Subgroups — C₁₃×#25834 #15712173

Order 3328.

1246 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	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2567	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2058	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1988	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1864	C₂	1	4	yes	maximal
9	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₁₃	—	2	1	no	—
11	D₄×Q₈×C₁₃	—	2	4	no	—
12	D₄×Q₈×C₁₃	—	2	4	no	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
17	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
18	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#498	—	2	4	no	—
22	C₁₃×#476	—	2	4	no	—
23	C₂×C₁₃×#106	C₂²	1	2	yes	—
24	C₂×C₁₃×#106	C₂²	1	4	yes	—
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#102	C₂²	1	2	yes	—
27	C₂×C₁₃×#102	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#395	—	2	2	no	—
30	C₁₃×#391	—	2	1	no	—
31	C₁₃×#389	C₂²	1	4	yes	—
32	C₁₃×#384	—	2	1	no	—
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₁₃×#340	C₂²	1	4	yes	—
35	C₁₃×#340	C₂²	1	2	yes	—
36	C₁₃×#336	C₂²	1	4	yes	—
37	C₂²×Q₈×C₁₃	—	2	8	no	—
38	C₂²×Q₈×C₁₃	—	2	2	no	—
39	C₂²×Q₈×C₁₃	—	2	1	no	—
40	C₂²×Q₈×C₁₃	—	2	1	no	—
41	C₂²×Q₈×C₁₃	—	4	4	no	—
42	C₂²×Q₈×C₁₃	—	4	4	no	—
43	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	—	2	2	no	—
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₁₃×C₄⋊Q₈	—	2	4	no	—
50	C₁₃×C₄⋊Q₈	—	2	4	no	—
51	C₁₃×C₄⋊Q₈	—	2	2	no	—
52	C₁₃×C₄⋊Q₈	—	2	2	no	—
53	C₁₃×C₄⋊Q₈	—	2	2	no	—
54	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
55	C₁₃×C₂²⋊Q₈	—	2	8	no	—
56	C₁₃×C₂²⋊Q₈	—	2	16	no	—
57	C₄×Q₈×C₁₃	—	2	2	no	—
58	C₄×Q₈×C₁₃	—	2	2	no	—
59	C₄×D₄×C₁₃	—	2	4	no	—
60	C₄×D₄×C₁₃	—	2	4	no	—
61	C₄×D₄×C₁₃	—	2	2	no	—
62	C₄×D₄×C₁₃	D₄	1	4	yes	—
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
67	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₄²×C₁₃	—	2	1	no	—
76	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×#106	—	2	4	no	—
79	C₁₃×#106	—	2	8	no	—
80	C₁₃×C₄⋊C₈	—	2	2	no	—
81	C₁₃×#102	—	2	4	no	—
82	C₁₃×#102	Q₈	1	8	yes	complemented
83	C₄×C₈×C₁₃	—	2	2	no	—
84	C₁₃×#95	—	2	1	no	—
85	C₁₃×#95	—	2	4	no	—
86	#25834	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₃	—	2	1	no	—
88	C₂×Q₈×C₁₃	—	2	8	no	—
89	C₂×Q₈×C₁₃	—	2	2	no	—
90	C₂×Q₈×C₁₃	—	2	4	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	4	4	no	—
93	C₂×Q₈×C₁₃	—	4	32	no	—
94	C₂×Q₈×C₁₃	—	4	2	no	—
95	C₂×Q₈×C₁₃	—	4	4	no	—
96	C₂×Q₈×C₁₃	—	4	2	no	—
97	C₂×Q₈×C₁₃	—	4	2	no	—
98	C₂×Q₈×C₁₃	—	8	2	no	—
99	C₂×Q₈×C₁₃	SD₁₆	1	4	yes	—
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
103	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
104	C₂²×C₄×C₁₃	—	2	8	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	4	4	no	—
111	C₂²×C₄×C₁₃	—	4	4	no	—
112	C₂²×C₄×C₁₃	—	4	2	no	—
113	C₂²×C₄×C₁₃	—	4	2	no	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	4	no	—
123	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	complemented
124	C₁₃×C₄⋊C₄	—	2	8	no	—
125	C₁₃×C₄⋊C₄	—	2	4	no	—
126	C₁₃×C₄⋊C₄	—	2	4	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	4	2	no	—
134	C₁₃×C₄⋊C₄	—	8	4	no	—
135	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
136	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
137	C₁₃×C₄⋊C₄	C₂×Q₈	1	4	yes	complemented
138	C₁₃×C₂²⋊C₄	—	2	8	no	—
139	C₁₃×C₂²⋊C₄	—	2	4	no	—
140	C₄²×C₁₃	—	2	2	no	—
141	C₄²×C₁₃	—	2	2	no	—
142	C₄²×C₁₃	—	4	2	no	—
143	C₄²×C₁₃	C₂×D₄	1	2	yes	—
144	C₄²×C₁₃	C₂×D₄	1	2	yes	—
145	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic
146	C₂×#498	C₂×C₁₃	1	1	yes	characteristic, complemented
147	C₂×#476	C₂×C₁₃	1	1	yes	characteristic
148	#2567	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#2058	C₂×C₁₃	1	4	yes	complemented
150	#1988	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#1864	C₂×C₁₃	1	4	yes	—
153	C₄×#102	C₂×C₁₃	1	1	yes	characteristic
154	C₂³×C₁₃	—	2	2	no	—
155	C₂³×C₁₃	—	2	4	no	—
156	C₂³×C₁₃	—	4	1	no	—
