Subgroups — C₁₃×#22643 #15708982

Order 3328.

780 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1939	C₂	1	2	yes	maximal, complemented
3	C₁₃×#1924	C₂	1	4	yes	maximal
4	C₁₃×#1839	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1770	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1767	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₃×#117	C₄	1	1	yes	characteristic
10	C₂×C₁₃×#117	C₄	1	1	yes	characteristic
11	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×C₄⋊C₈	C₂²	1	4	yes	—
13	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₃×#97	C₂²	1	4	yes	—
17	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
18	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
19	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
20	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₄×C₁₃×C₂²⋊C₄	C₄	1	2	yes	—
23	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₁₃×#376	C₄	1	2	yes	—
25	C₄³×C₁₃	C₂²	1	2	yes	—
26	C₁₃×#336	C₂²	1	1	yes	characteristic
27	C₁₃×#336	C₂²	1	1	yes	characteristic
28	C₁₃×#336	C₂²	1	2	yes	—
29	C₁₃×#336	C₂²	1	4	yes	—
30	C₁₃×#336	C₂²	1	4	yes	—
31	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
34	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
35	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
36	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
37	C₁₃×#117	—	2	4	no	—
38	C₁₃×#117	—	2	4	no	—
39	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
40	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
41	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
42	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
43	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
44	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₁₃	—	2	4	no	—
46	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
53	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
54	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
56	C₁₃×C₄⋊C₈	—	2	8	no	—
57	C₁₃×C₄⋊C₈	—	2	4	no	—
58	C₁₃×C₂²⋊C₈	—	2	4	no	—
59	C₁₃×C₂²⋊C₈	—	4	2	no	—
60	C₁₃×#97	—	4	4	no	—
61	C₄×C₈×C₁₃	—	2	4	no	—
62	C₁₃×#95	C₂×C₄	1	2	yes	—
63	C₁₃×#95	C₂×C₄	1	2	yes	—
64	C₁₃×#95	C₂×C₄	1	2	yes	—
65	C₁₃×#95	C₂×C₄	1	2	yes	—
66	#22643	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
67	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₃	—	2	2	no	—
69	C₂²×C₄×C₁₃	—	2	2	no	—
70	C₂²×C₄×C₁₃	—	2	2	no	—
71	C₂²×C₄×C₁₃	—	2	2	no	—
72	C₂²×C₄×C₁₃	—	2	2	no	—
73	C₂²×C₄×C₁₃	—	2	2	no	—
74	C₂²×C₄×C₁₃	—	2	1	no	—
75	C₂²×C₄×C₁₃	—	2	1	no	—
76	C₂²×C₄×C₁₃	—	4	1	no	—
77	C₂²×C₄×C₁₃	M₁₆	1	4	yes	—
78	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
88	C₂×C₈×C₁₃	—	2	2	no	—
89	C₂×C₈×C₁₃	—	2	2	no	—
90	C₂×C₈×C₁₃	—	2	2	no	—
91	C₂×C₈×C₁₃	—	2	2	no	—
92	C₂×C₈×C₁₃	—	2	4	no	—
93	C₂×C₈×C₁₃	—	2	4	no	—
94	C₂×C₈×C₁₃	—	2	4	no	—
95	C₂×C₈×C₁₃	—	2	2	no	—
96	C₂×C₈×C₁₃	#41	1	4	yes	—
97	C₁₃×C₄⋊C₄	—	2	2	no	—
98	C₁₃×C₄⋊C₄	—	2	2	no	—
99	C₁₃×C₄⋊C₄	—	2	2	no	—
100	C₁₃×C₄⋊C₄	M₁₆	1	4	yes	—
101	C₁₃×C₂²⋊C₄	—	2	4	no	—
102	C₁₃×C₂²⋊C₄	—	2	4	no	—
103	C₄²×C₁₃	—	2	2	no	—
104	C₄²×C₁₃	—	2	2	no	—
105	C₄²×C₁₃	—	2	4	no	—
106	C₄²×C₁₃	—	2	4	no	—
107	C₄²×C₁₃	—	2	4	no	—
108	C₄²×C₁₃	—	2	4	no	—
109	C₄²×C₁₃	—	2	2	no	—
110	C₄²×C₁₃	—	2	2	no	—
111	C₄²×C₁₃	—	2	2	no	—
112	C₄²×C₁₃	—	4	2	no	—
113	C₄²×C₁₃	#41	1	4	yes	—
114	C₄×#117	C₂×C₁₃	1	1	yes	characteristic
115	#1939	C₂×C₁₃	1	2	yes	complemented
116	#1924	C₂×C₁₃	1	4	yes	—
117	#1839	C₂×C₁₃	1	2	yes	complemented
118	#1797	C₂×C₁₃	1	1	yes	characteristic
119	#1770	C₂×C₁₃	1	2	yes	complemented
120	#1767	C₂×C₁₃	1	2	yes	complemented
121	C₄×C₂²⋊C₈	C₂×C₁₃	1	1	yes	characteristic
122	C₂³×C₁₃	—	2	1	no	—
123	C₂³×C₁₃	—	2	1	no	—
124	C₂³×C₁₃	—	2	1	no	—
125	C₂³×C₁₃	—	2	1	no	—
126	C₂³×C₁₃	—	2	1	no	—
127	C₂³×C₁₃	—	2	1	no	—
128	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
129	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₃	—	2	1	no	—
131	C₂×C₄×C₁₃	—	2	1	no	—
132	C₂×C₄×C₁₃	—	2	2	no	—
133	C₂×C₄×C₁₃	—	2	1	no	—
134	C₂×C₄×C₁₃	—	2	1	no	—
135	C₂×C₄×C₁₃	—	2	1	no	—
