Subgroups — C₁₁₃×#25649 #43293669

Order 28928.

1346 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#550×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#486×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#476×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#2567	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁₃×#2041	C₂	1	4	yes	maximal, complemented
6	C₁₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁₃×#1864	C₂	1	4	yes	maximal, complemented
9	C₄×#102×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₁₃	—	2	1	no	—
11	#550×C₁₁₃	—	2	4	no	—
12	#550×C₁₁₃	—	2	4	no	—
13	C₂×C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
14	C₂×#127×C₁₁₃	C₂²	1	2	yes	—
15	C₂×#127×C₁₁₃	C₂²	1	1	yes	characteristic
16	C₂×#121×C₁₁₃	—	2	1	no	—
17	C₂×#121×C₁₁₃	—	2	2	no	—
18	C₂×C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
21	#486×C₁₁₃	—	2	4	no	—
22	#476×C₁₁₃	—	2	4	no	—
23	C₂×#106×C₁₁₃	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	1	yes	characteristic
25	C₂×#102×C₁₁₃	C₂²	1	2	yes	—
26	C₂×#102×C₁₁₃	C₂²	1	2	yes	—
27	C₂×#102×C₁₁₃	C₂²	1	4	yes	—
28	C₂×#102×C₁₁₃	C₂²	1	4	yes	—
29	C₂×C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
30	#395×C₁₁₃	—	2	2	no	—
31	#391×C₁₁₃	—	2	1	no	—
32	#389×C₁₁₃	C₂²	1	4	yes	—
33	#384×C₁₁₃	—	2	1	no	—
34	C₄×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
35	#340×C₁₁₃	C₂²	1	2	yes	—
36	#336×C₁₁₃	C₂²	1	4	yes	—
37	C₂×#41×C₁₁₃	—	2	8	no	—
38	C₂×#41×C₁₁₃	—	4	4	no	—
39	C₂×#41×C₁₁₃	—	4	4	no	—
40	C₂²×Q₈×C₁₁₃	—	2	1	no	—
41	C₂²×Q₈×C₁₁₃	D₄	1	1	yes	characteristic
42	C₂²×D₄×C₁₁₃	—	2	2	no	—
43	C₂²×D₄×C₁₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₁₃	—	2	2	no	—
45	C₂²×D₄×C₁₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₁₃	C₂³	1	2	yes	—
47	C₂²×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₁₃	—	2	2	no	—
49	C₂³×C₄×C₁₁₃	—	2	1	no	—
50	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₁₁₃	—	2	2	no	—
53	C₄⋊Q₈×C₁₁₃	—	2	2	no	—
54	#127×C₁₁₃	—	2	4	no	—
55	#127×C₁₁₃	—	2	4	no	—
56	#127×C₁₁₃	—	2	2	no	—
57	#127×C₁₁₃	D₄	1	4	yes	—
58	#121×C₁₁₃	—	2	8	no	—
59	#121×C₁₁₃	—	2	16	no	—
60	C₄×Q₈×C₁₁₃	—	2	2	no	—
61	C₄×Q₈×C₁₁₃	—	2	2	no	—
62	C₄×D₄×C₁₁₃	—	2	4	no	—
63	C₄×D₄×C₁₁₃	—	2	4	no	—
64	C₄×D₄×C₁₁₃	—	2	2	no	—
65	C₄×D₄×C₁₁₃	D₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
68	C₂×C₄⋊C₄×C₁₁₃	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₁₃	D₄	1	2	yes	—
70	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
73	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
75	C₂×C₄²×C₁₁₃	—	2	1	no	—
76	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
77	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
78	#106×C₁₁₃	—	2	4	no	—
79	C₄⋊C₈×C₁₁₃	—	2	2	no	—
80	#102×C₁₁₃	—	2	4	no	—
