Subgroups — C₁₃×#26022 #15712361

Order 3328.

710 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2551	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2355	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2066	C₂	1	2	yes	maximal
4	C₁₃×#2024	C₂	1	2	yes	maximal
5	C₁₃×#1988	C₂	1	2	yes	maximal
6	C₁₃×#1948	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1919	C₂	1	2	yes	maximal
9	C₁₃×#1834	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₃×#103	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#106	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#103	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#395	—	2	2	no	—
23	C₁₃×#391	C₂²	1	2	yes	—
24	C₁₃×#389	—	2	1	no	—
25	C₁₃×#389	C₂²	1	2	yes	—
26	C₁₃×#387	—	2	2	no	—
27	C₁₃×#384	C₂²	1	1	yes	characteristic
28	C₁₃×#384	C₂²	1	1	yes	characteristic
29	C₁₃×#382	—	2	1	no	—
30	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
31	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
32	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₁₃×#340	C₂²	1	1	yes	characteristic
35	C₁₃×#340	C₂²	1	2	yes	—
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	1	yes	characteristic
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃	—	2	2	no	—
42	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₁₃×C₄⋊Q₈	—	2	4	no	—
47	C₁₃×C₄⋊Q₈	—	4	2	no	—
48	C₁₃×C₄⋊Q₈	—	4	4	no	—
49	C₄×Q₈×C₁₃	—	2	2	no	—
50	C₄×Q₈×C₁₃	Q₈	1	4	yes	complemented
51	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
59	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	—	2	1	no	—
66	C₂×C₄²×C₁₃	—	2	1	no	—
67	C₂×C₄²×C₁₃	—	2	2	no	—
68	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×#106	—	2	4	no	—
71	C₁₃×C₄⋊C₈	—	2	2	no	—
72	C₁₃×C₄⋊C₈	—	4	2	no	—
73	C₁₃×#103	—	2	2	no	—
74	C₁₃×#103	—	2	2	no	—
75	C₁₃×#103	—	4	2	no	—
76	C₄×C₈×C₁₃	—	2	2	no	—
77	C₁₃×#95	—	2	2	no	—
78	C₁₃×#95	—	2	2	no	—
79	C₁₃×#95	—	2	1	no	—
80	C₁₃×#95	—	2	2	no	—
81	C₁₃×#95	—	2	2	no	—
82	C₁₃×#95	D₄	1	2	yes	—
83	#26022	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂×Q₈×C₁₃	—	2	1	no	—
85	C₂×Q₈×C₁₃	—	2	1	no	—
86	C₂×Q₈×C₁₃	—	2	1	no	—
87	C₂×Q₈×C₁₃	—	2	1	no	—
88	C₂×Q₈×C₁₃	—	2	1	no	—
89	C₂×Q₈×C₁₃	—	4	4	no	—
90	C₂×Q₈×C₁₃	—	4	4	no	—
91	C₂×Q₈×C₁₃	—	8	2	no	—
92	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
93	C₂²×C₄×C₁₃	—	2	1	no	—
94	C₂²×C₄×C₁₃	—	2	1	no	—
95	C₂²×C₄×C₁₃	—	2	1	no	—
96	C₂²×C₄×C₁₃	—	2	1	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
104	C₂×C₈×C₁₃	—	2	1	no	—
105	C₂×C₈×C₁₃	—	2	1	no	—
106	C₂×C₈×C₁₃	—	2	1	no	—
107	C₂×C₈×C₁₃	—	2	1	no	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	—	2	1	no	—
113	C₁₃×C₄⋊C₄	—	2	4	no	—
114	C₁₃×C₄⋊C₄	—	2	2	no	—
115	C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₁₃×C₄⋊C₄	—	2	1	no	—
117	C₁₃×C₄⋊C₄	—	2	1	no	—
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	4	4	no	—
123	C₁₃×C₄⋊C₄	—	4	4	no	—
124	C₁₃×C₄⋊C₄	—	4	2	no	—
125	C₁₃×C₄⋊C₄	—	4	2	no	—
126	C₁₃×C₄⋊C₄	—	8	1	no	—
127	C₁₃×C₄⋊C₄	—	8	1	no	—
128	C₁₃×C₄⋊C₄	SD₁₆	1	4	yes	—
129	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
130	C₁₃×C₄⋊C₄	#41	1	2	yes	—
131	C₁₃×C₄⋊C₄	#41	1	2	yes	—
132	C₄²×C₁₃	—	2	4	no	—
133	C₄²×C₁₃	—	2	2	no	—
134	C₄²×C₁₃	—	2	2	no	—
135	C₄²×C₁₃	—	4	2	no	—
136	C₄²×C₁₃	—	8	2	no	—
137	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
138	C₄²×C₁₃	#41	1	2	yes	—
139	#2551	C₂×C₁₃	1	1	yes	characteristic
140	#2355	C₂×C₁₃	1	1	yes	characteristic
141	#2066	C₂×C₁₃	1	2	yes	—
142	#2024	C₂×C₁₃	1	2	yes	—
143	#1988	C₂×C₁₃	1	2	yes	—
144	#1948	C₂×C₁₃	1	1	yes	characteristic
