Subgroups — C₁₃×#32799 #15719138

Order 3328.

814 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2863	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2858	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2043	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2042	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2042	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2041	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2016	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2015	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2015	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2014	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1839	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
13	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#124	C₂²	1	2	yes	—
17	C₂×C₁₃×#124	C₂²	1	2	yes	—
18	C₂×C₁₃×#103	C₂²	1	2	yes	—
19	C₂×C₁₃×#103	C₂²	1	2	yes	—
20	C₂×C₁₃×#103	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	C₁₃×#391	C₂²	1	1	yes	characteristic
25	C₁₃×#391	C₂²	1	1	yes	characteristic
26	C₁₃×#391	C₂²	1	1	yes	characteristic
27	C₁₃×#390	—	2	1	no	—
28	C₁₃×#390	—	2	1	no	—
29	C₁₃×#390	—	2	1	no	—
30	C₁₃×#390	—	2	1	no	—
31	C₁₃×#389	C₂²	1	1	yes	characteristic
32	C₁₃×#389	C₂²	1	1	yes	characteristic
33	C₁₃×#389	C₂²	1	1	yes	characteristic
34	C₁₃×#387	—	2	1	no	—
35	C₁₃×#387	—	2	1	no	—
36	C₁₃×#387	—	2	1	no	—
37	C₁₃×#383	—	2	1	no	—
38	C₄³×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#336	C₂²	1	1	yes	characteristic
40	C₁₃×#336	C₂²	1	2	yes	—
41	C₁₃×#336	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
45	C₂²×D₄×C₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₃	—	2	1	no	—
47	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
48	C₂×C₁₃×Q₁₆	—	4	2	no	—
49	C₂×C₁₃×Q₁₆	—	4	2	no	—
50	C₂×C₁₃×Q₁₆	—	4	2	no	—
51	C₂×C₁₃×SD₁₆	—	4	2	no	—
52	C₂×C₁₃×SD₁₆	—	4	2	no	—
53	C₂×C₁₃×SD₁₆	—	4	2	no	—
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
56	C₁₃×C₄⋊Q₈	—	4	2	no	—
57	C₁₃×#127	—	4	2	no	—
58	C₁₃×#124	—	4	2	no	—
59	C₁₃×#124	—	4	2	no	—
60	C₁₃×#124	—	4	2	no	—
61	C₁₃×#124	—	4	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
81	C₁₃×#103	—	4	2	no	—
82	C₁₃×#103	—	4	2	no	—
83	C₁₃×#103	—	4	2	no	—
84	C₁₃×#102	—	4	2	no	—
85	C₁₃×#102	—	4	2	no	—
86	C₁₃×#102	—	4	2	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	C₁₃×#95	—	2	1	no	—
94	C₁₃×#95	—	2	1	no	—
95	C₁₃×#95	—	2	1	no	—
96	#32799	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂⁴×C₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₃	—	2	2	no	—
99	C₂×Q₈×C₁₃	—	2	2	no	—
100	C₂×Q₈×C₁₃	—	2	2	no	—
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	2	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₃	—	2	2	no	—
106	C₂×Q₈×C₁₃	—	2	2	no	—
107	C₂×Q₈×C₁₃	—	2	1	no	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	—	2	2	no	—
110	C₂×D₄×C₁₃	—	2	2	no	—
111	C₂×D₄×C₁₃	—	2	2	no	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	—	2	2	no	—
114	C₂×D₄×C₁₃	—	4	2	no	—
115	C₂×D₄×C₁₃	—	4	2	no	—
