Subgroups — C₂×C₁₃×#2629 #15720951

Order 3328.

2614 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2629	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#398	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×#396	C₂	1	4	yes	maximal
6	C₂×C₁₃×#389	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#384	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#380	C₂	1	2	yes	maximal
9	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#125	—	2	8	no	—
11	C₂×C₁₃×#125	C₂²	1	8	yes	complemented
12	C₂×C₁₃×#117	—	2	8	no	—
13	C₂×C₁₃×#117	C₂²	1	8	yes	—
14	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
20	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
22	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#398	C₂²	1	32	yes	complemented
25	C₁₃×#396	C₂²	1	32	yes	—
26	C₁₃×#389	C₂²	1	16	yes	complemented
27	C₁₃×#384	C₂²	1	8	yes	complemented
28	C₁₃×#380	C₂²	1	16	yes	—
29	C₂×C₁₃×#95	C₂²	1	4	yes	—
30	C₂×C₁₃×#95	C₂²	1	4	yes	—
31	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
32	C₂³×C₄×C₁₃	—	2	4	no	—
33	C₂³×C₄×C₁₃	—	2	4	no	—
34	C₂³×C₄×C₁₃	Q₈	1	8	yes	—
35	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
37	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
38	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
40	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₁₃×#125	—	2	32	no	—
43	C₁₃×#117	—	2	32	no	—
44	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
45	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
46	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
48	C₂×C₁₃×C₄⋊C₄	—	4	8	no	—
49	C₂×C₁₃×C₄⋊C₄	—	4	8	no	—
50	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
51	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
52	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
53	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
56	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
58	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
59	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
60	C₂×C₄²×C₁₃	—	2	4	no	—
61	C₂×C₄²×C₁₃	D₄	1	8	yes	—
62	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
63	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
64	C₁₃×#95	C₂³	1	16	yes	—
65	C₁₃×#95	C₂³	1	16	yes	—
66	C₂×#2629	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
67	C₂⁴×C₁₃	—	2	2	no	—
68	C₂⁴×C₁₃	—	2	2	no	—
69	C₂⁴×C₁₃	—	2	4	no	—
70	C₂⁴×C₁₃	—	2	4	no	—
71	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
72	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
73	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	—	2	2	no	—
75	C₂²×C₄×C₁₃	—	2	2	no	—
76	C₂²×C₄×C₁₃	—	2	4	no	—
77	C₂²×C₄×C₁₃	—	2	4	no	—
78	C₂²×C₄×C₁₃	—	2	32	no	—
79	C₂²×C₄×C₁₃	—	2	8	no	—
80	C₂²×C₄×C₁₃	—	2	8	no	—
81	C₂²×C₄×C₁₃	—	2	4	no	—
82	C₂²×C₄×C₁₃	—	2	8	no	—
83	C₂²×C₄×C₁₃	—	2	8	no	—
84	C₂²×C₄×C₁₃	—	2	8	no	—
85	C₂²×C₄×C₁₃	—	2	8	no	—
86	C₂²×C₄×C₁₃	—	2	4	no	—
87	C₂²×C₄×C₁₃	—	2	8	no	—
88	C₂²×C₄×C₁₃	—	2	4	no	—
89	C₂²×C₄×C₁₃	—	2	8	no	—
90	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
91	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
92	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
93	C₂²×C₄×C₁₃	C₂×Q₈	1	16	yes	—
94	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
95	C₂²×C₄×C₁₃	#41	1	4	yes	—
96	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
97	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
98	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
