Subgroups — C₁₃×#61587 #15747926

Order 3328.

2430 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3332	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3274	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3205	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3192	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3103	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3006	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2975	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×H(5,𝔽₂)	—	2	1	no	—
11	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
12	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
13	C₁₃×#550	—	2	4	no	—
14	C₁₃×#550	C₂²	1	8	yes	complemented
15	C₁₃×#547	C₂²	1	4	yes	complemented
16	C₁₃×#546	—	2	4	no	—
17	D₄²×C₁₃	C₂²	1	4	yes	complemented
18	C₁₃×#537	—	2	1	no	—
19	C₁₃×#534	—	2	2	no	—
20	C₁₃×#532	C₂²	1	2	yes	—
21	C₂×C₁₃×#127	—	2	1	no	—
22	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₃×#121	—	2	2	no	—
24	C₂×C₁₃×#121	C₂²	1	4	yes	—
25	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₄×D₄×C₁₃	—	2	1	no	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#493	C₂²	1	4	yes	complemented
30	C₁₃×#486	C₂²	1	4	yes	complemented
31	C₁₃×#481	C₂²	1	8	yes	complemented
32	C₁₃×#481	C₂²	1	4	yes	complemented
33	C₁₃×#475	C₂²	1	4	yes	complemented
34	C₁₃×#469	C₂²	1	16	yes	complemented
35	C₁₃×#460	C₂²	1	4	yes	complemented
36	C₁₃×#459	C₂²	1	8	yes	complemented
37	C₁₃×#449	C₂²	1	16	yes	complemented
38	C₁₃×#448	C₂²	1	4	yes	complemented
39	C₁₃×#447	C₂²	1	8	yes	complemented
40	C₁₃×#447	C₂²	1	8	yes	complemented
41	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
42	C₁₃×#436	C₂²	1	8	yes	complemented
43	C₁₃×#431	C₂²	1	2	yes	complemented
44	C₁₃×#417	C₂²	1	8	yes	complemented
45	C₁₃×#407	C₂²	1	4	yes	complemented
46	C₁₃×H(5,𝔽₂)	—	4	8	no	—
47	C₂×C₁₃×#41	—	2	4	no	—
48	C₂×C₁₃×#41	—	2	2	no	—
49	C₂×C₁₃×#41	—	2	4	no	—
50	C₂×C₁₃×#41	—	4	8	no	—
51	C₂×C₁₃×#41	C₂³	1	8	yes	—
52	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₃	—	2	2	no	—
54	C₂²×D₄×C₁₃	—	2	4	no	—
55	C₂²×D₄×C₁₃	—	2	2	no	—
56	C₂²×D₄×C₁₃	—	2	4	no	—
57	C₂²×D₄×C₁₃	—	2	1	no	—
58	C₂²×D₄×C₁₃	—	2	1	no	—
59	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
60	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
61	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
62	C₂³×C₄×C₁₃	—	2	2	no	—
63	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
64	C₁₃×AGL(1,ℤ/8)	—	4	16	no	—
65	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
66	C₂×C₁₃×D₈	C₂³	1	16	yes	—
67	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
68	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₁₃×#127	—	2	8	no	—
70	C₁₃×#127	—	2	2	no	—
71	C₁₃×#127	C₂³	1	4	yes	—
72	C₁₃×#127	C₂³	1	2	yes	—
73	C₁₃×#124	—	2	2	no	—
74	C₁₃×#123	—	2	8	no	—
75	C₁₃×C₂²⋊Q₈	—	2	4	no	—
76	C₁₃×#121	—	2	4	no	—
77	C₁₃×#121	—	2	4	no	—
78	C₁₃×#121	—	2	4	no	—
79	C₁₃×#121	—	2	2	no	—
80	C₁₃×#121	—	2	4	no	—
81	C₁₃×#121	—	2	16	no	—
82	C₁₃×#121	C₂³	1	4	yes	—
83	C₁₃×#121	C₂³	1	8	yes	—
