Subgroups — C₁₁₃×#20584 #43288604

Order 28928.

4006 conjugacy classes of subgroups.

The subgroup lattice has 474 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×#410×C₁₁₃	C₂	1	4	yes	maximal, complemented
3	C₁₁₃×#2280	C₂	1	2	yes	maximal, complemented
4	C₁₁₃×#1782	C₂	1	4	yes	maximal, complemented
5	C₁₁₃×#1781	C₂	1	4	yes	maximal, complemented
6	C₂²×#41×C₁₁₃	—	2	16	no	—
7	C₂²×#41×C₁₁₃	—	2	4	no	—
8	C₂²×#41×C₁₁₃	—	2	4	no	—
9	C₂²×#41×C₁₁₃	C₄	1	2	yes	complemented
10	C₂²×#41×C₁₁₃	C₄	1	2	yes	complemented
11	C₂²×#41×C₁₁₃	C₂²	1	2	yes	—
12	C₂²×#41×C₁₁₃	C₂²	1	2	yes	—
13	C₂³×Q₈×C₁₁₃	C₄	1	1	yes	characteristic, complemented
14	C₂³×D₄×C₁₁₃	C₄	1	1	yes	characteristic, complemented
15	C₂³×D₄×C₁₁₃	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₁₁₃	C₄	1	2	yes	complemented
17	C₂⁴×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
18	C₂×#117×C₁₁₃	C₂²	1	4	yes	complemented
19	#410×C₁₁₃	—	2	16	no	—
20	C₂×#99×C₁₁₃	C₂²	1	16	yes	complemented
21	#381×C₁₁₃	C₂²	1	4	yes	complemented
22	#380×C₁₁₃	—	2	4	no	—
23	#379×C₁₁₃	C₂²	1	4	yes	—
24	C₄×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
25	C₂⁵×C₁₁₃	C₂×C₄	1	2	yes	—
26	C₂⁵×C₁₁₃	C₂³	1	1	yes	characteristic
27	C₂×#41×C₁₁₃	—	2	64	no	—
28	C₂×#41×C₁₁₃	—	2	64	no	—
29	C₂×#41×C₁₁₃	—	2	8	no	—
30	C₂×#41×C₁₁₃	—	2	8	no	—
31	C₂×#41×C₁₁₃	—	2	16	no	—
32	C₂×#41×C₁₁₃	—	2	8	no	—
33	C₂×#41×C₁₁₃	—	2	4	no	—
34	C₂×#41×C₁₁₃	—	2	4	no	—
35	C₂×#41×C₁₁₃	—	2	16	no	—
36	C₂×#41×C₁₁₃	—	2	8	no	—
37	C₂×#41×C₁₁₃	—	2	4	no	—
38	C₂×#41×C₁₁₃	—	2	8	no	—
39	C₂×#41×C₁₁₃	—	2	4	no	—
40	C₂×#41×C₁₁₃	D₄	1	16	yes	—
41	C₂²×Q₈×C₁₁₃	—	2	8	no	—
42	C₂²×Q₈×C₁₁₃	—	2	4	no	—
43	C₂²×Q₈×C₁₁₃	C₂×C₄	1	2	yes	—
44	C₂²×Q₈×C₁₁₃	C₂×C₄	1	2	yes	—
45	C₂²×D₄×C₁₁₃	—	2	8	no	—
46	C₂²×D₄×C₁₁₃	—	2	8	no	—
47	C₂²×D₄×C₁₁₃	—	2	16	no	—
48	C₂²×D₄×C₁₁₃	—	2	4	no	—
49	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
50	C₂²×D₄×C₁₁₃	C₂×C₄	1	4	yes	—
51	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
52	C₂²×D₄×C₁₁₃	C₂³	1	4	yes	—
53	C₂³×C₄×C₁₁₃	—	2	4	no	—
54	C₂³×C₄×C₁₁₃	—	2	4	no	—
55	C₂³×C₄×C₁₁₃	—	2	16	no	—
56	C₂³×C₄×C₁₁₃	—	2	8	no	—
57	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
58	C₂³×C₄×C₁₁₃	C₂×C₄	1	4	yes	—
59	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₁₃	C₂×C₄	1	4	yes	—
64	C₂³×C₄×C₁₁₃	D₄	1	4	yes	—
65	C₂³×C₄×C₁₁₃	D₄	1	4	yes	—
66	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
68	#117×C₁₁₃	—	2	16	no	—
69	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
71	C₂×C₂²⋊C₄×C₁₁₃	C₂³	1	8	yes	—
72	C₂×C₄²×C₁₁₃	—	2	4	no	—
73	#99×C₁₁₃	—	2	32	no	—
74	#95×C₁₁₃	—	2	8	no	—
75	C₂⁴×C₁₁₃	—	2	8	no	—
76	C₂⁴×C₁₁₃	—	2	4	no	—
77	C₂⁴×C₁₁₃	—	2	4	no	—
78	C₂⁴×C₁₁₃	—	4	4	no	—
79	C₂⁴×C₁₁₃	—	4	8	no	—