145	#1939	C₂×C₁₃	1	1	yes	characteristic
146	#1919	C₂×C₁₃	1	2	yes	—
147	#1834	C₂×C₁₃	1	1	yes	characteristic
148	#1803	C₂×C₁₃	1	1	yes	characteristic
149	C₄×#103	C₂×C₁₃	1	1	yes	characteristic
150	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₁₃	—	2	2	no	—
152	Q₈×C₁₃	—	2	2	no	—
153	Q₈×C₁₃	—	4	1	no	—
154	Q₈×C₁₃	—	4	1	no	—
155	Q₈×C₁₃	—	8	8	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	1	no	—
159	C₂×C₄×C₁₃	—	2	1	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	4	1	no	—
168	C₂×C₄×C₁₃	—	4	1	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	4	1	no	—
171	C₂×C₄×C₁₃	—	4	1	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	—	4	2	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
182	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
183	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
184	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
185	C₂×C₄×C₁₃	#137	1	2	yes	—
186	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
192	C₈×C₁₃	—	4	1	no	—
193	C₈×C₁₃	—	4	2	no	—
194	C₈×C₁₃	—	4	1	no	—
195	C₂×C₄⋊Q₈	—	2	1	no	—
196	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
197	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×#106	C₂²×C₁₃	1	2	yes	—
199	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
201	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
203	C₂×#103	C₂²×C₁₃	1	2	yes	—
204	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
205	#395	—	2	2	no	—
206	#391	C₂²×C₁₃	1	2	yes	—
207	#389	—	2	1	no	—
208	#389	C₂²×C₁₃	1	2	yes	—
209	#387	—	2	2	no	—
210	#384	C₂²×C₁₃	1	1	yes	characteristic
211	#384	C₂²×C₁₃	1	1	yes	characteristic
212	#382	—	2	1	no	—
213	C₄×C₄⋊C₄	—	2	1	no	—
214	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
215	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
216	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
217	#340	C₂²×C₁₃	1	2	yes	—
218	#340	C₂²×C₁₃	1	2	yes	—
219	#340	C₂²×C₁₃	1	2	yes	—
220	#340	C₂²×C₁₃	1	1	yes	characteristic
221	#340	C₂²×C₁₃	1	2	yes	—
222	#340	C₂²×C₁₃	1	1	yes	characteristic
223	#336	C₂²×C₁₃	1	2	yes	—
224	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
225	C₂²×C₁₃	#546	1	1	yes	characteristic
226	C₂²×C₁₃	#548	1	1	yes	characteristic
227	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
228	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
229	C₂²×C₁₃	#576	1	1	yes	characteristic
230	C₂²×C₁₃	#578	1	1	yes	characteristic
231	C₄×C₁₃	—	2	2	no	—
232	C₄×C₁₃	—	2	4	no	—
233	C₄×C₁₃	—	4	2	no	—
234	C₄×C₁₃	—	4	2	no	—
235	C₄×C₁₃	—	4	2	no	—
236	C₄×C₁₃	—	4	2	no	—
237	C₄×C₁₃	—	4	2	no	—
238	C₄×C₁₃	—	8	2	no	—
239	C₄×C₁₃	—	8	2	no	—
240	C₄×C₁₃	#475	1	4	yes	—
241	C₄×C₁₃	#533	1	1	yes	characteristic
242	C₄×C₁₃	#544	1	1	yes	characteristic
243	C₄×C₁₃	#555	1	1	yes	characteristic
244	C₄×C₁₃	#556	1	1	yes	characteristic
245	C₂²×Q₈	—	2	2	no	—
246	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
249	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
250	C₄⋊Q₈	—	2	4	no	—
251	C₄⋊Q₈	—	4	2	no	—
252	C₄⋊Q₈	—	4	4	no	—
253	C₄×Q₈	—	2	2	no	—
254	C₄×Q₈	Q₈×C₁₃	1	4	yes	complemented
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
263	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
269	C₂×C₄²	—	2	1	no	—
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	—	2	2	no	—
272	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
273	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
274	#106	—	2	4	no	—
275	C₄⋊C₈	—	2	2	no	—
276	C₄⋊C₈	—	4	2	no	—
277	#103	—	2	2	no	—
278	#103	—	2	2	no	—
279	#103	—	4	2	no	—
280	C₄×C₈	—	2	2	no	—