99	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
100	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
102	C₁₃×C₄⋊C₄	—	2	16	no	—
103	C₁₃×C₄⋊C₄	—	2	32	no	—
104	C₁₃×C₄⋊C₄	—	2	16	no	—
105	C₁₃×C₄⋊C₄	—	2	16	no	—
106	C₁₃×C₄⋊C₄	—	4	16	no	—
107	C₁₃×C₄⋊C₄	—	4	16	no	—
108	C₁₃×C₂²⋊C₄	—	2	16	no	—
109	C₁₃×C₂²⋊C₄	—	4	16	no	—
110	C₄²×C₁₃	—	2	8	no	—
111	C₄²×C₁₃	C₂×D₄	1	16	yes	—
112	C₂²×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
113	C₂²×#117	C₂×C₁₃	1	1	yes	characteristic
114	#2629	C₂×C₁₃	1	16	yes	direct product factor
115	C₂×#398	C₂×C₁₃	1	4	yes	complemented
116	C₂×#396	C₂×C₁₃	1	4	yes	—
117	C₂×#389	C₂×C₁₃	1	2	yes	complemented
118	C₂×#384	C₂×C₁₃	1	1	yes	characteristic, complemented
119	C₂×#380	C₂×C₁₃	1	2	yes	—
120	C₂³×C₁₃	—	2	8	no	—
121	C₂³×C₁₃	—	2	16	no	—
122	C₂³×C₁₃	—	2	2	no	—
123	C₂³×C₁₃	—	2	2	no	—
124	C₂³×C₁₃	—	2	4	no	—
125	C₂³×C₁₃	—	2	4	no	—
126	C₂³×C₁₃	—	4	8	no	—
127	C₂³×C₁₃	—	4	4	no	—
128	C₂³×C₁₃	—	4	4	no	—
129	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
130	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
131	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
132	C₂³×C₁₃	C₂×#41	1	2	yes	—
133	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
134	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
135	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
136	C₂×C₄×C₁₃	—	2	8	no	—
137	C₂×C₄×C₁₃	—	2	16	no	—
138	C₂×C₄×C₁₃	—	2	2	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	—	2	4	no	—
141	C₂×C₄×C₁₃	—	2	4	no	—
142	C₂×C₄×C₁₃	—	2	32	no	—
143	C₂×C₄×C₁₃	—	2	4	no	—
144	C₂×C₄×C₁₃	—	2	8	no	—
145	C₂×C₄×C₁₃	—	2	8	no	—
146	C₂×C₄×C₁₃	—	2	8	no	—
147	C₂×C₄×C₁₃	—	2	8	no	—
148	C₂×C₄×C₁₃	—	2	4	no	—
149	C₂×C₄×C₁₃	—	2	8	no	—
150	C₂×C₄×C₁₃	—	2	4	no	—
151	C₂×C₄×C₁₃	—	2	8	no	—
152	C₂×C₄×C₁₃	—	4	8	no	—
153	C₂×C₄×C₁₃	—	4	16	no	—
154	C₂×C₄×C₁₃	—	4	16	no	—
155	C₂×C₄×C₁₃	C₂²⋊Q₈	1	16	yes	—
156	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
157	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
158	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
159	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
160	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
161	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
162	C₂×#125	—	2	8	no	—
163	C₂×#125	C₂²×C₁₃	1	8	yes	complemented
164	C₂×#117	—	2	8	no	—
165	C₂×#117	C₂²×C₁₃	1	8	yes	—
166	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
167	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
168	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
169	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
170	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
171	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
172	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
173	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
174	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
175	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
176	#398	C₂²×C₁₃	1	32	yes	complemented
177	#396	C₂²×C₁₃	1	32	yes	—
178	#389	C₂²×C₁₃	1	16	yes	complemented
179	#384	C₂²×C₁₃	1	8	yes	complemented
180	#380	C₂²×C₁₃	1	16	yes	—
181	C₂×#95	C₂²×C₁₃	1	4	yes	—
182	C₂×#95	C₂²×C₁₃	1	4	yes	—
183	C₂²×C₁₃	—	2	4	no	—
184	C₂²×C₁₃	—	2	8	no	—
185	C₂²×C₁₃	—	4	16	no	—
186	C₂²×C₁₃	—	4	4	no	—
187	C₂²×C₁₃	—	4	2	no	—
188	C₂²×C₁₃	—	4	2	no	—
189	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
190	C₂²×C₁₃	#537	1	8	yes	—
191	C₂²×C₁₃	#540	1	4	yes	—
192	C₂²×C₁₃	#541	1	4	yes	—
193	C₂²×C₁₃	#544	1	8	yes	—
