Subgroups — C₁₃×#29148 #15715487

Order 3328.

830 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2868	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2024	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2023	C₂	1	2	yes	maximal
5	C₁₃×#1959	C₂	1	2	yes	maximal
6	C₁₃×#1836	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1803	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1802	C₂	1	2	yes	maximal
9	C₁₃×#1767	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
11	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
13	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₃×#103	C₂²	1	4	yes	—
18	C₂×C₁₃×#102	C₂²	1	4	yes	—
19	C₂×C₁₃×#97	C₂²	1	2	yes	—
20	C₁₃×#391	C₂²	1	1	yes	characteristic
21	C₁₃×#390	C₂²	1	1	yes	characteristic
22	C₁₃×#388	—	2	1	no	—
23	C₁₃×#388	—	2	1	no	—
24	C₁₃×#384	—	2	1	no	—
25	C₁₃×#384	—	2	1	no	—
26	C₁₃×#384	C₂²	1	2	yes	—
27	C₁₃×#384	C₂²	1	2	yes	—
28	C₁₃×#382	C₂²	1	1	yes	characteristic
29	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
30	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
31	C₄³×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#340	C₂²	1	4	yes	—
33	C₁₃×#340	C₂²	1	4	yes	—
34	C₁₃×#336	C₂²	1	2	yes	—
35	C₂²×Q₈×C₁₃	—	2	2	no	—
36	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
37	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₁₃	—	2	1	no	—
39	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
40	C₁₃×C₄⋊Q₈	—	4	4	no	—
41	C₁₃×C₄⋊Q₈	—	4	4	no	—
42	C₁₃×C₄⋊Q₈	—	4	4	no	—
43	C₁₃×#124	—	2	2	no	—
44	C₁₃×#124	Q₈	1	4	yes	complemented
45	C₄×Q₈×C₁₃	—	2	4	no	—
46	C₄×D₄×C₁₃	—	2	4	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
53	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
56	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
61	C₂×C₄²×C₁₃	—	2	1	no	—
62	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
69	C₁₃×C₄⋊C₈	—	2	4	no	—
70	C₁₃×#103	—	4	4	no	—
71	C₁₃×#102	—	4	4	no	—
72	C₁₃×#97	—	2	4	no	—
73	C₁₃×#95	—	2	1	no	—
74	C₁₃×#95	—	2	1	no	—
75	C₁₃×#95	—	2	1	no	—
76	C₁₃×#95	—	2	1	no	—
77	#29148	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂⁴×C₁₃	—	2	1	no	—
79	C₂×Q₈×C₁₃	—	2	1	no	—
80	C₂×Q₈×C₁₃	—	2	2	no	—
81	C₂×Q₈×C₁₃	—	2	2	no	—
82	C₂×Q₈×C₁₃	—	4	4	no	—
83	C₂×Q₈×C₁₃	—	4	4	no	—
84	C₂×Q₈×C₁₃	—	4	4	no	—
85	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
86	C₂×D₄×C₁₃	—	2	2	no	—
87	C₂×D₄×C₁₃	—	2	1	no	—
88	C₂×D₄×C₁₃	—	2	2	no	—
89	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
90	C₂²×C₄×C₁₃	—	2	1	no	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	—	2	1	no	—
93	C₂²×C₄×C₁₃	—	2	4	no	—
94	C₂²×C₄×C₁₃	—	4	2	no	—
95	C₂²×C₄×C₁₃	—	4	2	no	—
96	C₂²×C₄×C₁₃	—	4	2	no	—
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
104	C₂×C₈×C₁₃	—	2	4	no	—
105	C₂×C₈×C₁₃	—	2	4	no	—
106	C₂×C₈×C₁₃	—	2	4	no	—
107	C₁₃×C₄⋊C₄	—	2	2	no	—
108	C₁₃×C₄⋊C₄	—	2	2	no	—
109	C₁₃×C₄⋊C₄	—	2	4	no	—
110	C₁₃×C₄⋊C₄	—	2	4	no	—
111	C₁₃×C₄⋊C₄	—	4	4	no	—
