Subgroups — C₁₃×#29354 #15715693

Order 3328.

850 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2858	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2071	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2023	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1987	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1982	C₂	1	2	yes	maximal
7	C₁₃×#1936	C₂	1	4	yes	maximal, complemented
8	C₁₃×#1767	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#124	—	2	1	no	—
13	C₂×C₁₃×#124	—	2	1	no	—
14	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₃×#102	C₂²	1	4	yes	—
17	C₂×C₁₃×#102	C₂²	1	4	yes	—
18	C₂×C₁₃×#97	C₂²	1	2	yes	—
19	C₁₃×#391	—	2	1	no	—
20	C₁₃×#390	—	2	1	no	—
21	C₁₃×#390	—	2	1	no	—
22	C₁₃×#390	C₂²	1	2	yes	—
23	C₁₃×#390	C₂²	1	2	yes	—
24	C₁₃×#389	—	2	1	no	—
25	C₁₃×#389	C₂²	1	2	yes	—
26	C₁₃×#384	C₂²	1	1	yes	characteristic
27	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
28	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
29	C₄³×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#340	C₂²	1	4	yes	—
31	C₁₃×#340	C₂²	1	4	yes	—
32	C₁₃×#336	C₂²	1	2	yes	—
33	C₂²×Q₈×C₁₃	—	2	1	no	—
34	C₂²×Q₈×C₁₃	—	2	1	no	—
35	C₂²×D₄×C₁₃	—	2	1	no	—
36	C₂²×D₄×C₁₃	—	2	1	no	—
37	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
38	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
39	C₁₃×C₄⋊Q₈	—	2	4	no	—
40	C₁₃×C₄⋊Q₈	—	2	4	no	—
41	C₁₃×#127	—	2	4	no	—
42	C₁₃×#124	—	4	4	no	—
43	C₁₃×#124	—	4	4	no	—
44	C₄×Q₈×C₁₃	—	4	4	no	—
45	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
46	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
50	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
51	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
52	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
53	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
54	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
57	C₂×C₄²×C₁₃	—	2	2	no	—
58	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×C₄⋊C₈	—	2	4	no	—
66	C₁₃×#102	—	2	8	no	—
67	C₁₃×#102	—	4	4	no	—
68	C₁₃×#97	—	4	2	no	—
69	C₁₃×#95	—	2	2	no	—
70	C₁₃×#95	—	2	2	no	—
71	#29354	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂⁴×C₁₃	—	2	2	no	—
73	C₂×Q₈×C₁₃	—	2	4	no	—
74	C₂×Q₈×C₁₃	—	4	2	no	—
75	C₂×Q₈×C₁₃	—	4	2	no	—
76	C₂×Q₈×C₁₃	—	4	2	no	—
77	C₂×Q₈×C₁₃	—	4	2	no	—
78	C₂×Q₈×C₁₃	—	4	2	no	—
79	C₂×D₄×C₁₃	—	2	4	no	—
80	C₂×D₄×C₁₃	—	2	4	no	—
81	C₂×D₄×C₁₃	—	2	2	no	—
82	C₂×D₄×C₁₃	—	2	2	no	—
83	C₂×D₄×C₁₃	—	4	2	no	—
84	C₂×D₄×C₁₃	—	4	2	no	—
85	C₂×D₄×C₁₃	—	4	2	no	—
86	C₂×D₄×C₁₃	—	4	2	no	—
87	C₂×D₄×C₁₃	—	4	2	no	—
88	C₂×D₄×C₁₃	—	4	2	no	—
89	C₂²×C₄×C₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
99	C₂×C₈×C₁₃	—	2	4	no	—
100	C₂×C₈×C₁₃	—	2	4	no	—
101	C₂×C₈×C₁₃	—	2	4	no	—
102	C₁₃×C₄⋊C₄	—	2	4	no	—
103	C₁₃×C₄⋊C₄	—	2	2	no	—
104	C₁₃×C₄⋊C₄	—	2	4	no	—
105	C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₁₃×C₄⋊C₄	—	2	2	no	—
107	C₁₃×C₄⋊C₄	—	4	2	no	—
108	C₁₃×C₄⋊C₄	—	4	4	no	—
109	C₁₃×C₄⋊C₄	—	4	2	no	—
110	C₁₃×C₄⋊C₄	—	4	2	no	—
111	C₁₃×C₄⋊C₄	#41	1	4	yes	—
112	C₁₃×C₂²⋊C₄	—	4	4	no	—
113	C₁₃×C₂²⋊C₄	—	4	4	no	—
114	C₁₃×C₂²⋊C₄	—	4	4	no	—
115	C₁₃×C₂²⋊C₄	—	4	4	no	—
116	C₄²×C₁₃	—	2	2	no	—
117	C₄²×C₁₃	—	2	2	no	—
118	C₄²×C₁₃	—	2	2	no	—
119	C₄²×C₁₃	—	2	2	no	—
120	C₄²×C₁₃	—	2	2	no	—
121	C₄²×C₁₃	—	2	1	no	—
122	C₄²×C₁₃	—	2	1	no	—
123	C₄²×C₁₃	—	4	4	no	—
124	C₄²×C₁₃	#41	1	4	yes	—
125	#2858	C₂×C₁₃	1	1	yes	characteristic
126	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
127	#2071	C₂×C₁₃	1	2	yes	complemented
128	#2023	C₂×C₁₃	1	2	yes	complemented
129	#1987	C₂×C₁₃	1	2	yes	complemented
130	#1982	C₂×C₁₃	1	2	yes	—
131	#1936	C₂×C₁₃	1	4	yes	complemented
