Subgroups — C₁₃×#61907 #15748246

Order 3328.

2092 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×#3522	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3399	C₂	1	6	yes	maximal, complemented
4	C₁₃×#3391	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3366	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3362	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3217	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3205	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3109	C₂	1	3	yes	maximal, complemented
10	C₁₃×#3105	C₂	1	3	yes	maximal, complemented
11	C₁₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	—	2	1	no	—
13	C₁₃×#559	C₂²	1	3	yes	complemented
14	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
15	C₁₃×#554	C₂²	1	3	yes	complemented
16	C₁₃×#550	—	2	1	no	—
17	C₁₃×#550	—	2	3	no	—
18	C₁₃×#550	C₂²	1	2	yes	—
19	C₁₃×#550	C₂²	1	6	yes	—
20	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
21	C₁₃×#548	—	2	1	no	—
22	C₁₃×#547	—	2	3	no	—
23	C₁₃×#542	—	2	3	no	—
24	C₁₃×#532	C₂²	1	3	yes	—
25	C₂×C₁₃×#127	C₂²	1	3	yes	—
26	C₁₃×#529	C₂²	1	3	yes	—
27	C₂×C₁₃×#121	—	2	3	no	—
28	C₁₃×#520	—	2	1	no	—
29	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
31	C₁₃×#496	C₂²	1	6	yes	complemented
32	C₁₃×#493	C₂²	1	6	yes	complemented
33	C₁₃×#490	C₂²	1	6	yes	complemented
34	C₁₃×#486	C₂²	1	6	yes	complemented
35	C₁₃×#484	C₂²	1	1	yes	characteristic
36	C₁₃×#481	C₂²	1	3	yes	—
37	C₁₃×#478	C₂²	1	6	yes	complemented
38	C₁₃×#476	C₂²	1	6	yes	complemented
39	C₁₃×#463	C₂²	1	6	yes	complemented
40	C₁₃×#460	C₂²	1	6	yes	complemented
41	C₁₃×#459	C₂²	1	6	yes	complemented
42	C₁₃×#459	C₂²	1	6	yes	complemented
43	C₁₃×#459	C₂²	1	12	yes	complemented
44	C₁₃×#450	C₂²	1	3	yes	—
45	C₁₃×#447	C₂²	1	3	yes	—
46	C₁₃×#447	C₂²	1	6	yes	—
47	C₁₃×#446	C₂²	1	6	yes	complemented
48	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
49	C₁₃×#442	C₂²	1	12	yes	complemented
50	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	complemented
51	C₄×C₁₃×D₈	C₂²	1	6	yes	complemented
52	C₁₃×#432	C₂²	1	3	yes	—
53	C₁₃×#431	C₂²	1	3	yes	—
54	C₂×C₁₃×#41	—	2	1	no	—
55	C₂×C₁₃×#41	—	2	6	no	—
56	C₂×C₁₃×#41	—	2	2	no	—
57	C₂×C₁₃×#41	—	2	3	no	—
58	C₂×C₁₃×#41	—	4	8	no	—
59	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
60	C₂²×D₄×C₁₃	—	2	3	no	—
61	C₂²×D₄×C₁₃	—	2	3	no	—
62	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
63	C₂³×C₄×C₁₃	—	2	3	no	—
64	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
65	C₂×C₁₃×D₈	C₂³	1	6	yes	—
66	C₂×C₁₃×D₈	C₂³	1	12	yes	—
67	C₁₃×C₄⋊Q₈	—	2	3	no	—
68	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
69	C₁₃×#127	—	2	3	no	—
70	C₁₃×#127	—	2	3	no	—
71	C₁₃×#127	C₂³	1	6	yes	—
72	C₁₃×#127	C₂³	1	3	yes	—
73	C₁₃×#127	C₂³	1	6	yes	—
74	C₁₃×#126	—	2	3	no	—
75	C₁₃×#125	C₂³	1	3	yes	—
76	C₁₃×#124	—	2	3	no	—
77	C₁₃×#124	—	2	3	no	—
78	C₁₃×#124	C₂³	1	3	yes	—
79	C₁₃×#123	—	2	3	no	—
80	C₁₃×#123	—	2	6	no	—
81	C₁₃×C₂²⋊Q₈	—	2	3	no	—
82	C₁₃×C₂²⋊Q₈	—	2	6	no	—
83	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₃×#121	—	2	3	no	—
85	C₁₃×#121	—	2	6	no	—
