Subgroups — C₁₃×#25903 #15712242

Order 3328.

1446 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#486	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2856	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2023	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1990	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1874	C₂	1	4	yes	maximal, complemented
7	C₄×C₁₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×Q₈×C₁₃	—	2	1	no	—
9	C₂×C₁₃×C₄⋊Q₈	—	2	8	no	—
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×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#121	—	2	1	no	—
16	C₂×C₁₃×#121	—	2	1	no	—
17	C₂×C₁₃×#121	C₂²	1	2	yes	—
18	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#486	—	2	8	no	—
22	C₂×C₁₃×#102	C₂²	1	8	yes	—
23	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
25	C₁₃×#390	—	2	1	no	—
26	C₁₃×#390	—	2	1	no	—
27	C₁₃×#390	C₂²	1	2	yes	—
28	C₁₃×#384	C₂²	1	1	yes	characteristic
29	C₁₃×#340	C₂²	1	8	yes	—
30	C₁₃×#336	C₂²	1	2	yes	—
31	C₂²×Q₈×C₁₃	—	2	8	no	—
32	C₂²×Q₈×C₁₃	—	2	2	no	—
33	C₂²×Q₈×C₁₃	—	2	2	no	—
34	C₂²×Q₈×C₁₃	—	4	4	no	—
35	C₂²×Q₈×C₁₃	—	4	4	no	—
36	C₂²×D₄×C₁₃	—	2	2	no	—
37	C₂²×D₄×C₁₃	—	2	1	no	—
38	C₂²×D₄×C₁₃	—	2	1	no	—
39	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₃	—	2	2	no	—
41	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
45	C₁₃×C₄⋊Q₈	—	2	8	no	—
46	C₁₃×C₄⋊Q₈	—	2	8	no	—
47	C₁₃×C₄⋊Q₈	—	2	8	no	—
48	C₁₃×C₄⋊Q₈	—	2	4	no	—
49	C₁₃×C₄⋊Q₈	D₄	1	8	yes	complemented
50	C₁₃×#127	—	2	4	no	—
51	C₁₃×#121	—	2	8	no	—
52	C₁₃×#121	—	4	4	no	—
53	C₁₃×#121	—	4	4	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
66	C₂×C₄²×C₁₃	—	2	4	no	—
67	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#102	—	2	16	no	—
72	C₁₃×C₂²⋊C₈	—	2	4	no	—
73	C₄×C₈×C₁₃	—	2	4	no	—
74	#25903	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
75	C₂⁴×C₁₃	—	2	2	no	—
76	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
77	C₂×Q₈×C₁₃	—	2	8	no	—
78	C₂×Q₈×C₁₃	—	2	8	no	—
79	C₂×Q₈×C₁₃	—	4	4	no	—
80	C₂×Q₈×C₁₃	—	4	32	no	—
81	C₂×Q₈×C₁₃	—	4	4	no	—
82	C₂×Q₈×C₁₃	—	4	4	no	—
83	C₂×Q₈×C₁₃	—	4	4	no	—
84	C₂×D₄×C₁₃	—	2	4	no	—
85	C₂×D₄×C₁₃	—	2	4	no	—
86	C₂×D₄×C₁₃	—	2	4	no	—
87	C₂×D₄×C₁₃	—	4	4	no	—
88	C₂×D₄×C₁₃	—	4	4	no	—
89	C₂×D₄×C₁₃	—	4	4	no	—
90	C₂×D₄×C₁₃	—	4	2	no	—
91	C₂×D₄×C₁₃	—	4	2	no	—
92	C₂×D₄×C₁₃	—	4	2	no	—
93	C₂×D₄×C₁₃	—	4	2	no	—
94	C₂×D₄×C₁₃	—	4	2	no	—
95	C₂×D₄×C₁₃	—	4	2	no	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	2	8	no	—
103	C₂²×C₄×C₁₃	—	2	4	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	4	4	no	—
106	C₂²×C₄×C₁₃	—	4	4	no	—
107	C₂²×C₄×C₁₃	D₈	1	4	yes	—
108	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	#41	1	4	yes	—
115	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
116	C₂×C₈×C₁₃	—	2	4	no	—
117	C₂×C₈×C₁₃	—	2	4	no	—
118	C₂×C₈×C₁₃	—	2	4	no	—
119	C₁₃×C₄⋊C₄	—	2	8	no	—
120	C₁₃×C₄⋊C₄	—	2	8	no	—
121	C₁₃×C₄⋊C₄	—	2	8	no	—
122	C₁₃×C₄⋊C₄	—	2	4	no	—
123	C₁₃×C₄⋊C₄	—	2	4	no	—
124	C₁₃×C₄⋊C₄	—	4	2	no	—
125	C₁₃×C₄⋊C₄	—	4	2	no	—
126	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
