Subgroups — C₁₃×#10420 #15696759

Order 3328.

556 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2542	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1990	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#1948	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
10	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
11	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#106	—	2	1	no	—
13	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#102	—	2	1	no	—
16	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#399	—	2	2	no	—
18	C₁₃×#390	—	2	1	no	—
19	C₁₃×#384	—	2	1	no	—
20	C₁₃×#384	C₂²	1	1	yes	characteristic
21	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₁₃×#340	—	2	2	no	—
23	C₁₃×#340	—	2	1	no	—
24	C₁₃×#340	—	2	1	no	—
25	C₁₃×#332	—	2	2	no	—
26	C₁₃×D₄⋊C₈	—	2	2	no	—
27	C₂²×Q₈×C₁₃	—	2	1	no	—
28	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₃	—	2	1	no	—
30	C₂²×C₈×C₁₃	—	2	1	no	—
31	C₂²×C₈×C₁₃	—	2	1	no	—
32	C₂²×C₈×C₁₃	—	2	1	no	—
33	C₁₃×C₄⋊Q₈	—	2	1	no	—
34	C₁₃×C₄⋊Q₈	—	2	1	no	—
35	C₁₃×C₄⋊Q₈	—	2	1	no	—
36	C₁₃×C₄⋊Q₈	—	2	1	no	—
37	C₁₃×C₂²⋊Q₈	—	4	2	no	—
38	C₁₃×C₂²⋊Q₈	—	4	2	no	—
39	C₁₃×C₂²⋊Q₈	—	4	2	no	—
40	C₁₃×C₂²⋊Q₈	—	4	2	no	—
41	C₄×D₄×C₁₃	—	2	1	no	—
42	C₄×D₄×C₁₃	—	2	1	no	—
43	C₄×D₄×C₁₃	—	2	1	no	—
44	C₄×D₄×C₁₃	—	2	1	no	—
45	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
46	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
51	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
52	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
53	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
54	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
55	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
58	C₂×C₄²×C₁₃	—	2	1	no	—
59	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
60	C₁₃×#106	—	4	2	no	—
61	C₁₃×C₄⋊C₈	—	2	1	no	—
62	C₁₃×C₄⋊C₈	—	2	1	no	—
63	C₁₃×C₄⋊C₈	—	2	1	no	—
64	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
65	C₁₃×#102	—	4	2	no	—
66	C₄×C₈×C₁₃	—	2	1	no	—
67	C₄×C₈×C₁₃	—	2	1	no	—
68	C₁₃×#95	—	2	1	no	—
69	#10420	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂⁴×C₁₃	—	2	1	no	—
71	C₂×Q₈×C₁₃	—	4	1	no	—
72	C₂×Q₈×C₁₃	—	4	1	no	—
73	C₂×Q₈×C₁₃	—	4	1	no	—
74	C₂×Q₈×C₁₃	—	4	1	no	—
75	C₂×Q₈×C₁₃	—	4	1	no	—
76	C₂×Q₈×C₁₃	—	4	1	no	—
77	C₂×D₄×C₁₃	—	2	1	no	—
78	C₂×D₄×C₁₃	—	2	1	no	—
79	C₂×D₄×C₁₃	—	2	1	no	—
80	C₂×D₄×C₁₃	—	2	1	no	—
81	C₂×D₄×C₁₃	—	2	1	no	—
82	C₂×D₄×C₁₃	SD₁₆	1	2	yes	—
83	C₂²×C₄×C₁₃	—	2	1	no	—
84	C₂²×C₄×C₁₃	—	2	1	no	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	2	1	no	—
87	C₂²×C₄×C₁₃	—	4	1	no	—
88	C₂²×C₄×C₁₃	—	4	1	no	—
89	C₂²×C₄×C₁₃	—	4	1	no	—
90	C₂²×C₄×C₁₃	—	4	1	no	—
91	C₂²×C₄×C₁₃	—	4	1	no	—
92	C₂²×C₄×C₁₃	—	4	1	no	—
93	C₂²×C₄×C₁₃	—	4	1	no	—
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	C₂×C₈×C₁₃	—	2	2	no	—
98	C₂×C₈×C₁₃	—	2	2	no	—
99	C₂×C₈×C₁₃	—	4	1	no	—
100	C₂×C₈×C₁₃	—	4	1	no	—
101	C₂×C₈×C₁₃	—	4	1	no	—
102	C₂×C₈×C₁₃	—	4	1	no	—
103	C₂×C₈×C₁₃	—	4	1	no	—
104	C₂×C₈×C₁₃	—	4	1	no	—
105	C₂×C₈×C₁₃	—	4	1	no	—
106	C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₁₃×C₄⋊C₄	—	2	1	no	—
