Subgroups — C₁₁₃×#20600 #43288620

Order 28928.

3966 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#419×C₁₁₃	C₂	1	2	yes	maximal, complemented
3	C₂×#418×C₁₁₃	C₂	1	2	yes	maximal, complemented
4	C₂×#407×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁₃×#1788	C₂	1	8	yes	maximal, complemented
7	C₂²×#41×C₁₁₃	—	2	8	no	—
8	C₂²×#41×C₁₁₃	—	2	8	no	—
9	C₂²×#41×C₁₁₃	—	2	4	no	—
10	C₂²×#41×C₁₁₃	—	2	2	no	—
11	C₂²×#41×C₁₁₃	C₄	1	8	yes	complemented
12	C₂²×#41×C₁₁₃	C₂²	1	4	yes	—
13	C₂³×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₁₃	—	2	1	no	—
15	C₂³×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₁₃	—	2	1	no	—
17	C₂⁴×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₁₁₃	C₂²	1	2	yes	—
19	C₂×#117×C₁₁₃	C₂²	1	2	yes	—
20	#419×C₁₁₃	—	2	8	no	—
21	#418×C₁₁₃	—	2	8	no	—
22	C₂×#103×C₁₁₃	C₂²	1	8	yes	complemented
23	C₂×#102×C₁₁₃	C₂²	1	8	yes	complemented
24	#407×C₁₁₃	—	2	4	no	—
25	C₂×C₂²⋊C₈×C₁₁₃	C₂²	1	4	yes	complemented
26	#381×C₁₁₃	—	2	1	no	—
27	#380×C₁₁₃	C₂²	1	4	yes	complemented
28	#379×C₁₁₃	—	2	1	no	—
29	C₄×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
30	C₂⁵×C₁₁₃	—	2	1	no	—
31	C₂⁵×C₁₁₃	D₄	1	1	yes	characteristic
32	C₂×#41×C₁₁₃	—	2	32	no	—
33	C₂×#41×C₁₁₃	—	2	64	no	—
34	C₂×#41×C₁₁₃	—	2	32	no	—
35	C₂×#41×C₁₁₃	—	2	16	no	—
36	C₂×#41×C₁₁₃	—	2	32	no	—
37	C₂×#41×C₁₁₃	—	2	16	no	—
38	C₂×#41×C₁₁₃	—	2	16	no	—
39	C₂×#41×C₁₁₃	—	2	8	no	—
40	C₂×#41×C₁₁₃	C₂×C₄	1	16	yes	—
41	C₂²×Q₈×C₁₁₃	—	2	2	no	—
42	C₂²×Q₈×C₁₁₃	—	2	4	no	—
43	C₂²×Q₈×C₁₁₃	—	2	1	no	—
44	C₂²×Q₈×C₁₁₃	C₂×C₄	1	4	yes	—
45	C₂²×Q₈×C₁₁₃	D₄	1	8	yes	—
46	C₂²×Q₈×C₁₁₃	C₂³	1	2	yes	—
47	C₂²×D₄×C₁₁₃	—	2	16	no	—
48	C₂²×D₄×C₁₁₃	—	2	8	no	—
49	C₂²×D₄×C₁₁₃	—	2	4	no	—
50	C₂²×D₄×C₁₁₃	—	2	1	no	—
51	C₂²×D₄×C₁₁₃	—	2	4	no	—
52	C₂²×D₄×C₁₁₃	—	2	2	no	—
53	C₂²×D₄×C₁₁₃	C₂×C₄	1	4	yes	—
54	C₂²×D₄×C₁₁₃	D₄	1	8	yes	—
55	C₂²×D₄×C₁₁₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₁₃	—	2	16	no	—
57	C₂³×C₄×C₁₁₃	—	2	1	no	—
58	C₂³×C₄×C₁₁₃	—	2	8	no	—
59	C₂³×C₄×C₁₁₃	—	2	4	no	—
60	C₂³×C₄×C₁₁₃	—	2	4	no	—
61	C₂³×C₄×C₁₁₃	—	2	4	no	—
62	C₂³×C₄×C₁₁₃	C₂×C₄	1	4	yes	—
63	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₁₁₃	D₄	1	2	yes	—
65	C₂³×C₄×C₁₁₃	D₄	1	4	yes	—
66	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
68	C₂×M₁₆×C₁₁₃	—	2	4	no	—
69	C₂×M₁₆×C₁₁₃	—	2	4	no	—
70	C₂×M₁₆×C₁₁₃	—	2	4	no	—
71	C₂²×C₈×C₁₁₃	C₂³	1	4	yes	—
72	#117×C₁₁₃	—	2	4	no	—
73	#117×C₁₁₃	—	2	4	no	—
74	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
75	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
