
184	C₂×C₄×C₁₁₃	—	2	4	no	—
185	C₂×C₄×C₁₁₃	—	2	4	no	—
186	C₂×C₄×C₁₁₃	—	4	1	no	—
187	C₂×C₄×C₁₁₃	—	4	2	no	—
188	C₂×C₄×C₁₁₃	—	4	1	no	—
189	C₂×C₄×C₁₁₃	—	4	2	no	—
190	C₂×C₄×C₁₁₃	—	4	4	no	—
191	C₂×C₄×C₁₁₃	—	4	2	no	—
192	C₂×C₄×C₁₁₃	—	4	2	no	—
193	C₂×C₄×C₁₁₃	—	4	4	no	—
194	C₂×C₄×C₁₁₃	—	4	8	no	—
195	C₂×C₄×C₁₁₃	#120	1	2	yes	—
196	C₂×C₄×C₁₁₃	#120	1	2	yes	—
197	C₂×C₄×C₁₁₃	#135	1	2	yes	—
198	C₂×C₄×C₁₁₃	AGL(1,ℤ/8)	1	2	yes	—
199	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₁₃	C₂×#41	1	2	yes	—
202	C₂×C₄×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
203	C₈×C₁₁₃	—	4	2	no	—
204	C₈×C₁₁₃	—	4	2	no	—
205	C₂²×C₁₁₃	—	4	2	no	—
206	C₂²×C₁₁₃	—	4	2	no	—
207	C₂²×C₁₁₃	—	4	2	no	—
208	C₂²×C₁₁₃	—	4	2	no	—
209	C₂²×C₁₁₃	—	4	2	no	—
210	C₂²×C₁₁₃	—	4	2	no	—
211	C₂²×C₁₁₃	—	4	4	no	—
212	C₂²×C₁₁₃	—	4	4	no	—
213	C₂²×C₁₁₃	—	8	2	no	—
214	C₂²×C₁₁₃	—	8	2	no	—
215	C₂²×C₁₁₃	—	8	2	no	—
216	C₂²×C₁₁₃	—	8	2	no	—
217	C₂²×C₁₁₃	—	8	2	no	—
218	C₂²×C₁₁₃	—	8	4	no	—
219	C₂²×C₁₁₃	—	8	4	no	—
220	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
221	C₂²×C₁₁₃	#546	1	2	yes	—
222	C₂²×C₁₁₃	C₂×#135	1	1	yes	characteristic
223	C₂²×C₁₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
224	C₂²×C₁₁₃	#576	1	2	yes	—
225	C₄×C₁₁₃	—	2	2	no	—
226	C₄×C₁₁₃	—	4	2	no	—
227	C₄×C₁₁₃	—	4	2	no	—
228	C₄×C₁₁₃	—	4	4	no	—
229	C₄×C₁₁₃	—	4	4	no	—
230	C₄×C₁₁₃	#449	1	4	yes	—
231	C₄×C₁₁₃	#532	1	1	yes	characteristic
232	C₄×C₁₁₃	#535	1	1	yes	characteristic
233	C₄×C₁₁₃	#550	1	2	yes	—
234	#25572	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂×C₁₁₃	—	8	2	no	—
236	C₂×C₁₁₃	—	8	2	no	—
237	C₂×C₁₁₃	—	16	2	no	—
238	C₂×C₁₁₃	#2431	1	1	yes	characteristic
239	C₂×C₁₁₃	C₂×#449	1	1	yes	characteristic
240	C₂×C₁₁₃	#3008	1	1	yes	characteristic
241	C₂×C₁₁₃	#3305	1	2	yes	—
242	C₂×C₁₁₃	#3325	1	2	yes	—
243	C₂×#555	C₂×C₁₁₃	1	1	yes	characteristic, complemented
244	C₂×#486	C₂×C₁₁₃	1	1	yes	characteristic, complemented
245	C₂×#459	C₂×C₁₁₃	1	1	yes	characteristic, complemented
246	#2541	C₂×C₁₁₃	1	1	yes	characteristic, complemented
247	#1999	C₂×C₁₁₃	1	4	yes	complemented
248	#1987	C₂×C₁₁₃	1	1	yes	characteristic, complemented
249	#1954	C₂×C₁₁₃	1	1	yes	characteristic, complemented
250	#1875	C₂×C₁₁₃	1	4	yes	complemented
251	C₄×#102	C₂×C₁₁₃	1	1	yes	characteristic, complemented
252	C₁₁₃	#25572	1	1	yes	characteristic, direct product factor, Sylow
253	C₂²×D₈	C₂²×C₁₁₃	1	2	yes	—
254	#555	—	2	4	no	—
255	#555	—	2	4	no	—
256	C₂×C₄⋊Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
257	C₂×#127	—	2	1	no	—
258	C₂×#127	C₂²×C₁₁₃	1	1	yes	characteristic
259	C₂×#124	—	2	2	no	—
260	C₂×#121	—	2	1	no	—
261	C₂×#121	C₂²×C₁₁₃	1	2	yes	—
262	C₂×#121	C₂²×C₁₁₃	1	4	yes	—
263	C₂×C₄×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
264	C₂×C₄×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
265	C₂×#117	—	2	1	no	—
266	C₂×#117	C₂²×C₁₁₃	1	2	yes	—
