Subgroups — C₁₃×#29195 #15715534

Order 3328.

858 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2864	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₁₃×#127	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2067	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2065	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1961	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1961	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1864	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1862	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1847	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1836	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1767	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₃	—	2	1	no	—
14	C₂×C₄×D₄×C₁₃	—	2	1	no	—
15	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
16	C₂×C₁₃×#107	C₂²	1	2	yes	—
17	C₂×C₁₃×#106	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#102	C₂²	1	2	yes	—
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×#97	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
25	C₁₃×#390	—	2	1	no	—
26	C₁₃×#390	—	2	1	no	—
27	C₁₃×#390	C₂²	1	2	yes	—
28	C₁₃×#389	C₂²	1	1	yes	characteristic
29	C₁₃×#389	C₂²	1	1	yes	characteristic
30	C₁₃×#389	C₂²	1	1	yes	characteristic
31	C₁₃×#389	C₂²	1	1	yes	characteristic
32	C₁₃×#387	—	2	1	no	—
33	C₁₃×#387	—	2	1	no	—
34	C₁₃×#387	—	2	1	no	—
35	C₁₃×#387	—	2	1	no	—
36	C₁₃×#384	C₂²	1	1	yes	characteristic
37	C₁₃×#382	C₂²	1	1	yes	characteristic
38	C₁₃×#382	C₂²	1	1	yes	characteristic
39	C₄³×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×D₄×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	—	2	1	no	—
45	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₃	—	2	2	no	—
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₁₃×#127	—	2	2	no	—
50	C₁₃×#127	Q₈	1	4	yes	—
51	C₄×D₄×C₁₃	—	4	2	no	—
52	C₄×D₄×C₁₃	—	4	2	no	—
53	C₄×D₄×C₁₃	—	4	4	no	—
54	C₄×D₄×C₁₃	—	4	4	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
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×C₄⋊C₄	C₂³	1	2	yes	—
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	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#107	—	4	2	no	—
77	C₁₃×#106	—	4	2	no	—
78	C₁₃×C₄⋊C₈	—	2	4	no	—
79	C₁₃×#102	—	2	4	no	—
80	C₁₃×#102	—	2	4	no	—
81	C₁₃×#102	—	4	2	no	—
82	C₁₃×#102	—	4	2	no	—
83	C₁₃×#97	—	2	2	no	—
84	C₁₃×#97	—	2	2	no	—
85	C₁₃×#95	—	2	1	no	—
86	C₁₃×#95	—	2	1	no	—
87	C₁₃×#95	—	2	1	no	—
88	C₁₃×#95	—	2	1	no	—
89	C₁₃×#95	—	2	1	no	—
90	C₁₃×#95	—	2	1	no	—
91	C₁₃×#95	—	2	1	no	—
92	C₁₃×#95	—	2	1	no	—
93	#29195	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂⁴×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	2	4	no	—
96	C₂×D₄×C₁₃	—	2	4	no	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	4	2	no	—
103	C₂×D₄×C₁₃	—	4	2	no	—
104	C₂×D₄×C₁₃	—	4	2	no	—
105	C₂×D₄×C₁₃	—	4	2	no	—
106	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	4	4	no	—
113	C₂²×C₄×C₁₃	—	4	4	no	—
114	C₂²×C₄×C₁₃	—	4	4	no	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	#41	1	4	yes	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	4	2	no	—
135	C₁₃×C₄⋊C₄	—	4	2	no	—
136	C₁₃×C₄⋊C₄	—	4	2	no	—
137	C₁₃×C₄⋊C₄	—	4	2	no	—
138	C₁₃×C₄⋊C₄	—	4	2	no	—
139	C₁₃×C₄⋊C₄	—	4	2	no	—
140	C₁₃×C₂²⋊C₄	—	4	4	no	—
141	C₁₃×C₂²⋊C₄	—	4	4	no	—
142	C₁₃×C₂²⋊C₄	—	4	4	no	—
143	C₄²×C₁₃	—	2	2	no	—
144	C₄²×C₁₃	—	2	2	no	—
145	C₄²×C₁₃	—	2	2	no	—
146	C₄²×C₁₃	—	2	2	no	—
147	C₄²×C₁₃	—	4	1	no	—
148	C₄²×C₁₃	—	4	1	no	—
149	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
150	C₄²×C₁₃	#41	1	2	yes	—
151	#2864	C₂×C₁₃	1	1	yes	characteristic, complemented
152	C₄×#127	C₂×C₁₃	1	1	yes	characteristic
153	#2067	C₂×C₁₃	1	2	yes	complemented
154	#2065	C₂×C₁₃	1	2	yes	complemented
155	#1961	C₂×C₁₃	1	1	yes	characteristic
156	#1961	C₂×C₁₃	1	1	yes	characteristic