77	C₂×C₄²×C₁₁₃	—	2	2	no	—
78	#103×C₁₁₃	—	2	16	no	—
79	#102×C₁₁₃	—	2	16	no	—
80	C₂²⋊C₈×C₁₁₃	—	2	8	no	—
81	#95×C₁₁₃	—	2	4	no	—
82	C₂⁴×C₁₁₃	—	2	4	no	—
83	C₂⁴×C₁₁₃	—	2	4	no	—
84	C₂⁴×C₁₁₃	—	2	8	no	—
85	C₂⁴×C₁₁₃	—	2	2	no	—
86	C₂⁴×C₁₁₃	—	4	4	no	—
87	C₂⁴×C₁₁₃	—	4	8	no	—
88	C₂⁴×C₁₁₃	C₂²⋊C₄	1	4	yes	—
89	C₂⁴×C₁₁₃	C₂×D₄	1	2	yes	—
90	C₂⁴×C₁₁₃	C₂×D₄	1	1	yes	characteristic
91	#41×C₁₁₃	—	2	64	no	—
92	#41×C₁₁₃	—	2	128	no	—
93	#41×C₁₁₃	—	2	32	no	—
94	#41×C₁₁₃	—	2	32	no	—
95	C₂×Q₈×C₁₁₃	—	2	4	no	—
96	C₂×Q₈×C₁₁₃	—	2	8	no	—
97	C₂×Q₈×C₁₁₃	—	2	8	no	—
98	C₂×Q₈×C₁₁₃	—	2	16	no	—
99	C₂×Q₈×C₁₁₃	—	2	2	no	—
100	C₂×Q₈×C₁₁₃	—	2	4	no	—
101	C₂×Q₈×C₁₁₃	C₂²⋊C₄	1	16	yes	complemented
102	C₂×Q₈×C₁₁₃	C₂²×C₄	1	4	yes	—
103	C₂×Q₈×C₁₁₃	C₂×D₄	1	8	yes	—
104	C₂×D₄×C₁₁₃	—	2	32	no	—
105	C₂×D₄×C₁₁₃	—	2	64	no	—
106	C₂×D₄×C₁₁₃	—	2	16	no	—
107	C₂×D₄×C₁₁₃	—	2	8	no	—
108	C₂×D₄×C₁₁₃	—	2	4	no	—
109	C₂×D₄×C₁₁₃	—	2	16	no	—
110	C₂×D₄×C₁₁₃	—	2	8	no	—
111	C₂×D₄×C₁₁₃	—	2	4	no	—
112	C₂×D₄×C₁₁₃	—	2	2	no	—
113	C₂×D₄×C₁₁₃	C₂²⋊C₄	1	16	yes	complemented
114	C₂×D₄×C₁₁₃	C₂²×C₄	1	4	yes	—
115	C₂×D₄×C₁₁₃	C₂×D₄	1	8	yes	—
116	C₂²×C₄×C₁₁₃	—	2	32	no	—
117	C₂²×C₄×C₁₁₃	—	2	64	no	—
118	C₂²×C₄×C₁₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₁₃	—	2	4	no	—
120	C₂²×C₄×C₁₁₃	—	2	8	no	—
121	C₂²×C₄×C₁₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₁₃	—	2	16	no	—
123	C₂²×C₄×C₁₁₃	—	2	8	no	—
124	C₂²×C₄×C₁₁₃	—	2	8	no	—
125	C₂²×C₄×C₁₁₃	—	2	8	no	—
126	C₂²×C₄×C₁₁₃	—	2	16	no	—
127	C₂²×C₄×C₁₁₃	—	2	4	no	—
128	C₂²×C₄×C₁₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
131	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	8	yes	—
132	C₂²×C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
133	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
134	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
136	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
139	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
141	M₁₆×C₁₁₃	—	4	8	no	—
142	C₂×C₈×C₁₁₃	—	2	4	no	—
143	C₂×C₈×C₁₁₃	—	2	4	no	—
144	C₂×C₈×C₁₁₃	—	2	4	no	—
145	C₄⋊C₄×C₁₁₃	—	2	4	no	—
146	C₄⋊C₄×C₁₁₃	—	2	4	no	—
147	C₂²⋊C₄×C₁₁₃	—	4	8	no	—
148	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
149	C₄²×C₁₁₃	—	4	4	no	—
150	C₂³×C₁₁₃	—	2	4	no	—
151	C₂³×C₁₁₃	—	2	4	no	—
152	C₂³×C₁₁₃	—	2	4	no	—
153	C₂³×C₁₁₃	—	2	8	no	—
154	C₂³×C₁₁₃	—	2	4	no	—
155	C₂³×C₁₁₃	—	2	4	no	—
156	C₂³×C₁₁₃	—	2	8	no	—
157	C₂³×C₁₁₃	—	2	16	no	—
158	C₂³×C₁₁₃	—	4	8	no	—
159	C₂³×C₁₁₃	—	4	16	no	—
160	C₂³×C₁₁₃	—	4	16	no	—
161	C₂³×C₁₁₃	—	4	32	no	—
