Subgroups — C₁₃×#62595 #15748934

Order 3328.

1966 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3517	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3359	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3358	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3332	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3330	C₂	1	6	yes	maximal, complemented
7	C₁₃×#3239	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3214	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3171	C₂	1	3	yes	maximal, complemented
10	C₁₃×#3141	C₂	1	3	yes	maximal, complemented
11	C₁₃×#2971	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×2₋¹⁺⁴	—	2	1	no	—
13	C₁₃×#557	C₂²	1	1	yes	characteristic
14	C₁₃×#553	—	2	3	no	—
15	C₁₃×#550	—	2	1	no	—
16	C₁₃×#550	C₂²	1	3	yes	—
17	C₁₃×#550	C₂²	1	1	yes	characteristic
18	D₄×Q₈×C₁₃	—	2	1	no	—
19	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
20	C₁₃×#547	—	2	3	no	—
21	C₁₃×#547	C₂²	1	3	yes	—
22	C₁₃×#547	C₂²	1	6	yes	—
23	C₁₃×#540	—	2	3	no	—
24	C₁₃×#536	—	2	3	no	—
25	C₁₃×#532	C₂²	1	3	yes	—
26	C₁₃×#532	C₂²	1	3	yes	—
27	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	—
28	C₁₃×#529	C₂²	1	3	yes	—
29	C₁₃×#520	—	2	1	no	—
30	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
31	C₁₃×#501	C₂²	1	3	yes	—
32	C₁₃×#496	C₂²	1	3	yes	—
33	C₁₃×#490	C₂²	1	1	yes	characteristic
34	C₁₃×#489	C₂²	1	3	yes	—
35	C₁₃×#489	C₂²	1	6	yes	—
36	C₁₃×#487	C₂²	1	6	yes	—
37	C₁₃×#486	C₂²	1	6	yes	—
38	C₁₃×#484	C₂²	1	6	yes	—
39	C₁₃×#481	C₂²	1	6	yes	—
40	C₁₃×#475	C₂²	1	6	yes	—
41	C₁₃×#474	C₂²	1	6	yes	—
42	C₁₃×#469	C₂²	1	6	yes	—
43	C₁₃×#468	C₂²	1	6	yes	—
44	C₁₃×#461	C₂²	1	6	yes	—
45	C₁₃×#459	C₂²	1	6	yes	—
46	C₁₃×#449	C₂²	1	12	yes	—
47	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
48	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	—
49	C₄×C₁₃×D₈	C₂²	1	6	yes	—
50	C₁₃×#436	C₂²	1	6	yes	—
51	C₁₃×#432	C₂²	1	3	yes	—
52	C₁₃×#417	C₂²	1	12	yes	—
53	C₄×C₁₃×M₁₆	C₂²	1	3	yes	—
54	C₁₃×2₋¹⁺⁴	—	4	8	no	—
55	C₂×C₁₃×#41	—	2	1	no	—
56	C₂×C₁₃×#41	—	2	6	no	—
57	C₂×C₁₃×#41	—	2	3	no	—
58	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
59	C₂×C₁₃×#41	C₂³	1	6	yes	—
60	C₂²×Q₈×C₁₃	—	2	2	no	—
61	C₂²×Q₈×C₁₃	—	2	3	no	—
62	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
63	C₂×C₁₃×D₈	C₂³	1	6	yes	—
64	C₂×C₁₃×M₁₆	C₂³	1	6	yes	—
65	C₁₃×C₄⋊Q₈	—	2	3	no	—
66	C₁₃×C₄⋊Q₈	—	2	3	no	—
67	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
68	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
69	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
70	C₁₃×#127	—	2	3	no	—
71	C₁₃×#127	C₂³	1	3	yes	—
72	C₁₃×#127	C₂³	1	1	yes	characteristic
73	C₁₃×#126	—	2	3	no	—
74	C₁₃×#125	—	2	3	no	—
75	C₁₃×#125	C₂³	1	1	yes	characteristic
76	C₁₃×#124	—	2	3	no	—
