Subgroups — C₂×C₁₁₃×#1492 #43285490

Order 28928.

1430 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#423×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#1492	C₂	1	8	yes	maximal, direct product factor
5	C₂×D₄⋊C₈×C₁₁₃	C₂	1	4	yes	maximal, complemented
6	C₂²×#41×C₁₁₃	—	2	1	no	—
7	C₂²×M₁₆×C₁₁₃	—	2	1	no	—
8	C₂³×C₈×C₁₁₃	—	2	1	no	—
9	#532×C₁₁₃	—	2	2	no	—
10	#532×C₁₁₃	—	2	2	no	—
11	#532×C₁₁₃	C₄	1	4	yes	—
12	#532×C₁₁₃	C₂²	1	4	yes	—
13	C₂×C₄⋊Q₈×C₁₁₃	C₄	1	1	yes	characteristic
14	C₂×#127×C₁₁₃	C₄	1	1	yes	characteristic
15	C₂×#124×C₁₁₃	—	2	1	no	—
16	C₂×#121×C₁₁₃	—	2	1	no	—
17	C₂×#121×C₁₁₃	C₄	1	2	yes	—
18	C₂×C₄×D₄×C₁₁₃	—	2	1	no	—
19	C₂×C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
20	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
21	#423×C₁₁₃	—	2	2	no	—
22	#423×C₁₁₃	C₂²	1	4	yes	complemented
23	C₂×C₄⋊C₈×C₁₁₃	—	2	1	no	—
24	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₁₃	—	2	2	no	—
26	C₂×C₄×C₈×C₁₁₃	—	2	1	no	—
27	C₂×C₄×C₈×C₁₁₃	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₁₃	C₂²	1	4	yes	complemented
29	D₄⋊C₈×C₁₁₃	C₂²	1	16	yes	complemented
30	C₂×#41×C₁₁₃	—	2	4	no	—
31	C₂×#41×C₁₁₃	—	2	4	no	—
32	C₂×#41×C₁₁₃	—	4	4	no	—
33	C₂×#41×C₁₁₃	—	4	4	no	—
34	C₂²×Q₈×C₁₁₃	—	2	1	no	—
35	C₂²×D₄×C₁₁₃	—	2	2	no	—
36	C₂²×D₄×C₁₁₃	—	2	1	no	—
37	C₂²×D₄×C₁₁₃	—	2	1	no	—
38	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
39	C₂³×C₄×C₁₁₃	—	2	2	no	—
40	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
43	C₂×M₁₆×C₁₁₃	—	2	4	no	—
44	C₂×M₁₆×C₁₁₃	—	4	4	no	—
45	C₂²×C₈×C₁₁₃	—	2	8	no	—
46	C₂²×C₈×C₁₁₃	—	2	2	no	—
47	C₂²×C₈×C₁₁₃	—	2	4	no	—
48	C₂²×C₈×C₁₁₃	—	2	2	no	—
49	C₄⋊Q₈×C₁₁₃	—	2	2	no	—
50	C₄⋊Q₈×C₁₁₃	C₂×C₄	1	4	yes	—
51	#127×C₁₁₃	—	2	2	no	—
52	#127×C₁₁₃	C₂×C₄	1	4	yes	—
53	#124×C₁₁₃	—	2	4	no	—
54	#124×C₁₁₃	—	2	4	no	—
55	#121×C₁₁₃	—	2	4	no	—
56	#121×C₁₁₃	—	2	4	no	—
57	#121×C₁₁₃	—	2	4	no	—
58	#121×C₁₁₃	C₂×C₄	1	8	yes	—
59	C₄×D₄×C₁₁₃	—	2	4	no	—
60	C₄×D₄×C₁₁₃	—	2	4	no	—
61	C₄×D₄×C₁₁₃	—	2	2	no	—
62	C₄×D₄×C₁₁₃	—	2	2	no	—
63	C₄×D₄×C₁₁₃	C₂×C₄	1	4	yes	—
64	C₄×D₄×C₁₁₃	C₂³	1	4	yes	—
65	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
67	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
69	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₁₃	C₂×C₄	1	2	yes	—
71	C₂×C₄²×C₁₁₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₁₃	D₄	1	2	yes	—
73	C₂×C₄²×C₁₁₃	D₄	1	2	yes	—
74	C₂×C₄²×C₁₁₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
76	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
77	C₄⋊C₈×C₁₁₃	—	2	4	no	—
78	C₄⋊C₈×C₁₁₃	—	2	2	no	—
79	C₄⋊C₈×C₁₁₃	C₂³	1	4	yes	—
80	C₄×C₈×C₁₁₃	—	2	2	no	—
81	C₄×C₈×C₁₁₃	—	2	4	no	—
82	C₄×C₈×C₁₁₃	C₂³	1	4	yes	—
83	C₂⁴×C₁₁₃	—	2	2	no	—
84	C₂⁴×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
85	#41×C₁₁₃	—	4	16	no	—
86	#41×C₁₁₃	—	4	8	no	—