162	C₂³×C₁₁₃	—	4	8	no	—
163	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
164	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂³×C₁₁₃	#120	1	4	yes	—
166	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₁₁₃	—	2	4	no	—
168	Q₈×C₁₁₃	—	2	8	no	—
169	Q₈×C₁₁₃	—	2	16	no	—
170	Q₈×C₁₁₃	C₂×C₂²⋊C₄	1	8	yes	—
171	D₄×C₁₁₃	—	2	64	no	—
172	D₄×C₁₁₃	—	2	4	no	—
173	D₄×C₁₁₃	—	2	8	no	—
174	D₄×C₁₁₃	—	2	16	no	—
175	D₄×C₁₁₃	C₂×C₂²⋊C₄	1	8	yes	—
176	C₂×C₄×C₁₁₃	—	2	64	no	—
177	C₂×C₄×C₁₁₃	—	2	4	no	—
178	C₂×C₄×C₁₁₃	—	2	4	no	—
179	C₂×C₄×C₁₁₃	—	2	8	no	—
180	C₂×C₄×C₁₁₃	—	2	8	no	—
181	C₂×C₄×C₁₁₃	—	2	16	no	—
182	C₂×C₄×C₁₁₃	—	2	4	no	—
183	C₂×C₄×C₁₁₃	—	2	4	no	—
184	C₂×C₄×C₁₁₃	—	2	8	no	—
185	C₂×C₄×C₁₁₃	—	2	16	no	—
186	C₂×C₄×C₁₁₃	—	4	4	no	—
187	C₂×C₄×C₁₁₃	—	4	8	no	—
188	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
189	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
190	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
191	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
192	C₂×C₄×C₁₁₃	#120	1	8	yes	—
193	C₂×C₄×C₁₁₃	#120	1	4	yes	—
194	C₂×C₄×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
196	C₂×C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
198	C₈×C₁₁₃	—	4	4	no	—
199	C₂²×C₁₁₃	—	2	4	no	—
200	C₂²×C₁₁₃	—	2	8	no	—
201	C₂²×C₁₁₃	—	2	4	no	—
202	C₂²×C₁₁₃	—	2	4	no	—
203	C₂²×C₁₁₃	—	2	4	no	—
204	C₂²×C₁₁₃	—	2	8	no	—
205	C₂²×C₁₁₃	—	4	16	no	—
206	C₂²×C₁₁₃	—	4	32	no	—
207	C₂²×C₁₁₃	—	4	8	no	—
208	C₂²×C₁₁₃	—	4	8	no	—
209	C₂²×C₁₁₃	—	4	16	no	—
210	C₂²×C₁₁₃	#379	1	4	yes	—
211	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
212	C₂²×C₁₁₃	C₂×#120	1	2	yes	—
213	C₂²×C₁₁₃	#575	1	4	yes	—
214	C₄×C₁₁₃	—	2	4	no	—
215	C₄×C₁₁₃	—	2	8	no	—
216	C₄×C₁₁₃	—	8	4	no	—
217	C₄×C₁₁₃	#379	1	4	yes	—
218	C₄×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
219	C₄×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
220	C₄×C₁₁₃	C₂×#120	1	2	yes	—
221	#20600	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂×C₁₁₃	—	2	4	no	—
223	C₂×C₁₁₃	—	4	4	no	—
224	C₂×C₁₁₃	—	4	8	no	—
225	C₂×C₁₁₃	C₂×#379	1	1	yes	characteristic
226	C₂×C₁₁₃	#2896	1	2	yes	—
227	C₂×C₁₁₃	#3005	1	4	yes	—
228	C₂³×#41	C₂×C₁₁₃	1	1	yes	characteristic
229	C₂×#419	C₂×C₁₁₃	1	2	yes	complemented
230	C₂×#418	C₂×C₁₁₃	1	2	yes	complemented
231	C₂×#407	C₂×C₁₁₃	1	1	yes	characteristic, complemented
232	#2280	C₂×C₁₁₃	1	1	yes	characteristic, complemented
233	#1788	C₂×C₁₁₃	1	8	yes	complemented
234	C₁₁₃	#20600	1	1	yes	characteristic, direct product factor, Sylow
235	C₂²×#41	—	2	8	no	—
