Subgroups — C₁₁₃×#25629 #43293649

Order 28928.

1178 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×#559×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#492×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#462×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#2568	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁₃×#2015	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
8	C₁₁₃×#1877	C₂	1	4	yes	maximal, complemented
9	C₄×#103×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₁₆×C₁₁₃	C₂²	1	2	yes	—
11	C₂²×SD₁₆×C₁₁₃	C₂²	1	4	yes	—
12	#559×C₁₁₃	—	2	4	no	—
13	#559×C₁₁₃	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
15	C₂×#127×C₁₁₃	C₂²	1	1	yes	characteristic
16	C₂×#124×C₁₁₃	—	2	1	no	—
17	C₂×#124×C₁₁₃	C₂²	1	2	yes	—
18	C₂×#123×C₁₁₃	—	2	2	no	—
19	C₂×C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₁₃	—	2	1	no	—
22	C₂×C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
23	#492×C₁₁₃	—	2	4	no	—
24	#462×C₁₁₃	—	2	4	no	—
25	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	1	yes	characteristic
26	C₂×#103×C₁₁₃	C₂²	1	2	yes	—
27	C₂×#103×C₁₁₃	C₂²	1	2	yes	—
28	C₂×#102×C₁₁₃	C₂²	1	4	yes	—
29	C₂×C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
30	#400×C₁₁₃	—	2	2	no	—
31	#391×C₁₁₃	—	2	1	no	—
32	#391×C₁₁₃	C₂²	1	4	yes	—
33	#382×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	C₂²×Q₈×C₁₁₃	D₄	1	1	yes	characteristic
38	C₂²×Q₈×C₁₁₃	C₂³	1	2	yes	—
39	C₂²×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₁₁₃	—	2	1	no	—
41	C₂²×D₄×C₁₁₃	—	2	1	no	—
42	C₂²×D₄×C₁₁₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₁₃	—	2	2	no	—
44	C₂×Q₁₆×C₁₁₃	—	2	4	no	—
45	C₂×Q₁₆×C₁₁₃	—	4	4	no	—
46	C₂×SD₁₆×C₁₁₃	—	2	8	no	—
47	C₂×SD₁₆×C₁₁₃	—	2	8	no	—
48	C₂×SD₁₆×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	—	2	2	no	—
53	#127×C₁₁₃	—	2	2	no	—
54	#127×C₁₁₃	D₄	1	4	yes	—
55	#124×C₁₁₃	—	2	8	no	—
56	#124×C₁₁₃	—	2	4	no	—
57	#124×C₁₁₃	—	2	4	no	—
58	#123×C₁₁₃	—	2	16	no	—
59	C₄×Q₈×C₁₁₃	—	2	2	no	—
60	C₄×Q₈×C₁₁₃	—	2	2	no	—
61	C₄×Q₈×C₁₁₃	—	2	2	no	—
62	C₄×Q₈×C₁₁₃	D₄	1	4	yes	—
63	C₄×D₄×C₁₁₃	—	2	8	no	—
64	C₄×D₄×C₁₁₃	—	2	4	no	—
65	C₄×D₄×C₁₁₃	—	2	4	no	—
66	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₁₃	D₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₁₃	D₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
76	C₂×C₄²×C₁₁₃	—	2	1	no	—
77	C₂×C₄²×C₁₁₃	—	2	1	no	—
78	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
79	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