80	C₂⁴×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂⁴×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₂⁴×C₁₁₃	C₂²×C₄	1	4	yes	—
83	C₂⁴×C₁₁₃	C₂×D₄	1	4	yes	—
84	C₂⁴×C₁₁₃	C₂⁴	1	1	yes	characteristic
85	#41×C₁₁₃	—	2	64	no	—
86	#41×C₁₁₃	—	2	64	no	—
87	#41×C₁₁₃	—	2	32	no	—
88	#41×C₁₁₃	—	2	32	no	—
89	#41×C₁₁₃	—	2	32	no	—
90	#41×C₁₁₃	—	2	32	no	—
91	C₂×Q₈×C₁₁₃	—	2	32	no	—
92	C₂×Q₈×C₁₁₃	—	2	8	no	—
93	C₂×Q₈×C₁₁₃	—	2	4	no	—
94	C₂×Q₈×C₁₁₃	—	2	4	no	—
95	C₂×Q₈×C₁₁₃	—	2	4	no	—
96	C₂×Q₈×C₁₁₃	C₂²⋊C₄	1	8	yes	complemented
97	C₂×D₄×C₁₁₃	—	2	64	no	—
98	C₂×D₄×C₁₁₃	—	2	32	no	—
99	C₂×D₄×C₁₁₃	—	2	8	no	—
100	C₂×D₄×C₁₁₃	—	2	8	no	—
101	C₂×D₄×C₁₁₃	—	2	8	no	—
102	C₂×D₄×C₁₁₃	—	2	8	no	—
103	C₂×D₄×C₁₁₃	—	2	8	no	—
104	C₂×D₄×C₁₁₃	—	2	8	no	—
105	C₂×D₄×C₁₁₃	—	2	4	no	—
106	C₂×D₄×C₁₁₃	—	2	4	no	—
107	C₂×D₄×C₁₁₃	—	2	4	no	—
108	C₂×D₄×C₁₁₃	C₂²⋊C₄	1	8	yes	complemented
109	C₂×D₄×C₁₁₃	C₂×D₄	1	16	yes	—
110	C₂²×C₄×C₁₁₃	—	2	32	no	—
111	C₂²×C₄×C₁₁₃	—	2	32	no	—
112	C₂²×C₄×C₁₁₃	—	2	4	no	—
113	C₂²×C₄×C₁₁₃	—	2	8	no	—
114	C₂²×C₄×C₁₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₁₃	—	2	8	no	—
117	C₂²×C₄×C₁₁₃	—	2	4	no	—
118	C₂²×C₄×C₁₁₃	—	2	8	no	—
119	C₂²×C₄×C₁₁₃	—	2	8	no	—
120	C₂²×C₄×C₁₁₃	—	2	4	no	—
121	C₂²×C₄×C₁₁₃	—	2	4	no	—
122	C₂²×C₄×C₁₁₃	—	2	4	no	—
123	C₂²×C₄×C₁₁₃	—	2	8	no	—
124	C₂²×C₄×C₁₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₁₃	—	2	16	no	—
126	C₂²×C₄×C₁₁₃	—	2	16	no	—
127	C₂²×C₄×C₁₁₃	—	2	8	no	—
128	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
129	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
130	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
131	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
132	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
133	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
134	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	16	yes	complemented
135	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
137	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₁₃	C₂×D₄	1	8	yes	—
143	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
144	C₄⋊C₄×C₁₁₃	—	4	8	no	—
145	C₂²⋊C₄×C₁₁₃	—	2	16	no	—
146	C₂²⋊C₄×C₁₁₃	—	4	16	no	—
147	C₄²×C₁₁₃	—	4	8	no	—
148	C₂³×C₁₁₃	—	2	2	no	—
149	C₂³×C₁₁₃	—	2	4	no	—
150	C₂³×C₁₁₃	—	2	16	no	—
151	C₂³×C₁₁₃	—	2	2	no	—
152	C₂³×C₁₁₃	—	2	4	no	—
153	C₂³×C₁₁₃	—	2	4	no	—
154	C₂³×C₁₁₃	—	2	8	no	—
155	C₂³×C₁₁₃	—	2	8	no	—
156	C₂³×C₁₁₃	—	4	2	no	—
157	C₂³×C₁₁₃	—	4	4	no	—
158	C₂³×C₁₁₃	—	4	2	no	—
159	C₂³×C₁₁₃	—	4	8	no	—
160	C₂³×C₁₁₃	—	4	16	no	—
161	C₂³×C₁₁₃	—	4	32	no	—
162	C₂³×C₁₁₃	—	4	8	no	—
163	C₂³×C₁₁₃	—	4	8	no	—
164	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	8	yes	—