236	C₂²×#41	—	2	8	no	—
237	C₂²×#41	—	2	4	no	—
238	C₂²×#41	—	2	2	no	—
239	C₂²×#41	C₄×C₁₁₃	1	8	yes	complemented
240	C₂²×#41	C₂²×C₁₁₃	1	4	yes	—
241	C₂³×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
242	C₂³×D₄	—	2	1	no	—
243	C₂³×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
244	C₂⁴×C₄	—	2	1	no	—
245	C₂⁴×C₄	C₂²×C₁₁₃	1	1	yes	characteristic
246	C₂²×M₁₆	C₂²×C₁₁₃	1	2	yes	—
247	C₂×#117	C₂²×C₁₁₃	1	2	yes	—
248	#419	—	2	8	no	—
249	#418	—	2	8	no	—
250	C₂×#103	C₂²×C₁₁₃	1	8	yes	complemented
251	C₂×#102	C₂²×C₁₁₃	1	8	yes	complemented
252	#407	—	2	4	no	—
253	C₂×C₂²⋊C₈	C₂²×C₁₁₃	1	4	yes	complemented
254	#381	—	2	1	no	—
255	#380	C₂²×C₁₁₃	1	4	yes	complemented
256	#379	—	2	1	no	—
257	C₄×C₂²⋊C₄	—	2	2	no	—
258	C₂⁵	—	2	1	no	—
259	C₂⁵	D₄×C₁₁₃	1	1	yes	characteristic
260	C₂×#41	—	2	32	no	—
261	C₂×#41	—	2	64	no	—
262	C₂×#41	—	2	32	no	—
263	C₂×#41	—	2	16	no	—
264	C₂×#41	—	2	32	no	—
265	C₂×#41	—	2	16	no	—
266	C₂×#41	—	2	16	no	—
267	C₂×#41	—	2	8	no	—
268	C₂×#41	C₂×C₄×C₁₁₃	1	16	yes	—
269	C₂²×Q₈	—	2	2	no	—
270	C₂²×Q₈	—	2	4	no	—
271	C₂²×Q₈	—	2	1	no	—
272	C₂²×Q₈	C₂×C₄×C₁₁₃	1	4	yes	—
273	C₂²×Q₈	D₄×C₁₁₃	1	8	yes	—
274	C₂²×Q₈	C₂³×C₁₁₃	1	2	yes	—
275	C₂²×D₄	—	2	16	no	—
276	C₂²×D₄	—	2	8	no	—
277	C₂²×D₄	—	2	4	no	—
278	C₂²×D₄	—	2	1	no	—
279	C₂²×D₄	—	2	4	no	—
280	C₂²×D₄	—	2	2	no	—
281	C₂²×D₄	C₂×C₄×C₁₁₃	1	4	yes	—
282	C₂²×D₄	D₄×C₁₁₃	1	8	yes	—
283	C₂²×D₄	C₂³×C₁₁₃	1	2	yes	—
284	C₂³×C₄	—	2	16	no	—
285	C₂³×C₄	—	2	1	no	—
286	C₂³×C₄	—	2	8	no	—
287	C₂³×C₄	—	2	4	no	—
288	C₂³×C₄	—	2	4	no	—
289	C₂³×C₄	—	2	4	no	—
290	C₂³×C₄	C₂×C₄×C₁₁₃	1	4	yes	—
291	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
292	C₂³×C₄	D₄×C₁₁₃	1	2	yes	—
293	C₂³×C₄	D₄×C₁₁₃	1	4	yes	—
294	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
295	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
296	C₂×M₁₆	—	2	4	no	—
297	C₂×M₁₆	—	2	4	no	—
298	C₂×M₁₆	—	2	4	no	—
299	C₂²×C₈	C₂³×C₁₁₃	1	4	yes	—
300	#117	—	2	4	no	—
301	#117	—	2	4	no	—
302	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	4	yes	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	—	2	4	no	—
305	C₂×C₄²	—	2	2	no	—
306	#103	—	2	16	no	—
307	#102	—	2	16	no	—
308	C₂²⋊C₈	—	2	8	no	—
309	#95	—	2	4	no	—
310	C₂⁴	—	2	4	no	—
311	C₂⁴	—	2	4	no	—
312	C₂⁴	—	2	8	no	—
313	C₂⁴	—	2	2	no	—
314	C₂⁴	—	4	4	no	—
315	C₂⁴	—	4	8	no	—
316	C₂⁴	C₂²⋊C₄×C₁₁₃	1	4	yes	—
317	C₂⁴	C₂×D₄×C₁₁₃	1	2	yes	—
318	C₂⁴	C₂×D₄×C₁₁₃	1	1	yes	characteristic
319	#41	—	2	64	no	—
320	#41	—	2	128	no	—
321	#41	—	2	32	no	—
322	#41	—	2	32	no	—