80	C₄⋊C₈×C₁₁₃	—	2	2	no	—
81	#103×C₁₁₃	—	2	4	no	—
82	#103×C₁₁₃	—	2	4	no	—
83	#102×C₁₁₃	—	4	4	no	—
84	C₄×C₈×C₁₁₃	—	2	2	no	—
85	#95×C₁₁₃	—	2	1	no	—
86	#95×C₁₁₃	—	2	4	no	—
87	#95×C₁₁₃	—	2	4	no	—
88	C₂⁴×C₁₁₃	—	2	2	no	—
89	C₂×Q₈×C₁₁₃	—	2	2	no	—
90	C₂×Q₈×C₁₁₃	—	2	2	no	—
91	C₂×Q₈×C₁₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₁₃	—	2	1	no	—
93	C₂×Q₈×C₁₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₁₃	—	2	2	no	—
96	C₂×Q₈×C₁₁₃	—	2	4	no	—
97	C₂×Q₈×C₁₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₁₃	—	2	4	no	—
99	C₂×Q₈×C₁₁₃	C₂×D₄	1	2	yes	—
100	C₂×D₄×C₁₁₃	—	2	4	no	—
101	C₂×D₄×C₁₁₃	—	2	4	no	—
102	C₂×D₄×C₁₁₃	—	2	2	no	—
103	C₂×D₄×C₁₁₃	—	2	4	no	—
104	C₂×D₄×C₁₁₃	—	2	4	no	—
105	C₂×D₄×C₁₁₃	—	4	2	no	—
106	C₂×D₄×C₁₁₃	—	4	2	no	—
107	C₂×D₄×C₁₁₃	—	8	2	no	—
108	C₂×D₄×C₁₁₃	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₁₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₁₃	—	2	8	no	—
112	C₂²×C₄×C₁₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₁₃	—	8	4	no	—
115	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
120	Q₁₆×C₁₁₃	—	4	8	no	—
121	SD₁₆×C₁₁₃	—	4	16	no	—
122	C₂×C₈×C₁₁₃	—	2	2	no	—
123	C₂×C₈×C₁₁₃	—	2	2	no	—
124	C₂×C₈×C₁₁₃	—	2	2	no	—
125	C₂×C₈×C₁₁₃	—	2	4	no	—
126	C₂×C₈×C₁₁₃	#41	1	4	yes	—
127	C₄⋊C₄×C₁₁₃	—	2	4	no	—
128	C₄⋊C₄×C₁₁₃	—	2	2	no	—
129	C₄⋊C₄×C₁₁₃	—	2	4	no	—
130	C₄⋊C₄×C₁₁₃	—	2	1	no	—
131	C₄⋊C₄×C₁₁₃	—	2	2	no	—
132	C₄⋊C₄×C₁₁₃	—	2	2	no	—
133	C₄⋊C₄×C₁₁₃	—	4	2	no	—
134	C₄⋊C₄×C₁₁₃	—	4	2	no	—
135	C₄⋊C₄×C₁₁₃	C₂×D₄	1	2	yes	—
136	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
137	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
138	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
139	C₄²×C₁₁₃	—	2	4	no	—
140	C₄²×C₁₁₃	—	2	2	no	—
141	C₄²×C₁₁₃	—	2	2	no	—
142	C₄²×C₁₁₃	—	4	2	no	—
143	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
144	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
145	C₂³×C₁₁₃	—	2	4	no	—
146	C₂³×C₁₁₃	—	4	4	no	—
147	C₂³×C₁₁₃	—	4	2	no	—
148	C₂³×C₁₁₃	—	4	2	no	—
149	C₂³×C₁₁₃	—	4	4	no	—
150	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₁₁₃	—	2	2	no	—
152	Q₈×C₁₁₃	—	2	2	no	—
153	Q₈×C₁₁₃	—	4	2	no	—
154	Q₈×C₁₁₃	—	4	4	no	—
155	Q₈×C₁₁₃	—	4	2	no	—
156	Q₈×C₁₁₃	—	4	2	no	—
157	Q₈×C₁₁₃	—	4	4	no	—
158	D₄×C₁₁₃	—	2	8	no	—
159	D₄×C₁₁₃	—	4	2	no	—
160	D₄×C₁₁₃	—	4	2	no	—
161	D₄×C₁₁₃	—	4	8	no	—
162	D₄×C₁₁₃	—	8	4	no	—
163	C₂×C₄×C₁₁₃	—	2	2	no	—
164	C₂×C₄×C₁₁₃	—	2	2	no	—
165	C₂×C₄×C₁₁₃	—	2	2	no	—
166	C₂×C₄×C₁₁₃	—	2	2	no	—
167	C₂×C₄×C₁₁₃	—	2	2	no	—
