Subgroups — C₁₃×#61661 #15748000

Order 3328.

2272 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3549	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3325	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3305	C₂	1	4	yes	maximal, complemented
5	D₄×C₁₃×D₈	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3274	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3205	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3199	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3106	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3008	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
13	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
14	C₂²×C₁₃×D₈	C₂²	1	4	yes	complemented
15	C₁₃×H(3,𝔽₄)	—	2	2	no	—
16	C₁₃×#555	—	2	1	no	—
17	C₁₃×#555	C₂²	1	4	yes	complemented
18	C₁₃×#550	C₂²	1	4	yes	complemented
19	D₄²×C₁₃	—	2	1	no	—
20	D₄²×C₁₃	—	2	4	no	—
21	D₄²×C₁₃	C₂²	1	4	yes	complemented
22	D₄²×C₁₃	C₂²	1	4	yes	complemented
23	C₁₃×#535	—	2	2	no	—
24	C₁₃×#535	—	2	4	no	—
25	C₁₃×#535	C₂²	1	4	yes	complemented
26	C₁₃×#535	C₂²	1	2	yes	complemented
27	C₁₃×#532	—	2	1	no	—
28	C₁₃×#532	C₂²	1	1	yes	characteristic
29	C₁₃×#532	C₂²	1	2	yes	complemented
30	C₂×C₁₃×#127	—	2	1	no	—
31	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
32	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#493	C₂²	1	4	yes	complemented
34	C₁₃×#486	C₂²	1	4	yes	complemented
35	C₁₃×#482	C₂²	1	8	yes	complemented
36	C₁₃×#482	C₂²	1	4	yes	complemented
37	C₁₃×#477	C₂²	1	2	yes	complemented
38	C₁₃×#476	C₂²	1	2	yes	complemented
39	C₁₃×#469	C₂²	1	8	yes	complemented
40	C₁₃×#466	C₂²	1	8	yes	complemented
41	C₁₃×#460	C₂²	1	2	yes	complemented
42	C₁₃×#459	C₂²	1	4	yes	complemented
43	C₁₃×#459	C₂²	1	2	yes	complemented
44	C₁₃×#459	C₂²	1	4	yes	complemented
45	C₁₃×#449	C₂²	1	4	yes	complemented
46	C₁₃×#449	C₂²	1	8	yes	complemented
47	C₁₃×#447	C₂²	1	8	yes	complemented
48	C₁₃×#447	C₂²	1	8	yes	complemented
49	C₁₃×#447	C₂²	1	8	yes	complemented
50	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
51	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
52	C₁₃×#436	C₂²	1	4	yes	complemented
53	C₈×D₄×C₁₃	C₂²	1	4	yes	complemented
54	C₁₃×#431	C₂²	1	2	yes	complemented
55	C₁₃×#418	C₂²	1	4	yes	complemented
56	C₁₃×#416	C₂²	1	4	yes	complemented
57	C₁₃×#408	C₂²	1	4	yes	complemented
58	C₁₃×H(5,𝔽₂)	—	4	4	no	—
59	C₁₃×H(5,𝔽₂)	—	4	4	no	—
60	C₂×C₁₃×#41	—	2	2	no	—
61	C₂×C₁₃×#41	—	2	2	no	—
62	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×#41	C₂³	1	4	yes	—
64	C₂×C₁₃×#41	C₂³	1	2	yes	—
65	C₂²×D₄×C₁₃	—	2	2	no	—
66	C₂²×D₄×C₁₃	—	2	4	no	—
67	C₂²×D₄×C₁₃	—	2	4	no	—
68	C₂²×D₄×C₁₃	—	2	4	no	—
69	C₂²×D₄×C₁₃	—	2	2	no	—
70	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