81	#102×C₁₁₃	—	2	8	no	—
82	#102×C₁₁₃	—	2	4	no	—
83	#102×C₁₁₃	—	2	8	no	—
84	C₄×C₈×C₁₁₃	—	2	2	no	—
85	#95×C₁₁₃	—	2	1	no	—
86	#95×C₁₁₃	—	2	4	no	—
87	C₂⁴×C₁₁₃	—	2	2	no	—
88	C₂⁴×C₁₁₃	—	2	1	no	—
89	#41×C₁₁₃	—	4	32	no	—
90	C₂×Q₈×C₁₁₃	—	2	2	no	—
91	C₂×Q₈×C₁₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₁₃	—	4	2	no	—
93	C₂×Q₈×C₁₁₃	—	8	2	no	—
94	C₂×Q₈×C₁₁₃	SD₁₆	1	4	yes	—
95	C₂×D₄×C₁₁₃	—	2	8	no	—
96	C₂×D₄×C₁₁₃	—	2	8	no	—
97	C₂×D₄×C₁₁₃	—	2	4	no	—
98	C₂×D₄×C₁₁₃	—	2	4	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	4	no	—
103	C₂×D₄×C₁₁₃	—	2	2	no	—
104	C₂×D₄×C₁₁₃	—	2	4	no	—
105	C₂×D₄×C₁₁₃	—	4	4	no	—
106	C₂×D₄×C₁₁₃	—	4	4	no	—
107	C₂×D₄×C₁₁₃	—	4	2	no	—
108	C₂×D₄×C₁₁₃	—	4	2	no	—
109	C₂×D₄×C₁₁₃	—	8	2	no	—
110	C₂×D₄×C₁₁₃	—	8	4	no	—
111	C₂×D₄×C₁₁₃	C₂×D₄	1	4	yes	—
112	C₂×D₄×C₁₁₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₁₃	—	2	8	no	—
114	C₂²×C₄×C₁₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₁₃	—	2	4	no	—
117	C₂²×C₄×C₁₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₁₃	—	4	4	no	—
119	C₂²×C₄×C₁₁₃	—	4	4	no	—
120	C₂²×C₄×C₁₁₃	—	4	2	no	—
121	C₂²×C₄×C₁₁₃	—	4	2	no	—
122	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
127	C₂×C₈×C₁₁₃	—	2	2	no	—
128	C₂×C₈×C₁₁₃	—	2	2	no	—
129	C₂×C₈×C₁₁₃	—	2	4	no	—
130	C₂×C₈×C₁₁₃	—	2	2	no	—
131	C₂×C₈×C₁₁₃	—	2	2	no	—
132	C₄⋊C₄×C₁₁₃	—	2	4	no	—
133	C₄⋊C₄×C₁₁₃	—	2	2	no	—
134	C₄⋊C₄×C₁₁₃	—	2	1	no	—
135	C₄⋊C₄×C₁₁₃	—	2	2	no	—
136	C₄⋊C₄×C₁₁₃	—	2	2	no	—
137	C₄⋊C₄×C₁₁₃	—	2	2	no	—
138	C₄⋊C₄×C₁₁₃	—	4	2	no	—
139	C₄⋊C₄×C₁₁₃	—	8	4	no	—
140	C₄⋊C₄×C₁₁₃	C₂×D₄	1	2	yes	—
141	C₄⋊C₄×C₁₁₃	#41	1	4	yes	complemented
142	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
143	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
144	C₄²×C₁₁₃	—	2	2	no	—
145	C₄²×C₁₁₃	—	2	2	no	—
146	C₄²×C₁₁₃	—	4	2	no	—
147	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
148	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
149	C₂³×C₁₁₃	—	2	4	no	—
150	C₂³×C₁₁₃	—	2	2	no	—
151	C₂³×C₁₁₃	—	4	2	no	—
152	C₂³×C₁₁₃	—	4	4	no	—
153	C₂³×C₁₁₃	—	4	2	no	—
154	C₂³×C₁₁₃	—	4	1	no	—
155	C₂³×C₁₁₃	—	4	2	no	—
156	C₂³×C₁₁₃	—	4	1	no	—
157	C₂³×C₁₁₃	—	4	4	no	—
158	C₂³×C₁₁₃	—	4	2	no	—
159	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
160	Q₈×C₁₁₃	—	2	8	no	—
161	Q₈×C₁₁₃	—	8	4	no	—
162	D₄×C₁₁₃	—	2	2	no	—
163	D₄×C₁₁₃	—	2	2	no	—
164	D₄×C₁₁₃	—	2	8	no	—
165	D₄×C₁₁₃	—	4	16	no	—
166	D₄×C₁₁₃	—	4	2	no	—
167	D₄×C₁₁₃	—	4	2	no	—
168	D₄×C₁₁₃	—	4	2	no	—
169	D₄×C₁₁₃	—	4	8	no	—
170	D₄×C₁₁₃	—	8	4	no	—
171	D₄×C₁₁₃	—	8	8	no	—
172	C₂×C₄×C₁₁₃	—	2	2	no	—
173	C₂×C₄×C₁₁₃	—	2	2	no	—
174	C₂×C₄×C₁₁₃	—	2	2	no	—
175	C₂×C₄×C₁₁₃	—	2	2	no	—
176	C₂×C₄×C₁₁₃	—	2	2	no	—
177	C₂×C₄×C₁₁₃	—	2	4	no	—
178	C₂×C₄×C₁₁₃	—	2	4	no	—
179	C₂×C₄×C₁₁₃	—	4	16	no	—
180	C₂×C₄×C₁₁₃	—	4	1	no	—