77	C₁₃×#124	C₂³	1	3	yes	—
78	C₁₃×#123	—	2	3	no	—
79	C₁₃×#123	—	2	12	no	—
80	C₁₃×#123	—	2	6	no	—
81	C₁₃×C₂²⋊Q₈	—	2	6	no	—
82	C₁₃×C₂²⋊Q₈	—	2	6	no	—
83	C₁₃×C₂²⋊Q₈	C₂³	1	3	yes	—
84	C₁₃×#121	—	2	3	no	—
85	C₁₃×#121	—	2	3	no	—
86	C₁₃×#121	—	2	3	no	—
87	C₁₃×#121	—	2	3	no	—
88	C₁₃×#121	—	2	3	no	—
89	C₁₃×#121	—	2	6	no	—
90	C₁₃×#121	C₂³	1	6	yes	—
91	C₁₃×#121	C₂³	1	3	yes	—
92	C₄×Q₈×C₁₃	—	2	1	no	—
93	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
94	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
95	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₁₃	—	2	3	no	—
97	C₄×D₄×C₁₃	—	2	3	no	—
98	C₄×D₄×C₁₃	—	2	3	no	—
99	C₄×D₄×C₁₃	—	2	3	no	—
100	C₄×D₄×C₁₃	—	2	3	no	—
101	C₄×D₄×C₁₃	D₄	1	3	yes	—
102	C₄×D₄×C₁₃	C₂³	1	3	yes	—
103	C₄×D₄×C₁₃	C₂³	1	6	yes	—
104	C₄×D₄×C₁₃	C₂³	1	3	yes	—
105	C₁₃×#117	—	2	3	no	—
106	C₁₃×#117	D₄	1	3	yes	—
107	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
110	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
111	C₁₃×#107	C₂³	1	6	yes	—
112	C₁₃×#106	C₂³	1	6	yes	—
113	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
114	C₁₃×#103	C₂³	1	6	yes	—
115	C₁₃×#103	C₂³	1	12	yes	—
116	C₁₃×#102	C₂³	1	6	yes	—
117	C₁₃×#102	C₂³	1	12	yes	—
118	C₁₃×#102	C₂³	1	2	yes	—
119	C₁₃×#102	C₂³	1	2	yes	—
120	C₁₃×C₂²⋊C₈	C₂³	1	6	yes	—
121	C₁₃×#97	C₂³	1	1	yes	characteristic
122	C₁₃×#97	C₂³	1	3	yes	—
123	C₄×C₈×C₁₃	C₂³	1	6	yes	—
124	#62595	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₁₃×#41	—	2	4	no	—
126	C₁₃×#41	—	4	12	no	—
127	C₁₃×#41	—	4	12	no	—
128	C₁₃×#41	—	4	24	no	—
129	C₁₃×#41	—	4	4	no	—
130	C₂×Q₈×C₁₃	—	2	6	no	—
131	C₂×Q₈×C₁₃	—	2	3	no	—
132	C₂×Q₈×C₁₃	—	4	12	no	—
133	C₂×Q₈×C₁₃	—	4	8	no	—
134	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
136	C₂×D₄×C₁₃	—	2	6	no	—
137	C₂×D₄×C₁₃	—	2	3	no	—
138	C₂×D₄×C₁₃	—	2	6	no	—
139	C₂×D₄×C₁₃	—	2	1	no	—
140	C₂×D₄×C₁₃	—	2	3	no	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	—	2	3	no	—
143	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
144	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
145	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₁₃	—	2	6	no	—
147	C₂²×C₄×C₁₃	—	2	3	no	—
148	C₂²×C₄×C₁₃	—	2	6	no	—
149	C₂²×C₄×C₁₃	—	2	6	no	—
150	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
151	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
153	C₁₃×SD₁₆	—	4	6	no	—
154	C₁₃×D₈	—	4	6	no	—
155	C₁₃×M₁₆	—	4	6	no	—
156	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
157	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
158	C₁₃×C₄⋊C₄	—	2	3	no	—
159	C₁₃×C₄⋊C₄	—	2	3	no	—
160	C₁₃×C₄⋊C₄	—	2	3	no	—
161	C₁₃×C₄⋊C₄	—	2	6	no	—
162	C₁₃×C₄⋊C₄	—	2	6	no	—
163	C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₁₃×C₄⋊C₄	—	2	3	no	—
166	C₁₃×C₄⋊C₄	—	2	3	no	—