73	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
74	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
75	C₂×C₁₃×D₈	—	4	8	no	—
76	C₂×C₁₃×D₈	C₂³	1	4	yes	—
77	C₂×C₁₃×D₈	C₂³	1	8	yes	—
78	C₂×C₁₃×D₈	C₂³	1	8	yes	—
79	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
80	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
81	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
82	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
83	C₁₃×#127	—	2	2	no	—
84	C₁₃×#127	—	2	4	no	—
85	C₁₃×#127	—	2	4	no	—
86	C₁₃×#127	—	2	1	no	—
87	C₁₃×#127	—	2	1	no	—
88	C₁₃×#127	D₄	1	1	yes	characteristic
89	C₁₃×#127	C₂³	1	4	yes	—
90	C₁₃×#127	C₂³	1	2	yes	—
91	C₁₃×#124	—	2	2	no	—
92	C₁₃×#124	—	2	4	no	—
93	C₁₃×#124	—	2	8	no	—
94	C₁₃×#124	—	2	2	no	—
95	C₁₃×#124	D₄	1	2	yes	—
96	C₁₃×#121	—	2	4	no	—
97	C₁₃×#121	—	2	2	no	—
98	C₁₃×#121	—	2	4	no	—
99	C₁₃×#121	—	2	4	no	—
100	C₁₃×#121	—	2	8	no	—
101	C₁₃×#121	D₄	1	4	yes	—
102	C₁₃×#121	C₂³	1	4	yes	—
103	C₁₃×#121	C₂³	1	8	yes	—
104	C₁₃×#121	C₂³	1	8	yes	—
105	C₁₃×#120	—	2	4	no	—
106	C₁₃×#120	—	2	4	no	—
107	C₁₃×#120	—	2	4	no	—
108	C₁₃×#120	—	2	8	no	—
109	C₁₃×#120	—	2	8	no	—
110	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
111	C₄×D₄×C₁₃	—	2	2	no	—
112	C₄×D₄×C₁₃	—	2	4	no	—
113	C₄×D₄×C₁₃	—	2	2	no	—
114	C₄×D₄×C₁₃	C₂³	1	2	yes	—
115	C₄×D₄×C₁₃	C₂³	1	4	yes	—
116	C₄×D₄×C₁₃	C₂³	1	4	yes	—
117	C₁₃×#117	—	2	4	no	—
118	C₁₃×#117	—	2	1	no	—
119	C₁₃×#117	C₂³	1	4	yes	—
120	C₁₃×#117	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₃	—	2	1	no	—
122	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
123	C₁₃×#107	C₂³	1	4	yes	—
124	C₁₃×#106	C₂³	1	4	yes	—
125	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
126	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
127	C₁₃×#103	C₂³	1	4	yes	—
128	C₁₃×#102	C₂³	1	8	yes	—
129	C₁₃×#102	C₂³	1	4	yes	—
130	C₁₃×#102	C₂³	1	8	yes	—
131	C₁₃×#102	C₂³	1	4	yes	—
132	C₁₃×#102	C₂³	1	4	yes	—
133	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
134	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
135	C₄×C₈×C₁₃	C₂³	1	4	yes	—
136	#61661	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂⁴×C₁₃	—	2	4	no	—
138	C₂⁴×C₁₃	—	2	2	no	—
139	C₂⁴×C₁₃	—	2	4	no	—
140	C₁₃×#41	—	2	2	no	—
141	C₁₃×#41	—	2	2	no	—
142	C₁₃×#41	—	2	8	no	—
143	C₁₃×#41	—	4	2	no	—
144	C₁₃×#41	—	4	2	no	—
145	C₁₃×#41	—	4	4	no	—
146	C₁₃×#41	—	4	8	no	—
147	C₁₃×#41	—	8	4	no	—
148	C₂×Q₈×C₁₃	—	2	2	no	—
149	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
150	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	2	8	no	—
153	C₂×D₄×C₁₃	—	2	4	no	—
154	C₂×D₄×C₁₃	—	2	8	no	—
155	C₂×D₄×C₁₃	—	2	8	no	—
156	C₂×D₄×C₁₃	—	2	4	no	—
157	C₂×D₄×C₁₃	—	2	2	no	—
158	C₂×D₄×C₁₃	—	2	4	no	—
159	C₂×D₄×C₁₃	—	2	4	no	—