181	C₂×C₄×C₁₁₃	—	4	2	no	—
182	C₂×C₄×C₁₁₃	—	4	1	no	—
183	C₂×C₄×C₁₁₃	—	4	2	no	—
184	C₂×C₄×C₁₁₃	—	4	8	no	—
185	C₂×C₄×C₁₁₃	—	4	2	no	—
186	C₂×C₄×C₁₁₃	—	4	4	no	—
187	C₂×C₄×C₁₁₃	#120	1	2	yes	—
188	C₂×C₄×C₁₁₃	#120	1	2	yes	—
189	C₂×C₄×C₁₁₃	C₂×SD₁₆	1	4	yes	—
190	C₂×C₄×C₁₁₃	C₂×SD₁₆	1	2	yes	—
191	C₂×C₄×C₁₁₃	AGL(1,ℤ/8)	1	2	yes	—
192	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₁₃	C₂×#41	1	2	yes	—
195	C₂×C₄×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
196	C₈×C₁₁₃	—	4	2	no	—
197	C₈×C₁₁₃	—	4	2	no	—
198	C₂²×C₁₁₃	—	4	2	no	—
199	C₂²×C₁₁₃	—	4	4	no	—
200	C₂²×C₁₁₃	—	4	4	no	—
201	C₂²×C₁₁₃	—	4	2	no	—
202	C₂²×C₁₁₃	—	4	4	no	—
203	C₂²×C₁₁₃	—	4	2	no	—
204	C₂²×C₁₁₃	—	8	2	no	—
205	C₂²×C₁₁₃	—	8	4	no	—
206	C₂²×C₁₁₃	—	8	4	no	—
207	C₂²×C₁₁₃	—	8	2	no	—
208	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
209	C₂²×C₁₁₃	#548	1	2	yes	—
210	C₂²×C₁₁₃	C₂²×SD₁₆	1	1	yes	characteristic
211	C₂²×C₁₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
212	C₂²×C₁₁₃	#576	1	2	yes	—
213	C₄×C₁₁₃	—	2	4	no	—
214	C₄×C₁₁₃	—	2	2	no	—
215	C₄×C₁₁₃	—	4	4	no	—
216	C₄×C₁₁₃	—	4	2	no	—
217	C₄×C₁₁₃	—	4	2	no	—
218	C₄×C₁₁₃	—	8	2	no	—
219	C₄×C₁₁₃	#450	1	4	yes	—
220	C₄×C₁₁₃	#532	1	1	yes	characteristic
221	C₄×C₁₁₃	#536	1	1	yes	characteristic
222	C₄×C₁₁₃	#547	1	2	yes	—
223	#25649	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₂×C₁₁₃	—	8	2	no	—
225	C₂×C₁₁₃	—	8	4	no	—
226	C₂×C₁₁₃	#2432	1	1	yes	characteristic
227	C₂×C₁₁₃	C₂×#450	1	1	yes	characteristic
228	C₂×C₁₁₃	#3008	1	1	yes	characteristic
229	C₂×C₁₁₃	#3362	1	2	yes	—
230	C₂×C₁₁₃	#3366	1	2	yes	—
231	C₂×#550	C₂×C₁₁₃	1	1	yes	characteristic
232	C₂×#486	C₂×C₁₁₃	1	1	yes	characteristic, complemented
233	C₂×#476	C₂×C₁₁₃	1	1	yes	characteristic, complemented
234	#2567	C₂×C₁₁₃	1	1	yes	characteristic, complemented
235	#2041	C₂×C₁₁₃	1	4	yes	complemented
236	#1984	C₂×C₁₁₃	1	1	yes	characteristic, complemented
237	#1982	C₂×C₁₁₃	1	1	yes	characteristic, complemented
238	#1864	C₂×C₁₁₃	1	4	yes	complemented
239	C₄×#102	C₂×C₁₁₃	1	1	yes	characteristic, complemented
240	C₁₁₃	#25649	1	1	yes	characteristic, direct product factor, Sylow
241	C₂²×#41	—	2	1	no	—
242	#550	—	2	4	no	—
243	#550	—	2	4	no	—
244	C₂×C₄⋊Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
245	C₂×#127	C₂²×C₁₁₃	1	2	yes	—
246	C₂×#127	C₂²×C₁₁₃	1	1	yes	characteristic
247	C₂×#121	—	2	1	no	—
248	C₂×#121	—	2	2	no	—
249	C₂×C₄×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
250	C₂×C₄×D₄	C₂²×C₁₁₃	1	2	yes	—
251	C₂×C₄×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
252	#486	—	2	4	no	—
253	#476	—	2	4	no	—
254	C₂×#106	C₂²×C₁₁₃	1	2	yes	—
255	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	1	yes	characteristic
256	C₂×#102	C₂²×C₁₁₃	1	4	yes	—
257	C₂×#102	C₂²×C₁₁₃	1	4	yes	—