168	C₂×C₄×C₁₁₃	—	2	2	no	—
169	C₂×C₄×C₁₁₃	—	2	2	no	—
170	C₂×C₄×C₁₁₃	—	2	4	no	—
171	C₂×C₄×C₁₁₃	—	4	2	no	—
172	C₂×C₄×C₁₁₃	—	4	2	no	—
173	C₂×C₄×C₁₁₃	—	4	2	no	—
174	C₂×C₄×C₁₁₃	—	4	2	no	—
175	C₂×C₄×C₁₁₃	—	4	4	no	—
176	C₂×C₄×C₁₁₃	—	4	2	no	—
177	C₂×C₄×C₁₁₃	—	4	2	no	—
178	C₂×C₄×C₁₁₃	—	8	8	no	—
179	C₂×C₄×C₁₁₃	#120	1	2	yes	—
180	C₂×C₄×C₁₁₃	#120	1	2	yes	—
181	C₂×C₄×C₁₁₃	#135	1	2	yes	—
182	C₂×C₄×C₁₁₃	#137	1	2	yes	—
183	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₁₃	C₂×#41	1	2	yes	—
186	C₂×C₄×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
187	C₈×C₁₁₃	—	2	4	no	—
188	C₈×C₁₁₃	—	4	2	no	—
189	C₂²×C₁₁₃	—	4	4	no	—
190	C₂²×C₁₁₃	—	4	4	no	—
191	C₂²×C₁₁₃	—	4	4	no	—
192	C₂²×C₁₁₃	—	8	4	no	—
193	C₂²×C₁₁₃	—	8	4	no	—
194	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
195	C₂²×C₁₁₃	#550	1	2	yes	—
196	C₂²×C₁₁₃	C₂×#135	1	1	yes	characteristic
197	C₂²×C₁₁₃	C₂×#137	1	1	yes	characteristic
198	C₂²×C₁₁₃	#577	1	2	yes	—
199	C₄×C₁₁₃	—	2	2	no	—
200	C₄×C₁₁₃	—	4	2	no	—
201	C₄×C₁₁₃	—	4	2	no	—
202	C₄×C₁₁₃	—	4	2	no	—
203	C₄×C₁₁₃	—	4	2	no	—
204	C₄×C₁₁₃	—	8	2	no	—
205	C₄×C₁₁₃	—	8	2	no	—
206	C₄×C₁₁₃	#452	1	4	yes	—
207	C₄×C₁₁₃	#532	1	1	yes	characteristic
208	C₄×C₁₁₃	#535	1	1	yes	characteristic
209	C₄×C₁₁₃	#546	1	2	yes	—
210	#25629	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂×C₁₁₃	—	8	4	no	—
212	C₂×C₁₁₃	#2431	1	1	yes	characteristic
213	C₂×C₁₁₃	C₂×#452	1	1	yes	characteristic
214	C₂×C₁₁₃	#3009	1	1	yes	characteristic
215	C₂×C₁₁₃	#3394	1	2	yes	—
216	C₂×C₁₁₃	#3400	1	2	yes	—
217	C₂×#559	C₂×C₁₁₃	1	1	yes	characteristic
218	C₂×#492	C₂×C₁₁₃	1	1	yes	characteristic
219	C₂×#462	C₂×C₁₁₃	1	1	yes	characteristic, complemented
220	#2568	C₂×C₁₁₃	1	1	yes	characteristic, complemented
221	#2015	C₂×C₁₁₃	1	4	yes	complemented
222	#1984	C₂×C₁₁₃	1	1	yes	characteristic, complemented
223	#1982	C₂×C₁₁₃	1	1	yes	characteristic
224	#1877	C₂×C₁₁₃	1	4	yes	complemented
225	C₄×#103	C₂×C₁₁₃	1	1	yes	characteristic, complemented
226	C₁₁₃	#25629	1	1	yes	characteristic, direct product factor, Sylow
227	C₂²×Q₁₆	C₂²×C₁₁₃	1	2	yes	—
228	C₂²×SD₁₆	C₂²×C₁₁₃	1	4	yes	—
229	#559	—	2	4	no	—
230	#559	—	2	4	no	—
231	C₂×C₄⋊Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
232	C₂×#127	C₂²×C₁₁₃	1	1	yes	characteristic
233	C₂×#124	—	2	1	no	—
234	C₂×#124	C₂²×C₁₁₃	1	2	yes	—
235	C₂×#123	—	2	2	no	—
236	C₂×C₄×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
237	C₂×C₄×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
238	C₂×C₄×D₄	—	2	1	no	—
239	C₂×C₄×D₄	C₂²×C₁₁₃	1	2	yes	—