167	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
168	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
169	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
170	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
171	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
172	C₁₃×C₂²⋊C₄	—	2	3	no	—
173	C₁₃×C₂²⋊C₄	—	2	3	no	—
174	C₁₃×C₂²⋊C₄	—	2	3	no	—
175	C₁₃×C₂²⋊C₄	—	2	3	no	—
176	C₁₃×C₂²⋊C₄	—	2	6	no	—
177	C₁₃×C₂²⋊C₄	—	2	3	no	—
178	C₁₃×C₂²⋊C₄	—	2	6	no	—
179	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
180	C₄²×C₁₃	—	2	3	no	—
181	C₄²×C₁₃	C₂×D₄	1	3	yes	—
182	C₄²×C₁₃	C₂×D₄	1	3	yes	—
183	C₄²×C₁₃	C₂⁴	1	3	yes	—
184	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
185	#3517	C₂×C₁₃	1	1	yes	characteristic, complemented
186	#3499	C₂×C₁₃	1	1	yes	characteristic, complemented
187	#3359	C₂×C₁₃	1	2	yes	complemented
188	#3358	C₂×C₁₃	1	2	yes	complemented
189	#3332	C₂×C₁₃	1	6	yes	complemented
190	#3330	C₂×C₁₃	1	6	yes	complemented
191	#3239	C₂×C₁₃	1	3	yes	complemented
192	#3214	C₂×C₁₃	1	3	yes	complemented
193	#3171	C₂×C₁₃	1	3	yes	complemented
194	#3141	C₂×C₁₃	1	3	yes	complemented
195	#2971	C₂×C₁₃	1	1	yes	characteristic, complemented
196	C₂³×C₁₃	—	2	2	no	—
197	C₂³×C₁₃	—	2	3	no	—
198	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
199	Q₈×C₁₃	—	2	6	no	—
200	Q₈×C₁₃	—	4	6	no	—
201	Q₈×C₁₃	—	4	12	no	—
202	Q₈×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
203	D₄×C₁₃	—	2	6	no	—
204	D₄×C₁₃	—	2	2	no	—
205	D₄×C₁₃	—	2	6	no	—
206	D₄×C₁₃	—	2	2	no	—
207	D₄×C₁₃	—	4	2	no	—
208	D₄×C₁₃	—	4	2	no	—
209	D₄×C₁₃	—	4	12	no	—
210	D₄×C₁₃	—	4	6	no	—
211	D₄×C₁₃	—	8	3	no	—
212	D₄×C₁₃	—	8	3	no	—
213	D₄×C₁₃	—	8	6	no	—
214	C₂×C₄×C₁₃	—	2	6	no	—
215	C₂×C₄×C₁₃	—	2	6	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	3	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	2	6	no	—
220	C₂×C₄×C₁₃	—	4	3	no	—
221	C₂×C₄×C₁₃	—	4	12	no	—
222	C₂×C₄×C₁₃	—	4	12	no	—
223	C₂×C₄×C₁₃	—	4	6	no	—
224	C₂×C₄×C₁₃	—	8	6	no	—
225	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
230	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
231	C₈×C₁₃	—	2	2	no	—
232	C₈×C₁₃	—	2	6	no	—
233	C₂×2₋¹⁺⁴	—	2	1	no	—
234	#557	C₂²×C₁₃	1	1	yes	characteristic
235	#553	—	2	3	no	—
236	#550	—	2	1	no	—
237	#550	C₂²×C₁₃	1	3	yes	—
238	#550	C₂²×C₁₃	1	1	yes	characteristic
239	D₄×Q₈	—	2	1	no	—
240	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
241	#547	—	2	3	no	—
242	#547	C₂²×C₁₃	1	3	yes	—
243	#547	C₂²×C₁₃	1	6	yes	—
244	#540	—	2	3	no	—
245	#536	—	2	3	no	—
246	#532	C₂²×C₁₃	1	3	yes	—
247	#532	C₂²×C₁₃	1	3	yes	—
248	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	—
249	#529	C₂²×C₁₃	1	3	yes	—
250	#520	—	2	1	no	—
251	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
252	#501	C₂²×C₁₃	1	3	yes	—
253	#496	C₂²×C₁₃	1	3	yes	—
