Subgroups — C₁₃×#26025 #15712364

Order 3328.

734 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2354	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2067	C₂	1	2	yes	maximal
4	C₁₃×#2025	C₂	1	2	yes	maximal
5	C₁₃×#1989	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1921	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1834	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#125	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#117	—	2	1	no	—
15	C₂×C₁₃×#107	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×#102	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#398	—	2	2	no	—
23	C₁₃×#390	C₂²	1	2	yes	—
24	C₁₃×#389	—	2	1	no	—
25	C₁₃×#389	C₂²	1	2	yes	—
26	C₁₃×#388	—	2	2	no	—
27	C₁₃×#384	—	2	1	no	—
28	C₁₃×#384	C₂²	1	1	yes	characteristic
29	C₁₃×#384	C₂²	1	1	yes	characteristic
30	C₁₃×#380	—	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×D₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	—	2	1	no	—
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×#125	—	2	4	no	—
47	C₁₃×#125	—	4	2	no	—
48	C₄×D₄×C₁₃	—	2	2	no	—
49	C₄×D₄×C₁₃	Q₈	1	4	yes	—
50	C₁₃×#117	—	4	4	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	2	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×C₁₃×C₂²⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₄²×C₁₃	—	2	1	no	—
69	C₂×C₄²×C₁₃	—	2	2	no	—
70	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
72	C₁₃×#107	—	2	4	no	—
73	C₁₃×C₄⋊C₈	—	2	2	no	—
74	C₁₃×C₄⋊C₈	—	4	2	no	—
75	C₁₃×#102	—	2	2	no	—
76	C₁₃×#102	—	2	2	no	—
77	C₁₃×#102	—	4	2	no	—
78	C₄×C₈×C₁₃	—	2	2	no	—
79	C₁₃×#95	—	2	2	no	—
80	C₁₃×#95	—	2	1	no	—
81	C₁₃×#95	—	2	2	no	—
82	C₁₃×#95	D₄	1	2	yes	—
83	#26025	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂⁴×C₁₃	—	2	1	no	—
85	C₂×D₄×C₁₃	—	2	1	no	—
86	C₂×D₄×C₁₃	—	2	1	no	—
87	C₂×D₄×C₁₃	—	2	1	no	—
88	C₂×D₄×C₁₃	—	2	1	no	—
89	C₂×D₄×C₁₃	—	2	1	no	—
90	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	—	2	1	no	—
93	C₂²×C₄×C₁₃	—	2	1	no	—
94	C₂²×C₄×C₁₃	—	2	4	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	4	2	no	—
98	C₂²×C₄×C₁₃	—	4	2	no	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	2	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	—	8	2	no	—
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	C₁₃×C₂²⋊C₄	—	2	4	no	—
133	C₁₃×C₂²⋊C₄	—	4	4	no	—
134	C₁₃×C₂²⋊C₄	—	8	2	no	—
135	C₄²×C₁₃	—	2	2	no	—
136	C₄²×C₁₃	—	2	2	no	—
137	C₄²×C₁₃	—	4	4	no	—
138	C₄²×C₁₃	—	4	2	no	—
139	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
140	C₄²×C₁₃	#41	1	2	yes	—
141	#2552	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#2354	C₂×C₁₃	1	1	yes	characteristic
143	#2067	C₂×C₁₃	1	2	yes	—
144	#2025	C₂×C₁₃	1	2	yes	—
145	#1989	C₂×C₁₃	1	2	yes	complemented
146	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#1921	C₂×C₁₃	1	2	yes	complemented
149	#1834	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#1802	C₂×C₁₃	1	1	yes	characteristic
151	C₄×#102	C₂×C₁₃	1	1	yes	characteristic
152	C₂³×C₁₃	—	2	2	no	—
153	C₂³×C₁₃	—	4	1	no	—
154	C₂³×C₁₃	—	4	1	no	—
155	C₂³×C₁₃	—	4	1	no	—
156	C₂³×C₁₃	—	4	1	no	—
157	C₂³×C₁₃	—	4	1	no	—
158	C₂³×C₁₃	—	4	1	no	—
159	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
160	D₄×C₁₃	—	2	2	no	—
161	D₄×C₁₃	—	2	2	no	—
162	D₄×C₁₃	—	4	1	no	—
163	D₄×C₁₃	—	4	1	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