84	C₁₃×#121	C₂³	1	8	yes	—
85	C₁₃×#120	—	2	8	no	—
86	C₄×Q₈×C₁₃	—	2	2	no	—
87	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
88	C₄×D₄×C₁₃	—	2	8	no	—
89	C₄×D₄×C₁₃	—	2	2	no	—
90	C₄×D₄×C₁₃	D₄	1	4	yes	—
91	C₄×D₄×C₁₃	C₂³	1	4	yes	—
92	C₄×D₄×C₁₃	C₂³	1	4	yes	—
93	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
99	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
100	C₂×C₄²×C₁₃	—	2	1	no	—
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₁₃×#106	C₂³	1	8	yes	—
103	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
104	C₁₃×#103	C₂³	1	8	yes	—
105	C₁₃×#102	C₂³	1	16	yes	—
106	C₁₃×#102	C₂³	1	8	yes	—
107	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
108	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
109	C₄×C₈×C₁₃	C₂³	1	4	yes	—
110	#61587	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂⁴×C₁₃	—	2	2	no	—
112	C₂⁴×C₁₃	—	2	4	no	—
113	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
114	C₁₃×#41	—	2	16	no	—
115	C₁₃×#41	—	4	8	no	—
116	C₁₃×#41	—	4	16	no	—
117	C₁₃×#41	—	4	16	no	—
118	C₁₃×#41	—	4	8	no	—
119	C₂×Q₈×C₁₃	—	2	4	no	—
120	C₂×Q₈×C₁₃	—	2	1	no	—
121	C₂×Q₈×C₁₃	—	2	2	no	—
122	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
123	C₂×D₄×C₁₃	—	2	8	no	—
124	C₂×D₄×C₁₃	—	2	4	no	—
125	C₂×D₄×C₁₃	—	2	8	no	—
126	C₂×D₄×C₁₃	—	2	8	no	—
127	C₂×D₄×C₁₃	—	2	4	no	—
128	C₂×D₄×C₁₃	—	2	4	no	—
129	C₂×D₄×C₁₃	—	2	2	no	—
130	C₂×D₄×C₁₃	—	2	2	no	—
131	C₂×D₄×C₁₃	—	2	2	no	—
132	C₂×D₄×C₁₃	—	2	4	no	—
133	C₂×D₄×C₁₃	—	2	4	no	—
134	C₂×D₄×C₁₃	—	4	4	no	—
135	C₂×D₄×C₁₃	—	4	8	no	—
136	C₂×D₄×C₁₃	—	4	8	no	—
137	C₂×D₄×C₁₃	—	4	16	no	—
138	C₂×D₄×C₁₃	—	4	16	no	—
139	C₂×D₄×C₁₃	—	4	4	no	—
140	C₂×D₄×C₁₃	—	8	2	no	—
141	C₂×D₄×C₁₃	—	8	4	no	—
142	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
143	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
144	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	2	4	no	—
148	C₂²×C₄×C₁₃	—	2	8	no	—
149	C₂²×C₄×C₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₃	—	4	4	no	—
151	C₂²×C₄×C₁₃	—	4	8	no	—
152	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
155	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
158	C₁₃×SD₁₆	—	2	16	no	—
159	C₁₃×D₈	—	4	16	no	—
160	C₁₃×M₁₆	—	4	8	no	—
161	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
162	C₁₃×C₄⋊C₄	—	2	4	no	—
163	C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₁₃×C₄⋊C₄	—	2	4	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
167	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
168	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
169	C₁₃×C₂²⋊C₄	—	2	4	no	—
170	C₁₃×C₂²⋊C₄	—	2	8	no	—
171	C₁₃×C₂²⋊C₄	—	2	8	no	—
172	C₁₃×C₂²⋊C₄	—	2	4	no	—
173	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
174	C₄²×C₁₃	—	2	4	no	—
175	C₄²×C₁₃	C₂×D₄	1	2	yes	—
176	C₄²×C₁₃	C₂⁴	1	2	yes	—
177	#3496	C₂×C₁₃	1	1	yes	characteristic, complemented
178	C₂×#550	C₂×C₁₃	1	1	yes	characteristic, complemented
179	#3332	C₂×C₁₃	1	8	yes	complemented
180	#3274	C₂×C₁₃	1	8	yes	complemented
181	#3205	C₂×C₁₃	1	2	yes	complemented
182	#3192	C₂×C₁₃	1	4	yes	complemented