116	C₂×D₄×C₁₃	—	4	2	no	—
117	C₂×D₄×C₁₃	—	4	2	no	—
118	C₂×D₄×C₁₃	—	4	2	no	—
119	C₂×D₄×C₁₃	—	4	2	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
132	C₁₃×Q₁₆	—	4	8	no	—
133	C₁₃×SD₁₆	—	4	8	no	—
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	2	1	no	—
144	C₁₃×C₄⋊C₄	—	4	2	no	—
145	C₁₃×C₄⋊C₄	—	4	2	no	—
146	C₁₃×C₄⋊C₄	—	4	2	no	—
147	C₁₃×C₄⋊C₄	—	4	2	no	—
148	C₁₃×C₄⋊C₄	—	4	2	no	—
149	C₁₃×C₂²⋊C₄	—	4	4	no	—
150	C₁₃×C₂²⋊C₄	—	4	4	no	—
151	C₁₃×C₂²⋊C₄	—	4	4	no	—
152	C₁₃×C₂²⋊C₄	—	4	4	no	—
153	C₄²×C₁₃	—	2	2	no	—
154	C₄²×C₁₃	—	2	2	no	—
155	C₄²×C₁₃	—	2	2	no	—
156	C₄²×C₁₃	—	2	1	no	—
157	C₄²×C₁₃	—	2	1	no	—
158	C₄²×C₁₃	—	2	2	no	—
159	C₄²×C₁₃	—	4	1	no	—
160	C₄²×C₁₃	—	4	1	no	—
161	#2863	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#2858	C₂×C₁₃	1	1	yes	characteristic
163	#2043	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#2042	C₂×C₁₃	1	2	yes	complemented
165	#2042	C₂×C₁₃	1	2	yes	complemented
166	#2041	C₂×C₁₃	1	1	yes	characteristic
167	#2016	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#2015	C₂×C₁₃	1	2	yes	complemented
169	#2015	C₂×C₁₃	1	2	yes	complemented
170	#2014	C₂×C₁₃	1	1	yes	characteristic
171	#1839	C₂×C₁₃	1	1	yes	characteristic, complemented
172	C₂³×C₁₃	—	4	2	no	—
173	C₂³×C₁₃	—	4	2	no	—
174	C₂³×C₁₃	—	4	2	no	—
175	C₂³×C₁₃	—	4	2	no	—
176	C₂³×C₁₃	—	4	2	no	—
177	C₂³×C₁₃	—	4	2	no	—
178	C₂³×C₁₃	—	4	2	no	—
179	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₁₃	—	4	2	no	—
181	Q₈×C₁₃	—	4	2	no	—
182	Q₈×C₁₃	—	4	2	no	—
183	Q₈×C₁₃	—	4	2	no	—
184	Q₈×C₁₃	—	4	2	no	—
185	Q₈×C₁₃	—	4	2	no	—
186	D₄×C₁₃	—	4	2	no	—
187	D₄×C₁₃	—	4	2	no	—
188	D₄×C₁₃	—	4	2	no	—
189	D₄×C₁₃	—	4	2	no	—
190	D₄×C₁₃	—	8	4	no	—
191	D₄×C₁₃	—	8	4	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	2	1	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	1	no	—
204	C₂×C₄×C₁₃	—	2	1	no	—
205	C₂×C₄×C₁₃	—	2	1	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	—	4	1	no	—
211	C₂×C₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	4	1	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	1	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	1	no	—
220	C₂×C₄×C₁₃	—	4	1	no	—
221	C₂×C₄×C₁₃	—	4	1	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	#135	1	2	yes	—
224	C₂×C₄×C₁₃	#137	1	2	yes	—
225	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
226	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
227	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
228	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
229	C₈×C₁₃	—	4	2	no	—
230	C₈×C₁₃	—	4	2	no	—
231	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
232	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
233	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×#124	C₂²×C₁₃	1	2	yes	—
236	C₂×#124	C₂²×C₁₃	1	2	yes	—
237	C₂×#103	C₂²×C₁₃	1	2	yes	—
238	C₂×#103	C₂²×C₁₃	1	2	yes	—
239	C₂×#103	C₂²×C₁₃	1	2	yes	—
240	C₂×#102	C₂²×C₁₃	1	2	yes	—
241	C₂×#102	C₂²×C₁₃	1	2	yes	—
242	C₂×#102	C₂²×C₁₃	1	2	yes	—
243	#391	C₂²×C₁₃	1	1	yes	characteristic