167	C₂³×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
168	C₂³×C₁₁₃	C₂²×D₄	1	2	yes	—
169	C₂³×C₁₁₃	C₂²×D₄	1	4	yes	—
170	Q₈×C₁₁₃	—	2	16	no	—
171	Q₈×C₁₁₃	—	2	16	no	—
172	D₄×C₁₁₃	—	2	32	no	—
173	D₄×C₁₁₃	—	2	16	no	—
174	D₄×C₁₁₃	—	2	32	no	—
175	D₄×C₁₁₃	—	2	16	no	—
176	C₂×C₄×C₁₁₃	—	2	16	no	—
177	C₂×C₄×C₁₁₃	—	2	32	no	—
178	C₂×C₄×C₁₁₃	—	2	2	no	—
179	C₂×C₄×C₁₁₃	—	2	4	no	—
180	C₂×C₄×C₁₁₃	—	2	2	no	—
181	C₂×C₄×C₁₁₃	—	2	4	no	—
182	C₂×C₄×C₁₁₃	—	2	8	no	—
183	C₂×C₄×C₁₁₃	—	2	4	no	—
184	C₂×C₄×C₁₁₃	—	2	4	no	—
185	C₂×C₄×C₁₁₃	—	2	8	no	—
186	C₂×C₄×C₁₁₃	—	2	8	no	—
187	C₂×C₄×C₁₁₃	—	2	4	no	—
188	C₂×C₄×C₁₁₃	—	2	4	no	—
189	C₂×C₄×C₁₁₃	—	2	16	no	—
190	C₂×C₄×C₁₁₃	—	2	16	no	—
191	C₂×C₄×C₁₁₃	—	4	16	no	—
192	C₂×C₄×C₁₁₃	—	4	8	no	—
193	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
194	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	8	yes	—
195	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
196	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
198	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
199	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
200	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₄×C₁₁₃	#120	1	8	yes	—
202	C₂×C₄×C₁₁₃	#120	1	8	yes	—
203	C₂²×C₁₁₃	—	2	8	no	—
204	C₂²×C₁₁₃	—	2	4	no	—
205	C₂²×C₁₁₃	—	2	2	no	—
206	C₂²×C₁₁₃	—	2	2	no	—
207	C₂²×C₁₁₃	—	2	2	no	—
208	C₂²×C₁₁₃	—	2	4	no	—
209	C₂²×C₁₁₃	—	2	2	no	—
210	C₂²×C₁₁₃	—	2	8	no	—
211	C₂²×C₁₁₃	—	4	4	no	—
212	C₂²×C₁₁₃	—	4	16	no	—
213	C₂²×C₁₁₃	—	4	8	no	—
214	C₂²×C₁₁₃	—	4	4	no	—
215	C₂²×C₁₁₃	—	4	8	no	—
216	C₂²×C₁₁₃	—	4	32	no	—
217	C₂²×C₁₁₃	—	4	8	no	—
218	C₂²×C₁₁₃	#410	1	4	yes	complemented
219	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	2	yes	—
220	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
221	C₂²×C₁₁₃	C₂×#120	1	4	yes	—
222	C₄×C₁₁₃	—	2	2	no	—
223	C₄×C₁₁₃	—	2	8	no	—
224	C₄×C₁₁₃	—	2	2	no	—
225	C₄×C₁₁₃	—	8	8	no	—
226	C₄×C₁₁₃	#379	1	2	yes	—
227	C₄×C₁₁₃	#379	1	2	yes	—
228	C₄×C₁₁₃	#379	1	4	yes	—
229	#20584	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂×C₁₁₃	—	2	4	no	—
231	C₂×C₁₁₃	—	2	2	no	—
232	C₂×C₁₁₃	—	2	4	no	—
233	C₂×C₁₁₃	—	4	2	no	—
234	C₂×C₁₁₃	—	4	8	no	—
235	C₂×C₁₁₃	C₂×#379	1	1	yes	characteristic
236	C₂×C₁₁₃	C₂×#410	1	2	yes	—
237	C₂³×#41	C₂×C₁₁₃	1	1	yes	characteristic
238	C₂×#410	C₂×C₁₁₃	1	4	yes	complemented
239	#2280	C₂×C₁₁₃	1	2	yes	complemented
240	#1782	C₂×C₁₁₃	1	4	yes	complemented
241	#1781	C₂×C₁₁₃	1	4	yes	complemented
242	C₁₁₃	#20584	1	1	yes	characteristic, direct product factor, Sylow
243	C₂²×#41	—	2	16	no	—
244	C₂²×#41	—	2	4	no	—
245	C₂²×#41	—	2	4	no	—
246	C₂²×#41	C₄×C₁₁₃	1	2	yes	complemented
247	C₂²×#41	C₄×C₁₁₃	1	2	yes	complemented
248	C₂²×#41	C₂²×C₁₁₃	1	2	yes	—