183	#3103	C₂×C₁₃	1	2	yes	complemented
184	#3006	C₂×C₁₃	1	4	yes	complemented
185	#2975	C₂×C₁₃	1	1	yes	characteristic, complemented
186	C₂³×C₁₃	—	2	4	no	—
187	C₂³×C₁₃	—	2	4	no	—
188	C₂³×C₁₃	—	2	4	no	—
189	C₂³×C₁₃	—	4	2	no	—
190	C₂³×C₁₃	—	4	2	no	—
191	C₂³×C₁₃	—	4	4	no	—
192	C₂³×C₁₃	—	4	4	no	—
193	C₂³×C₁₃	—	4	8	no	—
194	C₂³×C₁₃	—	4	4	no	—
195	C₂³×C₁₃	—	8	4	no	—
196	C₂³×C₁₃	—	8	4	no	—
197	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
198	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
199	Q₈×C₁₃	—	2	4	no	—
200	Q₈×C₁₃	—	2	2	no	—
201	Q₈×C₁₃	—	4	4	no	—
202	Q₈×C₁₃	H(5,𝔽₂)	1	4	yes	complemented
203	D₄×C₁₃	—	2	8	no	—
204	D₄×C₁₃	—	2	8	no	—
205	D₄×C₁₃	—	2	8	no	—
206	D₄×C₁₃	—	4	16	no	—
207	D₄×C₁₃	—	4	4	no	—
208	D₄×C₁₃	—	4	16	no	—
209	D₄×C₁₃	—	4	8	no	—
210	D₄×C₁₃	—	4	8	no	—
211	D₄×C₁₃	—	4	4	no	—
212	D₄×C₁₃	—	8	2	no	—
213	D₄×C₁₃	—	8	4	no	—
214	D₄×C₁₃	—	8	4	no	—
215	D₄×C₁₃	—	8	8	no	—
216	C₂×C₄×C₁₃	—	2	4	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	8	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	4	4	no	—
224	C₂×C₄×C₁₃	—	4	1	no	—
225	C₂×C₄×C₁₃	—	4	16	no	—
226	C₂×C₄×C₁₃	—	4	8	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	—	4	8	no	—
229	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
230	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
232	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
233	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
234	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
235	C₈×C₁₃	—	2	8	no	—
236	C₂×H(5,𝔽₂)	—	2	1	no	—
237	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
238	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	8	yes	complemented
239	#550	—	2	4	no	—
240	#550	C₂²×C₁₃	1	8	yes	complemented
241	#547	C₂²×C₁₃	1	4	yes	complemented
242	#546	—	2	4	no	—
243	D₄²	C₂²×C₁₃	1	4	yes	complemented
244	#537	—	2	1	no	—
245	#534	—	2	2	no	—
246	#532	C₂²×C₁₃	1	2	yes	—
247	C₂×#127	—	2	1	no	—
248	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
249	C₂×#121	—	2	2	no	—
250	C₂×#121	C₂²×C₁₃	1	4	yes	—
251	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
252	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
253	C₂×C₄×D₄	—	2	1	no	—
254	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
255	#493	C₂²×C₁₃	1	4	yes	complemented
256	#486	C₂²×C₁₃	1	4	yes	complemented
257	#481	C₂²×C₁₃	1	8	yes	complemented
258	#481	C₂²×C₁₃	1	4	yes	complemented
259	#475	C₂²×C₁₃	1	4	yes	complemented
260	#469	C₂²×C₁₃	1	16	yes	complemented
261	#460	C₂²×C₁₃	1	4	yes	complemented
262	#459	C₂²×C₁₃	1	8	yes	complemented
263	#449	C₂²×C₁₃	1	16	yes	complemented
264	#448	C₂²×C₁₃	1	4	yes	complemented
265	#447	C₂²×C₁₃	1	8	yes	complemented
266	#447	C₂²×C₁₃	1	8	yes	complemented
267	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
268	#436	C₂²×C₁₃	1	8	yes	complemented
269	#431	C₂²×C₁₃	1	2	yes	complemented
270	#417	C₂²×C₁₃	1	8	yes	complemented
271	#407	C₂²×C₁₃	1	4	yes	complemented
272	C₂²×C₁₃	—	2	1	no	—
273	C₂²×C₁₃	—	2	1	no	—
274	C₂²×C₁₃	—	2	4	no	—
275	C₂²×C₁₃	—	2	4	no	—