112	C₁₃×C₄⋊C₄	—	4	4	no	—
113	C₁₃×C₄⋊C₄	—	4	4	no	—
114	C₁₃×C₄⋊C₄	—	4	4	no	—
115	C₁₃×C₄⋊C₄	—	4	2	no	—
116	C₁₃×C₄⋊C₄	—	4	4	no	—
117	C₁₃×C₂²⋊C₄	—	2	4	no	—
118	C₁₃×C₂²⋊C₄	—	2	4	no	—
119	C₁₃×C₂²⋊C₄	—	4	2	no	—
120	C₁₃×C₂²⋊C₄	—	4	2	no	—
121	C₁₃×C₂²⋊C₄	—	4	2	no	—
122	C₄²×C₁₃	—	2	2	no	—
123	C₄²×C₁₃	—	2	2	no	—
124	C₄²×C₁₃	—	2	2	no	—
125	C₄²×C₁₃	—	2	2	no	—
126	C₄²×C₁₃	—	2	2	no	—
127	C₄²×C₁₃	—	4	2	no	—
128	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
129	C₄²×C₁₃	#41	1	2	yes	—
130	C₄²×C₁₃	#41	1	4	yes	—
131	#2868	C₂×C₁₃	1	1	yes	characteristic, complemented
132	C₄×#124	C₂×C₁₃	1	1	yes	characteristic
133	#2024	C₂×C₁₃	1	2	yes	complemented
134	#2023	C₂×C₁₃	1	2	yes	—
135	#1959	C₂×C₁₃	1	2	yes	—
136	#1836	C₂×C₁₃	1	2	yes	complemented
137	#1803	C₂×C₁₃	1	2	yes	complemented
138	#1802	C₂×C₁₃	1	2	yes	—
139	#1767	C₂×C₁₃	1	1	yes	characteristic, complemented
140	C₂³×C₁₃	—	2	2	no	—
141	C₂³×C₁₃	—	4	1	no	—
142	C₂³×C₁₃	—	4	1	no	—
143	C₂³×C₁₃	—	4	1	no	—
144	C₂³×C₁₃	—	4	1	no	—
145	C₂³×C₁₃	—	4	1	no	—
146	C₂³×C₁₃	—	4	1	no	—
147	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₁₃	—	2	4	no	—
149	Q₈×C₁₃	—	4	2	no	—
150	Q₈×C₁₃	—	8	8	no	—
151	D₄×C₁₃	—	2	4	no	—
152	D₄×C₁₃	—	4	2	no	—
153	C₂×C₄×C₁₃	—	2	1	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	—	2	1	no	—
161	C₂×C₄×C₁₃	—	2	1	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	4	1	no	—
165	C₂×C₄×C₁₃	—	4	1	no	—
166	C₂×C₄×C₁₃	—	4	1	no	—
167	C₂×C₄×C₁₃	—	4	1	no	—
168	C₂×C₄×C₁₃	—	4	4	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	4	4	no	—
171	C₂×C₄×C₁₃	—	4	4	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	—	4	1	no	—
175	C₂×C₄×C₁₃	—	8	4	no	—
176	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
177	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
178	C₂×C₄×C₁₃	#124	1	2	yes	—
179	C₂×C₄×C₁₃	#124	1	2	yes	—
180	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
181	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
182	C₂×C₄×C₁₃	#137	1	2	yes	—
183	C₂×C₄×C₁₃	#137	1	2	yes	—
184	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
186	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
188	C₈×C₁₃	—	4	4	no	—
189	C₂×C₄⋊Q₈	—	2	1	no	—
190	C₂×C₄⋊Q₈	—	2	1	no	—
191	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
192	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
193	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
194	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
196	C₂×#103	C₂²×C₁₃	1	4	yes	—
197	C₂×#102	C₂²×C₁₃	1	4	yes	—
198	C₂×#97	C₂²×C₁₃	1	2	yes	—
199	#391	C₂²×C₁₃	1	1	yes	characteristic
200	#390	C₂²×C₁₃	1	1	yes	characteristic
201	#388	—	2	1	no	—
202	#388	—	2	1	no	—
203	#384	—	2	1	no	—
204	#384	—	2	1	no	—
205	#384	C₂²×C₁₃	1	2	yes	—
206	#384	C₂²×C₁₃	1	2	yes	—
207	#382	C₂²×C₁₃	1	1	yes	characteristic
208	C₄×C₂²⋊C₄	—	2	1	no	—
209	C₄×C₂²⋊C₄	—	2	1	no	—
210	C₄³	C₂²×C₁₃	1	1	yes	characteristic
211	#340	C₂²×C₁₃	1	4	yes	—