157	#1864	C₂×C₁₃	1	2	yes	complemented
158	#1862	C₂×C₁₃	1	2	yes	complemented
159	#1847	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#1836	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#1767	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂³×C₁₃	—	2	4	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	—	4	2	no	—
168	C₂³×C₁₃	—	4	2	no	—
169	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
170	D₄×C₁₃	—	2	4	no	—
171	D₄×C₁₃	—	2	4	no	—
172	D₄×C₁₃	—	4	8	no	—
173	D₄×C₁₃	—	4	8	no	—
174	D₄×C₁₃	—	4	2	no	—
175	D₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	1	no	—
201	C₂×C₄×C₁₃	—	4	1	no	—
202	C₂×C₄×C₁₃	—	4	1	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	—	8	8	no	—
206	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
207	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
208	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
209	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
210	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
213	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
214	C₈×C₁₃	—	2	4	no	—
215	C₈×C₁₃	—	4	2	no	—
216	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×C₄×D₄	—	2	1	no	—
218	C₂×C₄×D₄	—	2	1	no	—
219	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
220	C₂×#107	C₂²×C₁₃	1	2	yes	—
221	C₂×#106	C₂²×C₁₃	1	2	yes	—
222	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
223	C₂×#102	C₂²×C₁₃	1	2	yes	—
224	C₂×#102	C₂²×C₁₃	1	2	yes	—
225	C₂×#102	C₂²×C₁₃	1	2	yes	—
226	C₂×#102	C₂²×C₁₃	1	2	yes	—
227	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
229	#390	—	2	1	no	—
230	#390	—	2	1	no	—
231	#390	C₂²×C₁₃	1	2	yes	—
232	#389	C₂²×C₁₃	1	1	yes	characteristic
233	#389	C₂²×C₁₃	1	1	yes	characteristic
234	#389	C₂²×C₁₃	1	1	yes	characteristic
235	#389	C₂²×C₁₃	1	1	yes	characteristic
236	#387	—	2	1	no	—
237	#387	—	2	1	no	—
238	#387	—	2	1	no	—
239	#387	—	2	1	no	—
240	#384	C₂²×C₁₃	1	1	yes	characteristic
241	#382	C₂²×C₁₃	1	1	yes	characteristic
242	#382	C₂²×C₁₃	1	1	yes	characteristic
243	C₄³	C₂²×C₁₃	1	1	yes	characteristic
244	#340	C₂²×C₁₃	1	2	yes	—
245	#340	C₂²×C₁₃	1	2	yes	—
246	#336	C₂²×C₁₃	1	2	yes	—
247	C₂²×C₁₃	—	4	4	no	—
248	C₂²×C₁₃	—	4	4	no	—
249	C₂²×C₁₃	—	4	4	no	—
250	C₂²×C₁₃	—	8	2	no	—
251	C₂²×C₁₃	—	8	2	no	—
252	C₂²×C₁₃	—	8	2	no	—
253	C₂²×C₁₃	—	8	2	no	—
254	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
255	C₂²×C₁₃	#532	1	1	yes	characteristic
256	C₂²×C₁₃	#535	1	1	yes	characteristic
257	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
258	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
259	C₂²×C₁₃	#575	1	1	yes	characteristic
260	C₂²×C₁₃	#575	1	1	yes	characteristic
261	C₄×C₁₃	—	2	2	no	—
262	C₄×C₁₃	—	2	2	no	—
263	C₄×C₁₃	—	2	2	no	—
264	C₄×C₁₃	—	2	2	no	—
265	C₄×C₁₃	—	4	1	no	—
266	C₄×C₁₃	—	4	1	no	—
267	C₄×C₁₃	—	8	1	no	—
268	C₄×C₁₃	—	8	1	no	—
269	C₄×C₁₃	—	8	1	no	—
270	C₄×C₁₃	—	8	2	no	—
271	C₄×C₁₃	—	8	1	no	—
272	C₄×C₁₃	#553	1	2	yes	—
273	C₄×C₁₃	#554	1	2	yes	—
274	C₂²×D₄	—	2	1	no	—
275	C₂²×D₄	—	2	1	no	—
276	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
277	C₂³×C₄	—	2	2	no	—
278	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
279	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
280	#127	—	2	2	no	—
281	#127	Q₈×C₁₃	1	4	yes	—
282	C₄×D₄	—	4	2	no	—
283	C₄×D₄	—	4	2	no	—
284	C₄×D₄	—	4	4	no	—
285	C₄×D₄	—	4	4	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
301	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
302	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
303	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
304	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
305	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
306	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
307	#107	—	4	2	no	—
308	#106	—	4	2	no	—
309	C₄⋊C₈	—	2	4	no	—
310	#102	—	2	4	no	—
311	#102	—	2	4	no	—
