Subgroups — C₂²×#11719191 #16769498

Order 3328.

14590 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#11719191	C₂	1	48	yes	maximal, direct product factor
3	C₂²×C₄×C₂²⋊D₁₃	C₂	1	4	yes	maximal, complemented
4	C₂²×#88135	C₂	1	4	yes	maximal, complemented
5	C₂²×#88131	C₂	1	2	yes	maximal, complemented
6	C₂³×C₂²⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₂²⋊C₄×D₁₃	C₂	1	2	yes	maximal, complemented
8	C₂³×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
10	C₂⁵×D₁₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
12	C₂³×C₂²⋊D₁₃	C₄	1	32	yes	complemented
13	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	—
14	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	—
15	C₂³×C₂²⋊D₁₃	C₂²	1	24	yes	—
16	C₂⁴×Dic₁₃	C₂²	1	1	yes	characteristic
17	C₂⁴×Dic₁₃	C₂²	1	2	yes	complemented
18	C₂³×C₄×D₁₃	C₂²	1	4	yes	complemented
19	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	24	yes	complemented
21	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
22	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
23	C₂²×C₂²⋊Dic₁₃	C₂²	1	24	yes	complemented
24	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
25	C₂×C₄×C₂²⋊D₁₃	C₂²	1	96	yes	complemented
26	C₂²×#6103	C₂²	1	4	yes	complemented
27	C₂²×#6101	C₂²	1	4	yes	complemented
28	C₂²×C₄×Dic₁₃	C₂²	1	4	yes	complemented
29	#11719191	C₂²	1	256	yes	direct product factor
30	C₂×#88135	C₂²	1	96	yes	complemented
31	C₂×C₂²⋊C₄×D₁₃	C₂²	1	48	yes	complemented
32	C₂×#88131	C₂²	1	48	yes	complemented
33	C₂⁵×C₁₃	—	4	8	no	—
34	C₂⁵×C₁₃	C₂×C₄	1	16	yes	complemented
35	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
36	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
37	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
38	C₂⁵×C₁₃	C₂³	1	12	yes	—
39	C₂⁴×D₁₃	—	4	8	no	—
40	C₂⁴×D₁₃	C₂×C₄	1	16	yes	complemented
41	C₂⁴×D₁₃	C₂³	1	2	yes	—
42	C₂⁴×D₁₃	C₂³	1	12	yes	—
43	C₂³×C₄×C₁₃	—	4	8	no	—
44	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
45	C₂³×C₄×C₁₃	C₂³	1	24	yes	complemented
46	C₂²×C₂²⋊D₁₃	C₂×C₄	1	32	yes	complemented
47	C₂²×C₂²⋊D₁₃	C₂×C₄	1	32	yes	complemented
48	C₂²×C₂²⋊D₁₃	C₂×C₄	1	384	yes	complemented
49	C₂²×C₂²⋊D₁₃	C₂³	1	24	yes	—
50	C₂²×C₂²⋊D₁₃	C₂³	1	64	yes	—
51	C₂²×C₂²⋊D₁₃	C₂³	1	24	yes	—
52	C₂³×Dic₁₃	—	4	8	no	—
53	C₂³×Dic₁₃	C₂×C₄	1	16	yes	complemented
54	C₂³×Dic₁₃	C₂³	1	4	yes	—
55	C₂³×Dic₁₃	C₂³	1	2	yes	—
56	C₂³×Dic₁₃	C₂³	1	12	yes	—
57	C₂³×Dic₁₃	C₂³	1	24	yes	complemented
58	C₂²×C₄×D₁₃	—	4	16	no	—
59	C₂²×C₄×D₁₃	C₂³	1	48	yes	complemented
60	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
61	C₂×C₁₃×C₂²⋊C₄	C₂³	1	64	yes	complemented