194	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
195	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
196	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
197	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
198	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
199	C₄×C₁₃	—	2	4	no	—
200	C₄×C₁₃	—	2	8	no	—
201	C₄×C₁₃	—	4	4	no	—
202	C₄×C₁₃	—	4	8	no	—
203	C₄×C₁₃	—	4	8	no	—
204	C₄×C₁₃	C₂×C₂²⋊Q₈	1	8	yes	—
205	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
206	C₂³×C₄	—	2	4	no	—
207	C₂³×C₄	—	2	4	no	—
208	C₂³×C₄	Q₈×C₁₃	1	8	yes	—
209	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
210	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
211	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
212	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
213	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
214	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
215	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
216	#125	—	2	32	no	—
217	#117	—	2	32	no	—
218	C₂×C₄⋊C₄	—	2	8	no	—
219	C₂×C₄⋊C₄	—	2	16	no	—
220	C₂×C₄⋊C₄	—	2	8	no	—
221	C₂×C₄⋊C₄	—	2	8	no	—
222	C₂×C₄⋊C₄	—	4	8	no	—
223	C₂×C₄⋊C₄	—	4	8	no	—
224	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
225	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
226	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
227	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
228	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
229	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
230	C₂×C₂²⋊C₄	—	2	8	no	—
231	C₂×C₂²⋊C₄	—	4	8	no	—
232	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
233	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
234	C₂×C₄²	—	2	4	no	—
235	C₂×C₄²	D₄×C₁₃	1	8	yes	—
236	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
237	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
238	#95	C₂³×C₁₃	1	16	yes	—
239	#95	C₂³×C₁₃	1	16	yes	—
240	C₂×C₁₃	—	4	4	no	—
241	C₂×C₁₃	#2629	1	8	yes	direct product factor
242	C₂×C₁₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
243	C₂×C₁₃	C₂×#537	1	2	yes	—
244	C₂×C₁₃	C₂×#540	1	1	yes	characteristic
245	C₂×C₁₃	C₂×#541	1	1	yes	characteristic
246	C₂×C₁₃	C₂×#544	1	2	yes	—
247	C₂⁴	—	2	2	no	—
248	C₂⁴	—	2	2	no	—
249	C₂⁴	—	2	4	no	—
250	C₂⁴	—	2	4	no	—
251	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
252	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
253	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	32	no	—
259	C₂²×C₄	—	2	8	no	—
260	C₂²×C₄	—	2	8	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	8	no	—
263	C₂²×C₄	—	2	8	no	—
264	C₂²×C₄	—	2	8	no	—
265	C₂²×C₄	—	2	8	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	8	no	—
268	C₂²×C₄	—	2	8	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
271	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
272	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
273	C₂²×C₄	C₂×Q₈×C₁₃	1	16	yes	—
274	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
275	C₂²×C₄	C₁₃×#41	1	4	yes	—
276	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
277	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
278	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
279	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
280	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
281	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
282	C₄⋊C₄	—	2	16	no	—
283	C₄⋊C₄	—	2	32	no	—
284	C₄⋊C₄	—	2	16	no	—
285	C₄⋊C₄	—	2	16	no	—