281	#95	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	—	2	1	no	—
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	#95	D₄×C₁₃	1	2	yes	—
287	C₂×C₁₃	#2439	1	1	yes	characteristic
288	C₂×C₁₃	C₂×#475	1	1	yes	characteristic
289	C₂×C₁₃	#3083	1	1	yes	characteristic
290	C₂×C₁₃	#3295	1	1	yes	characteristic
291	C₂×C₁₃	#3328	1	1	yes	characteristic
292	C₂×C₁₃	#3359	1	1	yes	characteristic
293	C₂×C₁₃	#3375	1	1	yes	characteristic
294	C₂×Q₈	—	2	1	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	4	4	no	—
300	C₂×Q₈	—	4	4	no	—
301	C₂×Q₈	—	8	2	no	—
302	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
313	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	4	4	no	—
333	C₄⋊C₄	—	4	4	no	—
334	C₄⋊C₄	—	4	2	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	—	8	1	no	—
337	C₄⋊C₄	—	8	1	no	—
338	C₄⋊C₄	C₁₃×SD₁₆	1	4	yes	—
339	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
340	C₄⋊C₄	C₁₃×#41	1	2	yes	—
341	C₄⋊C₄	C₁₃×#41	1	2	yes	—
342	C₄²	—	2	4	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	4	2	no	—
346	C₄²	—	8	2	no	—
347	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
348	C₄²	C₁₃×#41	1	2	yes	—
349	C₁₃	#26022	1	1	yes	characteristic, direct product factor, Sylow
350	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
351	Q₈	—	2	2	no	—
352	Q₈	—	2	2	no	—
353	Q₈	—	4	1	no	—
354	Q₈	—	4	1	no	—
355	Q₈	—	8	8	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	4	1	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	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
382	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
383	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
384	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
385	C₂×C₄	C₁₃×#137	1	2	yes	—
386	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
387	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
388	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
389	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
390	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
391	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
392	C₈	—	4	1	no	—
393	C₈	—	4	2	no	—
394	C₈	—	4	1	no	—
395	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
396	C₂²	C₁₃×#546	1	1	yes	characteristic
397	C₂²	C₁₃×#548	1	1	yes	characteristic
398	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
399	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
400	C₂²	C₁₃×#576	1	1	yes	characteristic
401	C₂²	C₁₃×#578	1	1	yes	characteristic
402	C₄	—	2	4	no	—
403	C₄	—	2	2	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	8	2	no	—
410	C₄	—	8	2	no	—
411	C₄	C₁₃×#475	1	4	yes	—
412	C₄	C₁₃×#533	1	1	yes	characteristic
413	C₄	C₁₃×#544	1	1	yes	characteristic
414	C₄	C₁₃×#555	1	1	yes	characteristic
415	C₄	C₁₃×#556	1	1	yes	characteristic
416	C₂	C₁₃×#2439	1	1	yes	characteristic
417	C₂	C₂×C₁₃×#475	1	1	yes	characteristic
418	C₂	C₁₃×#3083	1	1	yes	characteristic
419	C₂	C₁₃×#3295	1	1	yes	characteristic
420	C₂	C₁₃×#3328	1	1	yes	characteristic
421	C₂	C₁₃×#3359	1	1	yes	characteristic
422	C₂	C₁₃×#3375	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
50. C₄×Q₈×C₁₃	Q₈	semidirect
83. #26022	C₁₃	direct (N × H)
254. C₄×Q₈	Q₈×C₁₃	semidirect
349. C₁₃	#26022	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×#2551	2
C₁₃×#2355	2
C₁₃×#2066	2
C₁₃×#2024	2
C₁₃×#1988	2
C₁₃×#1948	2
C₁₃×#1939	2
C₁₃×#1919	2
C₁₃×#1834	2
C₁₃×#1803	2
C₄×C₁₃×#103	2
#26022	13

Subgroups — C13×#26022 #15712361

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26022 #15712361