160	C₂×D₄×C₁₃	—	2	2	no	—
161	C₂×D₄×C₁₃	—	2	2	no	—
162	C₂×D₄×C₁₃	—	2	4	no	—
163	C₂×D₄×C₁₃	—	2	4	no	—
164	C₂×D₄×C₁₃	—	4	4	no	—
165	C₂×D₄×C₁₃	—	4	2	no	—
166	C₂×D₄×C₁₃	—	4	2	no	—
167	C₂×D₄×C₁₃	—	4	4	no	—
168	C₂×D₄×C₁₃	—	4	4	no	—
169	C₂×D₄×C₁₃	—	4	8	no	—
170	C₂×D₄×C₁₃	—	4	16	no	—
171	C₂×D₄×C₁₃	—	8	4	no	—
172	C₂×D₄×C₁₃	—	8	8	no	—
173	C₂×D₄×C₁₃	—	8	8	no	—
174	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
175	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
176	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
177	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
178	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
179	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×C₁₃	—	2	1	no	—
181	C₂²×C₄×C₁₃	—	2	2	no	—
182	C₂²×C₄×C₁₃	—	2	4	no	—
183	C₂²×C₄×C₁₃	—	2	4	no	—
184	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
187	C₁₃×SD₁₆	—	2	8	no	—
188	C₁₃×D₈	—	2	8	no	—
189	C₁₃×D₈	—	4	8	no	—
190	C₁₃×D₈	—	4	8	no	—
191	C₁₃×M₁₆	—	4	4	no	—
192	C₂×C₈×C₁₃	—	4	4	no	—
193	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
194	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
195	C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₁₃×C₄⋊C₄	—	2	2	no	—
197	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
198	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
199	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
200	C₁₃×C₂²⋊C₄	—	2	1	no	—
201	C₁₃×C₂²⋊C₄	—	2	4	no	—
202	C₁₃×C₂²⋊C₄	—	2	2	no	—
203	C₁₃×C₂²⋊C₄	—	2	8	no	—
204	C₁₃×C₂²⋊C₄	—	2	8	no	—
205	C₁₃×C₂²⋊C₄	—	2	4	no	—
206	C₁₃×C₂²⋊C₄	—	2	4	no	—
207	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
208	C₄²×C₁₃	—	2	1	no	—
209	C₄²×C₁₃	—	2	2	no	—
210	C₄²×C₁₃	—	2	4	no	—
211	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₁₃	C₂⁴	1	2	yes	—
214	#3549	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#3498	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#3325	C₂×C₁₃	1	4	yes	complemented
217	#3305	C₂×C₁₃	1	4	yes	complemented
218	D₄×D₈	C₂×C₁₃	1	4	yes	complemented
219	#3274	C₂×C₁₃	1	4	yes	complemented
220	#3205	C₂×C₁₃	1	2	yes	complemented
221	#3199	C₂×C₁₃	1	4	yes	complemented
222	#3106	C₂×C₁₃	1	2	yes	complemented
223	#3008	C₂×C₁₃	1	4	yes	complemented
224	#2979	C₂×C₁₃	1	1	yes	characteristic, complemented
225	C₂³×C₁₃	—	2	1	no	—
226	C₂³×C₁₃	—	2	4	no	—
227	C₂³×C₁₃	—	2	4	no	—
228	C₂³×C₁₃	—	4	8	no	—
229	C₂³×C₁₃	—	4	4	no	—
230	C₂³×C₁₃	—	8	4	no	—
231	C₂³×C₁₃	—	8	4	no	—
232	C₂³×C₁₃	—	8	8	no	—
233	C₂³×C₁₃	—	8	8	no	—
234	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
235	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
236	Q₈×C₁₃	—	2	1	no	—
237	Q₈×C₁₃	—	4	2	no	—
238	Q₈×C₁₃	—	8	2	no	—
239	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