127	C₁₃×C₂²⋊C₄	—	4	4	no	—
128	C₁₃×C₂²⋊C₄	—	4	4	no	—
129	C₁₃×C₂²⋊C₄	—	4	4	no	—
130	C₄²×C₁₃	—	2	2	no	—
131	C₄²×C₁₃	—	2	2	no	—
132	C₄²×C₁₃	—	2	2	no	—
133	C₄²×C₁₃	C₂×D₄	1	4	yes	—
134	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
135	C₂×#486	C₂×C₁₃	1	2	yes	complemented
136	#2856	C₂×C₁₃	1	1	yes	characteristic
137	#2023	C₂×C₁₃	1	4	yes	complemented
138	#1990	C₂×C₁₃	1	2	yes	complemented
139	#1874	C₂×C₁₃	1	4	yes	complemented
140	C₄×C₂²⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
141	C₂³×C₁₃	—	2	1	no	—
142	C₂³×C₁₃	—	2	1	no	—
143	C₂³×C₁₃	—	2	1	no	—
144	C₂³×C₁₃	—	2	1	no	—
145	C₂³×C₁₃	—	4	2	no	—
146	C₂³×C₁₃	—	4	2	no	—
147	C₂³×C₁₃	—	4	2	no	—
148	C₂³×C₁₃	—	4	2	no	—
149	C₂³×C₁₃	—	4	2	no	—
150	C₂³×C₁₃	—	4	2	no	—
151	C₂³×C₁₃	—	4	2	no	—
152	C₂³×C₁₃	#124	1	2	yes	—
153	C₂³×C₁₃	C₂×D₈	1	2	yes	—
154	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
155	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₁₃	—	4	16	no	—
157	Q₈×C₁₃	—	4	16	no	—
158	D₄×C₁₃	—	4	8	no	—
159	D₄×C₁₃	—	8	8	no	—
160	D₄×C₁₃	—	8	4	no	—
161	D₄×C₁₃	—	8	4	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	8	no	—
169	C₂×C₄×C₁₃	—	2	8	no	—
170	C₂×C₄×C₁₃	—	2	8	no	—
171	C₂×C₄×C₁₃	—	2	8	no	—
172	C₂×C₄×C₁₃	—	4	16	no	—
173	C₂×C₄×C₁₃	—	4	4	no	—
174	C₂×C₄×C₁₃	—	4	4	no	—
175	C₂×C₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	#120	1	2	yes	—
179	C₂×C₄×C₁₃	#120	1	2	yes	—
180	C₂×C₄×C₁₃	#124	1	2	yes	—
181	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
182	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
183	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
184	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
185	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
186	C₂×C₄×C₁₃	#137	1	2	yes	—
187	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
188	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
189	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
190	C₈×C₁₃	—	4	4	no	—
191	C₂³×Q₈	—	2	1	no	—
192	C₂×C₄⋊Q₈	—	2	8	no	—
193	C₂×C₄⋊Q₈	—	2	1	no	—
194	C₂×C₄⋊Q₈	—	2	1	no	—
195	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
196	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
197	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×#121	—	2	1	no	—
199	C₂×#121	—	2	1	no	—
200	C₂×#121	C₂²×C₁₃	1	2	yes	—
201	C₂²×C₄⋊C₄	—	2	1	no	—
202	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
203	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
204	#486	—	2	8	no	—
205	C₂×#102	C₂²×C₁₃	1	8	yes	—
206	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
207	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
208	#390	—	2	1	no	—
209	#390	—	2	1	no	—
210	#390	C₂²×C₁₃	1	2	yes	—
211	#384	C₂²×C₁₃	1	1	yes	characteristic
212	#340	C₂²×C₁₃	1	8	yes	—
213	#336	C₂²×C₁₃	1	2	yes	—
214	C₂²×C₁₃	—	2	2	no	—
215	C₂²×C₁₃	—	2	2	no	—
216	C₂²×C₁₃	—	2	2	no	—
217	C₂²×C₁₃	—	2	2	no	—
218	C₂²×C₁₃	—	2	2	no	—
219	C₂²×C₁₃	—	2	2	no	—
220	C₂²×C₁₃	—	8	2	no	—
221	C₂²×C₁₃	—	8	2	no	—
222	C₂²×C₁₃	—	8	2	no	—
223	C₂²×C₁₃	—	8	2	no	—
224	C₂²×C₁₃	—	8	2	no	—
