Subgroups — C₁₃×#10062 #15696401

Order 3328.

806 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2541	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1988	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#331	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×SD₁₆	—	2	1	no	—
9	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#127	—	2	1	no	—
11	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#121	—	2	2	no	—
13	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#486	—	2	2	no	—
15	C₁₃×#486	—	2	2	no	—
16	C₁₃×#461	—	2	2	no	—
17	C₁₃×#461	—	2	2	no	—
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#103	—	2	1	no	—
21	C₂×C₁₃×#102	—	2	2	no	—
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#392	—	2	2	no	—
24	C₁₃×#390	—	2	1	no	—
25	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₁₃×#340	—	2	2	no	—
27	C₁₃×#331	—	2	2	no	—
28	C₁₃×D₄⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₁₃	—	2	1	no	—
30	C₂²×D₄×C₁₃	—	2	4	no	—
31	C₂²×D₄×C₁₃	—	2	1	no	—
32	C₂²×D₄×C₁₃	—	2	1	no	—
33	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
34	C₂²×D₄×C₁₃	D₄	1	2	yes	—
35	C₂³×C₄×C₁₃	—	2	1	no	—
36	C₂×C₁₃×SD₁₆	—	2	4	no	—
37	C₂×C₁₃×SD₁₆	—	4	2	no	—
38	C₂×C₁₃×SD₁₆	—	4	2	no	—
39	C₂²×C₈×C₁₃	—	2	1	no	—
40	C₂²×C₈×C₁₃	—	2	1	no	—
41	C₂²×C₈×C₁₃	—	2	1	no	—
42	C₁₃×C₄⋊Q₈	—	2	1	no	—
43	C₁₃×C₄⋊Q₈	—	2	1	no	—
44	C₁₃×C₄⋊Q₈	—	2	1	no	—
45	C₁₃×C₄⋊Q₈	D₄	1	2	yes	complemented
46	C₁₃×#127	—	2	1	no	—
47	C₁₃×#127	—	2	1	no	—
48	C₁₃×#127	—	2	1	no	—
49	C₁₃×#127	—	2	1	no	—
50	C₁₃×#127	—	4	2	no	—
51	C₁₃×#127	—	4	2	no	—
52	C₁₃×#121	—	4	4	no	—
53	C₁₃×#121	—	4	4	no	—
54	C₄×D₄×C₁₃	—	2	1	no	—
55	C₄×D₄×C₁₃	—	2	1	no	—
56	C₄×D₄×C₁₃	—	2	1	no	—
57	C₄×D₄×C₁₃	—	2	1	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
64	C₂×C₄²×C₁₃	—	2	1	no	—
65	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	C₁₃×C₄⋊C₈	—	2	1	no	—
67	C₁₃×C₄⋊C₈	—	2	1	no	—
68	C₁₃×C₄⋊C₈	—	2	1	no	—
69	C₁₃×C₄⋊C₈	D₄	1	2	yes	complemented
70	C₁₃×#103	—	2	4	no	—
71	C₁₃×#102	—	2	8	no	—
72	C₄×C₈×C₁₃	—	2	1	no	—
73	C₄×C₈×C₁₃	D₄	1	2	yes	complemented
74	C₁₃×#95	—	2	1	no	—
75	#10062	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂⁴×C₁₃	—	2	1	no	—
77	C₂⁴×C₁₃	—	2	2	no	—
78	C₂×Q₈×C₁₃	—	2	2	no	—
79	C₂×Q₈×C₁₃	—	4	1	no	—
80	C₂×Q₈×C₁₃	—	4	1	no	—
81	C₂×Q₈×C₁₃	—	4	1	no	—
82	C₂×Q₈×C₁₃	—	4	1	no	—
83	C₂×Q₈×C₁₃	—	4	1	no	—
84	C₂×D₄×C₁₃	—	2	1	no	—
85	C₂×D₄×C₁₃	—	2	2	no	—
86	C₂×D₄×C₁₃	—	2	1	no	—
87	C₂×D₄×C₁₃	—	2	2	no	—
88	C₂×D₄×C₁₃	—	2	1	no	—
89	C₂×D₄×C₁₃	—	2	1	no	—
90	C₂×D₄×C₁₃	—	2	1	no	—
91	C₂×D₄×C₁₃	—	4	4	no	—
92	C₂×D₄×C₁₃	—	4	8	no	—
93	C₂×D₄×C₁₃	—	4	8	no	—
94	C₂×D₄×C₁₃	—	4	1	no	—
95	C₂×D₄×C₁₃	—	4	1	no	—
96	C₂×D₄×C₁₃	—	4	1	no	—
97	C₂×D₄×C₁₃	—	4	1	no	—
98	C₂×D₄×C₁₃	—	4	1	no	—
99	C₂×D₄×C₁₃	—	4	2	no	—
100	C₂×D₄×C₁₃	—	4	1	no	—
101	C₂×D₄×C₁₃	—	4	2	no	—
102	C₂×D₄×C₁₃	—	4	1	no	—
103	C₂×D₄×C₁₃	—	4	1	no	—
104	C₂×D₄×C₁₃	—	8	4	no	—
105	C₂×D₄×C₁₃	D₈	1	2	yes	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	4	1	no	—
109	C₂²×C₄×C₁₃	—	4	1	no	—
110	C₂²×C₄×C₁₃	—	4	1	no	—
111	C₂²×C₄×C₁₃	—	4	2	no	—
112	C₂²×C₄×C₁₃	—	4	2	no	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₁₃×SD₁₆	—	4	8	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	4	2	no	—