240	D₄×C₁₃	—	2	4	no	—
241	D₄×C₁₃	—	2	8	no	—
242	D₄×C₁₃	—	2	1	no	—
243	D₄×C₁₃	—	2	4	no	—
244	D₄×C₁₃	—	2	4	no	—
245	D₄×C₁₃	—	2	4	no	—
246	D₄×C₁₃	—	2	4	no	—
247	D₄×C₁₃	—	4	2	no	—
248	D₄×C₁₃	—	4	4	no	—
249	D₄×C₁₃	—	4	8	no	—
250	D₄×C₁₃	—	4	8	no	—
251	D₄×C₁₃	—	4	4	no	—
252	D₄×C₁₃	—	4	4	no	—
253	D₄×C₁₃	—	4	8	no	—
254	D₄×C₁₃	—	8	4	no	—
255	D₄×C₁₃	—	8	4	no	—
256	D₄×C₁₃	—	8	2	no	—
257	D₄×C₁₃	—	8	8	no	—
258	D₄×C₁₃	—	8	8	no	—
259	D₄×C₁₃	—	8	4	no	—
260	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
261	C₂×C₄×C₁₃	—	2	4	no	—
262	C₂×C₄×C₁₃	—	2	1	no	—
263	C₂×C₄×C₁₃	—	2	4	no	—
264	C₂×C₄×C₁₃	—	2	4	no	—
265	C₂×C₄×C₁₃	—	2	4	no	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	2	1	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	2	4	no	—
270	C₂×C₄×C₁₃	—	4	8	no	—
271	C₂×C₄×C₁₃	—	4	4	no	—
272	C₂×C₄×C₁₃	—	4	8	no	—
273	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
275	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
276	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
277	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
278	C₈×C₁₃	—	2	4	no	—
279	C₈×C₁₃	—	2	4	no	—
280	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	complemented
281	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
282	C₂²×D₈	C₂²×C₁₃	1	4	yes	complemented
283	H(3,𝔽₄)	—	2	2	no	—
284	#555	—	2	1	no	—
285	#555	C₂²×C₁₃	1	4	yes	complemented
286	#550	C₂²×C₁₃	1	4	yes	complemented
287	D₄²	—	2	1	no	—
288	D₄²	—	2	4	no	—
289	D₄²	C₂²×C₁₃	1	4	yes	complemented
290	D₄²	C₂²×C₁₃	1	4	yes	complemented
291	#535	—	2	2	no	—
292	#535	—	2	4	no	—
293	#535	C₂²×C₁₃	1	2	yes	complemented
294	#535	C₂²×C₁₃	1	4	yes	complemented
295	#532	—	2	1	no	—
296	#532	C₂²×C₁₃	1	1	yes	characteristic
297	#532	C₂²×C₁₃	1	2	yes	complemented
298	C₂×#127	—	2	1	no	—
299	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
300	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
301	#493	C₂²×C₁₃	1	4	yes	complemented
302	#486	C₂²×C₁₃	1	4	yes	complemented
303	#482	C₂²×C₁₃	1	4	yes	complemented
304	#482	C₂²×C₁₃	1	8	yes	complemented
305	#477	C₂²×C₁₃	1	2	yes	complemented
306	#476	C₂²×C₁₃	1	2	yes	complemented
307	#469	C₂²×C₁₃	1	8	yes	complemented
308	#466	C₂²×C₁₃	1	8	yes	complemented
309	#460	C₂²×C₁₃	1	2	yes	complemented
310	#459	C₂²×C₁₃	1	2	yes	complemented
311	#459	C₂²×C₁₃	1	4	yes	complemented
312	#459	C₂²×C₁₃	1	4	yes	complemented
313	#449	C₂²×C₁₃	1	4	yes	complemented
314	#449	C₂²×C₁₃	1	8	yes	complemented
315	#447	C₂²×C₁₃	1	8	yes	complemented
316	#447	C₂²×C₁₃	1	8	yes	complemented
317	#447	C₂²×C₁₃	1	8	yes	complemented
318	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
319	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
320	#436	C₂²×C₁₃	1	4	yes	complemented