286	C₄⋊C₄	—	4	16	no	—
287	C₄⋊C₄	—	4	16	no	—
288	C₂²⋊C₄	—	2	16	no	—
289	C₂²⋊C₄	—	4	16	no	—
290	C₄²	—	2	8	no	—
291	C₄²	C₂×D₄×C₁₃	1	16	yes	—
292	C₁₃	C₂×#2629	1	1	yes	characteristic, direct product factor, Sylow
293	C₂³	—	2	8	no	—
294	C₂³	—	2	16	no	—
295	C₂³	—	2	2	no	—
296	C₂³	—	2	2	no	—
297	C₂³	—	2	4	no	—
298	C₂³	—	2	4	no	—
299	C₂³	—	4	8	no	—
300	C₂³	—	4	4	no	—
301	C₂³	—	4	4	no	—
302	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
303	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
304	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
305	C₂³	C₂×C₁₃×#41	1	2	yes	—
306	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
307	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
308	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
309	C₂×C₄	—	2	8	no	—
310	C₂×C₄	—	2	16	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	32	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	8	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	8	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	8	no	—
325	C₂×C₄	—	4	8	no	—
326	C₂×C₄	—	4	16	no	—
327	C₂×C₄	—	4	16	no	—
328	C₂×C₄	C₁₃×C₂²⋊Q₈	1	16	yes	—
329	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
330	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
331	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
332	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
333	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
334	C₂²	—	2	4	no	—
335	C₂²	—	2	8	no	—
336	C₂²	—	4	16	no	—
337	C₂²	—	4	4	no	—
338	C₂²	—	4	2	no	—
339	C₂²	—	4	2	no	—
340	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
341	C₂²	C₁₃×#537	1	8	yes	—
342	C₂²	C₁₃×#540	1	4	yes	—
343	C₂²	C₁₃×#541	1	4	yes	—
344	C₂²	C₁₃×#544	1	8	yes	—
345	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
346	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
347	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
348	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
349	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
350	C₄	—	2	4	no	—
351	C₄	—	2	8	no	—
352	C₄	—	4	4	no	—
353	C₄	—	4	8	no	—
354	C₄	—	4	8	no	—
355	C₄	C₂×C₁₃×C₂²⋊Q₈	1	8	yes	—
356	C₂	—	4	4	no	—
357	C₂	C₁₃×#2629	1	8	yes	direct product factor
358	C₂	C₂²×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
359	C₂	C₂×C₁₃×#537	1	2	yes	—
360	C₂	C₂×C₁₃×#540	1	1	yes	characteristic
361	C₂	C₂×C₁₃×#541	1	1	yes	characteristic
362	C₂	C₂×C₁₃×#544	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁵×C₁₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#125	C₂	semidirect
3. C₁₃×#2629	C₂	direct (N × H)
4. C₂×C₁₃×#398	C₂	semidirect
6. C₂×C₁₃×#389	C₂	semidirect
7. C₂×C₁₃×#384	C₂	semidirect
11. C₂×C₁₃×#125	C₂²	semidirect
24. C₁₃×#398	C₂²	semidirect
26. C₁₃×#389	C₂²	semidirect
27. C₁₃×#384	C₂²	semidirect
66. C₂×#2629	C₁₃	direct (N × H)
112. C₂²×#125	C₂×C₁₃	semidirect
114. #2629	C₂×C₁₃	direct (N × H)
115. C₂×#398	C₂×C₁₃	semidirect
117. C₂×#389	C₂×C₁₃	semidirect
118. C₂×#384	C₂×C₁₃	semidirect
163. C₂×#125	C₂²×C₁₃	semidirect
176. #398	C₂²×C₁₃	semidirect
178. #389	C₂²×C₁₃	semidirect
179. #384	C₂²×C₁₃	semidirect
241. C₂×C₁₃	#2629	direct (N × H)
292. C₁₃	C₂×#2629	direct (N × H)
357. C₂	C₁₃×#2629	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#125	2
C₂²×C₁₃×#117	2
C₁₃×#2629	2
C₂×C₁₃×#398	2
C₂×C₁₃×#396	2
C₂×C₁₃×#389	2
C₂×C₁₃×#384	2
C₂×C₁₃×#380	2
C₂×#2629	13

Subgroups — C2×C13×#2629 #15720951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2629 #15720951