120	C₂×C₈×C₁₃	—	4	1	no	—
121	C₂×C₈×C₁₃	—	4	1	no	—
122	C₂×C₈×C₁₃	—	4	1	no	—
123	C₂×C₈×C₁₃	—	4	2	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	4	1	no	—
130	C₁₃×C₄⋊C₄	—	4	1	no	—
131	C₁₃×C₄⋊C₄	SD₁₆	1	4	yes	complemented
132	C₁₃×C₂²⋊C₄	—	4	8	no	—
133	C₁₃×C₂²⋊C₄	—	4	1	no	—
134	C₁₃×C₂²⋊C₄	—	4	1	no	—
135	C₄²×C₁₃	—	4	1	no	—
136	C₄²×C₁₃	—	4	1	no	—
137	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₁₃	#41	1	1	yes	characteristic
141	C₂×#486	C₂×C₁₃	1	1	yes	characteristic, complemented
142	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#2541	C₂×C₁₃	1	1	yes	characteristic
144	#1988	C₂×C₁₃	1	1	yes	characteristic, complemented
145	C₂×#331	C₂×C₁₃	1	1	yes	characteristic, complemented
146	C₂×D₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#1279	C₂×C₁₃	1	1	yes	characteristic, complemented
148	C₂³×C₁₃	—	2	2	no	—
149	C₂³×C₁₃	—	4	1	no	—
150	C₂³×C₁₃	—	4	1	no	—
151	C₂³×C₁₃	—	4	2	no	—
152	C₂³×C₁₃	—	4	2	no	—
153	C₂³×C₁₃	—	4	2	no	—
154	C₂³×C₁₃	—	4	2	no	—
155	C₂³×C₁₃	—	4	2	no	—
156	C₂³×C₁₃	—	4	4	no	—
157	C₂³×C₁₃	—	4	4	no	—
158	C₂³×C₁₃	#120	1	1	yes	characteristic
159	Q₈×C₁₃	—	4	2	no	—
160	Q₈×C₁₃	—	4	2	no	—
161	Q₈×C₁₃	—	8	1	no	—
162	Q₈×C₁₃	—	8	1	no	—
163	D₄×C₁₃	—	2	2	no	—
164	D₄×C₁₃	—	2	2	no	—
165	D₄×C₁₃	—	4	4	no	—
166	D₄×C₁₃	—	4	1	no	—
167	D₄×C₁₃	—	4	1	no	—
168	D₄×C₁₃	—	8	2	no	—
169	D₄×C₁₃	—	8	16	no	—
170	D₄×C₁₃	—	8	1	no	—
171	D₄×C₁₃	—	8	1	no	—
172	D₄×C₁₃	—	8	2	no	—
173	D₄×C₁₃	—	8	1	no	—
174	D₄×C₁₃	—	8	1	no	—
175	D₄×C₁₃	—	8	1	no	—
176	D₄×C₁₃	—	8	1	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	4	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	8	1	no	—
185	C₂×C₄×C₁₃	—	8	1	no	—
186	C₂×C₄×C₁₃	—	8	2	no	—
187	C₂×C₄×C₁₃	—	8	1	no	—
188	C₂×C₄×C₁₃	—	8	1	no	—
189	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
190	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
191	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
192	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
193	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
194	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
197	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
198	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
200	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
201	C₈×C₁₃	—	4	2	no	—
202	C₈×C₁₃	—	4	2	no	—
203	C₈×C₁₃	—	8	1	no	—
204	C₂²×SD₁₆	—	2	1	no	—
205	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×#127	—	2	1	no	—
207	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×#121	—	2	2	no	—
209	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
210	#486	—	2	2	no	—
211	#486	—	2	2	no	—
212	#461	—	2	2	no	—
213	#461	—	2	2	no	—
214	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×#103	—	2	1	no	—
217	C₂×#102	—	2	2	no	—
218	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
219	#392	—	2	2	no	—
220	#390	—	2	1	no	—
221	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
222	#340	—	2	2	no	—
223	#331	—	2	2	no	—
224	D₄⋊C₈	—	2	2	no	—
225	C₂²×C₁₃	—	4	4	no	—
226	C₂²×C₁₃	—	4	2	no	—
227	C₂²×C₁₃	—	8	2	no	—
228	C₂²×C₁₃	—	8	1	no	—
229	C₂²×C₁₃	—	8	1	no	—