109	C₁₃×C₄⋊C₄	—	2	2	no	—
110	C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₁₃×C₄⋊C₄	—	2	2	no	—
112	C₁₃×C₄⋊C₄	—	4	4	no	—
113	C₁₃×C₄⋊C₄	—	4	4	no	—
114	C₁₃×C₄⋊C₄	—	4	2	no	—
115	C₁₃×C₄⋊C₄	—	4	1	no	—
116	C₁₃×C₄⋊C₄	—	4	1	no	—
117	C₁₃×C₄⋊C₄	—	4	1	no	—
118	C₁₃×C₄⋊C₄	—	4	1	no	—
119	C₁₃×C₄⋊C₄	—	4	1	no	—
120	C₁₃×C₄⋊C₄	—	4	1	no	—
121	C₁₃×C₄⋊C₄	D₈	1	2	yes	—
122	C₁₃×C₄⋊C₄	SD₁₆	1	2	yes	—
123	C₁₃×C₂²⋊C₄	—	4	4	no	—
124	C₁₃×C₂²⋊C₄	—	4	4	no	—
125	C₁₃×C₂²⋊C₄	—	4	1	no	—
126	C₁₃×C₂²⋊C₄	—	4	1	no	—
127	C₄²×C₁₃	—	4	1	no	—
128	C₄²×C₁₃	—	4	1	no	—
129	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₃	#41	1	1	yes	characteristic
131	C₄²×C₁₃	#41	1	1	yes	characteristic
132	C₄²×C₁₃	#41	1	1	yes	characteristic
133	#2542	C₂×C₁₃	1	1	yes	characteristic
134	#1990	C₂×C₁₃	1	1	yes	characteristic, complemented
135	#1948	C₂×C₁₃	1	1	yes	characteristic, complemented
136	#1802	C₂×C₁₃	1	1	yes	characteristic
137	C₂×#332	C₂×C₁₃	1	1	yes	characteristic, complemented
138	C₂×D₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
139	#1279	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	#120	1	1	yes	characteristic
148	Q₈×C₁₃	—	8	1	no	—
149	Q₈×C₁₃	—	8	1	no	—
150	Q₈×C₁₃	—	8	1	no	—
151	Q₈×C₁₃	—	8	1	no	—
152	D₄×C₁₃	—	2	2	no	—
153	D₄×C₁₃	—	2	2	no	—
154	D₄×C₁₃	—	4	1	no	—
155	D₄×C₁₃	—	4	1	no	—
156	C₂×C₄×C₁₃	—	2	1	no	—
157	C₂×C₄×C₁₃	—	2	1	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	4	1	no	—
161	C₂×C₄×C₁₃	—	4	1	no	—
162	C₂×C₄×C₁₃	—	4	1	no	—
163	C₂×C₄×C₁₃	—	4	1	no	—
164	C₂×C₄×C₁₃	—	4	1	no	—
165	C₂×C₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	4	1	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	8	1	no	—
171	C₂×C₄×C₁₃	—	8	1	no	—
172	C₂×C₄×C₁₃	—	8	1	no	—
173	C₂×C₄×C₁₃	—	8	1	no	—
174	C₂×C₄×C₁₃	—	8	1	no	—
175	C₂×C₄×C₁₃	—	8	1	no	—
176	C₂×C₄×C₁₃	—	8	1	no	—
177	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
178	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
179	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
180	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
181	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
182	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
186	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
187	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
190	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
191	C₈×C₁₃	—	4	2	no	—
192	C₈×C₁₃	—	4	2	no	—
193	C₈×C₁₃	—	8	1	no	—
194	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×C₂²⋊Q₈	—	2	1	no	—
196	C₂×C₂²⋊Q₈	—	2	1	no	—
197	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×#106	—	2	1	no	—
199	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
201	C₂×#102	—	2	1	no	—
202	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
203	#399	—	2	2	no	—
204	#390	—	2	1	no	—
205	#384	—	2	1	no	—
206	#384	C₂²×C₁₃	1	1	yes	characteristic
207	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
208	#340	—	2	1	no	—
209	#340	—	2	1	no	—
210	#340	—	2	2	no	—
211	#332	—	2	2	no	—
212	D₄⋊C₈	—	2	2	no	—
213	C₂²×C₁₃	—	4	2	no	—