86	C₁₃×#121	—	2	6	no	—
87	C₁₃×#121	—	2	12	no	—
88	C₁₃×#121	—	2	3	no	—
89	C₁₃×#121	C₂³	1	3	yes	—
90	C₄×Q₈×C₁₃	—	2	1	no	—
91	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
92	C₄×Q₈×C₁₃	D₄	1	3	yes	—
93	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
94	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
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	C₂³	1	3	yes	—
102	C₄×D₄×C₁₃	C₂³	1	6	yes	—
103	C₄×D₄×C₁₃	C₂³	1	6	yes	—
104	C₄×D₄×C₁₃	C₂³	1	6	yes	—
105	C₁₃×#117	—	2	3	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
107	C₂×C₁₃×C₄⋊C₄	D₄	1	3	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
110	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
111	C₁₃×#107	C₂³	1	2	yes	—
112	C₁₃×#106	C₂³	1	6	yes	—
113	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
114	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
115	C₁₃×#103	C₂³	1	2	yes	—
116	C₁₃×#102	C₂³	1	6	yes	—
117	C₁₃×#102	C₂³	1	6	yes	—
118	C₁₃×#102	C₂³	1	6	yes	—
119	C₁₃×#102	C₂³	1	12	yes	—
120	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₃×C₂²⋊C₈	C₂³	1	3	yes	—
122	C₁₃×#97	C₂³	1	6	yes	—
123	C₄×C₈×C₁₃	C₂³	1	6	yes	—
124	#61907	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂⁴×C₁₃	—	2	3	no	—
126	C₁₃×#41	—	4	24	no	—
127	C₁₃×#41	—	4	4	no	—
128	C₁₃×#41	—	4	8	no	—
129	C₁₃×#41	—	8	6	no	—
130	C₂×Q₈×C₁₃	—	2	4	no	—
131	C₂×Q₈×C₁₃	—	2	3	no	—
132	C₂×Q₈×C₁₃	C₂×D₄	1	3	yes	—
133	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₂×D₄×C₁₃	—	2	3	no	—
136	C₂×D₄×C₁₃	—	2	3	no	—
137	C₂×D₄×C₁₃	—	2	3	no	—
138	C₂×D₄×C₁₃	—	2	6	no	—
139	C₂×D₄×C₁₃	—	2	6	no	—
140	C₂×D₄×C₁₃	—	2	6	no	—
141	C₂×D₄×C₁₃	—	2	6	no	—
142	C₂×D₄×C₁₃	—	2	3	no	—
143	C₂×D₄×C₁₃	—	4	6	no	—
144	C₂×D₄×C₁₃	—	4	12	no	—
145	C₂×D₄×C₁₃	—	8	6	no	—
146	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
147	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	2	3	no	—
150	C₂²×C₄×C₁₃	—	2	6	no	—
151	C₂²×C₄×C₁₃	—	2	6	no	—
152	C₂²×C₄×C₁₃	—	2	6	no	—
153	C₂²×C₄×C₁₃	—	4	12	no	—
154	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
155	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
157	C₁₃×SD₁₆	—	4	6	no	—
158	C₁₃×D₈	—	4	6	no	—
159	C₁₃×D₈	—	4	12	no	—
160	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
161	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
162	C₁₃×C₄⋊C₄	—	2	3	no	—
163	C₁₃×C₄⋊C₄	—	2	3	no	—
164	C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₁₃×C₄⋊C₄	—	2	1	no	—
166	C₁₃×C₄⋊C₄	—	2	3	no	—
167	C₁₃×C₄⋊C₄	—	2	3	no	—
168	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
169	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
170	C₁₃×C₄⋊C₄	C₂×D₄	1	6	yes	—
171	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
172	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
173	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
174	C₁₃×C₂²⋊C₄	—	2	1	no	—
175	C₁₃×C₂²⋊C₄	—	2	6	no	—
176	C₁₃×C₂²⋊C₄	—	2	6	no	—
177	C₁₃×C₂²⋊C₄	—	2	3	no	—
178	C₁₃×C₂²⋊C₄	—	2	3	no	—
179	C₁₃×C₂²⋊C₄	—	2	3	no	—
180	C₁₃×C₂²⋊C₄	—	2	3	no	—
181	C₁₃×C₂²⋊C₄	—	2	6	no	—
182	C₄²×C₁₃	—	2	3	no	—
183	C₄²×C₁₃	C₂×D₄	1	3	yes	—