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	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	8	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
189	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
190	C₂×C₄×C₁₃	#135	1	2	yes	—
191	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
192	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
197	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
198	C₈×C₁₃	—	4	1	no	—
199	C₈×C₁₃	—	4	2	no	—
200	C₈×C₁₃	—	4	1	no	—
201	C₂×#125	C₂²×C₁₃	1	2	yes	—
202	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
203	C₂×#117	—	2	1	no	—
204	C₂×#107	C₂²×C₁₃	1	2	yes	—
205	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
207	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×#102	C₂²×C₁₃	1	2	yes	—
210	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
211	#398	—	2	2	no	—
212	#390	C₂²×C₁₃	1	2	yes	—
213	#389	—	2	1	no	—
214	#389	C₂²×C₁₃	1	2	yes	—
215	#388	—	2	2	no	—
216	#384	—	2	1	no	—
217	#384	C₂²×C₁₃	1	1	yes	characteristic
218	#384	C₂²×C₁₃	1	1	yes	characteristic
219	#380	—	2	1	no	—
220	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
221	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
222	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
223	#340	C₂²×C₁₃	1	2	yes	—
224	#340	C₂²×C₁₃	1	2	yes	—
225	#340	C₂²×C₁₃	1	2	yes	—
226	#340	C₂²×C₁₃	1	1	yes	characteristic
227	#340	C₂²×C₁₃	1	2	yes	—
228	#340	C₂²×C₁₃	1	1	yes	characteristic
229	#336	C₂²×C₁₃	1	2	yes	—
230	C₂²×C₁₃	—	4	2	no	—
231	C₂²×C₁₃	—	4	2	no	—
232	C₂²×C₁₃	—	4	2	no	—
233	C₂²×C₁₃	—	8	1	no	—
234	C₂²×C₁₃	—	8	1	no	—
235	C₂²×C₁₃	—	8	1	no	—
236	C₂²×C₁₃	—	8	1	no	—
237	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
238	C₂²×C₁₃	#546	1	1	yes	characteristic
239	C₂²×C₁₃	#548	1	1	yes	characteristic
240	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
241	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
242	C₂²×C₁₃	#576	1	1	yes	characteristic
243	C₂²×C₁₃	#578	1	1	yes	characteristic
244	C₄×C₁₃	—	2	2	no	—
245	C₄×C₁₃	—	4	2	no	—
246	C₄×C₁₃	—	4	2	no	—
247	C₄×C₁₃	—	4	2	no	—
248	C₄×C₁₃	—	4	2	no	—
249	C₄×C₁₃	—	4	2	no	—
250	C₄×C₁₃	—	8	2	no	—
251	C₄×C₁₃	—	8	2	no	—
252	C₄×C₁₃	#478	1	4	yes	—
253	C₄×C₁₃	#533	1	1	yes	characteristic
254	C₄×C₁₃	#544	1	1	yes	characteristic
255	C₄×C₁₃	#555	1	1	yes	characteristic
256	C₄×C₁₃	#556	1	1	yes	characteristic
257	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
258	C₂³×C₄	—	2	1	no	—
259	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
261	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
262	#125	—	2	4	no	—
263	#125	—	4	2	no	—
264	C₄×D₄	—	2	2	no	—
265	C₄×D₄	Q₈×C₁₃	1	4	yes	—
266	#117	—	4	4	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
275	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₄²	—	2	2	no	—
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
287	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
288	#107	—	2	4	no	—
289	C₄⋊C₈	—	2	2	no	—
290	C₄⋊C₈	—	4	2	no	—
291	#102	—	2	2	no	—
292	#102	—	2	2	no	—
293	#102	—	4	2	no	—
294	C₄×C₈	—	2	2	no	—
295	#95	—	2	2	no	—
296	#95	—	2	1	no	—
297	#95	—	2	2	no	—
298	#95	D₄×C₁₃	1	2	yes	—
299	C₂×C₁₃	—	8	2	no	—
300	C₂×C₁₃	#2439	1	1	yes	characteristic
301	C₂×C₁₃	C₂×#478	1	1	yes	characteristic
302	C₂×C₁₃	#3083	1	1	yes	characteristic
303	C₂×C₁₃	#3305	1	1	yes	characteristic
304	C₂×C₁₃	#3330	1	1	yes	characteristic
305	C₂×C₁₃	#3364	1	1	yes	characteristic