267	#486	—	2	4	no	—
268	#459	—	2	4	no	—
269	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	1	yes	characteristic
270	C₂×#102	C₂²×C₁₁₃	1	4	yes	—
271	C₂×#102	C₂²×C₁₁₃	1	2	yes	—
272	C₂×#102	C₂²×C₁₁₃	1	2	yes	—
273	C₂×C₂²⋊C₈	C₂²×C₁₁₃	1	4	yes	—
274	C₂×C₄×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
275	#392	—	2	2	no	—
276	#390	—	2	1	no	—
277	C₄×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
278	#340	C₂²×C₁₁₃	1	2	yes	—
279	#340	C₂²×C₁₁₃	1	4	yes	—
280	C₂²×Q₈	—	2	1	no	—
281	C₂²×D₄	—	2	2	no	—
282	C₂²×D₄	—	2	4	no	—
283	C₂²×D₄	—	2	1	no	—
284	C₂²×D₄	—	2	1	no	—
285	C₂²×D₄	D₄×C₁₁₃	1	1	yes	characteristic
286	C₂²×D₄	C₂³×C₁₁₃	1	2	yes	—
287	C₂²×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
288	C₂³×C₄	—	2	1	no	—
289	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
290	C₂×D₈	—	2	4	no	—
291	C₂×D₈	—	4	4	no	—
292	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
293	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
294	C₄⋊Q₈	—	2	2	no	—
295	C₄⋊Q₈	D₄×C₁₁₃	1	4	yes	complemented
296	#127	—	2	2	no	—
297	#127	—	2	2	no	—
298	#127	—	4	4	no	—
299	#124	—	2	16	no	—
300	#121	—	2	8	no	—
301	#121	—	2	4	no	—
302	#121	—	2	4	no	—
303	#121	—	2	8	no	—
304	#121	—	4	4	no	—
305	C₄×D₄	—	2	2	no	—
306	C₄×D₄	—	2	2	no	—
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	D₄×C₁₁₃	1	4	yes	complemented
309	#117	—	2	8	no	—
310	#117	—	2	4	no	—
311	#117	—	2	4	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	D₄×C₁₁₃	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₂²⋊C₄	—	2	4	no	—
321	C₂×C₂²⋊C₄	D₄×C₁₁₃	1	2	yes	—
322	C₂×C₄²	—	2	2	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
325	C₄⋊C₈	—	2	2	no	—
326	#102	—	2	4	no	—
327	#102	—	2	8	no	—
328	#102	—	2	4	no	—
329	C₂²⋊C₈	—	4	4	no	—
330	C₄×C₈	—	2	2	no	—
331	#95	—	2	1	no	—
332	C₂⁴	—	2	1	no	—
333	C₂⁴	—	2	2	no	—
334	C₂⁴	C₂×D₄×C₁₁₃	1	2	yes	—
335	C₂×Q₈	—	2	4	no	—
336	C₂×Q₈	—	8	2	no	—
337	C₂×D₄	—	2	8	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	4	8	no	—
349	C₂×D₄	—	4	8	no	—
350	C₂×D₄	—	4	2	no	—
351	C₂×D₄	—	4	2	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	4	2	no	—
354	C₂×D₄	—	8	2	no	—
355	C₂×D₄	—	8	4	no	—
356	C₂×D₄	—	8	4	no	—
357	C₂×D₄	C₂×D₄×C₁₁₃	1	2	yes	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
371	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
372	D₈	—	4	8	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	4	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	C₂×D₄×C₁₁₃	1	2	yes	—
384	C₄⋊C₄	C₂×D₄×C₁₁₃	1	4	yes	—
385	C₄⋊C₄	#41×C₁₁₃	1	4	yes	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	2	4	no	—
390	C₂²⋊C₄	—	4	8	no	—
391	C₄²	—	2	8	no	—
392	C₄²	—	4	2	no	—
393	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