214	C₂²×C₁₃	—	4	2	no	—
215	C₂²×C₁₃	—	4	2	no	—
216	C₂²×C₁₃	—	8	1	no	—
217	C₂²×C₁₃	—	8	1	no	—
218	C₂²×C₁₃	—	8	1	no	—
219	C₂²×C₁₃	—	8	1	no	—
220	C₂²×C₁₃	#394	1	1	yes	characteristic
221	C₂²×C₁₃	#447	1	1	yes	characteristic
222	C₂²×C₁₃	#448	1	1	yes	characteristic
223	C₂²×C₁₃	#450	1	1	yes	characteristic
224	C₂²×C₁₃	#452	1	1	yes	characteristic
225	C₂²×C₁₃	#454	1	1	yes	characteristic
226	C₂²×C₁₃	#456	1	1	yes	characteristic
227	C₄×C₁₃	—	2	1	no	—
228	C₄×C₁₃	—	2	1	no	—
229	C₄×C₁₃	—	4	2	no	—
230	C₄×C₁₃	—	4	2	no	—
231	C₄×C₁₃	—	8	1	no	—
232	C₄×C₁₃	—	8	2	no	—
233	C₄×C₁₃	—	16	1	no	—
234	C₄×C₁₃	#459	1	1	yes	characteristic
235	C₄×C₁₃	#460	1	1	yes	characteristic
236	C₄×C₁₃	#465	1	1	yes	characteristic
237	C₄×C₁₃	#470	1	1	yes	characteristic
238	C₄×C₁₃	#483	1	1	yes	characteristic
239	C₄×C₁₃	#485	1	1	yes	characteristic
240	C₄×C₁₃	#486	1	1	yes	characteristic
241	C₄×C₁₃	#490	1	1	yes	characteristic
242	C₂²×Q₈	—	2	1	no	—
243	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
244	C₂³×C₄	—	2	1	no	—
245	C₂²×C₈	—	2	1	no	—
246	C₂²×C₈	—	2	1	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₂²⋊Q₈	—	4	2	no	—
253	C₂²⋊Q₈	—	4	2	no	—
254	C₂²⋊Q₈	—	4	2	no	—
255	C₂²⋊Q₈	—	4	2	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
267	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
268	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
269	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	1	no	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
275	#106	—	4	2	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
280	#102	—	4	2	no	—
281	C₄×C₈	—	2	1	no	—
282	C₄×C₈	—	2	1	no	—
283	#95	—	2	1	no	—
284	C₂×C₁₃	—	8	2	no	—
285	C₂×C₁₃	#1627	1	1	yes	characteristic
286	C₂×C₁₃	#1635	1	1	yes	characteristic
287	C₂×C₁₃	#1647	1	1	yes	characteristic
288	C₂×C₁₃	#1651	1	1	yes	characteristic
289	C₂×C₁₃	#2035	1	1	yes	characteristic
290	C₂×C₁₃	#2038	1	1	yes	characteristic
291	C₂×C₁₃	#2041	1	1	yes	characteristic
292	C₂⁴	—	2	1	no	—
293	C₂×Q₈	—	4	1	no	—
294	C₂×Q₈	—	4	1	no	—
295	C₂×Q₈	—	4	1	no	—
296	C₂×Q₈	—	4	1	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	C₁₃×SD₁₆	1	2	yes	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	4	1	no	—
316	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	4	1	no	—
322	C₂×C₈	—	4	1	no	—
323	C₂×C₈	—	4	1	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	4	4	no	—
335	C₄⋊C₄	—	4	4	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	4	1	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	—	4	1	no	—
343	C₄⋊C₄	C₁₃×D₈	1	2	yes	—
344	C₄⋊C₄	C₁₃×SD₁₆	1	2	yes	—
345	C₂²⋊C₄	—	4	4	no	—
346	C₂²⋊C₄	—	4	4	no	—
347	C₂²⋊C₄	—	4	1	no	—
348	C₂²⋊C₄	—	4	1	no	—
349	C₄²	—	4	1	no	—
350	C₄²	—	4	1	no	—
351	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
352	C₄²	C₁₃×#41	1	1	yes	characteristic
353	C₄²	C₁₃×#41	1	1	yes	characteristic
354	C₄²	C₁₃×#41	1	1	yes	characteristic
355	C₁₃	#10420	1	1	yes	characteristic, direct product factor, Sylow
356	C₂³	—	2	2	no	—
357	C₂³	—	4	1	no	—
358	C₂³	—	4	1	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	4	1	no	—