132	#1767	C₂×C₁₃	1	1	yes	characteristic, complemented
133	C₂³×C₁₃	—	4	2	no	—
134	C₂³×C₁₃	—	4	2	no	—
135	C₂³×C₁₃	—	4	2	no	—
136	C₂³×C₁₃	—	4	2	no	—
137	C₂³×C₁₃	—	4	2	no	—
138	C₂³×C₁₃	—	4	2	no	—
139	C₂³×C₁₃	—	4	2	no	—
140	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₁₃	—	4	8	no	—
142	Q₈×C₁₃	—	8	4	no	—
143	D₄×C₁₃	—	4	4	no	—
144	D₄×C₁₃	—	4	4	no	—
145	D₄×C₁₃	—	8	4	no	—
146	D₄×C₁₃	—	8	4	no	—
147	C₂×C₄×C₁₃	—	2	1	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	1	no	—
150	C₂×C₄×C₁₃	—	2	1	no	—
151	C₂×C₄×C₁₃	—	2	1	no	—
152	C₂×C₄×C₁₃	—	2	1	no	—
153	C₂×C₄×C₁₃	—	2	4	no	—
154	C₂×C₄×C₁₃	—	2	1	no	—
155	C₂×C₄×C₁₃	—	2	1	no	—
156	C₂×C₄×C₁₃	—	2	1	no	—
157	C₂×C₄×C₁₃	—	2	1	no	—
158	C₂×C₄×C₁₃	—	2	1	no	—
159	C₂×C₄×C₁₃	—	2	1	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	—	4	2	no	—
162	C₂×C₄×C₁₃	—	4	2	no	—
163	C₂×C₄×C₁₃	—	4	2	no	—
164	C₂×C₄×C₁₃	—	4	2	no	—
165	C₂×C₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	#124	1	2	yes	—
169	C₂×C₄×C₁₃	#124	1	2	yes	—
170	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
171	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
172	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
173	C₂×C₄×C₁₃	#137	1	2	yes	—
174	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
175	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
176	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
178	C₈×C₁₃	—	4	4	no	—
179	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
180	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
181	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
182	C₂×#124	—	2	1	no	—
183	C₂×#124	—	2	1	no	—
184	C₂×C₄×Q₈	—	2	1	no	—
185	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
186	C₂×#102	C₂²×C₁₃	1	4	yes	—
187	C₂×#102	C₂²×C₁₃	1	4	yes	—
188	C₂×#97	C₂²×C₁₃	1	2	yes	—
189	#391	—	2	1	no	—
190	#390	—	2	1	no	—
191	#390	—	2	1	no	—
192	#390	C₂²×C₁₃	1	2	yes	—
193	#390	C₂²×C₁₃	1	2	yes	—
194	#389	—	2	1	no	—
195	#389	C₂²×C₁₃	1	2	yes	—
196	#384	C₂²×C₁₃	1	1	yes	characteristic
197	C₄×C₄⋊C₄	—	2	1	no	—
198	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
199	C₄³	C₂²×C₁₃	1	1	yes	characteristic
200	#340	C₂²×C₁₃	1	4	yes	—
201	#340	C₂²×C₁₃	1	4	yes	—
202	#336	C₂²×C₁₃	1	2	yes	—
203	C₂²×C₁₃	—	8	2	no	—
204	C₂²×C₁₃	—	8	2	no	—
205	C₂²×C₁₃	—	8	2	no	—
206	C₂²×C₁₃	—	8	2	no	—
207	C₂²×C₁₃	—	8	2	no	—
208	C₂²×C₁₃	—	8	2	no	—
209	C₂²×C₁₃	—	8	2	no	—
210	C₂²×C₁₃	#525	1	1	yes	characteristic
211	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
212	C₂²×C₁₃	#537	1	1	yes	characteristic
213	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
214	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
215	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
216	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
217	C₄×C₁₃	—	2	2	no	—
218	C₄×C₁₃	—	2	2	no	—
219	C₄×C₁₃	—	2	2	no	—
220	C₄×C₁₃	—	4	4	no	—
221	C₄×C₁₃	—	4	1	no	—
222	C₄×C₁₃	—	4	1	no	—
223	C₄×C₁₃	—	8	2	no	—
224	C₄×C₁₃	—	8	2	no	—
225	C₄×C₁₃	#489	1	4	yes	—
226	C₄×C₁₃	#556	1	2	yes	—
227	C₄×C₁₃	#559	1	2	yes	—
228	C₂²×Q₈	—	2	1	no	—
229	C₂²×Q₈	—	2	1	no	—
230	C₂²×D₄	—	2	1	no	—
231	C₂²×D₄	—	2	1	no	—
232	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
233	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
234	C₄⋊Q₈	—	2	4	no	—
235	C₄⋊Q₈	—	2	4	no	—
236	#127	—	2	4	no	—
237	#124	—	4	4	no	—
238	#124	—	4	4	no	—
239	C₄×Q₈	—	4	4	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
246	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
247	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
254	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
255	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
