Subgroups — C₁₃×#26316 #15712655

Order 3328.

802 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2548	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2093	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2071	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1982	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1957	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1925	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1925	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#124	—	2	1	no	—
14	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
15	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#107	C₂²	1	2	yes	—
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₁₃×#102	C₂²	1	2	yes	—
22	C₂×C₁₃×#102	C₂²	1	2	yes	—
23	C₂×C₁₃×#102	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#394	—	2	2	no	—
26	C₁₃×#390	—	2	1	no	—
27	C₁₃×#390	C₂²	1	2	yes	—
28	C₁₃×#390	C₂²	1	2	yes	—
29	C₁₃×#389	—	2	1	no	—
30	C₁₃×#389	—	2	2	no	—
31	C₁₃×#384	C₂²	1	2	yes	—
32	C₁₃×#384	C₂²	1	1	yes	characteristic
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
36	C₁₃×#340	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	1	yes	characteristic
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	2	yes	—
40	C₁₃×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
42	C₂²×D₄×C₁₃	—	2	1	no	—
43	C₂²×D₄×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₁₃×#127	—	2	2	no	—
49	C₁₃×#127	—	2	2	no	—
50	C₁₃×#124	—	4	4	no	—
51	C₄×Q₈×C₁₃	—	2	2	no	—
52	C₄×Q₈×C₁₃	—	2	2	no	—
53	C₄×Q₈×C₁₃	—	4	4	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	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	2	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₁₃×C₂²⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₄²×C₁₃	—	2	2	no	—
70	C₂×C₄²×C₁₃	—	2	1	no	—
71	C₂×C₄²×C₁₃	—	2	1	no	—
72	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×#107	—	2	2	no	—
75	C₁₃×#107	—	2	2	no	—
76	C₁₃×#107	—	4	2	no	—
77	C₁₃×C₄⋊C₈	—	2	2	no	—
78	C₁₃×#102	—	2	4	no	—
79	C₁₃×#102	—	2	4	no	—
80	C₁₃×#102	—	4	2	no	—
81	C₁₃×#102	—	4	2	no	—
82	C₄×C₈×C₁₃	—	2	2	no	—
83	C₁₃×#95	—	2	2	no	—
84	C₁₃×#95	—	2	1	no	—
85	C₁₃×#95	—	2	1	no	—
86	#26316	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₃	—	2	2	no	—
88	C₂×Q₈×C₁₃	—	2	2	no	—
89	C₂×Q₈×C₁₃	—	2	2	no	—
90	C₂×Q₈×C₁₃	D₈	1	4	yes	—
91	C₂×D₄×C₁₃	—	2	2	no	—
92	C₂×D₄×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	—	2	2	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	4	2	no	—
98	C₂×D₄×C₁₃	—	4	2	no	—
99	C₂×D₄×C₁₃	—	4	2	no	—
100	C₂×D₄×C₁₃	—	4	2	no	—
101	C₂×D₄×C₁₃	—	8	1	no	—
102	C₂×D₄×C₁₃	—	8	1	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	1	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	—	2	1	no	—
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	#41	1	2	yes	—
122	C₁₃×C₄⋊C₄	—	2	4	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	1	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	4	4	no	—
134	C₁₃×C₄⋊C₄	—	4	2	no	—
135	C₁₃×C₄⋊C₄	—	8	1	no	—
136	C₁₃×C₄⋊C₄	—	8	2	no	—
137	C₁₃×C₄⋊C₄	#41	1	2	yes	—
138	C₁₃×C₂²⋊C₄	—	4	4	no	—
139	C₁₃×C₂²⋊C₄	—	4	4	no	—
140	C₁₃×C₂²⋊C₄	—	8	2	no	—
141	C₁₃×C₂²⋊C₄	—	8	2	no	—
142	C₄²×C₁₃	—	2	2	no	—
143	C₄²×C₁₃	—	2	2	no	—
144	C₄²×C₁₃	—	4	4	no	—
145	C₄²×C₁₃	—	4	2	no	—
146	C₄²×C₁₃	—	4	2	no	—
147	C₄²×C₁₃	#41	1	2	yes	—
148	C₄²×C₁₃	#41	1	2	yes	—
149	#2548	C₂×C₁₃	1	1	yes	characteristic
150	Q₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#2093	C₂×C₁₃	1	2	yes	complemented
152	#2071	C₂×C₁₃	1	2	yes	complemented
153	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#1982	C₂×C₁₃	1	1	yes	characteristic
155	#1957	C₂×C₁₃	1	1	yes	characteristic
156	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#1925	C₂×C₁₃	1	2	yes	complemented
158	#1925	C₂×C₁₃	1	2	yes	complemented