184	C₄²×C₁₃	C₂×D₄	1	3	yes	—
185	C₄²×C₁₃	C₂⁴	1	3	yes	—
186	C₄²×C₁₃	C₂⁴	1	3	yes	—
187	#3522	C₂×C₁₃	1	1	yes	characteristic, complemented
188	C₂×#550	C₂×C₁₃	1	1	yes	characteristic, complemented
189	#3399	C₂×C₁₃	1	6	yes	complemented
190	#3391	C₂×C₁₃	1	2	yes	complemented
191	#3366	C₂×C₁₃	1	6	yes	complemented
192	#3362	C₂×C₁₃	1	2	yes	complemented
193	#3217	C₂×C₁₃	1	3	yes	complemented
194	#3205	C₂×C₁₃	1	3	yes	complemented
195	#3109	C₂×C₁₃	1	3	yes	complemented
196	#3105	C₂×C₁₃	1	3	yes	complemented
197	#2984	C₂×C₁₃	1	1	yes	characteristic, complemented
198	C₂³×C₁₃	—	2	3	no	—
199	C₂³×C₁₃	—	2	6	no	—
200	C₂³×C₁₃	—	4	6	no	—
201	C₂³×C₁₃	—	4	6	no	—
202	C₂³×C₁₃	—	4	6	no	—
203	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₁₃	—	2	6	no	—
205	Q₈×C₁₃	—	2	2	no	—
206	Q₈×C₁₃	—	8	3	no	—
207	Q₈×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
208	D₄×C₁₃	—	2	6	no	—
209	D₄×C₁₃	—	2	6	no	—
210	D₄×C₁₃	—	2	6	no	—
211	D₄×C₁₃	—	4	6	no	—
212	D₄×C₁₃	—	4	12	no	—
213	D₄×C₁₃	—	4	6	no	—
214	D₄×C₁₃	—	4	12	no	—
215	D₄×C₁₃	—	4	6	no	—
216	D₄×C₁₃	—	8	6	no	—
217	D₄×C₁₃	—	8	6	no	—
218	D₄×C₁₃	—	8	3	no	—
219	C₂×C₄×C₁₃	—	2	6	no	—
220	C₂×C₄×C₁₃	—	2	6	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	2	3	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	4	12	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	—	4	12	no	—
229	C₂×C₄×C₁₃	—	4	6	no	—
230	C₂×C₄×C₁₃	—	8	6	no	—
231	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
233	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
234	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
235	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
236	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
237	C₈×C₁₃	—	2	2	no	—
238	C₈×C₁₃	—	2	6	no	—
239	C₂²×#41	—	2	1	no	—
240	#559	C₂²×C₁₃	1	3	yes	complemented
241	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
242	#554	C₂²×C₁₃	1	3	yes	complemented
243	#550	—	2	1	no	—
244	#550	—	2	3	no	—
245	#550	C₂²×C₁₃	1	2	yes	—
246	#550	C₂²×C₁₃	1	6	yes	—
247	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
248	#548	—	2	1	no	—
249	#547	—	2	3	no	—
250	#542	—	2	3	no	—
251	#532	C₂²×C₁₃	1	3	yes	—
252	C₂×#127	C₂²×C₁₃	1	3	yes	—
253	#529	C₂²×C₁₃	1	3	yes	—
254	C₂×#121	—	2	3	no	—
255	#520	—	2	1	no	—
256	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
258	#496	C₂²×C₁₃	1	6	yes	complemented
259	#493	C₂²×C₁₃	1	6	yes	complemented
260	#490	C₂²×C₁₃	1	6	yes	complemented
261	#486	C₂²×C₁₃	1	6	yes	complemented
262	#484	C₂²×C₁₃	1	1	yes	characteristic
263	#481	C₂²×C₁₃	1	3	yes	—
264	#478	C₂²×C₁₃	1	6	yes	complemented
265	#476	C₂²×C₁₃	1	6	yes	complemented
266	#463	C₂²×C₁₃	1	6	yes	complemented
267	#460	C₂²×C₁₃	1	6	yes	complemented
268	#459	C₂²×C₁₃	1	6	yes	complemented
269	#459	C₂²×C₁₃	1	6	yes	complemented
270	#459	C₂²×C₁₃	1	12	yes	complemented
271	#450	C₂²×C₁₃	1	3	yes	—
272	#447	C₂²×C₁₃	1	3	yes	—
273	#447	C₂²×C₁₃	1	6	yes	—
274	#446	C₂²×C₁₃	1	6	yes	complemented
275	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
276	#442	C₂²×C₁₃	1	12	yes	complemented
277	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	complemented