62	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	complemented
63	C₂×C₂²⋊Dic₁₃	C₂³	1	24	yes	—
64	C₂×C₂²⋊Dic₁₃	C₂³	1	64	yes	complemented
65	C₂×C₂²⋊Dic₁₃	C₂³	1	24	yes	complemented
66	C₄×C₂²⋊D₁₃	C₂³	1	256	yes	complemented
67	C₂×#6103	C₂³	1	48	yes	complemented
68	C₂×#6101	C₂³	1	48	yes	complemented
69	C₂×C₄×Dic₁₃	C₂³	1	48	yes	complemented
70	#88135	C₂³	1	256	yes	complemented
71	C₂²⋊C₄×D₁₃	C₂³	1	128	yes	complemented
72	#88131	C₂³	1	128	yes	complemented
73	C₂²×#518	—	13	1	no	maximal, Sylow
74	C₂⁴×C₁₃	—	2	8	no	—
75	C₂⁴×C₁₃	—	2	8	no	—
76	C₂⁴×C₁₃	—	2	8	no	—
77	C₂⁴×C₁₃	—	4	64	no	—
78	C₂⁴×C₁₃	—	4	48	no	—
79	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
80	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
81	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
82	C₂⁴×C₁₃	C₂²×C₄	1	96	yes	complemented
83	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
84	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
85	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
86	C₂⁴×C₁₃	C₂⁴	1	16	yes	—
87	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
88	C₂³×D₁₃	—	2	16	no	—
89	C₂³×D₁₃	—	4	64	no	—
90	C₂³×D₁₃	—	4	48	no	—
91	C₂³×D₁₃	C₂²×C₄	1	16	yes	—
92	C₂³×D₁₃	C₂²×C₄	1	96	yes	complemented
93	C₂³×D₁₃	C₂⁴	1	12	yes	—
94	C₂³×D₁₃	C₂⁴	1	16	yes	—
95	C₂²×C₄×C₁₃	—	2	16	no	—
96	C₂²×C₄×C₁₃	—	4	48	no	—
97	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
98	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	complemented
99	C₂×C₂²⋊D₁₃	C₂²×C₄	1	192	yes	complemented
100	C₂×C₂²⋊D₁₃	C₂²×C₄	1	192	yes	complemented
101	C₂×C₂²⋊D₁₃	C₂²×C₄	1	512	yes	complemented
102	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
103	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
104	C₂²×Dic₁₃	—	2	16	no	—
105	C₂²×Dic₁₃	—	4	48	no	—
106	C₂²×Dic₁₃	C₂²×C₄	1	16	yes	—
107	C₂²×Dic₁₃	C₂²×C₄	1	96	yes	complemented
108	C₂²×Dic₁₃	C₂⁴	1	24	yes	—
109	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
110	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
111	C₂²×Dic₁₃	C₂⁴	1	32	yes	complemented
112	C₂×C₄×D₁₃	—	4	96	no	—
113	C₂×C₄×D₁₃	C₂⁴	1	64	yes	complemented
114	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
115	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	complemented
116	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
117	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	complemented
118	#6103	C₂⁴	1	64	yes	complemented
119	#6101	C₂⁴	1	64	yes	complemented
120	C₄×Dic₁₃	C₂⁴	1	64	yes	complemented
121	C₂⁴×D₄	—	13	1	no	—
122	C₂×#518	—	13	48	no	—
123	C₂²×C₄×D₄	—	13	4	no	—
124	C₂²×C₄×D₄	—	13	4	no	—
125	C₂²×#117	—	13	2	no	—
126	C₂³×C₂²⋊C₄	—	13	1	no	—