249	C₂²×#41	C₂²×C₁₁₃	1	2	yes	—
250	C₂³×Q₈	C₄×C₁₁₃	1	1	yes	characteristic, complemented
251	C₂³×D₄	C₄×C₁₁₃	1	1	yes	characteristic, complemented
252	C₂³×D₄	C₂²×C₁₁₃	1	2	yes	—
253	C₂⁴×C₄	C₄×C₁₁₃	1	2	yes	complemented
254	C₂⁴×C₄	C₂²×C₁₁₃	1	1	yes	characteristic
255	C₂×#117	C₂²×C₁₁₃	1	4	yes	complemented
256	#410	—	2	16	no	—
257	C₂×#99	C₂²×C₁₁₃	1	16	yes	complemented
258	#381	C₂²×C₁₁₃	1	4	yes	complemented
259	#380	—	2	4	no	—
260	#379	C₂²×C₁₁₃	1	4	yes	—
261	C₄×C₂²⋊C₄	—	2	4	no	—
262	C₂⁵	C₂×C₄×C₁₁₃	1	2	yes	—
263	C₂⁵	C₂³×C₁₁₃	1	1	yes	characteristic
264	C₂×#41	—	2	64	no	—
265	C₂×#41	—	2	64	no	—
266	C₂×#41	—	2	8	no	—
267	C₂×#41	—	2	8	no	—
268	C₂×#41	—	2	16	no	—
269	C₂×#41	—	2	8	no	—
270	C₂×#41	—	2	4	no	—
271	C₂×#41	—	2	4	no	—
272	C₂×#41	—	2	16	no	—
273	C₂×#41	—	2	8	no	—
274	C₂×#41	—	2	4	no	—
275	C₂×#41	—	2	4	no	—
276	C₂×#41	—	2	8	no	—
277	C₂×#41	D₄×C₁₁₃	1	16	yes	—
278	C₂²×Q₈	—	2	8	no	—
279	C₂²×Q₈	—	2	4	no	—
280	C₂²×Q₈	C₂×C₄×C₁₁₃	1	2	yes	—
281	C₂²×Q₈	C₂×C₄×C₁₁₃	1	2	yes	—
282	C₂²×D₄	—	2	8	no	—
283	C₂²×D₄	—	2	8	no	—
284	C₂²×D₄	—	2	16	no	—
285	C₂²×D₄	—	2	4	no	—
286	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
287	C₂²×D₄	C₂×C₄×C₁₁₃	1	4	yes	—
288	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
289	C₂²×D₄	C₂³×C₁₁₃	1	4	yes	—
290	C₂³×C₄	—	2	4	no	—
291	C₂³×C₄	—	2	4	no	—
292	C₂³×C₄	—	2	16	no	—
293	C₂³×C₄	—	2	8	no	—
294	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
295	C₂³×C₄	C₂×C₄×C₁₁₃	1	4	yes	—
296	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
297	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
298	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
299	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
300	C₂³×C₄	C₂×C₄×C₁₁₃	1	4	yes	—
301	C₂³×C₄	D₄×C₁₁₃	1	4	yes	—
302	C₂³×C₄	D₄×C₁₁₃	1	4	yes	—
303	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
304	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
305	#117	—	2	16	no	—
306	C₂×C₄⋊C₄	—	2	4	no	—
307	C₂×C₂²⋊C₄	—	2	8	no	—
308	C₂×C₂²⋊C₄	C₂³×C₁₁₃	1	8	yes	—
309	C₂×C₄²	—	2	4	no	—
310	#99	—	2	32	no	—
311	#95	—	2	8	no	—
312	C₂⁴	—	2	8	no	—
313	C₂⁴	—	2	4	no	—
314	C₂⁴	—	2	4	no	—
315	C₂⁴	—	4	4	no	—
316	C₂⁴	—	4	8	no	—
317	C₂⁴	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
318	C₂⁴	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
319	C₂⁴	C₂²×C₄×C₁₁₃	1	4	yes	—
320	C₂⁴	C₂×D₄×C₁₁₃	1	4	yes	—
321	C₂⁴	C₂⁴×C₁₁₃	1	1	yes	characteristic
322	#41	—	2	64	no	—
323	#41	—	2	64	no	—
324	#41	—	2	32	no	—
325	#41	—	2	32	no	—
326	#41	—	2	32	no	—
327	#41	—	2	32	no	—
328	C₂×Q₈	—	2	32	no	—
329	C₂×Q₈	—	2	8	no	—
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	2	4	no	—
332	C₂×Q₈	—	2	4	no	—