136	C₂×C₄×C₁₃	—	2	2	no	—
137	C₂×C₄×C₁₃	—	2	1	no	—
138	C₂×C₄×C₁₃	—	2	8	no	—
139	C₂×C₄×C₁₃	—	2	1	no	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	2	1	no	—
142	C₂×C₄×C₁₃	—	2	2	no	—
143	C₂×C₄×C₁₃	—	2	2	no	—
144	C₂×C₄×C₁₃	—	2	1	no	—
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	4	4	no	—
152	C₂×C₄×C₁₃	—	4	2	no	—
153	C₂×C₄×C₁₃	—	4	2	no	—
154	C₂×C₄×C₁₃	#117	1	2	yes	—
155	C₂×C₄×C₁₃	#117	1	2	yes	—
156	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
157	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
158	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
159	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
160	C₂×C₄×C₁₃	#131	1	2	yes	—
161	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
162	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
163	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
164	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
165	C₈×C₁₃	—	2	4	no	—
166	C₈×C₁₃	—	4	4	no	—
167	C₈×C₁₃	—	4	2	no	—
168	C₂×#117	C₄×C₁₃	1	1	yes	characteristic
169	C₂×#117	C₄×C₁₃	1	1	yes	characteristic
170	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
171	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
172	C₂×C₄⋊C₈	C₂²×C₁₃	1	4	yes	—
173	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
174	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
175	C₂×#97	C₂²×C₁₃	1	4	yes	—
176	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
177	C₄×C₄⋊C₄	C₄×C₁₃	1	1	yes	characteristic
178	C₄×C₄⋊C₄	C₄×C₁₃	1	1	yes	characteristic
179	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
180	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
181	C₄×C₂²⋊C₄	C₄×C₁₃	1	2	yes	—
182	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
183	#376	C₄×C₁₃	1	2	yes	—
184	C₄³	C₂²×C₁₃	1	2	yes	—
185	#336	C₂²×C₁₃	1	2	yes	—
186	#336	C₂²×C₁₃	1	1	yes	characteristic
187	#336	C₂²×C₁₃	1	4	yes	—
188	#336	C₂²×C₁₃	1	4	yes	—
189	#336	C₂²×C₁₃	1	1	yes	characteristic
190	C₂²×C₁₃	—	2	2	no	—
191	C₂²×C₁₃	—	2	2	no	—
192	C₂²×C₁₃	—	2	2	no	—
193	C₂²×C₁₃	—	4	1	no	—
194	C₂²×C₁₃	—	4	1	no	—
195	C₂²×C₁₃	—	4	1	no	—
196	C₂²×C₁₃	—	4	1	no	—
197	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
198	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
199	C₂²×C₁₃	#520	1	1	yes	characteristic
200	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
201	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
202	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
203	C₂²×C₁₃	#568	1	1	yes	characteristic
204	C₄×C₁₃	—	2	2	no	—
205	C₄×C₁₃	—	2	2	no	—
206	C₄×C₁₃	—	2	2	no	—
207	C₄×C₁₃	—	2	4	no	—
208	C₄×C₁₃	—	4	1	no	—
209	C₄×C₁₃	—	4	2	no	—
210	C₄×C₁₃	—	4	2	no	—
211	C₄×C₁₃	—	4	2	no	—
212	C₄×C₁₃	#432	1	4	yes	—
213	C₄×C₁₃	#553	1	2	yes	—
214	C₄×C₁₃	#556	1	2	yes	—
215	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
216	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
217	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
218	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
219	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
220	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
221	#117	—	2	4	no	—
222	#117	—	2	4	no	—
223	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
224	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
227	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
228	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
229	C₂×C₄²	—	2	4	no	—
230	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
231	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
232	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
233	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
234	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
235	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
236	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
237	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
238	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