230	C₂²×C₁₃	—	8	4	no	—
231	C₂²×C₁₃	—	8	4	no	—
232	C₂²×C₁₃	—	8	2	no	—
233	C₂²×C₁₃	—	8	2	no	—
234	C₂²×C₁₃	—	8	2	no	—
235	C₂²×C₁₃	#392	1	1	yes	characteristic
236	C₂²×C₁₃	#447	1	1	yes	characteristic
237	C₂²×C₁₃	#449	1	1	yes	characteristic
238	C₂²×C₁₃	#450	1	2	yes	—
239	C₂²×C₁₃	#455	1	2	yes	—
240	C₄×C₁₃	—	2	1	no	—
241	C₄×C₁₃	—	2	1	no	—
242	C₄×C₁₃	—	4	4	no	—
243	C₄×C₁₃	—	8	2	no	—
244	C₄×C₁₃	—	8	1	no	—
245	C₄×C₁₃	#447	1	1	yes	characteristic
246	C₄×C₁₃	#449	1	1	yes	characteristic
247	C₄×C₁₃	#460	1	2	yes	—
248	C₄×C₁₃	#466	1	1	yes	characteristic
249	C₄×C₁₃	#469	1	1	yes	characteristic
250	C₄×C₁₃	#492	1	1	yes	characteristic
251	C₄×C₁₃	#496	1	1	yes	characteristic
252	C₂²×Q₈	—	2	1	no	—
253	C₂²×D₄	—	2	4	no	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
257	C₂²×D₄	D₄×C₁₃	1	2	yes	—
258	C₂³×C₄	—	2	1	no	—
259	C₂×SD₁₆	—	2	4	no	—
260	C₂×SD₁₆	—	4	2	no	—
261	C₂×SD₁₆	—	4	2	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	2	1	no	—
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	—	2	1	no	—
267	C₄⋊Q₈	—	2	1	no	—
268	C₄⋊Q₈	D₄×C₁₃	1	2	yes	complemented
269	#127	—	2	1	no	—
270	#127	—	2	1	no	—
271	#127	—	2	1	no	—
272	#127	—	2	1	no	—
273	#127	—	4	2	no	—
274	#127	—	4	2	no	—
275	#121	—	4	4	no	—
276	#121	—	4	4	no	—
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
284	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
285	C₂×C₂²⋊C₄	—	2	4	no	—
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	D₄×C₁₃	1	2	yes	complemented
293	#103	—	2	4	no	—
294	#102	—	2	8	no	—
295	C₄×C₈	—	2	1	no	—
296	C₄×C₈	D₄×C₁₃	1	2	yes	complemented
297	#95	—	2	1	no	—
298	C₂×C₁₃	—	8	2	no	—
299	C₂×C₁₃	—	16	2	no	—
300	C₂×C₁₃	#1639	1	2	yes	—
301	C₂×C₁₃	#1642	1	2	yes	—
302	C₂×C₁₃	#1999	1	1	yes	characteristic
303	C₂×C₁₃	#2004	1	1	yes	characteristic
304	C₂×C₁₃	#2014	1	1	yes	characteristic
305	C₂⁴	—	2	1	no	—
306	C₂⁴	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	4	1	no	—
309	C₂×Q₈	—	4	1	no	—
310	C₂×Q₈	—	4	1	no	—
311	C₂×Q₈	—	4	1	no	—
312	C₂×Q₈	—	4	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	4	4	no	—
321	C₂×D₄	—	4	8	no	—
322	C₂×D₄	—	4	8	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂×D₄	—	4	2	no	—
331	C₂×D₄	—	4	1	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	8	4	no	—
334	C₂×D₄	C₁₃×D₈	1	2	yes	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
345	SD₁₆	—	4	8	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	4	2	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	4	1	no	—
352	C₂×C₈	—	4	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	4	1	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₄⋊C₄	C₁₃×SD₁₆	1	4	yes	complemented
361	C₂²⋊C₄	—	4	8	no	—
362	C₂²⋊C₄	—	4	1	no	—
363	C₂²⋊C₄	—	4	1	no	—
364	C₄²	—	4	1	no	—
365	C₄²	—	4	1	no	—
366	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
367	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
368	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
369	C₄²	C₁₃×#41	1	1	yes	characteristic
370	C₁₃	#10062	1	1	yes	characteristic, direct product factor, Sylow
371	C₂³	—	2	2	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	4	no	—
380	C₂³	—	4	4	no	—
