Subgroups — C₁₁₃×#15181 #43283201

Order 28928.

2314 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#389×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#380×C₁₁₃	C₂	1	2	yes	maximal, complemented
4	C₂×#380×C₁₁₃	C₂	1	2	yes	maximal, complemented
5	C₁₁₃×#1442	C₂	1	2	yes	maximal, complemented
6	C₁₁₃×#1439	C₂	1	4	yes	maximal, complemented
7	C₁₁₃×#1438	C₂	1	2	yes	maximal
8	C₁₁₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₁₃	C₂²	1	2	yes	—
11	C₂×C₄×D₄×C₁₁₃	—	2	8	no	—
12	C₂×C₄×D₄×C₁₁₃	—	2	4	no	—
13	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₁₁₃	C₂²	1	4	yes	—
20	C₂²×C₂²⋊C₄×C₁₁₃	C₂²	1	4	yes	—
21	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
22	#389×C₁₁₃	—	2	4	no	—
23	#380×C₁₁₃	—	2	8	no	—
24	#380×C₁₁₃	—	2	8	no	—
25	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
26	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
27	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
28	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
29	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
30	C₂⁵×C₁₁₃	C₂³	1	2	yes	—
31	C₂²×D₄×C₁₁₃	—	2	4	no	—
32	C₂²×D₄×C₁₁₃	—	2	4	no	—
33	C₂²×D₄×C₁₁₃	—	2	2	no	—
34	C₂²×D₄×C₁₁₃	—	2	2	no	—
35	C₂²×D₄×C₁₁₃	Q₈	1	4	yes	—
36	C₂³×C₄×C₁₁₃	—	2	4	no	—
37	C₂³×C₄×C₁₁₃	—	2	4	no	—
38	C₂³×C₄×C₁₁₃	—	2	4	no	—
39	C₂³×C₄×C₁₁₃	—	2	4	no	—
40	C₂³×C₄×C₁₁₃	—	2	4	no	—
41	C₂³×C₄×C₁₁₃	—	2	4	no	—
42	C₂³×C₄×C₁₁₃	D₄	1	8	yes	—
43	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₁₃	C₂³	1	4	yes	—
45	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
50	C₄×D₄×C₁₁₃	—	2	32	no	—
51	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
52	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
56	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
58	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
59	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
61	C₂×C₄⋊C₄×C₁₁₃	—	4	4	no	—
62	C₂×C₄⋊C₄×C₁₁₃	D₄	1	4	yes	complemented
63	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
67	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
68	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
69	C₂×C₂²⋊C₄×C₁₁₃	—	4	4	no	—
70	C₂×C₂²⋊C₄×C₁₁₃	—	4	4	no	—
71	C₂×C₂²⋊C₄×C₁₁₃	—	4	4	no	—
72	C₂×C₄²×C₁₁₃	—	2	4	no	—
73	C₂×C₄²×C₁₁₃	D₄	1	4	yes	—
74	#95×C₁₁₃	—	2	8	no	—
75	#95×C₁₁₃	—	2	8	no	—
76	#95×C₁₁₃	—	2	4	no	—
77	#95×C₁₁₃	—	2	4	no	—
78	#95×C₁₁₃	—	4	2	no	—
79	C₂⁴×C₁₁₃	—	2	2	no	—
80	C₂⁴×C₁₁₃	—	2	2	no	—
81	C₂⁴×C₁₁₃	—	2	2	no	—
82	C₂⁴×C₁₁₃	—	2	2	no	—