361	C₂³	—	4	1	no	—
362	C₂³	—	4	1	no	—
363	C₂³	C₁₃×#120	1	1	yes	characteristic
364	Q₈	—	8	1	no	—
365	Q₈	—	8	1	no	—
366	Q₈	—	8	1	no	—
367	Q₈	—	8	1	no	—
368	D₄	—	2	2	no	—
369	D₄	—	2	2	no	—
370	D₄	—	4	1	no	—
371	D₄	—	4	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	8	1	no	—
387	C₂×C₄	—	8	1	no	—
388	C₂×C₄	—	8	1	no	—
389	C₂×C₄	—	8	1	no	—
390	C₂×C₄	—	8	1	no	—
391	C₂×C₄	—	8	1	no	—
392	C₂×C₄	—	8	1	no	—
393	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
394	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
395	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
396	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
397	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
398	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
399	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
400	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
401	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
402	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
403	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
404	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
405	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
406	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
407	C₈	—	4	2	no	—
408	C₈	—	4	2	no	—
409	C₈	—	8	1	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	1	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	8	1	no	—
417	C₂²	C₁₃×#394	1	1	yes	characteristic
418	C₂²	C₁₃×#447	1	1	yes	characteristic
419	C₂²	C₁₃×#448	1	1	yes	characteristic
420	C₂²	C₁₃×#450	1	1	yes	characteristic
421	C₂²	C₁₃×#452	1	1	yes	characteristic
422	C₂²	C₁₃×#454	1	1	yes	characteristic
423	C₂²	C₁₃×#456	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	8	1	no	—
429	C₄	—	8	2	no	—
430	C₄	—	16	1	no	—
431	C₄	C₁₃×#459	1	1	yes	characteristic
432	C₄	C₁₃×#460	1	1	yes	characteristic
433	C₄	C₁₃×#465	1	1	yes	characteristic
434	C₄	C₁₃×#470	1	1	yes	characteristic
435	C₄	C₁₃×#483	1	1	yes	characteristic
436	C₄	C₁₃×#485	1	1	yes	characteristic
437	C₄	C₁₃×#486	1	1	yes	characteristic
438	C₄	C₁₃×#490	1	1	yes	characteristic
439	C₂	—	8	2	no	—
440	C₂	C₁₃×#1627	1	1	yes	characteristic
441	C₂	C₁₃×#1635	1	1	yes	characteristic
442	C₂	C₁₃×#1647	1	1	yes	characteristic
443	C₂	C₁₃×#1651	1	1	yes	characteristic
444	C₂	C₁₃×#2035	1	1	yes	characteristic
445	C₂	C₁₃×#2038	1	1	yes	characteristic
446	C₂	C₁₃×#2041	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂²×D₄×C₁₃	D₄
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
2. C₁₃×#1990	C₂	semidirect
3. C₁₃×#1948	C₂	semidirect
5. C₂×C₁₃×#332	C₂	semidirect
7. C₁₃×#1279	C₂	semidirect
69. #10420	C₁₃	direct (N × H)
134. #1990	C₂×C₁₃	semidirect
135. #1948	C₂×C₁₃	semidirect
137. C₂×#332	C₂×C₁₃	semidirect
139. #1279	C₂×C₁₃	semidirect
355. C₁₃	#10420	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×#2542	2
C₁₃×#1990	2
C₁₃×#1948	2
C₁₃×#1802	2
C₂×C₁₃×#332	2
C₂×C₁₃×D₄⋊C₈	2
C₁₃×#1279	2
#10420	13

Subgroups — C13×#10420 #15696759

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10420 #15696759