157	C₂³×C₁₃	—	4	1	no	—
158	C₂³×C₁₃	—	4	2	no	—
159	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
160	Q₈×C₁₃	—	2	8	no	—
161	Q₈×C₁₃	—	4	16	no	—
162	Q₈×C₁₃	—	4	8	no	—
163	Q₈×C₁₃	—	8	4	no	—
164	D₄×C₁₃	—	2	2	no	—
165	D₄×C₁₃	—	2	4	no	—
166	D₄×C₁₃	C₄⋊Q₈	1	4	yes	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	4	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	2	4	no	—
175	C₂×C₄×C₁₃	—	4	16	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	8	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	4	no	—
185	C₂×C₄×C₁₃	#120	1	2	yes	—
186	C₂×C₄×C₁₃	#120	1	2	yes	—
187	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
188	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
189	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
190	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
193	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
194	C₈×C₁₃	—	2	4	no	—
195	C₈×C₁₃	—	4	2	no	—
196	C₂³×Q₈	—	2	1	no	—
197	D₄×Q₈	—	2	4	no	—
198	D₄×Q₈	—	2	4	no	—
199	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
201	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×C₂²⋊Q₈	—	2	1	no	—
203	C₂×C₂²⋊Q₈	—	2	2	no	—
204	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
206	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
207	#498	—	2	4	no	—
208	#476	—	2	4	no	—
209	C₂×#106	C₂²×C₁₃	1	2	yes	—
210	C₂×#106	C₂²×C₁₃	1	4	yes	—
211	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×#102	C₂²×C₁₃	1	2	yes	—
213	C₂×#102	C₂²×C₁₃	1	2	yes	—
214	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
215	#395	—	2	2	no	—
216	#391	—	2	1	no	—
217	#389	C₂²×C₁₃	1	4	yes	—
218	#384	—	2	1	no	—
219	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
220	#340	C₂²×C₁₃	1	2	yes	—
221	#340	C₂²×C₁₃	1	4	yes	—
222	#336	C₂²×C₁₃	1	4	yes	—
223	C₂²×C₁₃	—	2	4	no	—
224	C₂²×C₁₃	—	4	4	no	—
225	C₂²×C₁₃	—	4	4	no	—
226	C₂²×C₁₃	—	4	2	no	—
227	C₂²×C₁₃	—	4	2	no	—
228	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
229	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
230	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
231	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
232	C₂²×C₁₃	#577	1	2	yes	—
233	C₄×C₁₃	—	2	4	no	—
234	C₄×C₁₃	—	2	2	no	—
235	C₄×C₁₃	—	4	4	no	—
236	C₄×C₁₃	—	4	4	no	—
237	C₄×C₁₃	—	4	2	no	—
238	C₄×C₁₃	—	4	2	no	—
239	C₄×C₁₃	—	8	2	no	—
240	C₄×C₁₃	#450	1	4	yes	—
241	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
242	C₄×C₁₃	#536	1	1	yes	characteristic
243	C₄×C₁₃	D₄×Q₈	1	2	yes	—
244	C₂²×Q₈	—	2	8	no	—
245	C₂²×Q₈	—	2	2	no	—
246	C₂²×Q₈	—	2	1	no	—
247	C₂²×Q₈	—	2	1	no	—
248	C₂²×Q₈	—	4	4	no	—
249	C₂²×Q₈	—	4	4	no	—
250	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
251	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
252	C₂³×C₄	—	2	2	no	—
253	C₂³×C₄	—	2	1	no	—
254	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
255	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
256	C₄⋊Q₈	—	2	4	no	—
257	C₄⋊Q₈	—	2	4	no	—
258	C₄⋊Q₈	—	2	2	no	—
259	C₄⋊Q₈	—	2	2	no	—
260	C₄⋊Q₈	—	2	2	no	—
261	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
262	C₂²⋊Q₈	—	2	8	no	—
263	C₂²⋊Q₈	—	2	16	no	—
264	C₄×Q₈	—	2	2	no	—
265	C₄×Q₈	—	2	2	no	—
266	C₄×D₄	—	2	4	no	—
267	C₄×D₄	—	2	4	no	—
268	C₄×D₄	—	2	2	no	—
269	C₄×D₄	D₄×C₁₃	1	4	yes	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	4	no	—
274	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
275	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
284	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
285	#106	—	2	4	no	—
286	#106	—	2	8	no	—
287	C₄⋊C₈	—	2	2	no	—
288	#102	—	2	4	no	—
289	#102	Q₈×C₁₃	1	8	yes	complemented
290	C₄×C₈	—	2	2	no	—
291	#95	—	2	1	no	—
292	#95	—	2	4	no	—
293	C₂×C₁₃	—	4	4	no	—
294	C₂×C₁₃	#2434	1	1	yes	characteristic
295	C₂×C₁₃	C₂×#450	1	1	yes	characteristic
296	C₂×C₁₃	#3010	1	1	yes	characteristic
297	C₂×C₁₃	Q₈×SD₁₆	1	2	yes	—
298	C₂×C₁₃	#3384	1	2	yes	—
299	C₂⁴	—	2	1	no	—
300	C₂×Q₈	—	2	8	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	4	4	no	—