87	#41×C₁₁₃	—	4	8	no	—
88	C₂×Q₈×C₁₁₃	—	2	4	no	—
89	C₂×Q₈×C₁₁₃	—	4	4	no	—
90	C₂×D₄×C₁₁₃	—	2	8	no	—
91	C₂×D₄×C₁₁₃	—	2	2	no	—
92	C₂×D₄×C₁₁₃	—	2	4	no	—
93	C₂×D₄×C₁₁₃	—	2	4	no	—
94	C₂×D₄×C₁₁₃	—	2	8	no	—
95	C₂×D₄×C₁₁₃	—	4	8	no	—
96	C₂×D₄×C₁₁₃	—	4	4	no	—
97	C₂×D₄×C₁₁₃	—	4	4	no	—
98	C₂×D₄×C₁₁₃	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₁₁₃	—	2	4	no	—
100	C₂²×C₄×C₁₁₃	—	2	4	no	—
101	C₂²×C₄×C₁₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₁₃	—	2	4	no	—
103	C₂²×C₄×C₁₁₃	—	2	4	no	—
104	C₂²×C₄×C₁₁₃	—	4	4	no	—
105	C₂²×C₄×C₁₁₃	—	4	4	no	—
106	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
107	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
109	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
111	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₁₃	D₈	1	4	yes	—
113	C₂²×C₄×C₁₁₃	SD₁₆	1	4	yes	—
114	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
120	M₁₆×C₁₁₃	—	4	8	no	—
121	C₂×C₈×C₁₁₃	—	2	8	no	—
122	C₂×C₈×C₁₁₃	—	2	16	no	—
123	C₂×C₈×C₁₁₃	—	2	4	no	—
124	C₂×C₈×C₁₁₃	—	2	4	no	—
125	C₂×C₈×C₁₁₃	—	4	4	no	—
126	C₄⋊C₄×C₁₁₃	—	2	4	no	—
127	C₄⋊C₄×C₁₁₃	—	2	2	no	—
128	C₄⋊C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
129	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
130	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
131	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
132	C₄²×C₁₁₃	C₂²⋊C₄	1	2	yes	—
133	C₄²×C₁₁₃	C₂²⋊C₄	1	2	yes	—
134	C₄²×C₁₁₃	C₂²⋊C₄	1	2	yes	—
135	C₄²×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₁₁₃	C₂²×C₄	1	2	yes	—
137	C₄²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
139	C₄²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
141	C₄²×C₁₁₃	C₂⁴	1	1	yes	characteristic
142	C₂³×C₁₁₃	—	2	2	no	—
143	C₂³×C₁₁₃	—	2	2	no	—
144	C₂³×C₁₁₃	—	2	4	no	—
145	C₂³×C₁₁₃	—	4	4	no	—
146	C₂³×C₁₁₃	—	4	4	no	—
147	C₂³×C₁₁₃	—	4	4	no	—
148	C₂³×C₁₁₃	#102	1	4	yes	—
149	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	Q₈×C₁₁₃	—	4	8	no	—
152	D₄×C₁₁₃	—	2	8	no	—
153	D₄×C₁₁₃	—	4	16	no	—
154	D₄×C₁₁₃	—	4	4	no	—
155	D₄×C₁₁₃	—	4	8	no	—
156	D₄×C₁₁₃	—	4	8	no	—
157	C₂×C₄×C₁₁₃	—	2	2	no	—
158	C₂×C₄×C₁₁₃	—	2	2	no	—
159	C₂×C₄×C₁₁₃	—	2	4	no	—
160	C₂×C₄×C₁₁₃	—	2	4	no	—
161	C₂×C₄×C₁₁₃	—	2	4	no	—
162	C₂×C₄×C₁₁₃	—	2	4	no	—
163	C₂×C₄×C₁₁₃	—	2	4	no	—
164	C₂×C₄×C₁₁₃	—	4	4	no	—
165	C₂×C₄×C₁₁₃	—	4	4	no	—
166	C₂×C₄×C₁₁₃	—	4	4	no	—
167	C₂×C₄×C₁₁₃	—	4	8	no	—
168	C₂×C₄×C₁₁₃	#102	1	4	yes	—
169	C₂×C₄×C₁₁₃	#102	1	8	yes	—
170	C₂×C₄×C₁₁₃	#104	1	4	yes	—
171	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
176	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂×C₄×C₁₁₃	#131	1	4	yes	—
178	C₂×C₄×C₁₁₃	C₂×D₈	1	2	yes	—
179	C₂×C₄×C₁₁₃	C₂×D₈	1	4	yes	—
180	C₂×C₄×C₁₁₃	C₂×SD₁₆	1	2	yes	—
181	C₂×C₄×C₁₁₃	C₂×SD₁₆	1	4	yes	—
182	C₂×C₄×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