83	C₂⁴×C₁₁₃	—	2	2	no	—
84	C₂⁴×C₁₁₃	—	2	2	no	—
85	C₂⁴×C₁₁₃	—	2	2	no	—
86	C₂⁴×C₁₁₃	—	2	2	no	—
87	C₂⁴×C₁₁₃	—	2	2	no	—
88	C₂⁴×C₁₁₃	—	2	2	no	—
89	C₂⁴×C₁₁₃	—	2	2	no	—
90	C₂⁴×C₁₁₃	—	2	2	no	—
91	C₂⁴×C₁₁₃	C₂×D₄	1	4	yes	—
92	C₂⁴×C₁₁₃	C₂×Q₈	1	4	yes	—
93	C₂⁴×C₁₁₃	#41	1	4	yes	—
94	C₂⁴×C₁₁₃	C₂⁴	1	1	yes	characteristic
95	C₂×D₄×C₁₁₃	—	2	8	no	—
96	C₂×D₄×C₁₁₃	—	2	8	no	—
97	C₂×D₄×C₁₁₃	—	2	16	no	—
98	C₂×D₄×C₁₁₃	—	2	16	no	—
99	C₂×D₄×C₁₁₃	—	2	8	no	—
100	C₂²×C₄×C₁₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₁₃	—	2	4	no	—
108	C₂²×C₄×C₁₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₁₃	—	2	16	no	—
117	C₂²×C₄×C₁₁₃	—	2	16	no	—
118	C₂²×C₄×C₁₁₃	—	2	16	no	—
119	C₂²×C₄×C₁₁₃	—	2	4	no	—
120	C₂²×C₄×C₁₁₃	—	2	4	no	—
121	C₂²×C₄×C₁₁₃	—	2	4	no	—
122	C₂²×C₄×C₁₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₁₃	—	2	4	no	—
126	C₂²×C₄×C₁₁₃	—	2	4	no	—
127	C₂²×C₄×C₁₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₁₃	—	4	8	no	—
132	C₂²×C₄×C₁₁₃	—	4	8	no	—
133	C₂²×C₄×C₁₁₃	—	4	8	no	—
134	C₂²×C₄×C₁₁₃	—	4	8	no	—
135	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
136	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
137	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
140	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₁₃	C₂×Q₈	1	2	yes	—
143	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
144	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
145	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
146	C₄⋊C₄×C₁₁₃	—	2	8	no	—
147	C₄⋊C₄×C₁₁₃	—	2	8	no	—
148	C₄⋊C₄×C₁₁₃	—	4	8	no	—
149	C₄⋊C₄×C₁₁₃	—	4	4	no	—
150	C₄⋊C₄×C₁₁₃	—	4	8	no	—
151	C₂²⋊C₄×C₁₁₃	—	2	16	no	—
152	C₂²⋊C₄×C₁₁₃	—	4	16	no	—
153	C₂²⋊C₄×C₁₁₃	—	4	16	no	—
154	C₄²×C₁₁₃	—	2	8	no	—
155	C₂³×C₁₁₃	—	2	4	no	—
156	C₂³×C₁₁₃	—	2	4	no	—
157	C₂³×C₁₁₃	—	2	4	no	—
158	C₂³×C₁₁₃	—	2	4	no	—
159	C₂³×C₁₁₃	—	2	4	no	—
160	C₂³×C₁₁₃	—	2	4	no	—
161	C₂³×C₁₁₃	—	2	4	no	—
162	C₂³×C₁₁₃	—	2	4	no	—
163	C₂³×C₁₁₃	—	2	4	no	—
164	C₂³×C₁₁₃	—	2	4	no	—
165	C₂³×C₁₁₃	—	2	4	no	—
166	C₂³×C₁₁₃	—	2	4	no	—
167	C₂³×C₁₁₃	—	2	4	no	—
168	C₂³×C₁₁₃	—	2	4	no	—
169	C₂³×C₁₁₃	—	2	4	no	—
170	C₂³×C₁₁₃	—	2	4	no	—
171	C₂³×C₁₁₃	—	2	4	no	—
172	C₂³×C₁₁₃	—	2	4	no	—
173	C₂³×C₁₁₃	—	4	2	no	—
174	C₂³×C₁₁₃	—	4	2	no	—
175	C₂³×C₁₁₃	—	4	2	no	—
176	C₂³×C₁₁₃	—	4	2	no	—
177	C₂³×C₁₁₃	—	4	2	no	—
178	C₂³×C₁₁₃	—	4	2	no	—
179	C₂³×C₁₁₃	—	4	2	no	—
180	C₂³×C₁₁₃	—	4	2	no	—
181	C₂³×C₁₁₃	—	4	2	no	—
182	C₂³×C₁₁₃	—	4	2	no	—
183	C₂³×C₁₁₃	—	4	2	no	—
184	C₂³×C₁₁₃	—	4	2	no	—