258	C₂×#102	C₂²×C₁₁₃	1	2	yes	—
259	C₂×#102	C₂²×C₁₁₃	1	2	yes	—
260	C₂×C₄×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
261	#395	—	2	2	no	—
262	#391	—	2	1	no	—
263	#389	C₂²×C₁₁₃	1	4	yes	—
264	#384	—	2	1	no	—
265	C₄×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
266	#340	C₂²×C₁₁₃	1	2	yes	—
267	#336	C₂²×C₁₁₃	1	4	yes	—
268	C₂×#41	—	2	8	no	—
269	C₂×#41	—	4	4	no	—
270	C₂×#41	—	4	4	no	—
271	C₂²×Q₈	—	2	1	no	—
272	C₂²×Q₈	D₄×C₁₁₃	1	1	yes	characteristic
273	C₂²×D₄	—	2	2	no	—
274	C₂²×D₄	—	2	1	no	—
275	C₂²×D₄	—	2	2	no	—
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	C₂³×C₁₁₃	1	2	yes	—
278	C₂²×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
279	C₂³×C₄	—	2	2	no	—
280	C₂³×C₄	—	2	1	no	—
281	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
282	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
283	C₄⋊Q₈	—	2	2	no	—
284	C₄⋊Q₈	—	2	2	no	—
285	#127	—	2	4	no	—
286	#127	—	2	4	no	—
287	#127	—	2	2	no	—
288	#127	D₄×C₁₁₃	1	4	yes	—
289	#121	—	2	8	no	—
290	#121	—	2	16	no	—
291	C₄×Q₈	—	2	2	no	—
292	C₄×Q₈	—	2	2	no	—
293	C₄×D₄	—	2	4	no	—
294	C₄×D₄	—	2	4	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	D₄×C₁₁₃	1	4	yes	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	4	no	—
299	C₂×C₄⋊C₄	D₄×C₁₁₃	1	1	yes	characteristic
300	C₂×C₄⋊C₄	D₄×C₁₁₃	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
308	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
309	#106	—	2	4	no	—
310	C₄⋊C₈	—	2	2	no	—
311	#102	—	2	4	no	—
312	#102	—	2	8	no	—
313	#102	—	2	8	no	—
314	#102	—	2	4	no	—
315	C₄×C₈	—	2	2	no	—
316	#95	—	2	1	no	—
317	#95	—	2	4	no	—
318	C₂⁴	—	2	2	no	—
319	C₂⁴	—	2	1	no	—
320	#41	—	4	32	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	4	2	no	—
324	C₂×Q₈	—	8	2	no	—
325	C₂×Q₈	SD₁₆×C₁₁₃	1	4	yes	—
326	C₂×D₄	—	2	8	no	—
327	C₂×D₄	—	2	8	no	—
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	4	4	no	—
337	C₂×D₄	—	4	4	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	8	2	no	—
341	C₂×D₄	—	8	4	no	—
342	C₂×D₄	C₂×D₄×C₁₁₃	1	4	yes	—
343	C₂×D₄	C₂×D₄×C₁₁₃	1	2	yes	—
344	C₂²×C₄	—	2	8	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	4	4	no	—
350	C₂²×C₄	—	4	4	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	—	4	2	no	—
353	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
357	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	4	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄⋊C₄	—	8	4	no	—
371	C₄⋊C₄	C₂×D₄×C₁₁₃	1	2	yes	—
372	C₄⋊C₄	#41×C₁₁₃	1	4	yes	complemented
373	C₂²⋊C₄	—	2	8	no	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	4	2	no	—
378	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
379	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