159	C₄×#107	C₂×C₁₃	1	1	yes	characteristic, complemented
160	C₂³×C₁₃	—	4	2	no	—
161	C₂³×C₁₃	—	4	2	no	—
162	C₂³×C₁₃	—	4	2	no	—
163	C₂³×C₁₃	—	4	2	no	—
164	C₂³×C₁₃	—	4	2	no	—
165	C₂³×C₁₃	—	4	2	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
168	Q₈×C₁₃	—	2	8	no	—
169	D₄×C₁₃	—	4	2	no	—
170	D₄×C₁₃	—	4	2	no	—
171	D₄×C₁₃	—	4	2	no	—
172	D₄×C₁₃	—	4	2	no	—
173	D₄×C₁₃	—	8	4	no	—
174	D₄×C₁₃	—	8	4	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	#123	1	2	yes	—
198	C₂×C₄×C₁₃	#123	1	2	yes	—
199	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
200	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
201	C₂×C₄×C₁₃	#137	1	2	yes	—
202	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
207	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
208	C₈×C₁₃	—	2	2	no	—
209	C₈×C₁₃	—	4	1	no	—
210	C₈×C₁₃	—	4	2	no	—
211	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×#124	—	2	1	no	—
213	C₂×C₄×Q₈	—	2	1	no	—
214	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×#107	C₂²×C₁₃	1	2	yes	—
218	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×#102	C₂²×C₁₃	1	2	yes	—
220	C₂×#102	C₂²×C₁₃	1	2	yes	—
221	C₂×#102	C₂²×C₁₃	1	2	yes	—
222	C₂×#102	C₂²×C₁₃	1	2	yes	—
223	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
224	#394	—	2	2	no	—
225	#390	—	2	1	no	—
226	#390	C₂²×C₁₃	1	2	yes	—
227	#390	C₂²×C₁₃	1	2	yes	—
228	#389	—	2	1	no	—
229	#389	—	2	2	no	—
230	#384	C₂²×C₁₃	1	2	yes	—
231	#384	C₂²×C₁₃	1	1	yes	characteristic
232	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
233	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
234	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
235	#340	C₂²×C₁₃	1	1	yes	characteristic
236	#340	C₂²×C₁₃	1	2	yes	—
237	#340	C₂²×C₁₃	1	1	yes	characteristic
238	#336	C₂²×C₁₃	1	2	yes	—
239	#336	C₂²×C₁₃	1	2	yes	—
240	C₂²×C₁₃	—	8	2	no	—
241	C₂²×C₁₃	—	8	2	no	—
242	C₂²×C₁₃	—	8	2	no	—
243	C₂²×C₁₃	—	8	2	no	—
244	C₂²×C₁₃	—	8	2	no	—
245	C₂²×C₁₃	—	8	2	no	—
246	C₂²×C₁₃	—	8	2	no	—
247	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
248	C₂²×C₁₃	#548	1	1	yes	characteristic
249	C₂²×C₁₃	#550	1	1	yes	characteristic
250	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
251	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
252	C₂²×C₁₃	#576	1	1	yes	characteristic
253	C₂²×C₁₃	#577	1	1	yes	characteristic
254	C₄×C₁₃	—	2	4	no	—
255	C₄×C₁₃	—	2	2	no	—
256	C₄×C₁₃	—	4	2	no	—
257	C₄×C₁₃	—	4	2	no	—
258	C₄×C₁₃	—	8	1	no	—
259	C₄×C₁₃	—	8	1	no	—
260	C₄×C₁₃	—	8	2	no	—
261	C₄×C₁₃	—	8	1	no	—
262	C₄×C₁₃	#480	1	4	yes	—
263	C₄×C₁₃	#529	1	1	yes	characteristic
264	C₄×C₁₃	#542	1	1	yes	characteristic
265	C₄×C₁₃	#556	1	1	yes	characteristic
266	C₄×C₁₃	#559	1	1	yes	characteristic
267	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	—	2	1	no	—
270	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
271	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
272	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
273	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
274	#127	—	2	2	no	—
275	#127	—	2	2	no	—
276	#124	—	4	4	no	—
277	C₄×Q₈	—	2	2	no	—
278	C₄×Q₈	—	2	2	no	—
279	C₄×Q₈	—	4	4	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
285	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₄²	—	2	2	no	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
299	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
300	#107	—	2	2	no	—
301	#107	—	2	2	no	—
302	#107	—	4	2	no	—
303	C₄⋊C₈	—	2	2	no	—
304	#102	—	2	4	no	—
305	#102	—	2	4	no	—
306	#102	—	4	2	no	—
307	#102	—	4	2	no	—
308	C₄×C₈	—	2	2	no	—
309	#95	—	2	2	no	—
310	#95	—	2	1	no	—
311	#95	—	2	1	no	—
312	C₂×C₁₃	—	16	2	no	—
313	C₂×C₁₃	#2448	1	1	yes	characteristic
314	C₂×C₁₃	C₂×#480	1	1	yes	characteristic
315	C₂×C₁₃	#3096	1	1	yes	characteristic
316	C₂×C₁₃	#3358	1	1	yes	characteristic
317	C₂×C₁₃	#3375	1	1	yes	characteristic