321	C₈×D₄	C₂²×C₁₃	1	4	yes	complemented
322	#431	C₂²×C₁₃	1	2	yes	complemented
323	#418	C₂²×C₁₃	1	4	yes	complemented
324	#416	C₂²×C₁₃	1	4	yes	complemented
325	#408	C₂²×C₁₃	1	4	yes	complemented
326	C₂²×C₁₃	—	2	1	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	4	no	—
329	C₂²×C₁₃	—	2	2	no	—
330	C₂²×C₁₃	—	2	8	no	—
331	C₂²×C₁₃	—	4	2	no	—
332	C₂²×C₁₃	—	4	4	no	—
333	C₂²×C₁₃	—	4	4	no	—
334	C₂²×C₁₃	—	4	4	no	—
335	C₂²×C₁₃	—	4	8	no	—
336	C₂²×C₁₃	—	4	4	no	—
337	C₂²×C₁₃	—	16	8	no	—
338	C₂²×C₁₃	—	16	4	no	—
339	C₂²×C₁₃	—	16	8	no	—
340	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
341	C₄×C₁₃	—	2	1	no	—
342	C₄×C₁₃	—	2	2	no	—
343	C₄×C₁₃	—	2	4	no	—
344	C₄×C₁₃	—	2	2	no	—
345	C₄×C₁₃	—	4	2	no	—
346	C₄×C₁₃	—	4	4	no	—
347	C₄×C₁₃	#576	1	4	yes	—
348	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
349	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
350	H(5,𝔽₂)	—	4	4	no	—
351	H(5,𝔽₂)	—	4	4	no	—
352	C₂×#41	—	2	2	no	—
353	C₂×#41	—	2	2	no	—
354	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
355	C₂×#41	C₂³×C₁₃	1	4	yes	—
356	C₂×#41	C₂³×C₁₃	1	2	yes	—
357	C₂²×D₄	—	2	2	no	—
358	C₂²×D₄	—	2	4	no	—
359	C₂²×D₄	—	2	4	no	—
360	C₂²×D₄	—	2	4	no	—
361	C₂²×D₄	—	2	2	no	—
362	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
363	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
364	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
365	AGL(1,ℤ/8)	—	4	8	no	—
366	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
367	C₂×D₈	—	4	8	no	—
368	C₂×D₈	C₂³×C₁₃	1	4	yes	—
369	C₂×D₈	C₂³×C₁₃	1	8	yes	—
370	C₂×D₈	C₂³×C₁₃	1	8	yes	—
371	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
372	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
373	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
374	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
375	#127	—	2	2	no	—
376	#127	—	2	4	no	—
377	#127	—	2	4	no	—
378	#127	—	2	1	no	—
379	#127	—	2	1	no	—
380	#127	D₄×C₁₃	1	1	yes	characteristic
381	#127	C₂³×C₁₃	1	4	yes	—
382	#127	C₂³×C₁₃	1	2	yes	—
383	#124	—	2	2	no	—
384	#124	—	2	4	no	—
385	#124	—	2	8	no	—
386	#124	—	2	2	no	—
387	#124	D₄×C₁₃	1	2	yes	—
388	#121	—	2	4	no	—
389	#121	—	2	2	no	—
390	#121	—	2	4	no	—
391	#121	—	2	4	no	—
392	#121	—	2	8	no	—
393	#121	D₄×C₁₃	1	4	yes	—
394	#121	C₂³×C₁₃	1	4	yes	—
395	#121	C₂³×C₁₃	1	8	yes	—
396	#121	C₂³×C₁₃	1	8	yes	—
397	#120	—	2	4	no	—
398	#120	—	2	4	no	—
399	#120	—	2	4	no	—
400	#120	—	2	8	no	—
401	#120	—	2	8	no	—
402	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	4	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	C₂³×C₁₃	1	2	yes	—
407	C₄×D₄	C₂³×C₁₃	1	4	yes	—
408	C₄×D₄	C₂³×C₁₃	1	4	yes	—
409	#117	—	2	4	no	—
410	#117	—	2	1	no	—
411	#117	C₂³×C₁₃	1	1	yes	characteristic
412	#117	C₂³×C₁₃	1	4	yes	—