212	#340	C₂²×C₁₃	1	4	yes	—
213	#336	C₂²×C₁₃	1	2	yes	—
214	C₂²×C₁₃	—	4	2	no	—
215	C₂²×C₁₃	—	4	2	no	—
216	C₂²×C₁₃	—	4	2	no	—
217	C₂²×C₁₃	—	8	1	no	—
218	C₂²×C₁₃	—	8	1	no	—
219	C₂²×C₁₃	—	8	1	no	—
220	C₂²×C₁₃	—	8	1	no	—
221	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
222	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
223	C₂²×C₁₃	#535	1	1	yes	characteristic
224	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
225	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
226	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
227	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
228	C₄×C₁₃	—	2	2	no	—
229	C₄×C₁₃	—	2	2	no	—
230	C₄×C₁₃	—	2	2	no	—
231	C₄×C₁₃	—	2	2	no	—
232	C₄×C₁₃	—	2	2	no	—
233	C₄×C₁₃	—	4	2	no	—
234	C₄×C₁₃	—	8	1	no	—
235	C₄×C₁₃	—	8	1	no	—
236	C₄×C₁₃	—	8	4	no	—
237	C₄×C₁₃	#489	1	4	yes	—
238	C₄×C₁₃	#554	1	2	yes	—
239	C₄×C₁₃	#555	1	2	yes	—
240	C₂²×Q₈	—	2	2	no	—
241	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
242	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
243	C₂³×C₄	—	2	1	no	—
244	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
245	C₄⋊Q₈	—	4	4	no	—
246	C₄⋊Q₈	—	4	4	no	—
247	C₄⋊Q₈	—	4	4	no	—
248	#124	—	2	2	no	—
249	#124	Q₈×C₁₃	1	4	yes	complemented
250	C₄×Q₈	—	2	4	no	—
251	C₄×D₄	—	2	4	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
261	C₂×C₂²⋊C₄	—	2	1	no	—
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₄²	—	2	1	no	—
267	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
268	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
269	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
270	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
273	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
274	C₄⋊C₈	—	2	4	no	—
275	#103	—	4	4	no	—
276	#102	—	4	4	no	—
277	#97	—	2	4	no	—
278	#95	—	2	1	no	—
279	#95	—	2	1	no	—
280	#95	—	2	1	no	—
281	#95	—	2	1	no	—
282	C₂×C₁₃	—	8	2	no	—
283	C₂×C₁₃	#2563	1	1	yes	characteristic
284	C₂×C₁₃	#3079	1	1	yes	characteristic
285	C₂×C₁₃	#3079	1	1	yes	characteristic
286	C₂×C₁₃	C₂×#489	1	1	yes	characteristic
287	C₂×C₁₃	#3141	1	1	yes	characteristic
288	C₂×C₁₃	#3217	1	1	yes	characteristic
289	C₂×C₁₃	#3218	1	1	yes	characteristic
290	C₂⁴	—	2	1	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	4	4	no	—
295	C₂×Q₈	—	4	4	no	—
296	C₂×Q₈	—	4	4	no	—
297	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
315	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	2	4	no	—
318	C₂×C₈	—	2	4	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	4	4	no	—
324	C₄⋊C₄	—	4	4	no	—
325	C₄⋊C₄	—	4	4	no	—
326	C₄⋊C₄	—	4	4	no	—
327	C₄⋊C₄	—	4	2	no	—
328	C₄⋊C₄	—	4	4	no	—
329	C₂²⋊C₄	—	2	4	no	—
330	C₂²⋊C₄	—	2	4	no	—
331	C₂²⋊C₄	—	4	2	no	—
332	C₂²⋊C₄	—	4	2	no	—
333	C₂²⋊C₄	—	4	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	4	2	no	—
340	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
341	C₄²	C₁₃×#41	1	2	yes	—
342	C₄²	C₁₃×#41	1	4	yes	—