305	C₂×Q₈	—	4	32	no	—
306	C₂×Q₈	—	4	2	no	—
307	C₂×Q₈	—	4	4	no	—
308	C₂×Q₈	—	4	2	no	—
309	C₂×Q₈	—	4	2	no	—
310	C₂×Q₈	—	8	2	no	—
311	C₂×Q₈	C₁₃×SD₁₆	1	4	yes	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
315	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	4	4	no	—
323	C₂²×C₄	—	4	4	no	—
324	C₂²×C₄	—	4	2	no	—
325	C₂²×C₄	—	4	2	no	—
326	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
327	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
330	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	4	no	—
335	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	complemented
336	C₄⋊C₄	—	2	8	no	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	—	8	4	no	—
347	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
348	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
349	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	complemented
350	C₂²⋊C₄	—	2	8	no	—
351	C₂²⋊C₄	—	2	4	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	4	2	no	—
355	C₄²	C₂×D₄×C₁₃	1	2	yes	—
356	C₄²	C₂×D₄×C₁₃	1	2	yes	—
357	C₁₃	#25834	1	1	yes	characteristic, direct product factor, Sylow
358	C₂³	—	2	2	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	4	1	no	—
361	C₂³	—	4	1	no	—
362	C₂³	—	4	2	no	—
363	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
364	Q₈	—	2	8	no	—
365	Q₈	—	4	16	no	—
366	Q₈	—	4	8	no	—
367	Q₈	—	8	4	no	—
368	D₄	—	2	2	no	—
369	D₄	—	2	4	no	—
370	D₄	C₁₃×C₄⋊Q₈	1	4	yes	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	4	16	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	8	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	C₁₃×#120	1	2	yes	—
390	C₂×C₄	C₁₃×#120	1	2	yes	—
391	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
392	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
393	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
394	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
395	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
396	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
397	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
398	C₈	—	2	4	no	—
399	C₈	—	4	2	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	4	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	4	2	no	—
405	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
406	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
407	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
408	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
409	C₂²	C₁₃×#577	1	2	yes	—
410	C₄	—	2	2	no	—
411	C₄	—	2	4	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	4	no	—
414	C₄	—	4	4	no	—
415	C₄	—	4	2	no	—
416	C₄	—	8	2	no	—
417	C₄	C₁₃×#450	1	4	yes	—
418	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
419	C₄	C₁₃×#536	1	1	yes	characteristic
420	C₄	D₄×Q₈×C₁₃	1	2	yes	—
421	C₂	—	4	4	no	—
422	C₂	C₁₃×#2434	1	1	yes	characteristic
423	C₂	C₂×C₁₃×#450	1	1	yes	characteristic
424	C₂	C₁₃×#3010	1	1	yes	characteristic
425	C₂	Q₈×C₁₃×SD₁₆	1	2	yes	—
426	C₂	C₁₃×#3384	1	2	yes	—

	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 ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#498	C₂	semidirect
4. C₁₃×#2567	C₂	semidirect
5. C₁₃×#2058	C₂	semidirect
6. C₁₃×#1988	C₂	semidirect
7. C₁₃×#1984	C₂	semidirect
82. C₁₃×#102	Q₈	semidirect
86. #25834	C₁₃	direct (N × H)
123. C₂×C₈×C₁₃	C₂×Q₈	semidirect
137. C₁₃×C₄⋊C₄	C₂×Q₈	semidirect
146. C₂×#498	C₂×C₁₃	semidirect
148. #2567	C₂×C₁₃	semidirect
149. #2058	C₂×C₁₃	semidirect
150. #1988	C₂×C₁₃	semidirect
151. #1984	C₂×C₁₃	semidirect
289. #102	Q₈×C₁₃	semidirect
335. C₂×C₈	C₂×Q₈×C₁₃	semidirect
349. C₄⋊C₄	C₂×Q₈×C₁₃	semidirect
357. C₁₃	#25834	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₁₃	2
C₂×C₁₃×#498	2
C₂×C₁₃×#476	2
C₁₃×#2567	2
C₁₃×#2058	2
C₁₃×#1988	2
C₁₃×#1984	2
C₁₃×#1864	2
C₄×C₁₃×#102	2
#25834	13

Subgroups — C13×#25834 #15712173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25834 #15712173