254	#490	C₂²×C₁₃	1	1	yes	characteristic
255	#489	C₂²×C₁₃	1	3	yes	—
256	#489	C₂²×C₁₃	1	6	yes	—
257	#487	C₂²×C₁₃	1	6	yes	—
258	#486	C₂²×C₁₃	1	6	yes	—
259	#484	C₂²×C₁₃	1	6	yes	—
260	#481	C₂²×C₁₃	1	6	yes	—
261	#475	C₂²×C₁₃	1	6	yes	—
262	#474	C₂²×C₁₃	1	6	yes	—
263	#469	C₂²×C₁₃	1	6	yes	—
264	#468	C₂²×C₁₃	1	6	yes	—
265	#461	C₂²×C₁₃	1	6	yes	—
266	#459	C₂²×C₁₃	1	6	yes	—
267	#449	C₂²×C₁₃	1	12	yes	—
268	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
269	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	—
270	C₄×D₈	C₂²×C₁₃	1	6	yes	—
271	#436	C₂²×C₁₃	1	6	yes	—
272	#432	C₂²×C₁₃	1	3	yes	—
273	#417	C₂²×C₁₃	1	12	yes	—
274	C₄×M₁₆	C₂²×C₁₃	1	3	yes	—
275	C₂²×C₁₃	—	2	3	no	—
276	C₂²×C₁₃	—	2	3	no	—
277	C₂²×C₁₃	—	2	3	no	—
278	C₂²×C₁₃	—	4	2	no	—
279	C₂²×C₁₃	—	4	3	no	—
280	C₂²×C₁₃	—	4	3	no	—
281	C₂²×C₁₃	—	4	2	no	—
282	C₂²×C₁₃	—	4	2	no	—
283	C₂²×C₁₃	—	4	3	no	—
284	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
285	C₄×C₁₃	—	2	1	no	—
286	C₄×C₁₃	—	2	3	no	—
287	C₄×C₁₃	—	2	3	no	—
288	C₄×C₁₃	—	2	1	no	—
289	C₄×C₁₃	—	4	1	no	—
290	C₄×C₁₃	—	4	3	no	—
291	C₄×C₁₃	—	4	1	no	—
292	C₄×C₁₃	—	4	6	no	—
293	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	6	yes	—
294	C₄×C₁₃	#585	1	2	yes	—
295	2₋¹⁺⁴	—	4	8	no	—
296	C₂×#41	—	2	1	no	—
297	C₂×#41	—	2	6	no	—
298	C₂×#41	—	2	3	no	—
299	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
300	C₂×#41	C₂³×C₁₃	1	6	yes	—
301	C₂²×Q₈	—	2	2	no	—
302	C₂²×Q₈	—	2	3	no	—
303	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
304	C₂×D₈	C₂³×C₁₃	1	6	yes	—
305	C₂×M₁₆	C₂³×C₁₃	1	6	yes	—
306	C₄⋊Q₈	—	2	3	no	—
307	C₄⋊Q₈	—	2	3	no	—
308	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
309	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
310	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
311	#127	—	2	3	no	—
312	#127	C₂³×C₁₃	1	1	yes	characteristic
313	#127	C₂³×C₁₃	1	3	yes	—
314	#126	—	2	3	no	—
315	#125	—	2	3	no	—
316	#125	C₂³×C₁₃	1	1	yes	characteristic
317	#124	—	2	3	no	—
318	#124	C₂³×C₁₃	1	3	yes	—
319	#123	—	2	3	no	—
320	#123	—	2	12	no	—
321	#123	—	2	6	no	—
322	C₂²⋊Q₈	—	2	6	no	—
323	C₂²⋊Q₈	—	2	6	no	—
324	C₂²⋊Q₈	C₂³×C₁₃	1	3	yes	—
325	#121	—	2	3	no	—
326	#121	—	2	3	no	—
327	#121	—	2	3	no	—
328	#121	—	2	3	no	—
329	#121	—	2	3	no	—
330	#121	—	2	6	no	—
331	#121	C₂³×C₁₃	1	3	yes	—
332	#121	C₂³×C₁₃	1	6	yes	—
333	C₄×Q₈	—	2	1	no	—
334	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
335	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
336	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
337	C₄×D₄	—	2	3	no	—
338	C₄×D₄	—	2	3	no	—
339	C₄×D₄	—	2	3	no	—
340	C₄×D₄	—	2	3	no	—
341	C₄×D₄	—	2	3	no	—
342	C₄×D₄	D₄×C₁₃	1	3	yes	—
343	C₄×D₄	C₂³×C₁₃	1	3	yes	—
344	C₄×D₄	C₂³×C₁₃	1	6	yes	—
345	C₄×D₄	C₂³×C₁₃	1	3	yes	—