185	C₂³×C₁₁₃	—	4	2	no	—
186	C₂³×C₁₁₃	—	4	2	no	—
187	C₂³×C₁₁₃	—	4	2	no	—
188	C₂³×C₁₁₃	—	4	2	no	—
189	C₂³×C₁₁₃	C₂²⋊Q₈	1	8	yes	—
190	C₂³×C₁₁₃	C₂²×D₄	1	2	yes	—
191	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
192	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
193	C₂³×C₁₁₃	C₂²×Q₈	1	1	yes	characteristic
194	C₂³×C₁₁₃	C₂×#41	1	1	yes	characteristic
195	C₂³×C₁₁₃	C₂×#41	1	2	yes	—
196	C₂³×C₁₁₃	C₂×#41	1	2	yes	—
197	C₂³×C₁₁₃	C₂×#41	1	1	yes	characteristic
198	C₂³×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
199	C₂³×C₁₁₃	H(5,𝔽₂)	1	1	yes	characteristic
200	C₂³×C₁₁₃	2₋¹⁺⁴	1	1	yes	characteristic
201	D₄×C₁₁₃	—	2	32	no	—
202	C₂×C₄×C₁₁₃	—	2	2	no	—
203	C₂×C₄×C₁₁₃	—	2	4	no	—
204	C₂×C₄×C₁₁₃	—	2	2	no	—
205	C₂×C₄×C₁₁₃	—	2	4	no	—
206	C₂×C₄×C₁₁₃	—	2	2	no	—
207	C₂×C₄×C₁₁₃	—	2	4	no	—
208	C₂×C₄×C₁₁₃	—	2	4	no	—
209	C₂×C₄×C₁₁₃	—	2	4	no	—
210	C₂×C₄×C₁₁₃	—	2	4	no	—
211	C₂×C₄×C₁₁₃	—	2	2	no	—
212	C₂×C₄×C₁₁₃	—	2	2	no	—
213	C₂×C₄×C₁₁₃	—	2	8	no	—
214	C₂×C₄×C₁₁₃	—	4	2	no	—
215	C₂×C₄×C₁₁₃	—	4	2	no	—
216	C₂×C₄×C₁₁₃	—	4	2	no	—
217	C₂×C₄×C₁₁₃	—	4	2	no	—
218	C₂×C₄×C₁₁₃	—	4	2	no	—
219	C₂×C₄×C₁₁₃	—	4	2	no	—
220	C₂×C₄×C₁₁₃	—	4	2	no	—
221	C₂×C₄×C₁₁₃	—	4	2	no	—
222	C₂×C₄×C₁₁₃	—	4	4	no	—
223	C₂×C₄×C₁₁₃	—	4	32	no	—
224	C₂×C₄×C₁₁₃	—	4	2	no	—
225	C₂×C₄×C₁₁₃	—	4	4	no	—
226	C₂×C₄×C₁₁₃	—	4	4	no	—
227	C₂×C₄×C₁₁₃	—	4	4	no	—
228	C₂×C₄×C₁₁₃	—	4	4	no	—
229	C₂×C₄×C₁₁₃	—	4	2	no	—
230	C₂×C₄×C₁₁₃	—	4	2	no	—
231	C₂×C₄×C₁₁₃	—	4	4	no	—
232	C₂×C₄×C₁₁₃	—	4	4	no	—
233	C₂×C₄×C₁₁₃	—	4	4	no	—
234	C₂×C₄×C₁₁₃	—	4	4	no	—
235	C₂×C₄×C₁₁₃	—	4	4	no	—
236	C₂×C₄×C₁₁₃	#120	1	4	yes	—
237	C₂×C₄×C₁₁₃	#121	1	4	yes	—
238	C₂×C₄×C₁₁₃	#121	1	8	yes	—
239	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	4	yes	—
240	C₂×C₄×C₁₁₃	#123	1	8	yes	—
241	C₂×C₄×C₁₁₃	#124	1	4	yes	—
242	C₂²×C₁₁₃	—	2	8	no	—
243	C₂²×C₁₁₃	—	2	8	no	—
244	C₂²×C₁₁₃	—	2	8	no	—
245	C₂²×C₁₁₃	—	4	4	no	—
246	C₂²×C₁₁₃	—	4	4	no	—
247	C₂²×C₁₁₃	—	4	4	no	—
248	C₂²×C₁₁₃	—	4	4	no	—
249	C₂²×C₁₁₃	—	4	4	no	—
250	C₂²×C₁₁₃	—	4	4	no	—
251	C₂²×C₁₁₃	—	4	4	no	—
252	C₂²×C₁₁₃	—	4	4	no	—
253	C₂²×C₁₁₃	—	4	4	no	—
254	C₂²×C₁₁₃	—	4	4	no	—
255	C₂²×C₁₁₃	—	4	4	no	—
256	C₂²×C₁₁₃	—	4	4	no	—
257	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
258	C₂²×C₁₁₃	C₂×#121	1	2	yes	—
259	C₂²×C₁₁₃	C₂×#121	1	1	yes	characteristic
260	C₂²×C₁₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
261	C₂²×C₁₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
262	C₂²×C₁₁₃	C₂×#123	1	2	yes	—