244	#391	C₂²×C₁₃	1	1	yes	characteristic
245	#391	C₂²×C₁₃	1	1	yes	characteristic
246	#390	—	2	1	no	—
247	#390	—	2	1	no	—
248	#390	—	2	1	no	—
249	#390	—	2	1	no	—
250	#389	C₂²×C₁₃	1	1	yes	characteristic
251	#389	C₂²×C₁₃	1	1	yes	characteristic
252	#389	C₂²×C₁₃	1	1	yes	characteristic
253	#387	—	2	1	no	—
254	#387	—	2	1	no	—
255	#387	—	2	1	no	—
256	#383	—	2	1	no	—
257	C₄³	C₂²×C₁₃	1	1	yes	characteristic
258	#336	C₂²×C₁₃	1	1	yes	characteristic
259	#336	C₂²×C₁₃	1	2	yes	—
260	#336	C₂²×C₁₃	1	2	yes	—
261	#336	C₂²×C₁₃	1	1	yes	characteristic
262	C₂²×C₁₃	—	8	2	no	—
263	C₂²×C₁₃	—	8	2	no	—
264	C₂²×C₁₃	—	8	2	no	—
265	C₂²×C₁₃	—	8	2	no	—
266	C₂²×C₁₃	—	8	2	no	—
267	C₂²×C₁₃	—	8	2	no	—
268	C₂²×C₁₃	—	8	2	no	—
269	C₂²×C₁₃	#535	1	1	yes	characteristic
270	C₂²×C₁₃	#535	1	1	yes	characteristic
271	C₂²×C₁₃	#535	1	1	yes	characteristic
272	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
273	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
274	C₂²×C₁₃	#575	1	1	yes	characteristic
275	C₂²×C₁₃	#575	1	1	yes	characteristic
276	C₄×C₁₃	—	2	2	no	—
277	C₄×C₁₃	—	2	2	no	—
278	C₄×C₁₃	—	4	1	no	—
279	C₄×C₁₃	—	4	1	no	—
280	C₄×C₁₃	—	4	1	no	—
281	C₄×C₁₃	—	4	1	no	—
282	C₄×C₁₃	—	8	2	no	—
283	C₄×C₁₃	—	8	1	no	—
284	C₄×C₁₃	—	8	1	no	—
285	C₄×C₁₃	—	8	1	no	—
286	C₄×C₁₃	—	8	1	no	—
287	C₄×C₁₃	#560	1	2	yes	—
288	C₄×C₁₃	#560	1	2	yes	—
289	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
290	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
294	C₂×Q₁₆	—	4	2	no	—
295	C₂×Q₁₆	—	4	2	no	—
296	C₂×Q₁₆	—	4	2	no	—
297	C₂×SD₁₆	—	4	2	no	—
298	C₂×SD₁₆	—	4	2	no	—
299	C₂×SD₁₆	—	4	2	no	—
300	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
301	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
302	C₄⋊Q₈	—	4	2	no	—
303	#127	—	4	2	no	—
304	#124	—	4	2	no	—
305	#124	—	4	2	no	—
306	#124	—	4	2	no	—
307	#124	—	4	2	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
321	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
322	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
323	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
324	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
326	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
327	#103	—	4	2	no	—
328	#103	—	4	2	no	—
329	#103	—	4	2	no	—
330	#102	—	4	2	no	—
331	#102	—	4	2	no	—
332	#102	—	4	2	no	—
333	#95	—	2	1	no	—
334	#95	—	2	1	no	—
335	#95	—	2	1	no	—
336	#95	—	2	1	no	—
337	#95	—	2	1	no	—
338	#95	—	2	1	no	—
339	#95	—	2	1	no	—
340	#95	—	2	1	no	—
341	#95	—	2	1	no	—
342	C₂×C₁₃	—	16	2	no	—
343	C₂×C₁₃	#2818	1	1	yes	characteristic
344	C₂×C₁₃	#3210	1	1	yes	characteristic
345	C₂×C₁₃	#3211	1	1	yes	characteristic
346	C₂×C₁₃	#3212	1	1	yes	characteristic
347	C₂×C₁₃	#3215	1	1	yes	characteristic
348	C₂×C₁₃	#3216	1	1	yes	characteristic
349	C₂×C₁₃	#3219	1	1	yes	characteristic
350	C₂⁴	—	2	2	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	4	2	no	—
368	C₂×D₄	—	4	2	no	—
369	C₂×D₄	—	4	2	no	—
370	C₂×D₄	—	4	2	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