318	C₂×C₁₃	#3391	1	1	yes	characteristic
319	C₂×C₁₃	#3400	1	1	yes	characteristic
320	C₂⁴	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	C₁₃×D₈	1	4	yes	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	4	2	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	—	4	2	no	—
334	C₂×D₄	—	8	1	no	—
335	C₂×D₄	—	8	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
344	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
345	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	C₁₃×#41	1	2	yes	—
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	4	4	no	—
367	C₄⋊C₄	—	4	2	no	—
368	C₄⋊C₄	—	8	1	no	—
369	C₄⋊C₄	—	8	2	no	—
370	C₄⋊C₄	C₁₃×#41	1	2	yes	—
371	C₂²⋊C₄	—	4	4	no	—
372	C₂²⋊C₄	—	4	4	no	—
373	C₂²⋊C₄	—	8	2	no	—
374	C₂²⋊C₄	—	8	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	4	4	no	—
378	C₄²	—	4	2	no	—
379	C₄²	—	4	2	no	—
380	C₄²	C₁₃×#41	1	2	yes	—
381	C₄²	C₁₃×#41	1	2	yes	—
382	C₁₃	#26316	1	1	yes	characteristic, direct product factor, Sylow
383	C₂³	—	4	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
391	Q₈	—	2	8	no	—
392	D₄	—	4	2	no	—
393	D₄	—	4	2	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	8	4	no	—
397	D₄	—	8	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	C₁₃×#123	1	2	yes	—
421	C₂×C₄	C₁₃×#123	1	2	yes	—
422	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
423	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
424	C₂×C₄	C₁₃×#137	1	2	yes	—
425	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
426	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
427	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
428	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
429	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
430	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	4	1	no	—
433	C₈	—	4	2	no	—
434	C₂²	—	8	2	no	—
435	C₂²	—	8	2	no	—
436	C₂²	—	8	2	no	—
437	C₂²	—	8	2	no	—
438	C₂²	—	8	2	no	—
439	C₂²	—	8	2	no	—
440	C₂²	—	8	2	no	—
441	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
442	C₂²	C₁₃×#548	1	1	yes	characteristic
443	C₂²	C₁₃×#550	1	1	yes	characteristic
444	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
445	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
446	C₂²	C₁₃×#576	1	1	yes	characteristic
447	C₂²	C₁₃×#577	1	1	yes	characteristic
448	C₄	—	2	4	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	8	1	no	—
453	C₄	—	8	1	no	—
454	C₄	—	8	2	no	—
455	C₄	—	8	1	no	—
456	C₄	C₁₃×#480	1	4	yes	—
457	C₄	C₁₃×#529	1	1	yes	characteristic
458	C₄	C₁₃×#542	1	1	yes	characteristic
459	C₄	C₁₃×#556	1	1	yes	characteristic
460	C₄	C₁₃×#559	1	1	yes	characteristic
461	C₂	—	16	2	no	—
462	C₂	C₁₃×#2448	1	1	yes	characteristic
463	C₂	C₂×C₁₃×#480	1	1	yes	characteristic
464	C₂	C₁₃×#3096	1	1	yes	characteristic
465	C₂	C₁₃×#3358	1	1	yes	characteristic
466	C₂	C₁₃×#3375	1	1	yes	characteristic
467	C₂	C₁₃×#3391	1	1	yes	characteristic
468	C₂	C₁₃×#3400	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
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. Q₈×C₁₃×C₄⋊C₄	C₂	semidirect
3. C₁₃×#2093	C₂	semidirect
4. C₁₃×#2071	C₂	semidirect
5. C₁₃×#1984	C₂	semidirect
8. C₁₃×#1947	C₂	semidirect
9. C₁₃×#1925	C₂	semidirect
10. C₁₃×#1925	C₂	semidirect
11. C₄×C₁₃×#107	C₂	semidirect
86. #26316	C₁₃	direct (N × H)
150. Q₈×C₄⋊C₄	C₂×C₁₃	semidirect
151. #2093	C₂×C₁₃	semidirect
152. #2071	C₂×C₁₃	semidirect
153. #1984	C₂×C₁₃	semidirect
156. #1947	C₂×C₁₃	semidirect
157. #1925	C₂×C₁₃	semidirect
158. #1925	C₂×C₁₃	semidirect
159. C₄×#107	C₂×C₁₃	semidirect
382. C₁₃	#26316	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×#2548	2
Q₈×C₁₃×C₄⋊C₄	2
C₁₃×#2093	2
C₁₃×#2071	2
C₁₃×#1984	2
C₁₃×#1982	2
C₁₃×#1957	2
C₁₃×#1947	2
C₁₃×#1925	2
C₄×C₁₃×#107	2
#26316	13

Subgroups — C13×#26316 #15712655

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26316 #15712655