333	C₂×Q₈	C₂²⋊C₄×C₁₁₃	1	8	yes	complemented
334	C₂×D₄	—	2	64	no	—
335	C₂×D₄	—	2	32	no	—
336	C₂×D₄	—	2	8	no	—
337	C₂×D₄	—	2	8	no	—
338	C₂×D₄	—	2	8	no	—
339	C₂×D₄	—	2	8	no	—
340	C₂×D₄	—	2	8	no	—
341	C₂×D₄	—	2	8	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	C₂²⋊C₄×C₁₁₃	1	8	yes	complemented
346	C₂×D₄	C₂×D₄×C₁₁₃	1	16	yes	—
347	C₂²×C₄	—	2	32	no	—
348	C₂²×C₄	—	2	32	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	8	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	8	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	8	no	—
356	C₂²×C₄	—	2	8	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	8	no	—
362	C₂²×C₄	—	2	16	no	—
363	C₂²×C₄	—	2	16	no	—
364	C₂²×C₄	—	2	8	no	—
365	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
366	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
367	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
368	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
369	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
370	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
371	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	16	yes	complemented
372	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
373	C₂²×C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
374	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
375	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
376	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
378	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
379	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₁₁₃	1	8	yes	—
381	C₄⋊C₄	—	4	8	no	—
382	C₂²⋊C₄	—	2	16	no	—
383	C₂²⋊C₄	—	4	16	no	—
384	C₄²	—	4	8	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	4	no	—
387	C₂³	—	2	16	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	4	no	—
390	C₂³	—	2	4	no	—
391	C₂³	—	2	8	no	—
392	C₂³	—	2	8	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	4	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	8	no	—
397	C₂³	—	4	16	no	—
398	C₂³	—	4	32	no	—
399	C₂³	—	4	8	no	—
400	C₂³	—	4	8	no	—
401	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
402	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
403	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	8	yes	—
404	C₂³	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
405	C₂³	C₂²×D₄×C₁₁₃	1	2	yes	—
406	C₂³	C₂²×D₄×C₁₁₃	1	4	yes	—
407	Q₈	—	2	16	no	—
408	Q₈	—	2	16	no	—
409	D₄	—	2	32	no	—
410	D₄	—	2	16	no	—
411	D₄	—	2	32	no	—
412	D₄	—	2	16	no	—
413	C₂×C₄	—	2	16	no	—
414	C₂×C₄	—	2	32	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	8	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	16	no	—
427	C₂×C₄	—	2	16	no	—
428	C₂×C₄	—	4	16	no	—