346	#117	—	2	3	no	—
347	#117	D₄×C₁₃	1	3	yes	—
348	C₂×C₄⋊C₄	—	2	3	no	—
349	C₂×C₄⋊C₄	—	2	3	no	—
350	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
351	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
352	#107	C₂³×C₁₃	1	6	yes	—
353	#106	C₂³×C₁₃	1	6	yes	—
354	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
355	#103	C₂³×C₁₃	1	6	yes	—
356	#103	C₂³×C₁₃	1	12	yes	—
357	#102	C₂³×C₁₃	1	6	yes	—
358	#102	C₂³×C₁₃	1	12	yes	—
359	#102	C₂³×C₁₃	1	2	yes	—
360	#102	C₂³×C₁₃	1	2	yes	—
361	C₂²⋊C₈	C₂³×C₁₃	1	6	yes	—
362	#97	C₂³×C₁₃	1	1	yes	characteristic
363	#97	C₂³×C₁₃	1	3	yes	—
364	C₄×C₈	C₂³×C₁₃	1	6	yes	—
365	C₂×C₁₃	—	4	3	no	—
366	C₂×C₁₃	—	8	2	no	—
367	C₂×C₁₃	—	8	3	no	—
368	C₂×C₁₃	#3500	1	1	yes	characteristic
369	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
370	C₂×C₁₃	#3586	1	1	yes	characteristic
371	#41	—	2	4	no	—
372	#41	—	4	12	no	—
373	#41	—	4	12	no	—
374	#41	—	4	24	no	—
375	#41	—	4	4	no	—
376	C₂×Q₈	—	2	6	no	—
377	C₂×Q₈	—	2	3	no	—
378	C₂×Q₈	—	4	12	no	—
379	C₂×Q₈	—	4	8	no	—
380	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
381	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
382	C₂×D₄	—	2	6	no	—
383	C₂×D₄	—	2	3	no	—
384	C₂×D₄	—	2	6	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	3	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	3	no	—
389	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
390	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
391	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
392	C₂²×C₄	—	2	6	no	—
393	C₂²×C₄	—	2	3	no	—
394	C₂²×C₄	—	2	6	no	—
395	C₂²×C₄	—	2	6	no	—
396	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
397	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
398	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
399	SD₁₆	—	4	6	no	—
400	D₈	—	4	6	no	—
401	M₁₆	—	4	6	no	—
402	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
403	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
404	C₄⋊C₄	—	2	3	no	—
405	C₄⋊C₄	—	2	3	no	—
406	C₄⋊C₄	—	2	3	no	—
407	C₄⋊C₄	—	2	6	no	—
408	C₄⋊C₄	—	2	6	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	3	no	—
412	C₄⋊C₄	—	2	3	no	—
413	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
414	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
415	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
416	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
417	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
418	C₂²⋊C₄	—	2	3	no	—
419	C₂²⋊C₄	—	2	3	no	—
420	C₂²⋊C₄	—	2	3	no	—
421	C₂²⋊C₄	—	2	3	no	—
422	C₂²⋊C₄	—	2	6	no	—
423	C₂²⋊C₄	—	2	3	no	—
424	C₂²⋊C₄	—	2	6	no	—
425	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
426	C₄²	—	2	3	no	—
427	C₄²	C₂×D₄×C₁₃	1	3	yes	—
428	C₄²	C₂×D₄×C₁₃	1	3	yes	—
429	C₄²	C₂⁴×C₁₃	1	3	yes	—