384	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
385	Q₁₆	—	4	8	no	—
386	SD₁₆	—	4	8	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	4	2	no	—
398	C₄⋊C₄	—	4	2	no	—
399	C₄⋊C₄	—	4	2	no	—
400	C₄⋊C₄	—	4	2	no	—
401	C₄⋊C₄	—	4	2	no	—
402	C₂²⋊C₄	—	4	4	no	—
403	C₂²⋊C₄	—	4	4	no	—
404	C₂²⋊C₄	—	4	4	no	—
405	C₂²⋊C₄	—	4	4	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	2	1	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	4	1	no	—
413	C₄²	—	4	1	no	—
414	C₁₃	#32799	1	1	yes	characteristic, direct product factor, Sylow
415	C₂³	—	4	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
423	Q₈	—	4	2	no	—
424	Q₈	—	4	2	no	—
425	Q₈	—	4	2	no	—
426	Q₈	—	4	2	no	—
427	Q₈	—	4	2	no	—
428	Q₈	—	4	2	no	—
429	D₄	—	4	2	no	—
430	D₄	—	4	2	no	—
431	D₄	—	4	2	no	—
432	D₄	—	4	2	no	—
433	D₄	—	8	4	no	—
434	D₄	—	8	4	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	C₁₃×#135	1	2	yes	—
467	C₂×C₄	C₁₃×#137	1	2	yes	—
468	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
469	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
470	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
471	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
472	C₈	—	4	2	no	—
473	C₈	—	4	2	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	—	8	2	no	—
479	C₂²	—	8	2	no	—
480	C₂²	—	8	2	no	—
481	C₂²	C₁₃×#535	1	1	yes	characteristic
482	C₂²	C₁₃×#535	1	1	yes	characteristic
483	C₂²	C₁₃×#535	1	1	yes	characteristic
484	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
485	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
486	C₂²	C₁₃×#575	1	1	yes	characteristic
487	C₂²	C₁₃×#575	1	1	yes	characteristic
488	C₄	—	2	2	no	—
489	C₄	—	2	2	no	—
490	C₄	—	4	1	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	1	no	—
493	C₄	—	4	1	no	—
494	C₄	—	8	2	no	—
495	C₄	—	8	1	no	—
496	C₄	—	8	1	no	—
497	C₄	—	8	1	no	—
498	C₄	—	8	1	no	—
499	C₄	C₁₃×#560	1	2	yes	—
500	C₄	C₁₃×#560	1	2	yes	—
501	C₂	—	16	2	no	—
502	C₂	C₁₃×#2818	1	1	yes	characteristic
503	C₂	C₁₃×#3210	1	1	yes	characteristic
504	C₂	C₁₃×#3211	1	1	yes	characteristic
505	C₂	C₁₃×#3212	1	1	yes	characteristic
506	C₂	C₁₃×#3215	1	1	yes	characteristic
507	C₂	C₁₃×#3216	1	1	yes	characteristic
508	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×#2863	C₂	semidirect
3. C₁₃×#2043	C₂	semidirect
4. C₁₃×#2042	C₂	semidirect
5. C₁₃×#2042	C₂	semidirect
7. C₁₃×#2016	C₂	semidirect
8. C₁₃×#2015	C₂	semidirect
9. C₁₃×#2015	C₂	semidirect
11. C₁₃×#1839	C₂	semidirect
96. #32799	C₁₃	direct (N × H)
161. #2863	C₂×C₁₃	semidirect
163. #2043	C₂×C₁₃	semidirect
164. #2042	C₂×C₁₃	semidirect
165. #2042	C₂×C₁₃	semidirect
167. #2016	C₂×C₁₃	semidirect
168. #2015	C₂×C₁₃	semidirect
169. #2015	C₂×C₁₃	semidirect
171. #1839	C₂×C₁₃	semidirect
414. C₁₃	#32799	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×#2863	2
C₁₃×#2858	2
C₁₃×#2043	2
C₁₃×#2042	2
C₁₃×#2041	2
C₁₃×#2016	2
C₁₃×#2015	2
C₁₃×#2014	2
C₁₃×#1839	2
#32799	13

Subgroups — C13×#32799 #15719138

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32799 #15719138