263	C₂²×C₁₁₃	#525	1	1	yes	characteristic
264	C₂²×C₁₁₃	#525	1	2	yes	—
265	C₂²×C₁₁₃	C₂×#124	1	1	yes	characteristic
266	C₂²×C₁₁₃	#535	1	1	yes	characteristic
267	C₂²×C₁₁₃	#535	1	2	yes	—
268	C₂²×C₁₁₃	#537	1	1	yes	characteristic
269	C₂²×C₁₁₃	#537	1	2	yes	—
270	C₂²×C₁₁₃	#546	1	2	yes	—
271	C₂²×C₁₁₃	D₄×Q₈	1	1	yes	characteristic
272	C₂²×C₁₁₃	#550	1	1	yes	characteristic
273	C₂²×C₁₁₃	#552	1	2	yes	—
274	C₂²×C₁₁₃	#553	1	2	yes	—
275	C₂²×C₁₁₃	#553	1	2	yes	—
276	C₂²×C₁₁₃	#554	1	2	yes	—
277	C₂²×C₁₁₃	#554	1	1	yes	characteristic
278	C₂²×C₁₁₃	#555	1	2	yes	—
279	C₂²×C₁₁₃	#556	1	1	yes	characteristic
280	C₄×C₁₁₃	—	2	4	no	—
281	C₄×C₁₁₃	—	4	2	no	—
282	C₄×C₁₁₃	—	4	4	no	—
283	C₄×C₁₁₃	—	4	4	no	—
284	C₄×C₁₁₃	—	8	2	no	—
285	C₄×C₁₁₃	—	8	4	no	—
286	C₄×C₁₁₃	#394	1	8	yes	—
287	#15181	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
288	C₂×C₁₁₃	—	4	8	no	—
289	C₂×C₁₁₃	C₂×#394	1	1	yes	characteristic
290	C₂×C₁₁₃	#2414	1	2	yes	—
291	C₂×C₁₁₃	#2417	1	2	yes	—
292	C₂×C₁₁₃	#2485	1	2	yes	—
293	C₂×C₁₁₃	#2487	1	2	yes	—
294	C₂×C₁₁₃	#2535	1	1	yes	characteristic
295	C₂×C₁₁₃	#2538	1	1	yes	characteristic
296	C₂×C₁₁₃	#2562	1	1	yes	characteristic
297	C₂×C₁₁₃	#2563	1	1	yes	characteristic
298	C₂×C₁₁₃	#2615	1	1	yes	characteristic
299	C₂×C₁₁₃	#2848	1	1	yes	characteristic
300	C₂²×C₄×D₄	C₂×C₁₁₃	1	1	yes	characteristic
301	C₂×#389	C₂×C₁₁₃	1	1	yes	characteristic, complemented
302	C₂×#380	C₂×C₁₁₃	1	2	yes	complemented
303	C₂×#380	C₂×C₁₁₃	1	2	yes	complemented
304	#1442	C₂×C₁₁₃	1	2	yes	complemented
305	#1439	C₂×C₁₁₃	1	4	yes	complemented
306	#1438	C₂×C₁₁₃	1	2	yes	—
307	C₄⋊#95	C₂×C₁₁₃	1	1	yes	characteristic, complemented
308	C₁₁₃	#15181	1	1	yes	characteristic, direct product factor, Sylow
309	C₂³×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
310	C₂⁴×C₄	C₂²×C₁₁₃	1	2	yes	—
311	C₂×C₄×D₄	—	2	8	no	—
312	C₂×C₄×D₄	—	2	4	no	—
313	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
314	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
315	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
316	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
317	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
318	C₂²×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	—
319	C₂²×C₂²⋊C₄	C₂²×C₁₁₃	1	4	yes	—
320	C₂²×C₂²⋊C₄	C₂²×C₁₁₃	1	4	yes	—
321	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
322	#389	—	2	4	no	—
323	#380	—	2	8	no	—
324	#380	—	2	8	no	—
325	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