185	C₈×C₁₁₃	—	2	8	no	—
186	C₈×C₁₁₃	—	4	4	no	—
187	C₂²×C₁₁₃	—	2	2	no	—
188	C₂²×C₁₁₃	—	2	2	no	—
189	C₂²×C₁₁₃	—	2	8	no	—
190	C₂²×C₁₁₃	—	4	4	no	—
191	C₂²×C₁₁₃	—	4	4	no	—
192	C₂²×C₁₁₃	—	4	4	no	—
193	C₂²×C₁₁₃	—	8	8	no	—
194	C₂²×C₁₁₃	#408	1	2	yes	—
195	C₂²×C₁₁₃	C₂×#102	1	4	yes	—
196	C₂²×C₁₁₃	C₂×#102	1	2	yes	—
197	C₂²×C₁₁₃	C₂×#104	1	2	yes	—
198	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
199	C₄×C₁₁₃	—	2	2	no	—
200	C₄×C₁₁₃	—	2	1	no	—
201	C₄×C₁₁₃	—	2	1	no	—
202	C₄×C₁₁₃	—	4	4	no	—
203	C₄×C₁₁₃	#408	1	2	yes	—
204	C₄×C₁₁₃	C₂×#102	1	2	yes	—
205	C₄×C₁₁₃	C₂×#102	1	4	yes	—
206	C₄×C₁₁₃	C₂×#104	1	4	yes	—
207	C₄×C₁₁₃	C₂×#131	1	2	yes	—
208	C₄×C₁₁₃	C₂²×D₈	1	1	yes	characteristic
209	C₄×C₁₁₃	C₂²×SD₁₆	1	1	yes	characteristic
210	C₂×#1492	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂×C₁₁₃	—	2	4	no	—
212	C₂×C₁₁₃	—	8	4	no	—
213	C₂×C₁₁₃	#1492	1	4	yes	direct product factor
214	C₂×C₁₁₃	C₂×#408	1	1	yes	characteristic
215	C₂×C₁₁₃	C₂²×#102	1	1	yes	characteristic
216	C₂×C₁₁₃	C₂²×#104	1	1	yes	characteristic
217	C₂×#532	C₂×C₁₁₃	1	1	yes	characteristic
218	C₂×#423	C₂×C₁₁₃	1	1	yes	characteristic, complemented
219	C₂²×C₄×C₈	C₂×C₁₁₃	1	1	yes	characteristic, complemented
220	#1492	C₂×C₁₁₃	1	8	yes	direct product factor
221	C₂×D₄⋊C₈	C₂×C₁₁₃	1	4	yes	complemented
222	C₁₁₃	C₂×#1492	1	1	yes	characteristic, direct product factor, Sylow
223	C₂²×#41	—	2	1	no	—
224	C₂²×M₁₆	—	2	1	no	—
225	C₂³×C₈	—	2	1	no	—
226	#532	—	2	2	no	—
227	#532	—	2	2	no	—
228	#532	C₄×C₁₁₃	1	4	yes	—
229	#532	C₂²×C₁₁₃	1	4	yes	—
230	C₂×C₄⋊Q₈	C₄×C₁₁₃	1	1	yes	characteristic
231	C₂×#127	C₄×C₁₁₃	1	1	yes	characteristic
232	C₂×#124	—	2	1	no	—
233	C₂×#121	—	2	1	no	—
234	C₂×#121	C₄×C₁₁₃	1	2	yes	—
235	C₂×C₄×D₄	—	2	1	no	—
236	C₂×C₄×D₄	C₂²×C₁₁₃	1	2	yes	—
237	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
238	#423	—	2	2	no	—
239	#423	C₂²×C₁₁₃	1	4	yes	complemented
240	C₂×C₄⋊C₈	—	2	1	no	—
241	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
242	C₂×C₄×C₈	—	2	2	no	—
243	C₂×C₄×C₈	—	2	1	no	—
244	C₂×C₄×C₈	C₂²×C₁₁₃	1	2	yes	—
245	C₂×C₄×C₈	C₂²×C₁₁₃	1	4	yes	complemented
246	D₄⋊C₈	C₂²×C₁₁₃	1	16	yes	complemented
247	C₂×#41	—	2	4	no	—
248	C₂×#41	—	2	4	no	—
249	C₂×#41	—	4	4	no	—
250	C₂×#41	—	4	4	no	—
251	C₂²×Q₈	—	2	1	no	—
252	C₂²×D₄	—	2	2	no	—
253	C₂²×D₄	—	2	1	no	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
256	C₂³×C₄	—	2	2	no	—
257	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
258	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
259	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
260	C₂×M₁₆	—	2	4	no	—
261	C₂×M₁₆	—	4	4	no	—
262	C₂²×C₈	—	2	8	no	—
263	C₂²×C₈	—	2	2	no	—
264	C₂²×C₈	—	2	4	no	—
265	C₂²×C₈	—	2	2	no	—
266	C₄⋊Q₈	—	2	2	no	—
267	C₄⋊Q₈	C₂×C₄×C₁₁₃	1	4	yes	—
268	#127	—	2	2	no	—
269	#127	C₂×C₄×C₁₁₃	1	4	yes	—