278	C₄×D₈	C₂²×C₁₃	1	6	yes	complemented
279	#432	C₂²×C₁₃	1	3	yes	—
280	#431	C₂²×C₁₃	1	3	yes	—
281	C₂²×C₁₃	—	2	1	no	—
282	C₂²×C₁₃	—	2	1	no	—
283	C₂²×C₁₃	—	4	6	no	—
284	C₂²×C₁₃	—	4	3	no	—
285	C₂²×C₁₃	—	4	6	no	—
286	C₂²×C₁₃	—	4	3	no	—
287	C₂²×C₁₃	—	4	3	no	—
288	C₂²×C₁₃	—	4	6	no	—
289	C₂²×C₁₃	—	8	12	no	—
290	C₂²×C₁₃	#576	1	2	yes	—
291	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
292	C₄×C₁₃	—	2	1	no	—
293	C₄×C₁₃	—	2	3	no	—
294	C₄×C₁₃	—	2	3	no	—
295	C₄×C₁₃	—	2	3	no	—
296	C₄×C₁₃	—	4	1	no	—
297	C₄×C₁₃	—	4	1	no	—
298	C₄×C₁₃	—	4	2	no	—
299	C₄×C₁₃	—	4	3	no	—
300	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	6	yes	—
301	C₄×C₁₃	#585	1	2	yes	—
302	C₂×#41	—	2	1	no	—
303	C₂×#41	—	2	6	no	—
304	C₂×#41	—	2	2	no	—
305	C₂×#41	—	2	3	no	—
306	C₂×#41	—	4	8	no	—
307	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
308	C₂²×D₄	—	2	3	no	—
309	C₂²×D₄	—	2	3	no	—
310	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
311	C₂³×C₄	—	2	3	no	—
312	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
313	C₂×D₈	C₂³×C₁₃	1	6	yes	—
314	C₂×D₈	C₂³×C₁₃	1	12	yes	—
315	C₄⋊Q₈	—	2	3	no	—
316	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
317	#127	—	2	3	no	—
318	#127	—	2	3	no	—
319	#127	C₂³×C₁₃	1	6	yes	—
320	#127	C₂³×C₁₃	1	6	yes	—
321	#127	C₂³×C₁₃	1	3	yes	—
322	#126	—	2	3	no	—
323	#125	C₂³×C₁₃	1	3	yes	—
324	#124	—	2	3	no	—
325	#124	—	2	3	no	—
326	#124	C₂³×C₁₃	1	3	yes	—
327	#123	—	2	3	no	—
328	#123	—	2	6	no	—
329	C₂²⋊Q₈	—	2	3	no	—
330	C₂²⋊Q₈	—	2	6	no	—
331	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
332	#121	—	2	3	no	—
333	#121	—	2	6	no	—
334	#121	—	2	6	no	—
335	#121	—	2	12	no	—
336	#121	—	2	3	no	—
337	#121	C₂³×C₁₃	1	3	yes	—
338	C₄×Q₈	—	2	1	no	—
339	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
340	C₄×Q₈	D₄×C₁₃	1	3	yes	—
341	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
342	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
343	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
344	C₄×D₄	—	2	3	no	—
345	C₄×D₄	—	2	3	no	—
346	C₄×D₄	—	2	3	no	—
347	C₄×D₄	—	2	3	no	—
348	C₄×D₄	—	2	3	no	—
349	C₄×D₄	C₂³×C₁₃	1	6	yes	—
350	C₄×D₄	C₂³×C₁₃	1	6	yes	—
351	C₄×D₄	C₂³×C₁₃	1	3	yes	—
352	C₄×D₄	C₂³×C₁₃	1	6	yes	—
353	#117	—	2	3	no	—
354	C₂×C₄⋊C₄	—	2	3	no	—
355	C₂×C₄⋊C₄	D₄×C₁₃	1	3	yes	—
356	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
357	C₂×C₂²⋊C₄	—	2	3	no	—
358	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
359	#107	C₂³×C₁₃	1	2	yes	—
360	#106	C₂³×C₁₃	1	6	yes	—
361	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
362	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
363	#103	C₂³×C₁₃	1	2	yes	—
364	#102	C₂³×C₁₃	1	6	yes	—
365	#102	C₂³×C₁₃	1	6	yes	—
366	#102	C₂³×C₁₃	1	6	yes	—
367	#102	C₂³×C₁₃	1	12	yes	—
368	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
369	C₂²⋊C₈	C₂³×C₁₃	1	3	yes	—
370	#97	C₂³×C₁₃	1	6	yes	—
371	C₄×C₈	C₂³×C₁₃	1	6	yes	—
372	C₂×C₁₃	—	2	2	no	—
373	C₂×C₁₃	—	8	3	no	—
374	C₂×C₁₃	—	8	6	no	—
375	C₂×C₁₃	#3487	1	1	yes	characteristic
376	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