323	C₂×Q₈	—	2	4	no	—
324	C₂×Q₈	—	2	8	no	—
325	C₂×Q₈	—	2	8	no	—
326	C₂×Q₈	—	2	16	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	4	no	—
329	C₂×Q₈	C₂²⋊C₄×C₁₁₃	1	16	yes	complemented
330	C₂×Q₈	C₂²×C₄×C₁₁₃	1	4	yes	—
331	C₂×Q₈	C₂×D₄×C₁₁₃	1	8	yes	—
332	C₂×D₄	—	2	32	no	—
333	C₂×D₄	—	2	64	no	—
334	C₂×D₄	—	2	16	no	—
335	C₂×D₄	—	2	8	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	16	no	—
338	C₂×D₄	—	2	8	no	—
339	C₂×D₄	—	2	4	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	C₂²⋊C₄×C₁₁₃	1	16	yes	complemented
342	C₂×D₄	C₂²×C₄×C₁₁₃	1	4	yes	—
343	C₂×D₄	C₂×D₄×C₁₁₃	1	8	yes	—
344	C₂²×C₄	—	2	32	no	—
345	C₂²×C₄	—	2	64	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	8	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	16	no	—
351	C₂²×C₄	—	2	8	no	—
352	C₂²×C₄	—	2	8	no	—
353	C₂²×C₄	—	2	8	no	—
354	C₂²×C₄	—	2	16	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
359	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	8	yes	—
360	C₂²×C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
361	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
364	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
366	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
367	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
368	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
369	M₁₆	—	4	8	no	—
370	C₂×C₈	—	2	4	no	—
371	C₂×C₈	—	2	4	no	—
372	C₂×C₈	—	2	4	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	4	8	no	—
376	C₂²⋊C₄	—	4	4	no	—
377	C₄²	—	4	4	no	—
378	C₂³	—	2	4	no	—
379	C₂³	—	2	4	no	—
380	C₂³	—	2	4	no	—
381	C₂³	—	2	8	no	—
382	C₂³	—	2	4	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	2	8	no	—
385	C₂³	—	2	16	no	—
386	C₂³	—	4	8	no	—
387	C₂³	—	4	16	no	—
388	C₂³	—	4	16	no	—
389	C₂³	—	4	32	no	—
390	C₂³	—	4	8	no	—
391	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
392	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
393	C₂³	#120×C₁₁₃	1	4	yes	—
394	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
395	Q₈	—	2	4	no	—
396	Q₈	—	2	8	no	—
397	Q₈	—	2	16	no	—
398	Q₈	C₂×C₂²⋊C₄×C₁₁₃	1	8	yes	—
399	D₄	—	2	64	no	—
400	D₄	—	2	4	no	—
401	D₄	—	2	8	no	—
402	D₄	—	2	16	no	—
403	D₄	C₂×C₂²⋊C₄×C₁₁₃	1	8	yes	—
404	C₂×C₄	—	2	64	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	8	no	—
408	C₂×C₄	—	2	8	no	—
409	C₂×C₄	—	2	16	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	16	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	8	no	—
416	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
