Subgroups — C₁₃×#61707 #15748046

Order 3328.

2086 conjugacy classes of subgroups.

The subgroup lattice has 664 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×#553	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3345	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3318	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3234	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3192	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3186	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3109	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3094	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#481	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×H(5,𝔽₂)	—	2	1	no	—
13	C₁₃×#553	—	2	4	no	—
14	C₁₃×#553	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	1	no	—
20	C₁₃×#534	—	2	1	no	—
21	C₁₃×#532	C₂²	1	2	yes	—
22	C₂×C₁₃×#126	—	2	1	no	—
23	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₃×#123	—	2	1	no	—
25	C₂×C₁₃×#121	—	2	1	no	—
26	C₂×C₁₃×#121	C₂²	1	2	yes	—
27	C₂×C₁₃×#121	C₂²	1	2	yes	—
28	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄×D₄×C₁₃	—	2	1	no	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#501	C₂²	1	4	yes	complemented
36	C₁₃×#490	C₂²	1	4	yes	complemented
37	C₁₃×#482	C₂²	1	8	yes	complemented
38	C₁₃×#481	C₂²	1	8	yes	complemented
39	C₁₃×#481	C₂²	1	4	yes	complemented
40	C₁₃×#481	C₂²	1	4	yes	complemented
41	C₁₃×#481	C₂²	1	4	yes	complemented
42	C₁₃×#480	C₂²	1	4	yes	complemented
43	C₁₃×#480	C₂²	1	4	yes	complemented
44	C₁₃×#478	C₂²	1	8	yes	complemented
45	C₁₃×#476	C₂²	1	4	yes	complemented
46	C₁₃×#469	C₂²	1	8	yes	complemented
47	C₁₃×#466	C₂²	1	8	yes	complemented
48	C₁₃×#459	C₂²	1	4	yes	complemented
49	C₁₃×#447	C₂²	1	4	yes	complemented
50	C₁₃×#447	C₂²	1	4	yes	complemented
51	C₁₃×#447	C₂²	1	4	yes	complemented
52	C₁₃×#442	C₂²	1	8	yes	complemented
53	C₁₃×#435	C₂²	1	8	yes	complemented
54	C₁₃×#432	C₂²	1	2	yes	complemented
55	C₁₃×#428	C₂²	1	4	yes	complemented
56	C₂×C₁₃×#106	C₂²	1	4	yes	complemented
57	C₁₃×#418	C₂²	1	4	yes	complemented
58	C₂×C₁₃×#102	C₂²	1	4	yes	complemented
59	C₁₃×#407	C₂²	1	2	yes	complemented
60	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
61	C₁₃×H(5,𝔽₂)	—	4	8	no	—
62	C₂×C₁₃×#41	—	2	4	no	—
63	C₂×C₁₃×#41	—	2	2	no	—
64	C₂²×D₄×C₁₃	—	2	1	no	—
65	C₂²×D₄×C₁₃	—	2	2	no	—
66	C₂²×D₄×C₁₃	—	2	2	no	—
67	C₂²×D₄×C₁₃	—	2	1	no	—
68	C₂²×D₄×C₁₃	—	2	4	no	—
69	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
70	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	—	2	1	no	—
74	C₂³×C₄×C₁₃	—	2	1	no	—
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×D₈	C₂³	1	8	yes	—
78	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
79	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
80	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
81	C₁₃×#127	C₂³	1	2	yes	—
82	C₁₃×#126	—	2	8	no	—
83	C₁₃×#125	—	2	2	no	—
84	C₁₃×#125	C₂³	1	4	yes	—
85	C₁₃×#124	—	2	2	no	—
86	C₁₃×#123	—	2	8	no	—
87	C₁₃×#123	—	2	4	no	—
88	C₁₃×#123	—	2	4	no	—
89	C₁₃×C₂²⋊Q₈	—	2	4	no	—
90	C₁₃×#121	—	2	8	no	—
91	C₁₃×#121	—	2	2	no	—
92	C₁₃×#121	—	2	2	no	—
93	C₁₃×#121	—	2	2	no	—
94	C₁₃×#121	—	2	2	no	—
95	C₁₃×#121	—	2	2	no	—
96	C₁₃×#121	—	2	2	no	—
97	C₁₃×#121	—	2	2	no	—
98	C₁₃×#121	—	2	4	no	—
99	C₁₃×#121	C₂³	1	4	yes	—
100	C₁₃×#121	C₂³	1	4	yes	—
101	C₁₃×#121	C₂³	1	4	yes	—
102	C₁₃×#121	C₂³	1	4	yes	—
103	C₁₃×#121	C₂³	1	4	yes	—
104	C₁₃×#120	—	2	4	no	—
105	C₁₃×#120	—	2	4	no	—
106	C₄×D₄×C₁₃	—	2	8	no	—
107	C₄×D₄×C₁₃	—	2	2	no	—
108	C₄×D₄×C₁₃	—	2	2	no	—
109	C₄×D₄×C₁₃	D₄	1	4	yes	—
110	C₄×D₄×C₁₃	C₂³	1	4	yes	—
111	C₄×D₄×C₁₃	C₂³	1	4	yes	—
112	C₄×D₄×C₁₃	C₂³	1	4	yes	—
113	C₁₃×#117	—	2	2	no	—
114	C₁₃×#117	C₂³	1	4	yes	—
115	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
126	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