276	C₂²×C₁₃	—	2	4	no	—
277	C₂²×C₁₃	—	4	4	no	—
278	C₂²×C₁₃	—	4	4	no	—
279	C₂²×C₁₃	—	4	4	no	—
280	C₂²×C₁₃	—	4	4	no	—
281	C₂²×C₁₃	—	4	4	no	—
282	C₂²×C₁₃	—	4	4	no	—
283	C₂²×C₁₃	—	8	4	no	—
284	C₂²×C₁₃	—	8	8	no	—
285	C₂²×C₁₃	—	16	8	no	—
286	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
287	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
288	C₄×C₁₃	—	2	2	no	—
289	C₄×C₁₃	—	2	4	no	—
290	C₄×C₁₃	—	2	4	no	—
291	C₄×C₁₃	—	2	1	no	—
292	C₄×C₁₃	—	4	2	no	—
293	C₄×C₁₃	—	4	4	no	—
294	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
295	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
296	H(5,𝔽₂)	—	4	8	no	—
297	C₂×#41	—	2	4	no	—
298	C₂×#41	—	2	2	no	—
299	C₂×#41	—	2	4	no	—
300	C₂×#41	—	4	8	no	—
301	C₂×#41	C₂³×C₁₃	1	8	yes	—
302	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
303	C₂²×D₄	—	2	2	no	—
304	C₂²×D₄	—	2	4	no	—
305	C₂²×D₄	—	2	2	no	—
306	C₂²×D₄	—	2	4	no	—
307	C₂²×D₄	—	2	1	no	—
308	C₂²×D₄	—	2	1	no	—
309	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
310	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
311	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
312	C₂³×C₄	—	2	2	no	—
313	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
314	AGL(1,ℤ/8)	—	4	16	no	—
315	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
316	C₂×D₈	C₂³×C₁₃	1	16	yes	—
317	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
318	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
319	#127	—	2	8	no	—
320	#127	—	2	2	no	—
321	#127	C₂³×C₁₃	1	4	yes	—
322	#127	C₂³×C₁₃	1	2	yes	—
323	#124	—	2	2	no	—
324	#123	—	2	8	no	—
325	C₂²⋊Q₈	—	2	4	no	—
326	#121	—	2	4	no	—
327	#121	—	2	4	no	—
328	#121	—	2	4	no	—
329	#121	—	2	2	no	—
330	#121	—	2	4	no	—
331	#121	—	2	16	no	—
332	#121	C₂³×C₁₃	1	4	yes	—
333	#121	C₂³×C₁₃	1	8	yes	—
334	#121	C₂³×C₁₃	1	8	yes	—
335	#120	—	2	8	no	—
336	C₄×Q₈	—	2	2	no	—
337	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
338	C₄×D₄	—	2	8	no	—
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	D₄×C₁₃	1	4	yes	—
341	C₄×D₄	C₂³×C₁₃	1	4	yes	—
342	C₄×D₄	C₂³×C₁₃	1	4	yes	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	4	no	—
349	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
352	#106	C₂³×C₁₃	1	8	yes	—
353	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
354	#103	C₂³×C₁₃	1	8	yes	—
355	#102	C₂³×C₁₃	1	16	yes	—
356	#102	C₂³×C₁₃	1	8	yes	—
357	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
358	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
359	C₄×C₈	C₂³×C₁₃	1	4	yes	—
360	C₂×C₁₃	—	2	2	no	—
361	C₂×C₁₃	—	4	4	no	—
362	C₂×C₁₃	—	8	4	no	—
363	C₂×C₁₃	—	8	4	no	—
364	C₂×C₁₃	#3484	1	1	yes	characteristic
365	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
366	C₂×C₁₃	#3585	1	1	yes	characteristic
367	C₂⁴	—	2	2	no	—
368	C₂⁴	—	2	4	no	—
369	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
370	#41	—	2	16	no	—
371	#41	—	4	8	no	—
372	#41	—	4	16	no	—
373	#41	—	4	16	no	—
374	#41	—	4	8	no	—
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	2	1	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