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
415	#107	C₂³×C₁₃	1	4	yes	—
416	#106	C₂³×C₁₃	1	4	yes	—
417	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
418	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
419	#103	C₂³×C₁₃	1	4	yes	—
420	#102	C₂³×C₁₃	1	8	yes	—
421	#102	C₂³×C₁₃	1	4	yes	—
422	#102	C₂³×C₁₃	1	8	yes	—
423	#102	C₂³×C₁₃	1	4	yes	—
424	#102	C₂³×C₁₃	1	4	yes	—
425	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
426	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
427	C₄×C₈	C₂³×C₁₃	1	4	yes	—
428	C₂×C₁₃	—	4	1	no	—
429	C₂×C₁₃	—	4	4	no	—
430	C₂×C₁₃	—	4	2	no	—
431	C₂×C₁₃	—	8	4	no	—
432	C₂×C₁₃	—	8	4	no	—
433	C₂×C₁₃	#3484	1	1	yes	characteristic
434	C₂×C₁₃	C₂×#576	1	2	yes	—
435	C₂⁴	—	2	4	no	—
436	C₂⁴	—	2	2	no	—
437	C₂⁴	—	2	4	no	—
438	#41	—	2	2	no	—
439	#41	—	2	2	no	—
440	#41	—	2	8	no	—
441	#41	—	4	2	no	—
442	#41	—	4	2	no	—
443	#41	—	4	4	no	—
444	#41	—	4	8	no	—
445	#41	—	8	4	no	—
446	C₂×Q₈	—	2	2	no	—
447	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
448	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	8	no	—
451	C₂×D₄	—	2	4	no	—
452	C₂×D₄	—	2	8	no	—
453	C₂×D₄	—	2	8	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	2	4	no	—
462	C₂×D₄	—	4	4	no	—
463	C₂×D₄	—	4	2	no	—
464	C₂×D₄	—	4	2	no	—
465	C₂×D₄	—	4	4	no	—
466	C₂×D₄	—	4	4	no	—
467	C₂×D₄	—	4	8	no	—
468	C₂×D₄	—	4	16	no	—
469	C₂×D₄	—	8	4	no	—
470	C₂×D₄	—	8	8	no	—
471	C₂×D₄	—	8	8	no	—
472	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
473	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
474	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
475	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
476	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
477	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
483	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
484	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
485	SD₁₆	—	2	8	no	—
486	D₈	—	2	8	no	—
487	D₈	—	4	8	no	—
488	D₈	—	4	8	no	—
489	M₁₆	—	4	4	no	—
490	C₂×C₈	—	4	4	no	—
491	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
492	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
496	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
497	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	4	no	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₂²⋊C₄	—	2	8	no	—
502	C₂²⋊C₄	—	2	8	no	—
503	C₂²⋊C₄	—	2	4	no	—
504	C₂²⋊C₄	—	2	4	no	—
505	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	2	no	—
508	C₄²	—	2	4	no	—
509	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
510	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
511	C₄²	C₂⁴×C₁₃	1	2	yes	—
512	C₁₃	#61661	1	1	yes	characteristic, direct product factor, Sylow