127	C₂³×C₂²⋊C₄	—	13	2	no	—
128	C₂³×C₂²⋊C₄	D₁₃	1	1	yes	characteristic, complemented
129	C₂³×C₁₃	—	2	32	no	—
130	C₂³×C₁₃	—	2	32	no	—
131	C₂³×C₁₃	—	2	32	no	—
132	C₂³×C₁₃	—	2	24	no	—
133	C₂³×C₁₃	—	2	24	no	—
134	C₂³×C₁₃	—	2	24	no	—
135	C₂³×C₁₃	—	4	192	no	—
136	C₂³×C₁₃	—	4	32	no	—
137	C₂³×C₁₃	C₂³×C₄	1	24	yes	—
138	C₂³×C₁₃	C₂³×C₄	1	24	yes	—
139	C₂³×C₁₃	C₂³×C₄	1	24	yes	—
140	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
141	C₂³×C₁₃	C₂³×C₄	1	64	yes	complemented
142	C₂³×C₁₃	H(5,𝔽₂)	1	8	yes	—
143	C₂³×C₁₃	C₂⁵	1	4	yes	—
144	C₂³×C₁₃	C₂⁵	1	4	yes	—
145	C₂³×C₁₃	C₂⁵	1	4	yes	—
146	C₂³×C₁₃	C₂⁵	1	3	yes	—
147	C₂²×D₁₃	—	2	64	no	—
148	C₂²×D₁₃	—	2	48	no	—
149	C₂²×D₁₃	—	4	192	no	—
150	C₂²×D₁₃	—	4	32	no	—
151	C₂²×D₁₃	C₂³×C₄	1	48	yes	—
152	C₂²×D₁₃	C₂³×C₄	1	64	yes	complemented
153	C₂²×D₁₃	C₂⁵	1	8	yes	—
154	C₂×C₄×C₁₃	—	2	48	no	—
155	C₂×C₄×C₁₃	—	4	32	no	—
156	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
157	C₂²⋊D₁₃	C₂³×C₄	1	128	yes	complemented
158	C₂²⋊D₁₃	C₂³×C₄	1	128	yes	complemented
159	C₂×Dic₁₃	—	2	48	no	—
160	C₂×Dic₁₃	—	4	32	no	—
161	C₂×Dic₁₃	C₂³×C₄	1	48	yes	—
162	C₂×Dic₁₃	C₂³×C₄	1	64	yes	complemented
163	C₂×Dic₁₃	C₂⁵	1	16	yes	—
164	C₂×Dic₁₃	C₂⁵	1	8	yes	—
165	C₄×D₁₃	—	4	64	no	—
166	C₂⁶	—	13	1	no	—
167	C₂⁶	C₂×D₁₃	1	1	yes	characteristic
168	C₂³×D₄	—	13	32	no	—
169	C₂³×D₄	—	13	2	no	—
170	C₂³×D₄	—	13	2	no	—
171	C₂³×D₄	—	13	24	no	—
172	C₂⁴×C₄	—	13	1	no	—
173	C₂⁴×C₄	—	13	2	no	—
174	C₂⁴×C₄	—	13	4	no	—
175	C₂⁴×C₄	C₂×D₁₃	1	2	yes	complemented
176	#518	—	13	256	no	—
177	C₂×C₄×D₄	—	13	96	no	—
178	C₂×C₄×D₄	—	13	96	no	—
179	C₂×#117	—	13	48	no	—
180	C₂²×C₄⋊C₄	—	13	4	no	—
181	C₂²×C₂²⋊C₄	—	13	2	no	—
182	C₂²×C₂²⋊C₄	—	13	2	no	—
183	C₂²×C₂²⋊C₄	—	13	24	no	—
184	C₂²×C₂²⋊C₄	—	13	4	no	—
185	C₂²×C₂²⋊C₄	—	13	48	no	—
186	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
187	C₂²×C₂²⋊C₄	C₂×D₁₃	1	24	yes	complemented
188	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	complemented
189	C₂²×C₄²	—	13	4	no	—
190	C₂²×C₁₃	—	2	8	no	—
191	C₂²×C₁₃	—	2	8	no	—
192	C₂²×C₁₃	—	2	8	no	—
193	C₂²×C₁₃	—	2	48	no	—
194	C₂²×C₁₃	—	2	48	no	—
195	C₂²×C₁₃	—	2	48	no	—
196	C₂²×C₁₃	—	4	64	no	—
197	C₂²×C₁₃	#518	1	16	yes	complemented
198	C₂²×C₁₃	C₂⁴×C₄	1	8	yes	—
199	C₂²×C₁₃	C₂⁴×C₄	1	8	yes	—
200	C₂²×C₁₃	C₂⁴×C₄	1	8	yes	—
201	C₂²×C₁₃	C₂⁴×C₄	1	6	yes	—
202	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	12	yes	—
203	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
204	C₂×D₁₃	—	2	16	no	—
205	C₂×D₁₃	—	2	96	no	—
206	C₂×D₁₃	—	4	64	no	—
207	C₂×D₁₃	C₂⁴×C₄	1	16	yes	—
208	C₄×C₁₃	—	2	16	no	—
209	Dic₁₃	—	2	16	no	—
210	Dic₁₃	C₂⁴×C₄	1	16	yes	—
211	C₂⁵	—	4	8	no	—
212	C₂⁵	—	13	2	no	—