380	C₂³	—	2	4	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	4	4	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	4	no	—
389	C₂³	—	4	2	no	—
390	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
391	Q₈	—	2	8	no	—
392	Q₈	—	8	4	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	2	8	no	—
396	D₄	—	4	16	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	8	no	—
401	D₄	—	8	4	no	—
402	D₄	—	8	8	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	16	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	8	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	#120×C₁₁₃	1	2	yes	—
419	C₂×C₄	#120×C₁₁₃	1	2	yes	—
420	C₂×C₄	C₂×SD₁₆×C₁₁₃	1	4	yes	—
421	C₂×C₄	C₂×SD₁₆×C₁₁₃	1	2	yes	—
422	C₂×C₄	AGL(1,ℤ/8)×C₁₁₃	1	2	yes	—
423	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
425	C₂×C₄	C₂×#41×C₁₁₃	1	2	yes	—
426	C₂×C₄	2₋¹⁺⁴×C₁₁₃	1	2	yes	—
427	C₈	—	4	2	no	—
428	C₈	—	4	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	4	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	8	2	no	—
436	C₂²	—	8	4	no	—
437	C₂²	—	8	4	no	—
438	C₂²	—	8	2	no	—
439	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
440	C₂²	#548×C₁₁₃	1	2	yes	—
441	C₂²	C₂²×SD₁₆×C₁₁₃	1	1	yes	characteristic
442	C₂²	C₂×AGL(1,ℤ/8)×C₁₁₃	1	1	yes	characteristic
443	C₂²	#576×C₁₁₃	1	2	yes	—
444	C₄	—	2	4	no	—
445	C₄	—	2	2	no	—
446	C₄	—	4	4	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	8	2	no	—
450	C₄	#450×C₁₁₃	1	4	yes	—
451	C₄	#532×C₁₁₃	1	1	yes	characteristic
452	C₄	#536×C₁₁₃	1	1	yes	characteristic
453	C₄	#547×C₁₁₃	1	2	yes	—
454	C₂	—	8	2	no	—
455	C₂	—	8	4	no	—
456	C₂	C₁₁₃×#2432	1	1	yes	characteristic
457	C₂	C₂×#450×C₁₁₃	1	1	yes	characteristic
458	C₂	C₁₁₃×#3008	1	1	yes	characteristic
459	C₂	C₁₁₃×#3362	1	2	yes	—
460	C₂	C₁₁₃×#3366	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
prime radical	C₂×#550×C₁₁₃	C₂
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×#486×C₁₁₃	C₂	semidirect
3. C₂×#476×C₁₁₃	C₂	semidirect
4. C₁₁₃×#2567	C₂	semidirect
5. C₁₁₃×#2041	C₂	semidirect
6. C₁₁₃×#1984	C₂	semidirect
7. C₁₁₃×#1982	C₂	semidirect
8. C₁₁₃×#1864	C₂	semidirect
9. C₄×#102×C₁₁₃	C₂	semidirect
141. C₄⋊C₄×C₁₁₃	#41	semidirect
223. #25649	C₁₁₃	direct (N × H)
232. C₂×#486	C₂×C₁₁₃	semidirect
233. C₂×#476	C₂×C₁₁₃	semidirect
234. #2567	C₂×C₁₁₃	semidirect
235. #2041	C₂×C₁₁₃	semidirect
236. #1984	C₂×C₁₁₃	semidirect
237. #1982	C₂×C₁₁₃	semidirect
238. #1864	C₂×C₁₁₃	semidirect
239. C₄×#102	C₂×C₁₁₃	semidirect
240. C₁₁₃	#25649	direct (N × H)
372. C₄⋊C₄	#41×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#550×C₁₁₃	2
C₂×#486×C₁₁₃	2
C₂×#476×C₁₁₃	2
C₁₁₃×#2567	2
C₁₁₃×#2041	2
C₁₁₃×#1984	2
C₁₁₃×#1982	2
C₁₁₃×#1864	2
C₄×#102×C₁₁₃	2
#25649	113

Subgroups — C113×#25649 #43293669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#25649 #43293669