513	C₂³	—	2	1	no	—
514	C₂³	—	2	4	no	—
515	C₂³	—	2	4	no	—
516	C₂³	—	4	8	no	—
517	C₂³	—	4	4	no	—
518	C₂³	—	8	4	no	—
519	C₂³	—	8	4	no	—
520	C₂³	—	8	8	no	—
521	C₂³	—	8	8	no	—
522	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
523	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
524	Q₈	—	2	1	no	—
525	Q₈	—	4	2	no	—
526	Q₈	—	8	2	no	—
527	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
528	D₄	—	2	4	no	—
529	D₄	—	2	8	no	—
530	D₄	—	2	1	no	—
531	D₄	—	2	4	no	—
532	D₄	—	2	4	no	—
533	D₄	—	2	4	no	—
534	D₄	—	2	4	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	4	no	—
537	D₄	—	4	8	no	—
538	D₄	—	4	8	no	—
539	D₄	—	4	4	no	—
540	D₄	—	4	4	no	—
541	D₄	—	4	8	no	—
542	D₄	—	8	4	no	—
543	D₄	—	8	4	no	—
544	D₄	—	8	2	no	—
545	D₄	—	8	8	no	—
546	D₄	—	8	8	no	—
547	D₄	—	8	4	no	—
548	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	4	8	no	—
559	C₂×C₄	—	4	4	no	—
560	C₂×C₄	—	4	8	no	—
561	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
562	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
563	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
564	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
565	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
566	C₈	—	2	4	no	—
567	C₈	—	2	4	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	8	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	4	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	4	4	no	—
575	C₂²	—	4	8	no	—
576	C₂²	—	4	4	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	4	4	no	—
579	C₂²	—	16	8	no	—
580	C₂²	—	16	4	no	—
581	C₂²	—	16	8	no	—
582	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
583	C₄	—	2	2	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	4	no	—
587	C₄	—	4	2	no	—
588	C₄	—	4	4	no	—
589	C₄	C₁₃×#576	1	4	yes	—
590	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
591	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
592	C₂	—	4	1	no	—
593	C₂	—	4	4	no	—
594	C₂	—	4	2	no	—
595	C₂	—	8	4	no	—
596	C₂	—	8	4	no	—
597	C₂	C₁₃×#3484	1	1	yes	characteristic
598	C₂	C₂×C₁₃×#576	1	2	yes	—

	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 ◁ C₁₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3549	C₂	semidirect
2. C₁₃×#3498	C₂	semidirect
3. C₁₃×#3325	C₂	semidirect
4. C₁₃×#3305	C₂	semidirect
5. D₄×C₁₃×D₈	C₂	semidirect
6. C₁₃×#3274	C₂	semidirect
7. C₁₃×#3205	C₂	semidirect
8. C₁₃×#3199	C₂	semidirect
9. C₁₃×#3106	C₂	semidirect
10. C₁₃×#3008	C₂	semidirect
11. C₁₃×#2979	C₂	semidirect
12. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
13. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
14. C₂²×C₁₃×D₈	C₂²	semidirect
17. C₁₃×#555	C₂²	semidirect
18. C₁₃×#550	C₂²	semidirect
21. D₄²×C₁₃	C₂²	semidirect
22. D₄²×C₁₃	C₂²	semidirect