213	C₂⁵	—	13	16	no	—
214	C₂⁵	—	13	12	no	—
215	C₂⁵	—	52	8	no	—
216	C₂⁵	C₄×D₁₃	1	16	yes	complemented
217	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
218	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
219	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
220	C₂⁵	C₂²×D₁₃	1	12	yes	—
221	C₂²×D₄	—	13	32	no	—
222	C₂²×D₄	—	13	32	no	—
223	C₂²×D₄	—	13	384	no	—
224	C₂²×D₄	—	13	24	no	—
225	C₂²×D₄	—	13	24	no	—
226	C₂²×D₄	—	13	64	no	—
227	C₂³×C₄	—	4	8	no	—
228	C₂³×C₄	—	13	16	no	—
229	C₂³×C₄	—	13	12	no	—
230	C₂³×C₄	—	13	2	no	—
231	C₂³×C₄	—	13	4	no	—
232	C₂³×C₄	—	13	24	no	—
233	C₂³×C₄	—	13	48	no	—
234	C₂³×C₄	—	52	16	no	—
235	C₂³×C₄	—	52	8	no	—
236	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
237	C₂³×C₄	C₂²×D₁₃	1	24	yes	complemented
238	C₄×D₄	—	13	256	no	—
239	C₄×D₄	—	13	256	no	—
240	#117	—	13	128	no	—
241	C₂×C₄⋊C₄	—	13	48	no	—
242	C₂×C₂²⋊C₄	—	13	24	no	—
243	C₂×C₂²⋊C₄	—	13	24	no	—
244	C₂×C₂²⋊C₄	—	13	64	no	—
245	C₂×C₂²⋊C₄	—	13	48	no	—
246	C₂×C₂²⋊C₄	—	13	128	no	—
247	C₂×C₂²⋊C₄	C₂²×D₁₃	1	24	yes	—
248	C₂×C₂²⋊C₄	C₂²×D₁₃	1	64	yes	complemented
249	C₂×C₂²⋊C₄	C₂²×D₁₃	1	24	yes	complemented
250	C₂×C₄²	—	13	48	no	—
251	C₂×C₁₃	—	2	8	no	—
252	C₂×C₁₃	—	2	8	no	—
253	C₂×C₁₃	—	2	8	no	—
254	C₂×C₁₃	C₂×#518	1	12	yes	complemented
255	C₂×C₁₃	C₂⁵×C₄	1	1	yes	characteristic
256	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	2	yes	—
257	D₁₃	—	2	16	no	—
258	C₂⁴	—	2	8	no	—
259	C₂⁴	—	2	8	no	—
260	C₂⁴	—	2	8	no	—
261	C₂⁴	—	4	64	no	—
262	C₂⁴	—	4	48	no	—
263	C₂⁴	—	13	16	no	—
264	C₂⁴	—	13	12	no	—
265	C₂⁴	—	13	96	no	—
266	C₂⁴	—	13	16	no	—
267	C₂⁴	—	26	16	no	—
268	C₂⁴	—	52	64	no	—
269	C₂⁴	—	52	48	no	—
270	C₂⁴	C₂×C₄×D₁₃	1	8	yes	—
271	C₂⁴	C₂×C₄×D₁₃	1	8	yes	—
272	C₂⁴	C₂×C₄×D₁₃	1	8	yes	—
273	C₂⁴	C₂×C₄×D₁₃	1	96	yes	complemented
274	C₂⁴	C₂³×D₁₃	1	6	yes	—
275	C₂⁴	C₂³×D₁₃	1	6	yes	—
276	C₂⁴	C₂³×D₁₃	1	6	yes	—
277	C₂⁴	C₂³×D₁₃	1	16	yes	—
278	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
279	C₂×D₄	—	13	192	no	—
280	C₂×D₄	—	13	192	no	—
281	C₂×D₄	—	13	512	no	—
282	C₂×D₄	—	13	32	no	—
283	C₂×D₄	—	13	32	no	—
284	C₂²×C₄	—	2	16	no	—
285	C₂²×C₄	—	4	48	no	—
286	C₂²×C₄	—	13	16	no	—
287	C₂²×C₄	—	13	96	no	—
288	C₂²×C₄	—	13	12	no	—
289	C₂²×C₄	—	13	16	no	—
290	C₂²×C₄	—	13	24	no	—
291	C₂²×C₄	—	13	32	no	—
292	C₂²×C₄	—	13	64	no	—
293	C₂²×C₄	—	26	16	no	—
294	C₂²×C₄	—	52	96	no	—
295	C₂²×C₄	—	52	48	no	—
296	C₂²×C₄	C₂³×D₁₃	1	24	yes	—
297	C₂²×C₄	C₂³×D₁₃	1	32	yes	complemented
298	C₄⋊C₄	—	13	64	no	—
299	C₂²⋊C₄	—	13	32	no	—
300	C₂²⋊C₄	—	13	32	no	—
301	C₂²⋊C₄	—	13	64	no	—
302	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	—