240	#492	—	2	4	no	—
241	#462	—	2	4	no	—
242	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	1	yes	characteristic
243	C₂×#103	C₂²×C₁₁₃	1	2	yes	—
244	C₂×#103	C₂²×C₁₁₃	1	2	yes	—
245	C₂×#102	C₂²×C₁₁₃	1	4	yes	—
246	C₂×C₄×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
247	#400	—	2	2	no	—
248	#391	—	2	1	no	—
249	#391	C₂²×C₁₁₃	1	4	yes	—
250	#382	—	2	1	no	—
251	C₄×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
252	#340	C₂²×C₁₁₃	1	2	yes	—
253	#336	C₂²×C₁₁₃	1	4	yes	—
254	C₂²×Q₈	D₄×C₁₁₃	1	1	yes	characteristic
255	C₂²×Q₈	C₂³×C₁₁₃	1	2	yes	—
256	C₂²×Q₈	C₂³×C₁₁₃	1	1	yes	characteristic
257	C₂²×D₄	—	2	1	no	—
258	C₂²×D₄	—	2	1	no	—
259	C₂²×D₄	C₂³×C₁₁₃	1	2	yes	—
260	C₂³×C₄	—	2	2	no	—
261	C₂×Q₁₆	—	2	4	no	—
262	C₂×Q₁₆	—	4	4	no	—
263	C₂×SD₁₆	—	2	8	no	—
264	C₂×SD₁₆	—	2	8	no	—
265	C₂×SD₁₆	—	4	4	no	—
266	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
267	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
268	C₄⋊Q₈	—	2	2	no	—
269	C₄⋊Q₈	—	2	2	no	—
270	#127	—	2	2	no	—
271	#127	D₄×C₁₁₃	1	4	yes	—
272	#124	—	2	8	no	—
273	#124	—	2	4	no	—
274	#124	—	2	4	no	—
275	#123	—	2	16	no	—
276	C₄×Q₈	—	2	2	no	—
277	C₄×Q₈	—	2	2	no	—
278	C₄×Q₈	—	2	2	no	—
279	C₄×Q₈	D₄×C₁₁₃	1	4	yes	—
280	C₄×D₄	—	2	8	no	—
281	C₄×D₄	—	2	4	no	—
282	C₄×D₄	—	2	4	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	D₄×C₁₁₃	1	1	yes	characteristic
287	C₂×C₄⋊C₄	D₄×C₁₁₃	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
296	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
297	C₄⋊C₈	—	2	2	no	—
298	#103	—	2	4	no	—
299	#103	—	2	4	no	—
300	#102	—	4	4	no	—
301	C₄×C₈	—	2	2	no	—
302	#95	—	2	1	no	—
303	#95	—	2	4	no	—
304	#95	—	2	4	no	—
305	C₂⁴	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	4	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	4	no	—
316	C₂×Q₈	C₂×D₄×C₁₁₃	1	2	yes	—
317	C₂×D₄	—	2	4	no	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	4	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	4	2	no	—
323	C₂×D₄	—	4	2	no	—
324	C₂×D₄	—	8	2	no	—
325	C₂×D₄	C₂×D₄×C₁₁₃	1	4	yes	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	8	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	8	4	no	—
332	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
336	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
337	Q₁₆	—	4	8	no	—
338	SD₁₆	—	4	16	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	4	no	—
343	C₂×C₈	#41×C₁₁₃	1	4	yes	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	C₂×D₄×C₁₁₃	1	2	yes	—