25. C₁₃×#535	C₂²	semidirect
26. C₁₃×#535	C₂²	semidirect
29. C₁₃×#532	C₂²	semidirect
31. C₂×C₁₃×#127	C₂²	semidirect
32. C₄×C₁₃×#41	C₂²	semidirect
33. C₁₃×#493	C₂²	semidirect
34. C₁₃×#486	C₂²	semidirect
35. C₁₃×#482	C₂²	semidirect
36. C₁₃×#482	C₂²	semidirect
37. C₁₃×#477	C₂²	semidirect
38. C₁₃×#476	C₂²	semidirect
39. C₁₃×#469	C₂²	semidirect
40. C₁₃×#466	C₂²	semidirect
41. C₁₃×#460	C₂²	semidirect
42. C₁₃×#459	C₂²	semidirect
43. C₁₃×#459	C₂²	semidirect
44. C₁₃×#459	C₂²	semidirect
45. C₁₃×#449	C₂²	semidirect
46. C₁₃×#449	C₂²	semidirect
47. C₁₃×#447	C₂²	semidirect
48. C₁₃×#447	C₂²	semidirect
49. C₁₃×#447	C₂²	semidirect
50. C₄×C₁₃×SD₁₆	C₂²	semidirect
51. C₄×C₁₃×D₈	C₂²	semidirect
52. C₁₃×#436	C₂²	semidirect
53. C₈×D₄×C₁₃	C₂²	semidirect
54. C₁₃×#431	C₂²	semidirect
55. C₁₃×#418	C₂²	semidirect
56. C₁₃×#416	C₂²	semidirect
57. C₁₃×#408	C₂²	semidirect
136. #61661	C₁₃	direct (N × H)
214. #3549	C₂×C₁₃	semidirect
215. #3498	C₂×C₁₃	semidirect
216. #3325	C₂×C₁₃	semidirect
217. #3305	C₂×C₁₃	semidirect
218. D₄×D₈	C₂×C₁₃	semidirect
219. #3274	C₂×C₁₃	semidirect
220. #3205	C₂×C₁₃	semidirect
221. #3199	C₂×C₁₃	semidirect
222. #3106	C₂×C₁₃	semidirect
223. #3008	C₂×C₁₃	semidirect
224. #2979	C₂×C₁₃	semidirect
280. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
281. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
282. C₂²×D₈	C₂²×C₁₃	semidirect
285. #555	C₂²×C₁₃	semidirect
286. #550	C₂²×C₁₃	semidirect
289. D₄²	C₂²×C₁₃	semidirect
290. D₄²	C₂²×C₁₃	semidirect
293. #535	C₂²×C₁₃	semidirect
294. #535	C₂²×C₁₃	semidirect
297. #532	C₂²×C₁₃	semidirect
299. C₂×#127	C₂²×C₁₃	semidirect
300. C₄×#41	C₂²×C₁₃	semidirect
301. #493	C₂²×C₁₃	semidirect
302. #486	C₂²×C₁₃	semidirect
303. #482	C₂²×C₁₃	semidirect
304. #482	C₂²×C₁₃	semidirect
305. #477	C₂²×C₁₃	semidirect
306. #476	C₂²×C₁₃	semidirect
307. #469	C₂²×C₁₃	semidirect
308. #466	C₂²×C₁₃	semidirect
309. #460	C₂²×C₁₃	semidirect
310. #459	C₂²×C₁₃	semidirect
311. #459	C₂²×C₁₃	semidirect
312. #459	C₂²×C₁₃	semidirect
313. #449	C₂²×C₁₃	semidirect
314. #449	C₂²×C₁₃	semidirect
315. #447	C₂²×C₁₃	semidirect
316. #447	C₂²×C₁₃	semidirect
317. #447	C₂²×C₁₃	semidirect
318. C₄×SD₁₆	C₂²×C₁₃	semidirect
319. C₄×D₈	C₂²×C₁₃	semidirect
320. #436	C₂²×C₁₃	semidirect
321. C₈×D₄	C₂²×C₁₃	semidirect
322. #431	C₂²×C₁₃	semidirect
323. #418	C₂²×C₁₃	semidirect
324. #416	C₂²×C₁₃	semidirect
325. #408	C₂²×C₁₃	semidirect
512. C₁₃	#61661	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×#3549	2
C₁₃×#3498	2
C₁₃×#3325	2
C₁₃×#3305	2
D₄×C₁₃×D₈	2
C₁₃×#3274	2
C₁₃×#3205	2
C₁₃×#3199	2
C₁₃×#3106	2
C₁₃×#3008	2
C₁₃×#2979	2
#61661	13

Subgroups — C13×#61661 #15748000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61661 #15748000