303	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	complemented
304	C₄²	—	13	64	no	—
305	C₁₃	C₂²×#518	1	1	yes	characteristic, complemented, Sylow
306	C₂³	—	2	32	no	—
307	C₂³	—	2	32	no	—
308	C₂³	—	2	32	no	—
309	C₂³	—	2	24	no	—
310	C₂³	—	2	24	no	—
311	C₂³	—	2	24	no	—
312	C₂³	—	4	192	no	—
313	C₂³	—	4	32	no	—
314	C₂³	—	13	48	no	—
315	C₂³	—	13	8	no	—
316	C₂³	—	13	64	no	—
317	C₂³	—	26	64	no	—
318	C₂³	—	26	48	no	—
319	C₂³	—	52	192	no	—
320	C₂³	—	52	32	no	—
321	C₂³	C₂²×C₄×D₁₃	1	24	yes	—
322	C₂³	C₂²×C₄×D₁₃	1	24	yes	—
323	C₂³	C₂²×C₄×D₁₃	1	24	yes	—
324	C₂³	C₂²×C₄×D₁₃	1	4	yes	—
325	C₂³	C₂²×C₄×D₁₃	1	64	yes	complemented
326	C₂³	#88251	1	8	yes	—
327	C₂³	C₂⁴×D₁₃	1	4	yes	—
328	C₂³	C₂⁴×D₁₃	1	4	yes	—
329	C₂³	C₂⁴×D₁₃	1	4	yes	—
330	C₂³	C₂⁴×D₁₃	1	3	yes	—
331	D₄	—	13	128	no	—
332	D₄	—	13	128	no	—
333	C₂×C₄	—	2	48	no	—
334	C₂×C₄	—	4	32	no	—
335	C₂×C₄	—	13	48	no	—
336	C₂×C₄	—	13	64	no	—
337	C₂×C₄	—	13	8	no	—
338	C₂×C₄	—	13	16	no	—
339	C₂×C₄	—	26	48	no	—
340	C₂×C₄	—	52	64	no	—
341	C₂×C₄	—	52	32	no	—
342	C₂×C₄	C₂⁴×D₁₃	1	16	yes	—
343	C₂²	—	2	48	no	—
344	C₂²	—	2	48	no	—
345	C₂²	—	2	48	no	—
346	C₂²	—	2	8	no	—
347	C₂²	—	2	8	no	—
348	C₂²	—	2	8	no	—
349	C₂²	—	4	64	no	—
350	C₂²	—	13	16	no	—
351	C₂²	—	26	96	no	—
352	C₂²	—	26	16	no	—
353	C₂²	—	52	64	no	—
354	C₂²	#11719191	1	16	yes	direct product factor
355	C₂²	C₂³×C₄×D₁₃	1	8	yes	—
356	C₂²	C₂³×C₄×D₁₃	1	8	yes	—
357	C₂²	C₂³×C₄×D₁₃	1	8	yes	—
358	C₂²	C₂³×C₄×D₁₃	1	6	yes	—
359	C₂²	C₂×#88251	1	12	yes	—
360	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
361	C₄	—	2	16	no	—
362	C₄	—	13	16	no	—
363	C₄	—	26	16	no	—
364	C₂	—	2	8	no	—
365	C₂	—	2	8	no	—
366	C₂	—	2	8	no	—
367	C₂	—	26	16	no	—
368	C₂	C₂×#11719191	1	12	yes	direct product factor
369	C₂	C₂⁴×C₄×D₁₃	1	1	yes	characteristic
370	C₂	C₂²×#88251	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₁₃
commutator	C₂×C₁₃	C₂⁵×C₄
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂³×C₁₃×C₂²⋊C₄	C₂
socle	C₂⁴×C₁₃	C₂⁴
prime radical	C₂⁴×C₂²⋊D₁₃	C₂
cosocle	C₂²×C₁₃	C₂⁶
hypercenter	C₂³×C₂²⋊C₄	D₁₃
hypocenter	C₁₃	C₂²×#518
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×#11719191	C₂	direct (N × H)
3. C₂²×C₄×C₂²⋊D₁₃	C₂	semidirect
4. C₂²×#88135	C₂	semidirect
5. C₂²×#88131	C₂	semidirect
6. C₂³×C₂²⋊Dic₁₃	C₂	semidirect
7. C₂²×C₂²⋊C₄×D₁₃	C₂	semidirect
8. C₂³×C₁₃×C₂²⋊C₄	C₂	semidirect
11. C₂⁴×C₄×C₁₃	C₂²	semidirect
12. C₂³×C₂²⋊D₁₃	C₄	semidirect
17. C₂⁴×Dic₁₃	C₂²	semidirect
18. C₂³×C₄×D₁₃	C₂²	semidirect
20. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
21. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
23. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
24. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
25. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
26. C₂²×#6103	C₂²	semidirect
27. C₂²×#6101	C₂²	semidirect
28. C₂²×C₄×Dic₁₃	C₂²	semidirect
29. #11719191	C₂²	direct (N × H)
30. C₂×#88135	C₂²	semidirect
31. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
32. C₂×#88131	C₂²	semidirect
34. C₂⁵×C₁₃	C₂×C₄	semidirect
40. C₂⁴×D₁₃	C₂×C₄	semidirect
45. C₂³×C₄×C₁₃	C₂³	semidirect
46. C₂²×C₂²⋊D₁₃	C₂×C₄	semidirect
47. C₂²×C₂²⋊D₁₃	C₂×C₄	semidirect
48. C₂²×C₂²⋊D₁₃	C₂×C₄	semidirect
53. C₂³×Dic₁₃	C₂×C₄	semidirect
57. C₂³×Dic₁₃	C₂³	semidirect
59. C₂²×C₄×D₁₃	C₂³	semidirect
61. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
62. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
64. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
65. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
66. C₄×C₂²⋊D₁₃	C₂³	semidirect
67. C₂×#6103	C₂³	semidirect
68. C₂×#6101	C₂³	semidirect
69. C₂×C₄×Dic₁₃	C₂³	semidirect
70. #88135	C₂³	semidirect
71. C₂²⋊C₄×D₁₃	C₂³	semidirect
72. #88131	C₂³	semidirect
82. C₂⁴×C₁₃	C₂²×C₄	semidirect
92. C₂³×D₁₃	C₂²×C₄	semidirect
98. C₂²×C₄×C₁₃	C₂⁴	semidirect
99. C₂×C₂²⋊D₁₃	C₂²×C₄	semidirect
100. C₂×C₂²⋊D₁₃	C₂²×C₄	semidirect
101. C₂×C₂²⋊D₁₃	C₂²×C₄	semidirect
107. C₂²×Dic₁₃	C₂²×C₄	semidirect
111. C₂²×Dic₁₃	C₂⁴	semidirect
113. C₂×C₄×D₁₃	C₂⁴	semidirect
115. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
117. C₂²⋊Dic₁₃	C₂⁴	semidirect
118. #6103	C₂⁴	semidirect
119. #6101	C₂⁴	semidirect
120. C₄×Dic₁₃	C₂⁴	semidirect
128. C₂³×C₂²⋊C₄	D₁₃	semidirect
141. C₂³×C₁₃	C₂³×C₄	semidirect
152. C₂²×D₁₃	C₂³×C₄	semidirect
157. C₂²⋊D₁₃	C₂³×C₄	semidirect
158. C₂²⋊D₁₃	C₂³×C₄	semidirect
162. C₂×Dic₁₃	C₂³×C₄	semidirect
175. C₂⁴×C₄	C₂×D₁₃	semidirect
187. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
188. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
197. C₂²×C₁₃	#518	semidirect
216. C₂⁵	C₄×D₁₃	semidirect
237. C₂³×C₄	C₂²×D₁₃	semidirect
248. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
249. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
254. C₂×C₁₃	C₂×#518	semidirect
273. C₂⁴	C₂×C₄×D₁₃	semidirect
297. C₂²×C₄	C₂³×D₁₃	semidirect
303. C₂²⋊C₄	C₂³×D₁₃	semidirect
305. C₁₃	C₂²×#518	semidirect
325. C₂³	C₂²×C₄×D₁₃	semidirect
354. C₂²	#11719191	direct (N × H)
368. C₂	C₂×#11719191	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₂²⋊D₁₃	2
C₂×#11719191	2
C₂²×C₄×C₂²⋊D₁₃	2
C₂²×#88135	2
C₂²×#88131	2
C₂³×C₂²⋊Dic₁₃	2
C₂²×C₂²⋊C₄×D₁₃	2
C₂³×C₁₃×C₂²⋊C₄	2
C₂²×#518	13

Subgroups — C22×#11719191 #16769498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11719191 #16769498