270	#124	—	2	4	no	—
271	#124	—	2	4	no	—
272	#121	—	2	4	no	—
273	#121	—	2	4	no	—
274	#121	—	2	4	no	—
275	#121	C₂×C₄×C₁₁₃	1	8	yes	—
276	C₄×D₄	—	2	4	no	—
277	C₄×D₄	—	2	4	no	—
278	C₄×D₄	—	2	2	no	—
279	C₄×D₄	—	2	2	no	—
280	C₄×D₄	C₂×C₄×C₁₁₃	1	4	yes	—
281	C₄×D₄	C₂³×C₁₁₃	1	4	yes	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
287	C₂×C₄²	C₂×C₄×C₁₁₃	1	2	yes	—
288	C₂×C₄²	D₄×C₁₁₃	1	1	yes	characteristic
289	C₂×C₄²	D₄×C₁₁₃	1	1	yes	characteristic
290	C₂×C₄²	D₄×C₁₁₃	1	2	yes	—
291	C₂×C₄²	D₄×C₁₁₃	1	2	yes	—
292	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
293	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
294	C₄⋊C₈	—	2	4	no	—
295	C₄⋊C₈	—	2	2	no	—
296	C₄⋊C₈	C₂³×C₁₁₃	1	4	yes	—
297	C₄×C₈	—	2	2	no	—
298	C₄×C₈	—	2	4	no	—
299	C₄×C₈	C₂³×C₁₁₃	1	4	yes	—
300	C₂⁴	—	2	2	no	—
301	C₂⁴	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
302	#41	—	4	16	no	—
303	#41	—	4	8	no	—
304	#41	—	4	8	no	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	—	4	4	no	—
307	C₂×D₄	—	2	8	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	2	4	no	—
311	C₂×D₄	—	2	8	no	—
312	C₂×D₄	—	4	8	no	—
313	C₂×D₄	—	4	4	no	—
314	C₂×D₄	—	4	4	no	—
315	C₂×D₄	C₂²×C₄×C₁₁₃	1	4	yes	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	4	4	no	—
322	C₂²×C₄	—	4	4	no	—
323	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
324	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
325	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
326	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
327	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
328	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
329	C₂²×C₄	D₈×C₁₁₃	1	4	yes	—
330	C₂²×C₄	SD₁₆×C₁₁₃	1	4	yes	—
331	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
332	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
337	M₁₆	—	4	8	no	—
338	C₂×C₈	—	2	8	no	—
339	C₂×C₈	—	2	16	no	—
340	C₂×C₈	—	2	4	no	—
341	C₂×C₈	—	2	4	no	—
342	C₂×C₈	—	4	4	no	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
346	C₂²⋊C₄	—	2	8	no	—
347	C₂²⋊C₄	—	2	4	no	—
348	C₂²⋊C₄	—	2	4	no	—
349	C₄²	C₂²⋊C₄×C₁₁₃	1	2	yes	—
350	C₄²	C₂²⋊C₄×C₁₁₃	1	2	yes	—
351	C₄²	C₂²⋊C₄×C₁₁₃	1	2	yes	—
352	C₄²	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
353	C₄²	C₂²×C₄×C₁₁₃	1	2	yes	—
354	C₄²	C₂×D₄×C₁₁₃	1	1	yes	characteristic
355	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
356	C₄²	C₂×D₄×C₁₁₃	1	1	yes	characteristic
357	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
358	C₄²	C₂⁴×C₁₁₃	1	1	yes	characteristic
359	C₂³	—	2	2	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	4	4	no	—
363	C₂³	—	4	4	no	—
364	C₂³	—	4	4	no	—
365	C₂³	#102×C₁₁₃	1	4	yes	—
366	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
367	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
368	Q₈	—	4	8	no	—