394	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	4	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	4	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	4	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	4	no	—
410	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
411	Q₈	—	8	4	no	—
412	D₄	—	2	2	no	—
413	D₄	—	2	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	4	no	—
418	D₄	—	4	4	no	—
419	D₄	—	8	4	no	—
420	D₄	—	8	8	no	—
421	D₄	—	8	16	no	—
422	D₄	—	8	4	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	8	no	—
438	C₂×C₄	#120×C₁₁₃	1	2	yes	—
439	C₂×C₄	#120×C₁₁₃	1	2	yes	—
440	C₂×C₄	#135×C₁₁₃	1	2	yes	—
441	C₂×C₄	AGL(1,ℤ/8)×C₁₁₃	1	2	yes	—
442	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
443	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
444	C₂×C₄	C₂×#41×C₁₁₃	1	2	yes	—
445	C₂×C₄	H(5,𝔽₂)×C₁₁₃	1	2	yes	—
446	C₈	—	4	2	no	—
447	C₈	—	4	2	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	8	2	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	8	4	no	—
459	C₂²	—	8	4	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	8	2	no	—
462	C₂²	—	8	2	no	—
463	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
464	C₂²	#546×C₁₁₃	1	2	yes	—
465	C₂²	C₂×#135×C₁₁₃	1	1	yes	characteristic
466	C₂²	C₂×AGL(1,ℤ/8)×C₁₁₃	1	1	yes	characteristic
467	C₂²	#576×C₁₁₃	1	2	yes	—
468	C₄	—	2	2	no	—
469	C₄	—	4	4	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	4	no	—
473	C₄	#449×C₁₁₃	1	4	yes	—
474	C₄	#532×C₁₁₃	1	1	yes	characteristic
475	C₄	#535×C₁₁₃	1	1	yes	characteristic
476	C₄	#550×C₁₁₃	1	2	yes	—
477	C₂	—	8	2	no	—
478	C₂	—	8	2	no	—
479	C₂	—	16	2	no	—
480	C₂	C₁₁₃×#2431	1	1	yes	characteristic
481	C₂	C₂×#449×C₁₁₃	1	1	yes	characteristic
482	C₂	C₁₁₃×#3008	1	1	yes	characteristic
483	C₂	C₁₁₃×#3305	1	2	yes	—
484	C₂	C₁₁₃×#3325	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
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
1. C₂×#555×C₁₁₃	C₂	semidirect
2. C₂×#486×C₁₁₃	C₂	semidirect
3. C₂×#459×C₁₁₃	C₂	semidirect
4. C₁₁₃×#2541	C₂	semidirect
5. C₁₁₃×#1999	C₂	semidirect
6. C₁₁₃×#1987	C₂	semidirect
7. C₁₁₃×#1954	C₂	semidirect
8. C₁₁₃×#1875	C₂	semidirect
9. C₄×#102×C₁₁₃	C₂	semidirect
52. C₄⋊Q₈×C₁₁₃	D₄	semidirect
65. C₄×D₄×C₁₁₃	D₄	semidirect
234. #25572	C₁₁₃	direct (N × H)
243. C₂×#555	C₂×C₁₁₃	semidirect
244. C₂×#486	C₂×C₁₁₃	semidirect
245. C₂×#459	C₂×C₁₁₃	semidirect
246. #2541	C₂×C₁₁₃	semidirect
247. #1999	C₂×C₁₁₃	semidirect
248. #1987	C₂×C₁₁₃	semidirect
249. #1954	C₂×C₁₁₃	semidirect
250. #1875	C₂×C₁₁₃	semidirect
251. C₄×#102	C₂×C₁₁₃	semidirect
252. C₁₁₃	#25572	direct (N × H)
295. C₄⋊Q₈	D₄×C₁₁₃	semidirect
308. C₄×D₄	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×#555×C₁₁₃	2
C₂×#486×C₁₁₃	2
C₂×#459×C₁₁₃	2
C₁₁₃×#2541	2
C₁₁₃×#1999	2
C₁₁₃×#1987	2
C₁₁₃×#1954	2
C₁₁₃×#1875	2
C₄×#102×C₁₁₃	2
#25572	113

Subgroups — C113×#25572 #43293592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#25572 #43293592