353	C₂²⋊C₄	—	2	8	no	—
354	C₂²⋊C₄	—	2	8	no	—
355	C₂²⋊C₄	—	2	8	no	—
356	C₄²	—	2	4	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	4	2	no	—
360	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
361	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
362	C₂³	—	2	4	no	—
363	C₂³	—	4	4	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	4	no	—
367	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	4	4	no	—
372	Q₈	—	4	2	no	—
373	Q₈	—	4	2	no	—
374	Q₈	—	4	4	no	—
375	D₄	—	2	8	no	—
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	4	8	no	—
379	D₄	—	8	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	8	8	no	—
396	C₂×C₄	#120×C₁₁₃	1	2	yes	—
397	C₂×C₄	#120×C₁₁₃	1	2	yes	—
398	C₂×C₄	#135×C₁₁₃	1	2	yes	—
399	C₂×C₄	#137×C₁₁₃	1	2	yes	—
400	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
402	C₂×C₄	C₂×#41×C₁₁₃	1	2	yes	—
403	C₂×C₄	H(5,𝔽₂)×C₁₁₃	1	2	yes	—
404	C₈	—	2	4	no	—
405	C₈	—	4	2	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	8	4	no	—
410	C₂²	—	8	4	no	—
411	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
412	C₂²	#550×C₁₁₃	1	2	yes	—
413	C₂²	C₂×#135×C₁₁₃	1	1	yes	characteristic
414	C₂²	C₂×#137×C₁₁₃	1	1	yes	characteristic
415	C₂²	#577×C₁₁₃	1	2	yes	—
416	C₄	—	2	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	8	2	no	—
422	C₄	—	8	2	no	—
423	C₄	#452×C₁₁₃	1	4	yes	—
424	C₄	#532×C₁₁₃	1	1	yes	characteristic
425	C₄	#535×C₁₁₃	1	1	yes	characteristic
426	C₄	#546×C₁₁₃	1	2	yes	—
427	C₂	—	8	4	no	—
428	C₂	C₁₁₃×#2431	1	1	yes	characteristic
429	C₂	C₂×#452×C₁₁₃	1	1	yes	characteristic
430	C₂	C₁₁₃×#3009	1	1	yes	characteristic
431	C₂	C₁₁₃×#3394	1	2	yes	—
432	C₂	C₁₁₃×#3400	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
prime radical	C₂×#127×C₁₁₃	C₂²
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
3. C₂×#462×C₁₁₃	C₂	semidirect
4. C₁₁₃×#2568	C₂	semidirect
5. C₁₁₃×#2015	C₂	semidirect
6. C₁₁₃×#1984	C₂	semidirect
8. C₁₁₃×#1877	C₂	semidirect
9. C₄×#103×C₁₁₃	C₂	semidirect
210. #25629	C₁₁₃	direct (N × H)
219. C₂×#462	C₂×C₁₁₃	semidirect
220. #2568	C₂×C₁₁₃	semidirect
221. #2015	C₂×C₁₁₃	semidirect
222. #1984	C₂×C₁₁₃	semidirect
224. #1877	C₂×C₁₁₃	semidirect
225. C₄×#103	C₂×C₁₁₃	semidirect
226. C₁₁₃	#25629	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×#559×C₁₁₃	2
C₂×#492×C₁₁₃	2
C₂×#462×C₁₁₃	2
C₁₁₃×#2568	2
C₁₁₃×#2015	2
C₁₁₃×#1984	2
C₁₁₃×#1982	2
C₁₁₃×#1877	2
C₄×#103×C₁₁₃	2
#25629	113

Subgroups — C113×#25629 #43293649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#25629 #43293649