326	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
327	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
328	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
329	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
330	C₂⁵	C₂³×C₁₁₃	1	2	yes	—
331	C₂²×D₄	—	2	4	no	—
332	C₂²×D₄	—	2	4	no	—
333	C₂²×D₄	—	2	2	no	—
334	C₂²×D₄	—	2	2	no	—
335	C₂²×D₄	Q₈×C₁₁₃	1	4	yes	—
336	C₂³×C₄	—	2	4	no	—
337	C₂³×C₄	—	2	4	no	—
338	C₂³×C₄	—	2	4	no	—
339	C₂³×C₄	—	2	4	no	—
340	C₂³×C₄	—	2	4	no	—
341	C₂³×C₄	—	2	4	no	—
342	C₂³×C₄	D₄×C₁₁₃	1	8	yes	—
343	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
344	C₂³×C₄	C₂³×C₁₁₃	1	4	yes	—
345	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
346	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
347	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
348	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
349	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
350	C₄×D₄	—	2	32	no	—
351	C₂×C₄⋊C₄	—	2	4	no	—
352	C₂×C₄⋊C₄	—	2	2	no	—
353	C₂×C₄⋊C₄	—	2	2	no	—
354	C₂×C₄⋊C₄	—	2	2	no	—
355	C₂×C₄⋊C₄	—	2	4	no	—
356	C₂×C₄⋊C₄	—	2	4	no	—
357	C₂×C₄⋊C₄	—	2	4	no	—
358	C₂×C₄⋊C₄	—	2	4	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	—	2	4	no	—
361	C₂×C₄⋊C₄	—	4	4	no	—
362	C₂×C₄⋊C₄	D₄×C₁₁₃	1	4	yes	complemented
363	C₂×C₂²⋊C₄	—	2	4	no	—
364	C₂×C₂²⋊C₄	—	2	4	no	—
365	C₂×C₂²⋊C₄	—	2	4	no	—
366	C₂×C₂²⋊C₄	—	2	8	no	—
367	C₂×C₂²⋊C₄	—	2	8	no	—
368	C₂×C₂²⋊C₄	—	2	8	no	—
369	C₂×C₂²⋊C₄	—	4	4	no	—
370	C₂×C₂²⋊C₄	—	4	4	no	—
371	C₂×C₂²⋊C₄	—	4	4	no	—
372	C₂×C₄²	—	2	4	no	—
373	C₂×C₄²	D₄×C₁₁₃	1	4	yes	—
374	#95	—	2	8	no	—
375	#95	—	2	8	no	—
376	#95	—	2	4	no	—
377	#95	—	2	4	no	—
378	#95	—	4	2	no	—
379	C₂⁴	—	2	2	no	—
380	C₂⁴	—	2	2	no	—
381	C₂⁴	—	2	2	no	—
382	C₂⁴	—	2	2	no	—
383	C₂⁴	—	2	2	no	—
384	C₂⁴	—	2	2	no	—
385	C₂⁴	—	2	2	no	—
386	C₂⁴	—	2	2	no	—
387	C₂⁴	—	2	2	no	—
388	C₂⁴	—	2	2	no	—
389	C₂⁴	—	2	2	no	—
390	C₂⁴	—	2	2	no	—
391	C₂⁴	C₂×D₄×C₁₁₃	1	4	yes	—
392	C₂⁴	C₂×Q₈×C₁₁₃	1	4	yes	—
393	C₂⁴	#41×C₁₁₃	1	4	yes	—
394	C₂⁴	C₂⁴×C₁₁₃	1	1	yes	characteristic
395	C₂×D₄	—	2	8	no	—
396	C₂×D₄	—	2	8	no	—
397	C₂×D₄	—	2	16	no	—
398	C₂×D₄	—	2	16	no	—
399	C₂×D₄	—	2	8	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	16	no	—
417	C₂²×C₄	—	2	16	no	—
418	C₂²×C₄	—	2	16	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	4	8	no	—
432	C₂²×C₄	—	4	8	no	—
433	C₂²×C₄	—	4	8	no	—
434	C₂²×C₄	—	4	8	no	—
435	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