312	#102	—	4	2	no	—
313	#102	—	4	2	no	—
314	#97	—	2	2	no	—
315	#97	—	2	2	no	—
316	#95	—	2	1	no	—
317	#95	—	2	1	no	—
318	#95	—	2	1	no	—
319	#95	—	2	1	no	—
320	#95	—	2	1	no	—
321	#95	—	2	1	no	—
322	#95	—	2	1	no	—
323	#95	—	2	1	no	—
324	C₂×C₁₃	—	8	4	no	—
325	C₂×C₁₃	#2566	1	1	yes	characteristic
326	C₂×C₁₃	#3077	1	1	yes	characteristic
327	C₂×C₁₃	#3077	1	1	yes	characteristic
328	C₂×C₁₃	#3171	1	1	yes	characteristic
329	C₂×C₁₃	#3180	1	1	yes	characteristic
330	C₂×C₁₃	#3217	1	1	yes	characteristic
331	C₂×C₁₃	#3219	1	1	yes	characteristic
332	C₂⁴	—	2	2	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	4	4	no	—
351	C₂²×C₄	—	4	4	no	—
352	C₂²×C₄	—	4	4	no	—
353	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
359	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	C₁₃×#41	1	4	yes	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₂²⋊C₄	—	4	4	no	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₂²⋊C₄	—	4	4	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	4	1	no	—
386	C₄²	—	4	1	no	—
387	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
388	C₄²	C₁₃×#41	1	2	yes	—
389	C₁₃	#29195	1	1	yes	characteristic, direct product factor, Sylow
390	C₂³	—	2	4	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
398	D₄	—	2	4	no	—
399	D₄	—	2	4	no	—
400	D₄	—	4	8	no	—
401	D₄	—	4	8	no	—
402	D₄	—	4	2	no	—
403	D₄	—	4	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	8	8	no	—
434	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
435	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
436	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
437	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
438	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
439	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
440	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
441	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
442	C₈	—	2	4	no	—
443	C₈	—	4	2	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	4	4	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	8	2	no	—
449	C₂²	—	8	2	no	—
450	C₂²	—	8	2	no	—
451	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
452	C₂²	C₁₃×#532	1	1	yes	characteristic
453	C₂²	C₁₃×#535	1	1	yes	characteristic
454	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
455	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
456	C₂²	C₁₃×#575	1	1	yes	characteristic
457	C₂²	C₁₃×#575	1	1	yes	characteristic
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	1	no	—
464	C₄	—	8	1	no	—
465	C₄	—	8	1	no	—
466	C₄	—	8	1	no	—
467	C₄	—	8	2	no	—
468	C₄	—	8	1	no	—
469	C₄	C₁₃×#553	1	2	yes	—
470	C₄	C₁₃×#554	1	2	yes	—
471	C₂	—	8	4	no	—
472	C₂	C₁₃×#2566	1	1	yes	characteristic
473	C₂	C₁₃×#3077	1	1	yes	characteristic
474	C₂	C₁₃×#3077	1	1	yes	characteristic
475	C₂	C₁₃×#3171	1	1	yes	characteristic
476	C₂	C₁₃×#3180	1	1	yes	characteristic
477	C₂	C₁₃×#3217	1	1	yes	characteristic
478	C₂	C₁₃×#3219	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 ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2864	C₂	semidirect
3. C₁₃×#2067	C₂	semidirect
4. C₁₃×#2065	C₂	semidirect
7. C₁₃×#1864	C₂	semidirect
8. C₁₃×#1862	C₂	semidirect
9. C₁₃×#1847	C₂	semidirect
10. C₁₃×#1836	C₂	semidirect
11. C₁₃×#1767	C₂	semidirect
93. #29195	C₁₃	direct (N × H)
151. #2864	C₂×C₁₃	semidirect
153. #2067	C₂×C₁₃	semidirect
154. #2065	C₂×C₁₃	semidirect
157. #1864	C₂×C₁₃	semidirect
158. #1862	C₂×C₁₃	semidirect
159. #1847	C₂×C₁₃	semidirect
160. #1836	C₂×C₁₃	semidirect
161. #1767	C₂×C₁₃	semidirect
389. C₁₃	#29195	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×#2864	2
C₄×C₁₃×#127	2
C₁₃×#2067	2
C₁₃×#2065	2
C₁₃×#1961	2
C₁₃×#1864	2
C₁₃×#1862	2
C₁₃×#1847	2
C₁₃×#1836	2
C₁₃×#1767	2
#29195	13

Subgroups — C13×#29195 #15715534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29195 #15715534