306	C₂×C₁₃	#3366	1	1	yes	characteristic
307	C₂⁴	—	2	1	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
323	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
326	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	4	4	no	—
346	C₄⋊C₄	—	4	4	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	—	8	1	no	—
350	C₄⋊C₄	—	8	1	no	—
351	C₄⋊C₄	—	8	2	no	—
352	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
353	C₄⋊C₄	C₁₃×#41	1	2	yes	—
354	C₄⋊C₄	C₁₃×#41	1	2	yes	—
355	C₂²⋊C₄	—	2	4	no	—
356	C₂²⋊C₄	—	4	4	no	—
357	C₂²⋊C₄	—	8	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	4	4	no	—
361	C₄²	—	4	2	no	—
362	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
363	C₄²	C₁₃×#41	1	2	yes	—
364	C₁₃	#26025	1	1	yes	characteristic, direct product factor, Sylow
365	C₂³	—	2	2	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
373	D₄	—	2	2	no	—
374	D₄	—	2	2	no	—
375	D₄	—	4	1	no	—
376	D₄	—	4	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	8	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
402	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
403	C₂×C₄	C₁₃×#135	1	2	yes	—
404	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
405	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
406	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
407	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
408	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
409	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
410	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
411	C₈	—	4	1	no	—
412	C₈	—	4	2	no	—
413	C₈	—	4	1	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	8	1	no	—
418	C₂²	—	8	1	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
422	C₂²	C₁₃×#546	1	1	yes	characteristic
423	C₂²	C₁₃×#548	1	1	yes	characteristic
424	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
425	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
426	C₂²	C₁₃×#576	1	1	yes	characteristic
427	C₂²	C₁₃×#578	1	1	yes	characteristic
428	C₄	—	2	2	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	8	2	no	—
435	C₄	—	8	2	no	—
436	C₄	C₁₃×#478	1	4	yes	—
437	C₄	C₁₃×#533	1	1	yes	characteristic
438	C₄	C₁₃×#544	1	1	yes	characteristic
439	C₄	C₁₃×#555	1	1	yes	characteristic
440	C₄	C₁₃×#556	1	1	yes	characteristic
441	C₂	—	8	2	no	—
442	C₂	C₁₃×#2439	1	1	yes	characteristic
443	C₂	C₂×C₁₃×#478	1	1	yes	characteristic
444	C₂	C₁₃×#3083	1	1	yes	characteristic
445	C₂	C₁₃×#3305	1	1	yes	characteristic
446	C₂	C₁₃×#3330	1	1	yes	characteristic
447	C₂	C₁₃×#3364	1	1	yes	characteristic
448	C₂	C₁₃×#3366	1	1	yes	characteristic

	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 ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2552	C₂	semidirect
5. C₁₃×#1989	C₂	semidirect
6. C₁₃×#1947	C₂	semidirect
7. C₁₃×#1939	C₂	semidirect
8. C₁₃×#1921	C₂	semidirect
9. C₁₃×#1834	C₂	semidirect
83. #26025	C₁₃	direct (N × H)
141. #2552	C₂×C₁₃	semidirect
145. #1989	C₂×C₁₃	semidirect
146. #1947	C₂×C₁₃	semidirect
147. #1939	C₂×C₁₃	semidirect
148. #1921	C₂×C₁₃	semidirect
149. #1834	C₂×C₁₃	semidirect
364. C₁₃	#26025	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×#2552	2
C₁₃×#2354	2
C₁₃×#2067	2
C₁₃×#2025	2
C₁₃×#1989	2
C₁₃×#1947	2
C₁₃×#1939	2
C₁₃×#1921	2
C₁₃×#1834	2
C₁₃×#1802	2
C₄×C₁₃×#102	2
#26025	13

Subgroups — C13×#26025 #15712364

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26025 #15712364