381	C₂³	C₁₃×#120	1	1	yes	characteristic
382	Q₈	—	4	2	no	—
383	Q₈	—	4	2	no	—
384	Q₈	—	8	1	no	—
385	Q₈	—	8	1	no	—
386	D₄	—	2	2	no	—
387	D₄	—	2	2	no	—
388	D₄	—	4	4	no	—
389	D₄	—	4	1	no	—
390	D₄	—	4	1	no	—
391	D₄	—	8	2	no	—
392	D₄	—	8	16	no	—
393	D₄	—	8	1	no	—
394	D₄	—	8	1	no	—
395	D₄	—	8	2	no	—
396	D₄	—	8	1	no	—
397	D₄	—	8	1	no	—
398	D₄	—	8	1	no	—
399	D₄	—	8	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	8	1	no	—
408	C₂×C₄	—	8	1	no	—
409	C₂×C₄	—	8	2	no	—
410	C₂×C₄	—	8	1	no	—
411	C₂×C₄	—	8	1	no	—
412	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
413	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
414	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
415	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
416	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
417	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
418	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
419	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
420	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
421	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
422	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
423	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
424	C₈	—	4	2	no	—
425	C₈	—	4	2	no	—
426	C₈	—	8	1	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	2	no	—
434	C₂²	—	8	2	no	—
435	C₂²	—	8	4	no	—
436	C₂²	—	8	4	no	—
437	C₂²	C₁₃×#392	1	1	yes	characteristic
438	C₂²	C₁₃×#447	1	1	yes	characteristic
439	C₂²	C₁₃×#449	1	1	yes	characteristic
440	C₂²	C₁₃×#450	1	2	yes	—
441	C₂²	C₁₃×#455	1	2	yes	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	4	4	no	—
445	C₄	—	8	2	no	—
446	C₄	—	8	1	no	—
447	C₄	C₁₃×#447	1	1	yes	characteristic
448	C₄	C₁₃×#449	1	1	yes	characteristic
449	C₄	C₁₃×#460	1	2	yes	—
450	C₄	C₁₃×#466	1	1	yes	characteristic
451	C₄	C₁₃×#469	1	1	yes	characteristic
452	C₄	C₁₃×#492	1	1	yes	characteristic
453	C₄	C₁₃×#496	1	1	yes	characteristic
454	C₂	—	8	2	no	—
455	C₂	—	16	2	no	—
456	C₂	C₁₃×#1639	1	2	yes	—
457	C₂	C₁₃×#1642	1	2	yes	—
458	C₂	C₁₃×#1999	1	1	yes	characteristic
459	C₂	C₁₃×#2004	1	1	yes	characteristic
460	C₂	C₁₃×#2014	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₁₃×#2541	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#486	C₂	semidirect
2. C₂×C₁₃×#461	C₂	semidirect
4. C₁₃×#1988	C₂	semidirect
5. C₂×C₁₃×#331	C₂	semidirect
6. C₂×C₁₃×D₄⋊C₈	C₂	semidirect
7. C₁₃×#1279	C₂	semidirect
45. C₁₃×C₄⋊Q₈	D₄	semidirect
69. C₁₃×C₄⋊C₈	D₄	semidirect
73. C₄×C₈×C₁₃	D₄	semidirect
75. #10062	C₁₃	direct (N × H)
131. C₁₃×C₄⋊C₄	SD₁₆	semidirect
141. C₂×#486	C₂×C₁₃	semidirect
142. C₂×#461	C₂×C₁₃	semidirect
144. #1988	C₂×C₁₃	semidirect
145. C₂×#331	C₂×C₁₃	semidirect
146. C₂×D₄⋊C₈	C₂×C₁₃	semidirect
147. #1279	C₂×C₁₃	semidirect
268. C₄⋊Q₈	D₄×C₁₃	semidirect
292. C₄⋊C₈	D₄×C₁₃	semidirect
296. C₄×C₈	D₄×C₁₃	semidirect
360. C₄⋊C₄	C₁₃×SD₁₆	semidirect
370. C₁₃	#10062	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×C₁₃×#486	2
C₂×C₁₃×#461	2
C₁₃×#2541	2
C₁₃×#1988	2
C₂×C₁₃×#331	2
C₂×C₁₃×D₄⋊C₈	2
C₁₃×#1279	2
#10062	13

Subgroups — C13×#10062 #15696401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10062 #15696401