377	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
378	C₂⁴	—	2	3	no	—
379	#41	—	4	24	no	—
380	#41	—	4	8	no	—
381	#41	—	4	4	no	—
382	#41	—	8	6	no	—
383	C₂×Q₈	—	2	4	no	—
384	C₂×Q₈	—	2	3	no	—
385	C₂×Q₈	C₂×D₄×C₁₃	1	3	yes	—
386	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
387	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
388	C₂×D₄	—	2	3	no	—
389	C₂×D₄	—	2	3	no	—
390	C₂×D₄	—	2	3	no	—
391	C₂×D₄	—	2	6	no	—
392	C₂×D₄	—	2	6	no	—
393	C₂×D₄	—	2	6	no	—
394	C₂×D₄	—	2	6	no	—
395	C₂×D₄	—	2	3	no	—
396	C₂×D₄	—	4	6	no	—
397	C₂×D₄	—	4	12	no	—
398	C₂×D₄	—	8	6	no	—
399	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
400	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	3	no	—
403	C₂²×C₄	—	2	6	no	—
404	C₂²×C₄	—	2	6	no	—
405	C₂²×C₄	—	2	6	no	—
406	C₂²×C₄	—	4	12	no	—
407	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
408	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
409	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
410	SD₁₆	—	4	6	no	—
411	D₈	—	4	6	no	—
412	D₈	—	4	12	no	—
413	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
414	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
415	C₄⋊C₄	—	2	3	no	—
416	C₄⋊C₄	—	2	3	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	3	no	—
420	C₄⋊C₄	—	2	3	no	—
421	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
422	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
423	C₄⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
424	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
425	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
426	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
427	C₂²⋊C₄	—	2	1	no	—
428	C₂²⋊C₄	—	2	6	no	—
429	C₂²⋊C₄	—	2	6	no	—
430	C₂²⋊C₄	—	2	3	no	—
431	C₂²⋊C₄	—	2	3	no	—
432	C₂²⋊C₄	—	2	3	no	—
433	C₂²⋊C₄	—	2	3	no	—
434	C₂²⋊C₄	—	2	6	no	—
435	C₄²	—	2	3	no	—
436	C₄²	C₂×D₄×C₁₃	1	3	yes	—
437	C₄²	C₂×D₄×C₁₃	1	3	yes	—
438	C₄²	C₂⁴×C₁₃	1	3	yes	—
439	C₄²	C₂⁴×C₁₃	1	3	yes	—
440	C₁₃	#61907	1	1	yes	characteristic, direct product factor, Sylow
441	C₂³	—	2	3	no	—
442	C₂³	—	2	6	no	—
443	C₂³	—	4	6	no	—
444	C₂³	—	4	6	no	—
445	C₂³	—	4	6	no	—
446	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
447	Q₈	—	2	6	no	—
448	Q₈	—	2	2	no	—
449	Q₈	—	8	3	no	—
450	Q₈	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
451	D₄	—	2	6	no	—
452	D₄	—	2	6	no	—
453	D₄	—	2	6	no	—
454	D₄	—	4	6	no	—
455	D₄	—	4	12	no	—
456	D₄	—	4	6	no	—
457	D₄	—	4	12	no	—
458	D₄	—	4	6	no	—
459	D₄	—	8	6	no	—
460	D₄	—	8	6	no	—
461	D₄	—	8	3	no	—
462	C₂×C₄	—	2	6	no	—
463	C₂×C₄	—	2	6	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	3	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	4	12	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	12	no	—
472	C₂×C₄	—	4	6	no	—
473	C₂×C₄	—	8	6	no	—
474	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
475	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
476	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
477	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
478	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