379	C₂×D₄	—	2	8	no	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	8	no	—
382	C₂×D₄	—	2	8	no	—
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	4	4	no	—
391	C₂×D₄	—	4	8	no	—
392	C₂×D₄	—	4	8	no	—
393	C₂×D₄	—	4	16	no	—
394	C₂×D₄	—	4	16	no	—
395	C₂×D₄	—	4	4	no	—
396	C₂×D₄	—	8	2	no	—
397	C₂×D₄	—	8	4	no	—
398	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
399	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
400	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	8	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	4	4	no	—
407	C₂²×C₄	—	4	8	no	—
408	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
410	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
411	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
412	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
413	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
414	SD₁₆	—	2	16	no	—
415	D₈	—	4	16	no	—
416	M₁₆	—	4	8	no	—
417	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
423	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
424	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₂²⋊C₄	—	2	8	no	—
427	C₂²⋊C₄	—	2	8	no	—
428	C₂²⋊C₄	—	2	4	no	—
429	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
430	C₄²	—	2	4	no	—
431	C₄²	C₂×D₄×C₁₃	1	2	yes	—
432	C₄²	C₂⁴×C₁₃	1	2	yes	—
433	C₁₃	#61587	1	1	yes	characteristic, direct product factor, Sylow
434	C₂³	—	2	4	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	2	4	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	4	no	—
440	C₂³	—	4	4	no	—
441	C₂³	—	4	8	no	—
442	C₂³	—	4	4	no	—
443	C₂³	—	8	4	no	—
444	C₂³	—	8	4	no	—
445	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
446	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
447	Q₈	—	2	4	no	—
448	Q₈	—	2	2	no	—
449	Q₈	—	4	4	no	—
450	Q₈	C₁₃×H(5,𝔽₂)	1	4	yes	complemented
451	D₄	—	2	8	no	—
452	D₄	—	2	8	no	—
453	D₄	—	2	8	no	—
454	D₄	—	4	16	no	—
455	D₄	—	4	4	no	—
456	D₄	—	4	16	no	—
457	D₄	—	4	8	no	—
458	D₄	—	4	4	no	—
459	D₄	—	4	8	no	—
460	D₄	—	8	4	no	—
461	D₄	—	8	4	no	—
462	D₄	—	8	2	no	—
463	D₄	—	8	8	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	16	no	—
474	C₂×C₄	—	4	8	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	8	no	—
477	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
478	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
479	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
480	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
481	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
482	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
483	C₈	—	2	8	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	4	no	—
487	C₂²	—	2	4	no	—
488	C₂²	—	2	4	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	4	4	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	8	4	no	—
496	C₂²	—	8	8	no	—
497	C₂²	—	16	8	no	—
498	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
499	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	4	no	—
502	C₄	—	2	4	no	—
503	C₄	—	2	1	no	—