429	C₂×C₄	—	4	8	no	—
430	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
431	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	8	yes	—
432	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
433	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
434	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
435	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
436	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
437	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
438	C₂×C₄	#120×C₁₁₃	1	8	yes	—
439	C₂×C₄	#120×C₁₁₃	1	8	yes	—
440	C₂²	—	2	8	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	8	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	16	no	—
450	C₂²	—	4	8	no	—
451	C₂²	—	4	4	no	—
452	C₂²	—	4	8	no	—
453	C₂²	—	4	32	no	—
454	C₂²	—	4	8	no	—
455	C₂²	#410×C₁₁₃	1	4	yes	complemented
456	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	2	yes	—
457	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
458	C₂²	C₂×#120×C₁₁₃	1	4	yes	—
459	C₄	—	2	2	no	—
460	C₄	—	2	8	no	—
461	C₄	—	2	2	no	—
462	C₄	—	8	8	no	—
463	C₄	#379×C₁₁₃	1	2	yes	—
464	C₄	#379×C₁₁₃	1	2	yes	—
465	C₄	#379×C₁₁₃	1	4	yes	—
466	C₂	—	2	4	no	—
467	C₂	—	2	2	no	—
468	C₂	—	2	4	no	—
469	C₂	—	4	2	no	—
470	C₂	—	4	8	no	—
471	C₂	C₂×#379×C₁₁₃	1	1	yes	characteristic
472	C₂	C₂×#410×C₁₁₃	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×#410×C₁₁₃	C₂	semidirect
3. C₁₁₃×#2280	C₂	semidirect
4. C₁₁₃×#1782	C₂	semidirect
5. C₁₁₃×#1781	C₂	semidirect
9. C₂²×#41×C₁₁₃	C₄	semidirect
10. C₂²×#41×C₁₁₃	C₄	semidirect
13. C₂³×Q₈×C₁₁₃	C₄	semidirect
14. C₂³×D₄×C₁₁₃	C₄	semidirect
16. C₂⁴×C₄×C₁₁₃	C₄	semidirect
18. C₂×#117×C₁₁₃	C₂²	semidirect
20. C₂×#99×C₁₁₃	C₂²	semidirect
21. #381×C₁₁₃	C₂²	semidirect
96. C₂×Q₈×C₁₁₃	C₂²⋊C₄	semidirect
108. C₂×D₄×C₁₁₃	C₂²⋊C₄	semidirect
134. C₂²×C₄×C₁₁₃	C₂²⋊C₄	semidirect
218. C₂²×C₁₁₃	#410	semidirect
229. #20584	C₁₁₃	direct (N × H)
238. C₂×#410	C₂×C₁₁₃	semidirect
239. #2280	C₂×C₁₁₃	semidirect
240. #1782	C₂×C₁₁₃	semidirect
241. #1781	C₂×C₁₁₃	semidirect
242. C₁₁₃	#20584	direct (N × H)
246. C₂²×#41	C₄×C₁₁₃	semidirect
247. C₂²×#41	C₄×C₁₁₃	semidirect
250. C₂³×Q₈	C₄×C₁₁₃	semidirect
251. C₂³×D₄	C₄×C₁₁₃	semidirect
253. C₂⁴×C₄	C₄×C₁₁₃	semidirect
255. C₂×#117	C₂²×C₁₁₃	semidirect
257. C₂×#99	C₂²×C₁₁₃	semidirect
258. #381	C₂²×C₁₁₃	semidirect
333. C₂×Q₈	C₂²⋊C₄×C₁₁₃	semidirect
345. C₂×D₄	C₂²⋊C₄×C₁₁₃	semidirect
371. C₂²×C₄	C₂²⋊C₄×C₁₁₃	semidirect
455. C₂²	#410×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×#410×C₁₁₃	2
C₁₁₃×#2280	2
C₁₁₃×#1782	2
C₁₁₃×#1781	2
#20584	113

Subgroups — C113×#20584 #43288604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#20584 #43288604