225	C₂²×C₁₃	—	8	2	no	—
226	C₂²×C₁₃	—	8	2	no	—
227	C₂²×C₁₃	#486	1	4	yes	complemented
228	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
229	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
230	C₂²×C₁₃	#536	1	1	yes	characteristic
231	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
232	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
233	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
234	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
235	C₄×C₁₃	—	2	2	no	—
236	C₄×C₁₃	—	2	2	no	—
237	C₄×C₁₃	—	2	2	no	—
238	C₄×C₁₃	—	4	8	no	—
239	C₄×C₁₃	—	8	2	no	—
240	C₄×C₁₃	#447	1	4	yes	—
241	C₄×C₁₃	#448	1	4	yes	—
242	C₄×C₁₃	#548	1	4	yes	—
243	C₂²×Q₈	—	2	8	no	—
244	C₂²×Q₈	—	2	2	no	—
245	C₂²×Q₈	—	2	2	no	—
246	C₂²×Q₈	—	4	4	no	—
247	C₂²×Q₈	—	4	4	no	—
248	C₂²×D₄	—	2	2	no	—
249	C₂²×D₄	—	2	1	no	—
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
252	C₂³×C₄	—	2	2	no	—
253	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
254	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
255	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
257	C₄⋊Q₈	—	2	8	no	—
258	C₄⋊Q₈	—	2	8	no	—
259	C₄⋊Q₈	—	2	8	no	—
260	C₄⋊Q₈	—	2	4	no	—
261	C₄⋊Q₈	D₄×C₁₃	1	8	yes	complemented
262	#127	—	2	4	no	—
263	#121	—	2	8	no	—
264	#121	—	4	4	no	—
265	#121	—	4	4	no	—
266	C₂×C₄⋊C₄	—	2	8	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	8	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₄²	—	2	4	no	—
279	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
280	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
281	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
283	#102	—	2	16	no	—
284	C₂²⋊C₈	—	2	4	no	—
285	C₄×C₈	—	2	4	no	—
286	C₂×C₁₃	—	2	4	no	—
287	C₂×C₁₃	—	16	2	no	—
288	C₂×C₁₃	#2436	1	1	yes	characteristic
289	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
290	C₂×C₁₃	C₂×#448	1	1	yes	characteristic
291	C₂×C₁₃	C₂×#486	1	1	yes	characteristic
292	C₂×C₁₃	#3141	1	1	yes	characteristic
293	C₂×C₁₃	#3226	1	1	yes	characteristic
294	C₂×C₁₃	#3227	1	1	yes	characteristic
295	C₂⁴	—	2	2	no	—
296	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
297	C₂×Q₈	—	2	8	no	—
298	C₂×Q₈	—	2	8	no	—
299	C₂×Q₈	—	4	4	no	—
300	C₂×Q₈	—	4	32	no	—
301	C₂×Q₈	—	4	4	no	—
302	C₂×Q₈	—	4	4	no	—
303	C₂×Q₈	—	4	4	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	4	4	no	—
308	C₂×D₄	—	4	4	no	—
309	C₂×D₄	—	4	4	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	8	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	4	4	no	—
326	C₂²×C₄	—	4	4	no	—
327	C₂²×C₄	C₁₃×D₈	1	4	yes	—
328	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	—
329	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
334	C₂²×C₄	C₁₃×#41	1	4	yes	—
335	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
336	C₂×C₈	—	2	4	no	—
337	C₂×C₈	—	2	4	no	—
338	C₂×C₈	—	2	4	no	—
339	C₄⋊C₄	—	2	8	no	—
340	C₄⋊C₄	—	2	8	no	—
341	C₄⋊C₄	—	2	8	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	4	2	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
347	C₂²⋊C₄	—	4	4	no	—
348	C₂²⋊C₄	—	4	4	no	—