479	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
480	C₈	—	2	2	no	—
481	C₈	—	2	6	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	4	6	no	—
485	C₂²	—	4	3	no	—
486	C₂²	—	4	3	no	—
487	C₂²	—	4	6	no	—
488	C₂²	—	4	6	no	—
489	C₂²	—	4	3	no	—
490	C₂²	—	8	12	no	—
491	C₂²	C₁₃×#576	1	2	yes	—
492	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
493	C₄	—	2	3	no	—
494	C₄	—	2	3	no	—
495	C₄	—	2	3	no	—
496	C₄	—	2	1	no	—
497	C₄	—	4	1	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	3	no	—
500	C₄	—	4	1	no	—
501	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	6	yes	—
502	C₄	C₁₃×#585	1	2	yes	—
503	C₂	—	2	2	no	—
504	C₂	—	8	6	no	—
505	C₂	—	8	3	no	—
506	C₂	C₁₃×#3487	1	1	yes	characteristic
507	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
508	C₂	C₂×C₁₃×#576	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 ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3522	C₂	semidirect
2. C₂×C₁₃×#550	C₂	semidirect
3. C₁₃×#3399	C₂	semidirect
4. C₁₃×#3391	C₂	semidirect
5. C₁₃×#3366	C₂	semidirect
6. C₁₃×#3362	C₂	semidirect
7. C₁₃×#3217	C₂	semidirect
8. C₁₃×#3205	C₂	semidirect
9. C₁₃×#3109	C₂	semidirect
10. C₁₃×#3105	C₂	semidirect
11. C₁₃×#2984	C₂	semidirect
13. C₁₃×#559	C₂²	semidirect
14. Q₈²×C₁₃	C₂²	semidirect
15. C₁₃×#554	C₂²	semidirect
20. C₁₃×#550	C₂²	semidirect
31. C₁₃×#496	C₂²	semidirect
32. C₁₃×#493	C₂²	semidirect
33. C₁₃×#490	C₂²	semidirect
34. C₁₃×#486	C₂²	semidirect
37. C₁₃×#478	C₂²	semidirect
38. C₁₃×#476	C₂²	semidirect
39. C₁₃×#463	C₂²	semidirect
40. C₁₃×#460	C₂²	semidirect
41. C₁₃×#459	C₂²	semidirect
42. C₁₃×#459	C₂²	semidirect
43. C₁₃×#459	C₂²	semidirect
47. C₁₃×#446	C₂²	semidirect
48. C₈×Q₈×C₁₃	C₂²	semidirect
49. C₁₃×#442	C₂²	semidirect
50. C₄×C₁₃×SD₁₆	C₂²	semidirect
51. C₄×C₁₃×D₈	C₂²	semidirect
124. #61907	C₁₃	direct (N × H)
187. #3522	C₂×C₁₃	semidirect
188. C₂×#550	C₂×C₁₃	semidirect
189. #3399	C₂×C₁₃	semidirect
190. #3391	C₂×C₁₃	semidirect
191. #3366	C₂×C₁₃	semidirect
192. #3362	C₂×C₁₃	semidirect
193. #3217	C₂×C₁₃	semidirect
194. #3205	C₂×C₁₃	semidirect
195. #3109	C₂×C₁₃	semidirect
196. #3105	C₂×C₁₃	semidirect
197. #2984	C₂×C₁₃	semidirect
240. #559	C₂²×C₁₃	semidirect
241. Q₈²	C₂²×C₁₃	semidirect
242. #554	C₂²×C₁₃	semidirect
247. #550	C₂²×C₁₃	semidirect
258. #496	C₂²×C₁₃	semidirect
259. #493	C₂²×C₁₃	semidirect
260. #490	C₂²×C₁₃	semidirect
261. #486	C₂²×C₁₃	semidirect
264. #478	C₂²×C₁₃	semidirect
265. #476	C₂²×C₁₃	semidirect
266. #463	C₂²×C₁₃	semidirect
267. #460	C₂²×C₁₃	semidirect
268. #459	C₂²×C₁₃	semidirect
269. #459	C₂²×C₁₃	semidirect
270. #459	C₂²×C₁₃	semidirect
274. #446	C₂²×C₁₃	semidirect
275. C₈×Q₈	C₂²×C₁₃	semidirect
276. #442	C₂²×C₁₃	semidirect
277. C₄×SD₁₆	C₂²×C₁₃	semidirect
278. C₄×D₈	C₂²×C₁₃	semidirect
440. C₁₃	#61907	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×#3522	2
C₂×C₁₃×#550	2
C₁₃×#3399	2
C₁₃×#3391	2
C₁₃×#3366	2
C₁₃×#3362	2
C₁₃×#3217	2
C₁₃×#3205	2
C₁₃×#3109	2
C₁₃×#3105	2
C₁₃×#2984	2
#61907	13

Subgroups — C13×#61907 #15748246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61907 #15748246