256	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
257	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
258	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
260	C₄⋊C₈	—	2	4	no	—
261	#102	—	2	8	no	—
262	#102	—	4	4	no	—
263	#97	—	4	2	no	—
264	#95	—	2	2	no	—
265	#95	—	2	2	no	—
266	C₂×C₁₃	—	16	2	no	—
267	C₂×C₁₃	#2592	1	1	yes	characteristic
268	C₂×C₁₃	#3109	1	1	yes	characteristic
269	C₂×C₁₃	#3112	1	1	yes	characteristic
270	C₂×C₁₃	C₂×#489	1	1	yes	characteristic
271	C₂×C₁₃	#3138	1	1	yes	characteristic
272	C₂×C₁₃	#3253	1	1	yes	characteristic
273	C₂×C₁₃	#3254	1	1	yes	characteristic
274	C₂⁴	—	2	2	no	—
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	—	4	2	no	—
277	C₂×Q₈	—	4	2	no	—
278	C₂×Q₈	—	4	2	no	—
279	C₂×Q₈	—	4	2	no	—
280	C₂×Q₈	—	4	2	no	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
301	C₂×C₈	—	2	4	no	—
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	2	4	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	4	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	C₁₃×#41	1	4	yes	—
314	C₂²⋊C₄	—	4	4	no	—
315	C₂²⋊C₄	—	4	4	no	—
316	C₂²⋊C₄	—	4	4	no	—
317	C₂²⋊C₄	—	4	4	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	4	4	no	—
326	C₄²	C₁₃×#41	1	4	yes	—
327	C₁₃	#29354	1	1	yes	characteristic, direct product factor, Sylow
328	C₂³	—	4	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
336	Q₈	—	4	8	no	—
337	Q₈	—	8	4	no	—
338	D₄	—	4	4	no	—
339	D₄	—	4	4	no	—
340	D₄	—	8	4	no	—
341	D₄	—	8	4	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	C₁₃×#124	1	2	yes	—
364	C₂×C₄	C₁₃×#124	1	2	yes	—
365	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
366	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
367	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
368	C₂×C₄	C₁₃×#137	1	2	yes	—
369	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
370	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
371	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
372	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
373	C₈	—	4	4	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	C₁₃×#525	1	1	yes	characteristic
382	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
383	C₂²	C₁₃×#537	1	1	yes	characteristic
384	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
385	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
386	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
387	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	4	4	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	1	no	—
394	C₄	—	8	2	no	—
395	C₄	—	8	2	no	—
396	C₄	C₁₃×#489	1	4	yes	—
397	C₄	C₁₃×#556	1	2	yes	—
398	C₄	C₁₃×#559	1	2	yes	—
399	C₂	—	16	2	no	—
400	C₂	C₁₃×#2592	1	1	yes	characteristic
401	C₂	C₁₃×#3109	1	1	yes	characteristic
402	C₂	C₁₃×#3112	1	1	yes	characteristic
403	C₂	C₂×C₁₃×#489	1	1	yes	characteristic
404	C₂	C₁₃×#3138	1	1	yes	characteristic
405	C₂	C₁₃×#3253	1	1	yes	characteristic
406	C₂	C₁₃×#3254	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
3. C₁₃×#2071	C₂	semidirect
4. C₁₃×#2023	C₂	semidirect
5. C₁₃×#1987	C₂	semidirect
7. C₁₃×#1936	C₂	semidirect
8. C₁₃×#1767	C₂	semidirect
71. #29354	C₁₃	direct (N × H)
126. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
127. #2071	C₂×C₁₃	semidirect
128. #2023	C₂×C₁₃	semidirect
129. #1987	C₂×C₁₃	semidirect
131. #1936	C₂×C₁₃	semidirect
132. #1767	C₂×C₁₃	semidirect
327. C₁₃	#29354	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2858	2
C₄×C₁₃×C₄⋊Q₈	2
C₁₃×#2071	2
C₁₃×#2023	2
C₁₃×#1987	2
C₁₃×#1982	2
C₁₃×#1936	2
C₁₃×#1767	2
#29354	13

Subgroups — C13×#29354 #15715693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29354 #15715693