436	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
437	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
438	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
439	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
440	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
441	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
442	C₂²×C₄	C₂×Q₈×C₁₁₃	1	2	yes	—
443	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
444	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
445	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
446	C₄⋊C₄	—	2	8	no	—
447	C₄⋊C₄	—	2	8	no	—
448	C₄⋊C₄	—	4	8	no	—
449	C₄⋊C₄	—	4	4	no	—
450	C₄⋊C₄	—	4	8	no	—
451	C₂²⋊C₄	—	2	16	no	—
452	C₂²⋊C₄	—	4	16	no	—
453	C₂²⋊C₄	—	4	16	no	—
454	C₄²	—	2	8	no	—
455	C₂³	—	2	4	no	—
456	C₂³	—	2	4	no	—
457	C₂³	—	2	4	no	—
458	C₂³	—	2	4	no	—
459	C₂³	—	2	4	no	—
460	C₂³	—	2	4	no	—
461	C₂³	—	2	4	no	—
462	C₂³	—	2	4	no	—
463	C₂³	—	2	4	no	—
464	C₂³	—	2	4	no	—
465	C₂³	—	2	4	no	—
466	C₂³	—	2	4	no	—
467	C₂³	—	2	4	no	—
468	C₂³	—	2	4	no	—
469	C₂³	—	2	4	no	—
470	C₂³	—	2	4	no	—
471	C₂³	—	2	4	no	—
472	C₂³	—	2	4	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	4	2	no	—
475	C₂³	—	4	2	no	—
476	C₂³	—	4	2	no	—
477	C₂³	—	4	2	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	2	no	—
489	C₂³	C₂²⋊Q₈×C₁₁₃	1	8	yes	—
490	C₂³	C₂²×D₄×C₁₁₃	1	2	yes	—
491	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
492	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
493	C₂³	C₂²×Q₈×C₁₁₃	1	1	yes	characteristic
494	C₂³	C₂×#41×C₁₁₃	1	1	yes	characteristic
495	C₂³	C₂×#41×C₁₁₃	1	2	yes	—
496	C₂³	C₂×#41×C₁₁₃	1	2	yes	—
497	C₂³	C₂×#41×C₁₁₃	1	1	yes	characteristic
498	C₂³	H(5,𝔽₂)×C₁₁₃	1	2	yes	—
499	C₂³	H(5,𝔽₂)×C₁₁₃	1	1	yes	characteristic
500	C₂³	2₋¹⁺⁴×C₁₁₃	1	1	yes	characteristic
501	D₄	—	2	32	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	8	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	4	no	—
523	C₂×C₄	—	4	32	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	4	no	—
526	C₂×C₄	—	4	4	no	—
527	C₂×C₄	—	4	4	no	—
528	C₂×C₄	—	4	4	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	4	no	—
532	C₂×C₄	—	4	4	no	—
533	C₂×C₄	—	4	4	no	—
534	C₂×C₄	—	4	4	no	—
535	C₂×C₄	—	4	4	no	—
536	C₂×C₄	#120×C₁₁₃	1	4	yes	—
537	C₂×C₄	#121×C₁₁₃	1	4	yes	—
538	C₂×C₄	#121×C₁₁₃	1	8	yes	—
539	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	4	yes	—
540	C₂×C₄	#123×C₁₁₃	1	8	yes	—
541	C₂×C₄	#124×C₁₁₃	1	4	yes	—
542	C₂²	—	2	8	no	—
543	C₂²	—	2	8	no	—