430	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
431	C₁₃	#62595	1	1	yes	characteristic, direct product factor, Sylow
432	C₂³	—	2	2	no	—
433	C₂³	—	2	3	no	—
434	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
435	Q₈	—	2	6	no	—
436	Q₈	—	4	6	no	—
437	Q₈	—	4	12	no	—
438	Q₈	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
439	D₄	—	2	6	no	—
440	D₄	—	2	2	no	—
441	D₄	—	2	6	no	—
442	D₄	—	2	2	no	—
443	D₄	—	4	2	no	—
444	D₄	—	4	2	no	—
445	D₄	—	4	12	no	—
446	D₄	—	4	6	no	—
447	D₄	—	8	3	no	—
448	D₄	—	8	3	no	—
449	D₄	—	8	6	no	—
450	C₂×C₄	—	2	6	no	—
451	C₂×C₄	—	2	6	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	3	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	6	no	—
456	C₂×C₄	—	4	3	no	—
457	C₂×C₄	—	4	12	no	—
458	C₂×C₄	—	4	12	no	—
459	C₂×C₄	—	4	6	no	—
460	C₂×C₄	—	8	6	no	—
461	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
464	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
465	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
466	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	2	6	no	—
469	C₂²	—	2	3	no	—
470	C₂²	—	2	3	no	—
471	C₂²	—	2	3	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	3	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	3	no	—
476	C₂²	—	4	3	no	—
477	C₂²	—	4	2	no	—
478	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	3	no	—
482	C₄	—	2	3	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	6	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	3	no	—
487	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	6	yes	—
488	C₄	C₁₃×#585	1	2	yes	—
489	C₂	—	4	3	no	—
490	C₂	—	8	2	no	—
491	C₂	—	8	3	no	—
492	C₂	C₁₃×#3500	1	1	yes	characteristic
493	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
494	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3517	C₂	semidirect
2. C₁₃×#3499	C₂	semidirect
3. C₁₃×#3359	C₂	semidirect
4. C₁₃×#3358	C₂	semidirect
5. C₁₃×#3332	C₂	semidirect
6. C₁₃×#3330	C₂	semidirect
7. C₁₃×#3239	C₂	semidirect
8. C₁₃×#3214	C₂	semidirect
9. C₁₃×#3171	C₂	semidirect
10. C₁₃×#3141	C₂	semidirect
11. C₁₃×#2971	C₂	semidirect
124. #62595	C₁₃	direct (N × H)
185. #3517	C₂×C₁₃	semidirect
186. #3499	C₂×C₁₃	semidirect
187. #3359	C₂×C₁₃	semidirect
188. #3358	C₂×C₁₃	semidirect
189. #3332	C₂×C₁₃	semidirect
190. #3330	C₂×C₁₃	semidirect
191. #3239	C₂×C₁₃	semidirect
192. #3214	C₂×C₁₃	semidirect
193. #3171	C₂×C₁₃	semidirect
194. #3141	C₂×C₁₃	semidirect
195. #2971	C₂×C₁₃	semidirect
431. C₁₃	#62595	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×#3517	2
C₁₃×#3499	2
C₁₃×#3359	2
C₁₃×#3358	2
C₁₃×#3332	2
C₁₃×#3330	2
C₁₃×#3239	2
C₁₃×#3214	2
C₁₃×#3171	2
C₁₃×#3141	2
C₁₃×#2971	2
#62595	13

Subgroups — C13×#62595 #15748934

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62595 #15748934