343	C₁₃	#29148	1	1	yes	characteristic, direct product factor, Sylow
344	C₂³	—	2	2	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	4	1	no	—
347	C₂³	—	4	1	no	—
348	C₂³	—	4	1	no	—
349	C₂³	—	4	1	no	—
350	C₂³	—	4	1	no	—
351	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
352	Q₈	—	2	4	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	8	8	no	—
355	D₄	—	2	4	no	—
356	D₄	—	4	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	8	4	no	—
380	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
381	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
382	C₂×C₄	C₁₃×#124	1	2	yes	—
383	C₂×C₄	C₁₃×#124	1	2	yes	—
384	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
385	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
386	C₂×C₄	C₁₃×#137	1	2	yes	—
387	C₂×C₄	C₁₃×#137	1	2	yes	—
388	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
389	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
390	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
391	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
392	C₈	—	4	4	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	8	1	no	—
397	C₂²	—	8	1	no	—
398	C₂²	—	8	1	no	—
399	C₂²	—	8	1	no	—
400	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
401	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
402	C₂²	C₁₃×#535	1	1	yes	characteristic
403	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
404	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
405	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
406	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
407	C₄	—	2	2	no	—
408	C₄	—	2	2	no	—
409	C₄	—	2	2	no	—
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	4	2	no	—
413	C₄	—	8	1	no	—
414	C₄	—	8	1	no	—
415	C₄	—	8	4	no	—
416	C₄	C₁₃×#489	1	4	yes	—
417	C₄	C₁₃×#554	1	2	yes	—
418	C₄	C₁₃×#555	1	2	yes	—
419	C₂	—	8	2	no	—
420	C₂	C₁₃×#2563	1	1	yes	characteristic
421	C₂	C₁₃×#3079	1	1	yes	characteristic
422	C₂	C₁₃×#3079	1	1	yes	characteristic
423	C₂	C₂×C₁₃×#489	1	1	yes	characteristic
424	C₂	C₁₃×#3141	1	1	yes	characteristic
425	C₂	C₁₃×#3217	1	1	yes	characteristic
426	C₂	C₁₃×#3218	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
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
1. C₁₃×#2868	C₂	semidirect
3. C₁₃×#2024	C₂	semidirect
6. C₁₃×#1836	C₂	semidirect
7. C₁₃×#1803	C₂	semidirect
9. C₁₃×#1767	C₂	semidirect
44. C₁₃×#124	Q₈	semidirect
77. #29148	C₁₃	direct (N × H)
131. #2868	C₂×C₁₃	semidirect
133. #2024	C₂×C₁₃	semidirect
136. #1836	C₂×C₁₃	semidirect
137. #1803	C₂×C₁₃	semidirect
139. #1767	C₂×C₁₃	semidirect
249. #124	Q₈×C₁₃	semidirect
343. C₁₃	#29148	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×#2868	2
C₄×C₁₃×#124	2
C₁₃×#2024	2
C₁₃×#2023	2
C₁₃×#1959	2
C₁₃×#1836	2
C₁₃×#1803	2
C₁₃×#1802	2
C₁₃×#1767	2
#29148	13

Subgroups — C13×#29148 #15715487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29148 #15715487