544	C₂²	—	2	8	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	4	4	no	—
547	C₂²	—	4	4	no	—
548	C₂²	—	4	4	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	4	no	—
552	C₂²	—	4	4	no	—
553	C₂²	—	4	4	no	—
554	C₂²	—	4	4	no	—
555	C₂²	—	4	4	no	—
556	C₂²	—	4	4	no	—
557	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
558	C₂²	C₂×#121×C₁₁₃	1	1	yes	characteristic
559	C₂²	C₂×#121×C₁₁₃	1	2	yes	—
560	C₂²	C₂×C₂²⋊Q₈×C₁₁₃	1	1	yes	characteristic
561	C₂²	C₂×C₂²⋊Q₈×C₁₁₃	1	2	yes	—
562	C₂²	C₂×#123×C₁₁₃	1	2	yes	—
563	C₂²	#525×C₁₁₃	1	1	yes	characteristic
564	C₂²	#525×C₁₁₃	1	2	yes	—
565	C₂²	C₂×#124×C₁₁₃	1	1	yes	characteristic
566	C₂²	#535×C₁₁₃	1	1	yes	characteristic
567	C₂²	#535×C₁₁₃	1	2	yes	—
568	C₂²	#537×C₁₁₃	1	1	yes	characteristic
569	C₂²	#537×C₁₁₃	1	2	yes	—
570	C₂²	#546×C₁₁₃	1	2	yes	—
571	C₂²	D₄×Q₈×C₁₁₃	1	1	yes	characteristic
572	C₂²	#550×C₁₁₃	1	1	yes	characteristic
573	C₂²	#552×C₁₁₃	1	2	yes	—
574	C₂²	#553×C₁₁₃	1	2	yes	—
575	C₂²	#553×C₁₁₃	1	2	yes	—
576	C₂²	#554×C₁₁₃	1	1	yes	characteristic
577	C₂²	#554×C₁₁₃	1	2	yes	—
578	C₂²	#555×C₁₁₃	1	2	yes	—
579	C₂²	#556×C₁₁₃	1	1	yes	characteristic
580	C₄	—	2	4	no	—
581	C₄	—	4	4	no	—
582	C₄	—	4	2	no	—
583	C₄	—	4	4	no	—
584	C₄	—	8	2	no	—
585	C₄	—	8	4	no	—
586	C₄	#394×C₁₁₃	1	8	yes	—
587	C₂	—	4	8	no	—
588	C₂	C₂×#394×C₁₁₃	1	1	yes	characteristic
589	C₂	C₁₁₃×#2414	1	2	yes	—
590	C₂	C₁₁₃×#2417	1	2	yes	—
591	C₂	C₁₁₃×#2485	1	2	yes	—
592	C₂	C₁₁₃×#2487	1	2	yes	—
593	C₂	C₁₁₃×#2535	1	1	yes	characteristic
594	C₂	C₁₁₃×#2538	1	1	yes	characteristic
595	C₂	C₁₁₃×#2562	1	1	yes	characteristic
596	C₂	C₁₁₃×#2563	1	1	yes	characteristic
597	C₂	C₁₁₃×#2615	1	1	yes	characteristic
598	C₂	C₁₁₃×#2848	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×#389×C₁₁₃	C₂	semidirect
3. C₂×#380×C₁₁₃	C₂	semidirect
4. C₂×#380×C₁₁₃	C₂	semidirect
5. C₁₁₃×#1442	C₂	semidirect
6. C₁₁₃×#1439	C₂	semidirect
8. C₁₁₃×C₄⋊#95	C₂	semidirect
62. C₂×C₄⋊C₄×C₁₁₃	D₄	semidirect
287. #15181	C₁₁₃	direct (N × H)
301. C₂×#389	C₂×C₁₁₃	semidirect
302. C₂×#380	C₂×C₁₁₃	semidirect
303. C₂×#380	C₂×C₁₁₃	semidirect
304. #1442	C₂×C₁₁₃	semidirect
305. #1439	C₂×C₁₁₃	semidirect
307. C₄⋊#95	C₂×C₁₁₃	semidirect
308. C₁₁₃	#15181	direct (N × H)
362. C₂×C₄⋊C₄	D₄×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₁₁₃	2
C₂×#389×C₁₁₃	2
C₂×#380×C₁₁₃	2
C₁₁₃×#1442	2
C₁₁₃×#1439	2
C₁₁₃×#1438	2
C₁₁₃×C₄⋊#95	2
#15181	113

Subgroups — C113×#15181 #43283201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#15181 #43283201