417	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
418	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
419	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
420	C₂×C₄	#120×C₁₁₃	1	8	yes	—
421	C₂×C₄	#120×C₁₁₃	1	4	yes	—
422	C₂×C₄	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₄×C₁₁₃	1	2	yes	—
424	C₂×C₄	C₂²×D₄×C₁₁₃	1	2	yes	—
425	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
426	C₈	—	4	4	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	2	8	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	2	8	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	4	16	no	—
434	C₂²	—	4	32	no	—
435	C₂²	—	4	8	no	—
436	C₂²	—	4	8	no	—
437	C₂²	—	4	16	no	—
438	C₂²	#379×C₁₁₃	1	4	yes	—
439	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
440	C₂²	C₂×#120×C₁₁₃	1	2	yes	—
441	C₂²	#575×C₁₁₃	1	4	yes	—
442	C₄	—	2	4	no	—
443	C₄	—	2	8	no	—
444	C₄	—	8	4	no	—
445	C₄	#379×C₁₁₃	1	4	yes	—
446	C₄	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
447	C₄	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
448	C₄	C₂×#120×C₁₁₃	1	2	yes	—
449	C₂	—	2	4	no	—
450	C₂	—	4	4	no	—
451	C₂	—	4	8	no	—
452	C₂	C₂×#379×C₁₁₃	1	1	yes	characteristic
453	C₂	C₁₁₃×#2896	1	2	yes	—
454	C₂	C₁₁₃×#3005	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
prime radical	C₂³×#41×C₁₁₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁₃ ◁ C₂⁴×C₄×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#419×C₁₁₃	C₂	semidirect
3. C₂×#418×C₁₁₃	C₂	semidirect
4. C₂×#407×C₁₁₃	C₂	semidirect
5. C₁₁₃×#2280	C₂	semidirect
6. C₁₁₃×#1788	C₂	semidirect
11. C₂²×#41×C₁₁₃	C₄	semidirect
22. C₂×#103×C₁₁₃	C₂²	semidirect
23. C₂×#102×C₁₁₃	C₂²	semidirect
25. C₂×C₂²⋊C₈×C₁₁₃	C₂²	semidirect
27. #380×C₁₁₃	C₂²	semidirect
101. C₂×Q₈×C₁₁₃	C₂²⋊C₄	semidirect
113. C₂×D₄×C₁₁₃	C₂²⋊C₄	semidirect
221. #20600	C₁₁₃	direct (N × H)
229. C₂×#419	C₂×C₁₁₃	semidirect
230. C₂×#418	C₂×C₁₁₃	semidirect
231. C₂×#407	C₂×C₁₁₃	semidirect
232. #2280	C₂×C₁₁₃	semidirect
233. #1788	C₂×C₁₁₃	semidirect
234. C₁₁₃	#20600	direct (N × H)
239. C₂²×#41	C₄×C₁₁₃	semidirect
250. C₂×#103	C₂²×C₁₁₃	semidirect
251. C₂×#102	C₂²×C₁₁₃	semidirect
253. C₂×C₂²⋊C₈	C₂²×C₁₁₃	semidirect
255. #380	C₂²×C₁₁₃	semidirect
329. C₂×Q₈	C₂²⋊C₄×C₁₁₃	semidirect
341. C₂×D₄	C₂²⋊C₄×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂³×#41×C₁₁₃	2
C₂×#419×C₁₁₃	2
C₂×#418×C₁₁₃	2
C₂×#407×C₁₁₃	2
C₁₁₃×#2280	2
C₁₁₃×#1788	2
#20600	113

Subgroups — C113×#20600 #43288620

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#20600 #43288620