504	C₄	—	4	4	no	—
505	C₄	—	4	2	no	—
506	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
507	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
508	C₂	—	2	2	no	—
509	C₂	—	4	4	no	—
510	C₂	—	8	4	no	—
511	C₂	—	8	4	no	—
512	C₂	C₁₃×#3484	1	1	yes	characteristic
513	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
514	C₂	C₁₃×#3585	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×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3496	C₂	semidirect
2. C₂×C₁₃×#550	C₂	semidirect
3. C₁₃×#3332	C₂	semidirect
4. C₁₃×#3274	C₂	semidirect
5. C₁₃×#3205	C₂	semidirect
6. C₁₃×#3192	C₂	semidirect
7. C₁₃×#3103	C₂	semidirect
8. C₁₃×#3006	C₂	semidirect
9. C₁₃×#2975	C₂	semidirect
11. C₂²×C₁₃×#41	C₂²	semidirect
12. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
14. C₁₃×#550	C₂²	semidirect
15. C₁₃×#547	C₂²	semidirect
17. D₄²×C₁₃	C₂²	semidirect
22. C₂×C₁₃×#127	C₂²	semidirect
25. C₂×C₁₃×#121	C₂²	semidirect
26. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
29. C₁₃×#493	C₂²	semidirect
30. C₁₃×#486	C₂²	semidirect
31. C₁₃×#481	C₂²	semidirect
32. C₁₃×#481	C₂²	semidirect
33. C₁₃×#475	C₂²	semidirect
34. C₁₃×#469	C₂²	semidirect
35. C₁₃×#460	C₂²	semidirect
36. C₁₃×#459	C₂²	semidirect
37. C₁₃×#449	C₂²	semidirect
38. C₁₃×#448	C₂²	semidirect
39. C₁₃×#447	C₂²	semidirect
40. C₁₃×#447	C₂²	semidirect
41. C₄×C₁₃×SD₁₆	C₂²	semidirect
42. C₁₃×#436	C₂²	semidirect
43. C₁₃×#431	C₂²	semidirect
44. C₁₃×#417	C₂²	semidirect
45. C₁₃×#407	C₂²	semidirect
110. #61587	C₁₃	direct (N × H)
177. #3496	C₂×C₁₃	semidirect
178. C₂×#550	C₂×C₁₃	semidirect
179. #3332	C₂×C₁₃	semidirect
180. #3274	C₂×C₁₃	semidirect
181. #3205	C₂×C₁₃	semidirect
182. #3192	C₂×C₁₃	semidirect
183. #3103	C₂×C₁₃	semidirect
184. #3006	C₂×C₁₃	semidirect
185. #2975	C₂×C₁₃	semidirect
202. Q₈×C₁₃	H(5,𝔽₂)	semidirect
229. C₂×C₄×C₁₃	AGL(1,ℤ/8)	semidirect
237. C₂²×#41	C₂²×C₁₃	semidirect
238. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
240. #550	C₂²×C₁₃	semidirect
241. #547	C₂²×C₁₃	semidirect
243. D₄²	C₂²×C₁₃	semidirect
248. C₂×#127	C₂²×C₁₃	semidirect
251. C₂×#121	C₂²×C₁₃	semidirect
252. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
255. #493	C₂²×C₁₃	semidirect
256. #486	C₂²×C₁₃	semidirect
257. #481	C₂²×C₁₃	semidirect
258. #481	C₂²×C₁₃	semidirect
259. #475	C₂²×C₁₃	semidirect
260. #469	C₂²×C₁₃	semidirect
261. #460	C₂²×C₁₃	semidirect
262. #459	C₂²×C₁₃	semidirect
263. #449	C₂²×C₁₃	semidirect
264. #448	C₂²×C₁₃	semidirect
265. #447	C₂²×C₁₃	semidirect
266. #447	C₂²×C₁₃	semidirect
267. C₄×SD₁₆	C₂²×C₁₃	semidirect
268. #436	C₂²×C₁₃	semidirect
269. #431	C₂²×C₁₃	semidirect
270. #417	C₂²×C₁₃	semidirect
271. #407	C₂²×C₁₃	semidirect
433. C₁₃	#61587	direct (N × H)
450. Q₈	C₁₃×H(5,𝔽₂)	semidirect
477. C₂×C₄	C₁₃×AGL(1,ℤ/8)	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3496	2
C₂×C₁₃×#550	2
C₁₃×#3332	2
C₁₃×#3274	2
C₁₃×#3205	2
C₁₃×#3192	2
C₁₃×#3103	2
C₁₃×#3006	2
C₁₃×#2975	2
#61587	13

Subgroups — C13×#61587 #15747926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61587 #15747926