239	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
240	C₄⋊C₈	—	2	8	no	—
241	C₄⋊C₈	—	2	4	no	—
242	C₂²⋊C₈	—	2	4	no	—
243	C₂²⋊C₈	—	4	2	no	—
244	#97	—	4	4	no	—
245	C₄×C₈	—	2	4	no	—
246	#95	C₂×C₄×C₁₃	1	2	yes	—
247	#95	C₂×C₄×C₁₃	1	2	yes	—
248	#95	C₂×C₄×C₁₃	1	2	yes	—
249	#95	C₂×C₄×C₁₃	1	2	yes	—
250	C₂×C₁₃	—	4	2	no	—
251	C₂×C₁₃	#2347	1	1	yes	characteristic
252	C₂×C₁₃	C₂×#432	1	1	yes	characteristic
253	C₂×C₁₃	#2924	1	1	yes	characteristic
254	C₂×C₁₃	#2965	1	1	yes	characteristic
255	C₂×C₁₃	#2970	1	1	yes	characteristic
256	C₂×C₁₃	#2989	1	1	yes	characteristic
257	C₂×C₁₃	#2991	1	1	yes	characteristic
258	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	4	1	no	—
268	C₂²×C₄	C₁₃×M₁₆	1	4	yes	—
269	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
270	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
271	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
272	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
273	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
275	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
276	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
277	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
278	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	C₁₃×#41	1	4	yes	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	C₁₃×M₁₆	1	4	yes	—
292	C₂²⋊C₄	—	2	4	no	—
293	C₂²⋊C₄	—	2	4	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	4	no	—
297	C₄²	—	2	4	no	—
298	C₄²	—	2	4	no	—
299	C₄²	—	2	4	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	4	2	no	—
304	C₄²	C₁₃×#41	1	4	yes	—
305	C₁₃	#22643	1	1	yes	characteristic, direct product factor, Sylow
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	—	2	1	no	—
311	C₂³	—	2	1	no	—
312	C₂³	C₂×C₁₃×M₁₆	1	2	yes	—
313	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	C₁₃×#117	1	2	yes	—
339	C₂×C₄	C₁₃×#117	1	2	yes	—
340	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
341	C₂×C₄	C₂×C₁₃×M₁₆	1	4	yes	—
342	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
343	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
344	C₂×C₄	C₁₃×#131	1	2	yes	—
345	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
346	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
347	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
348	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
349	C₈	—	2	4	no	—
350	C₈	—	4	4	no	—
351	C₈	—	4	2	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	1	no	—
357	C₂²	—	4	1	no	—
358	C₂²	—	4	1	no	—
359	C₂²	C₂×C₁₃×#117	1	1	yes	characteristic
360	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
361	C₂²	C₁₃×#520	1	1	yes	characteristic
362	C₂²	C₂²×C₁₃×M₁₆	1	1	yes	characteristic
363	C₂²	C₂²×C₁₃×M₁₆	1	1	yes	characteristic
364	C₂²	C₂×C₁₃×#131	1	1	yes	characteristic
365	C₂²	C₁₃×#568	1	1	yes	characteristic
366	C₄	—	2	2	no	—
367	C₄	—	2	2	no	—
368	C₄	—	2	2	no	—
369	C₄	—	2	4	no	—
370	C₄	—	4	1	no	—
371	C₄	—	4	2	no	—
372	C₄	—	4	2	no	—
373	C₄	—	4	2	no	—
374	C₄	C₁₃×#432	1	4	yes	—
375	C₄	C₁₃×#553	1	2	yes	—
376	C₄	C₁₃×#556	1	2	yes	—
377	C₂	—	4	2	no	—
378	C₂	C₁₃×#2347	1	1	yes	characteristic
379	C₂	C₂×C₁₃×#432	1	1	yes	characteristic
380	C₂	C₁₃×#2924	1	1	yes	characteristic
381	C₂	C₁₃×#2965	1	1	yes	characteristic
382	C₂	C₁₃×#2970	1	1	yes	characteristic
383	C₂	C₁₃×#2989	1	1	yes	characteristic
384	C₂	C₁₃×#2991	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂⁴×C₁₃	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#1939	C₂	semidirect
4. C₁₃×#1839	C₂	semidirect
6. C₁₃×#1770	C₂	semidirect
7. C₁₃×#1767	C₂	semidirect
66. #22643	C₁₃	direct (N × H)
115. #1939	C₂×C₁₃	semidirect
117. #1839	C₂×C₁₃	semidirect
119. #1770	C₂×C₁₃	semidirect
120. #1767	C₂×C₁₃	semidirect
305. C₁₃	#22643	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₃×#117	2
C₁₃×#1939	2
C₁₃×#1924	2
C₁₃×#1839	2
C₁₃×#1797	2
C₁₃×#1770	2
C₁₃×#1767	2
C₄×C₁₃×C₂²⋊C₈	2
#22643	13

Subgroups — C13×#22643 #15708982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22643 #15708982