349	C₂²⋊C₄	—	4	4	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	C₂×D₄×C₁₃	1	4	yes	—
354	C₁₃	#25903	1	1	yes	characteristic, direct product factor, Sylow
355	C₂³	—	2	1	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	C₁₃×#124	1	2	yes	—
367	C₂³	C₂×C₁₃×D₈	1	2	yes	—
368	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
369	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
370	Q₈	—	4	16	no	—
371	Q₈	—	4	16	no	—
372	D₄	—	4	8	no	—
373	D₄	—	8	8	no	—
374	D₄	—	8	4	no	—
375	D₄	—	8	4	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	4	16	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	C₁₃×#120	1	2	yes	—
393	C₂×C₄	C₁₃×#120	1	2	yes	—
394	C₂×C₄	C₁₃×#124	1	2	yes	—
395	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
396	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
397	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
398	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
399	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
400	C₂×C₄	C₁₃×#137	1	2	yes	—
401	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
402	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
403	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
404	C₈	—	4	4	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	2	no	—
418	C₂²	C₁₃×#486	1	4	yes	complemented
419	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
420	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
421	C₂²	C₁₃×#536	1	1	yes	characteristic
422	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
423	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
424	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
425	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	4	8	no	—
430	C₄	—	8	2	no	—
431	C₄	C₁₃×#447	1	4	yes	—
432	C₄	C₁₃×#448	1	4	yes	—
433	C₄	C₁₃×#548	1	4	yes	—
434	C₂	—	2	4	no	—
435	C₂	—	16	2	no	—
436	C₂	C₁₃×#2436	1	1	yes	characteristic
437	C₂	C₂×C₁₃×#447	1	1	yes	characteristic
438	C₂	C₂×C₁₃×#448	1	1	yes	characteristic
439	C₂	C₂×C₁₃×#486	1	1	yes	characteristic
440	C₂	C₁₃×#3141	1	1	yes	characteristic
441	C₂	C₁₃×#3226	1	1	yes	characteristic
442	C₂	C₁₃×#3227	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2856	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
2. C₂×C₁₃×#486	C₂	semidirect
4. C₁₃×#2023	C₂	semidirect
5. C₁₃×#1990	C₂	semidirect
6. C₁₃×#1874	C₂	semidirect
7. C₄×C₁₃×C₂²⋊C₈	C₂	semidirect
49. C₁₃×C₄⋊Q₈	D₄	semidirect
74. #25903	C₁₃	direct (N × H)
134. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
135. C₂×#486	C₂×C₁₃	semidirect
137. #2023	C₂×C₁₃	semidirect
138. #1990	C₂×C₁₃	semidirect
139. #1874	C₂×C₁₃	semidirect
140. C₄×C₂²⋊C₈	C₂×C₁₃	semidirect
227. C₂²×C₁₃	#486	semidirect
261. C₄⋊Q₈	D₄×C₁₃	semidirect
354. C₁₃	#25903	direct (N × H)
418. C₂²	C₁₃×#486	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×C₄⋊Q₈	2
C₂×C₁₃×#486	2
C₁₃×#2856	2
C₁₃×#2023	2
C₁₃×#1990	2
C₁₃×#1874	2
C₄×C₁₃×C₂²⋊C₈	2
#25903	13

Subgroups — C13×#25903 #15712242

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25903 #15712242