369	D₄	—	2	8	no	—
370	D₄	—	4	16	no	—
371	D₄	—	4	4	no	—
372	D₄	—	4	8	no	—
373	D₄	—	4	8	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	8	no	—
385	C₂×C₄	#102×C₁₁₃	1	4	yes	—
386	C₂×C₄	#102×C₁₁₃	1	8	yes	—
387	C₂×C₄	#104×C₁₁₃	1	4	yes	—
388	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
389	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
390	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
391	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
392	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
393	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
394	C₂×C₄	#131×C₁₁₃	1	4	yes	—
395	C₂×C₄	C₂×D₈×C₁₁₃	1	2	yes	—
396	C₂×C₄	C₂×D₈×C₁₁₃	1	4	yes	—
397	C₂×C₄	C₂×SD₁₆×C₁₁₃	1	2	yes	—
398	C₂×C₄	C₂×SD₁₆×C₁₁₃	1	4	yes	—
399	C₂×C₄	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
400	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
402	C₈	—	2	8	no	—
403	C₈	—	4	4	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	8	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	8	8	no	—
411	C₂²	#408×C₁₁₃	1	2	yes	—
412	C₂²	C₂×#102×C₁₁₃	1	4	yes	—
413	C₂²	C₂×#102×C₁₁₃	1	2	yes	—
414	C₂²	C₂×#104×C₁₁₃	1	2	yes	—
415	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	4	4	no	—
420	C₄	#408×C₁₁₃	1	2	yes	—
421	C₄	C₂×#102×C₁₁₃	1	2	yes	—
422	C₄	C₂×#102×C₁₁₃	1	4	yes	—
423	C₄	C₂×#104×C₁₁₃	1	4	yes	—
424	C₄	C₂×#131×C₁₁₃	1	2	yes	—
425	C₄	C₂²×D₈×C₁₁₃	1	1	yes	characteristic
426	C₄	C₂²×SD₁₆×C₁₁₃	1	1	yes	characteristic
427	C₂	—	2	4	no	—
428	C₂	—	8	4	no	—
429	C₂	C₁₁₃×#1492	1	4	yes	direct product factor
430	C₂	C₂×#408×C₁₁₃	1	1	yes	characteristic
431	C₂	C₂²×#102×C₁₁₃	1	1	yes	characteristic
432	C₂	C₂²×#104×C₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₁₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₁₃
socle	C₂³×C₁₁₃	C₂×C₂²⋊C₄
prime radical	C₂×#532×C₁₁₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁₃ ◁ C₂²×C₄²×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#423×C₁₁₃	C₂	semidirect
3. C₂²×C₄×C₈×C₁₁₃	C₂	semidirect
4. C₁₁₃×#1492	C₂	direct (N × H)
5. C₂×D₄⋊C₈×C₁₁₃	C₂	semidirect
22. #423×C₁₁₃	C₂²	semidirect
28. C₂×C₄×C₈×C₁₁₃	C₂²	semidirect
29. D₄⋊C₈×C₁₁₃	C₂²	semidirect
210. C₂×#1492	C₁₁₃	direct (N × H)
213. C₂×C₁₁₃	#1492	direct (N × H)
218. C₂×#423	C₂×C₁₁₃	semidirect
219. C₂²×C₄×C₈	C₂×C₁₁₃	semidirect
220. #1492	C₂×C₁₁₃	direct (N × H)
221. C₂×D₄⋊C₈	C₂×C₁₁₃	semidirect
222. C₁₁₃	C₂×#1492	direct (N × H)
239. #423	C₂²×C₁₁₃	semidirect
245. C₂×C₄×C₈	C₂²×C₁₁₃	semidirect
246. D₄⋊C₈	C₂²×C₁₁₃	semidirect
429. C₂	C₁₁₃×#1492	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#532×C₁₁₃	2
C₂×#423×C₁₁₃	2
C₂²×C₄×C₈×C₁₁₃	2
C₁₁₃×#1492	2
C₂×D₄⋊C₈×C₁₁₃	2
C₂×#1492	113

Subgroups — C2×C113×#1492 #43285490

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁₃×#1492 #43285490