127	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
128	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
129	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
130	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
131	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
132	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
133	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
134	C₂×C₄²×C₁₃	—	2	1	no	—
135	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
136	C₁₃×#107	C₂³	1	8	yes	—
137	C₁₃×#106	C₂³	1	8	yes	—
138	C₁₃×#106	C₂³	1	8	yes	—
139	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
140	C₁₃×#102	C₂³	1	8	yes	—
141	C₁₃×#102	C₂³	1	8	yes	—
142	C₁₃×#102	C₂³	1	8	yes	—
143	C₁₃×#102	C₂³	1	8	yes	—
144	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
145	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
146	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
147	C₁₃×#97	C₂³	1	4	yes	—
148	#61707	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂⁴×C₁₃	—	2	1	no	—
150	C₂⁴×C₁₃	—	2	2	no	—
151	C₂⁴×C₁₃	—	2	2	no	—
152	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₁₃×#41	—	4	8	no	—
155	C₁₃×#41	—	4	16	no	—
156	C₂×Q₈×C₁₃	—	2	2	no	—
157	C₂×D₄×C₁₃	—	2	4	no	—
158	C₂×D₄×C₁₃	—	2	4	no	—
159	C₂×D₄×C₁₃	—	2	4	no	—
160	C₂×D₄×C₁₃	—	2	4	no	—
161	C₂×D₄×C₁₃	—	2	4	no	—
162	C₂×D₄×C₁₃	—	2	4	no	—
163	C₂×D₄×C₁₃	—	2	1	no	—
164	C₂×D₄×C₁₃	—	2	2	no	—
165	C₂×D₄×C₁₃	—	2	2	no	—
166	C₂×D₄×C₁₃	—	2	2	no	—
167	C₂×D₄×C₁₃	—	2	2	no	—
168	C₂×D₄×C₁₃	—	4	2	no	—
169	C₂×D₄×C₁₃	—	4	4	no	—
170	C₂×D₄×C₁₃	—	4	4	no	—
171	C₂×D₄×C₁₃	—	4	16	no	—
172	C₂×D₄×C₁₃	—	4	8	no	—
173	C₂×D₄×C₁₃	—	4	4	no	—
174	C₂×D₄×C₁₃	—	4	8	no	—
175	C₂×D₄×C₁₃	—	8	2	no	—
176	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
177	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
178	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₃	—	2	1	no	—
180	C₂²×C₄×C₁₃	—	2	1	no	—
181	C₂²×C₄×C₁₃	—	2	1	no	—
182	C₂²×C₄×C₁₃	—	2	2	no	—
183	C₂²×C₄×C₁₃	—	2	2	no	—
184	C₂²×C₄×C₁₃	—	2	4	no	—
185	C₂²×C₄×C₁₃	—	2	4	no	—
186	C₂²×C₄×C₁₃	—	2	4	no	—
187	C₂²×C₄×C₁₃	—	4	2	no	—
188	C₂²×C₄×C₁₃	—	4	2	no	—
189	C₂²×C₄×C₁₃	—	8	2	no	—
190	C₂²×C₄×C₁₃	—	8	2	no	—
191	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
196	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
197	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
200	C₁₃×D₈	—	4	8	no	—
201	C₁₃×M₁₆	—	4	4	no	—
202	C₂×C₈×C₁₃	—	4	4	no	—
203	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
204	C₁₃×C₄⋊C₄	—	2	1	no	—
205	C₁₃×C₄⋊C₄	—	2	1	no	—
206	C₁₃×C₄⋊C₄	—	2	4	no	—
207	C₁₃×C₄⋊C₄	—	2	4	no	—
208	C₁₃×C₄⋊C₄	—	2	4	no	—
209	C₁₃×C₄⋊C₄	—	2	1	no	—
210	C₁₃×C₄⋊C₄	—	2	2	no	—
211	C₁₃×C₄⋊C₄	—	2	2	no	—
212	C₁₃×C₄⋊C₄	—	2	2	no	—
213	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
214	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
215	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
216	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
217	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
218	C₁₃×C₂²⋊C₄	—	2	4	no	—
219	C₁₃×C₂²⋊C₄	—	2	4	no	—
220	C₁₃×C₂²⋊C₄	—	2	4	no	—
221	C₁₃×C₂²⋊C₄	—	2	4	no	—
222	C₁₃×C₂²⋊C₄	—	2	4	no	—
223	C₁₃×C₂²⋊C₄	—	2	4	no	—
224	C₁₃×C₂²⋊C₄	—	2	4	no	—
225	C₁₃×C₂²⋊C₄	—	2	4	no	—
226	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
227	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
228	C₄²×C₁₃	—	2	4	no	—
229	C₄²×C₁₃	C₂×D₄	1	2	yes	—
230	C₄²×C₁₃	C₂⁴	1	2	yes	—
231	#3496	C₂×C₁₃	1	1	yes	characteristic, complemented
232	C₂×#553	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#3345	C₂×C₁₃	1	8	yes	complemented
234	#3318	C₂×C₁₃	1	8	yes	complemented
235	#3234	C₂×C₁₃	1	2	yes	complemented
236	#3192	C₂×C₁₃	1	2	yes	complemented
237	#3186	C₂×C₁₃	1	2	yes	complemented
238	#3109	C₂×C₁₃	1	2	yes	complemented
239	#3094	C₂×C₁₃	1	2	yes	complemented
240	C₂×#481	C₂×C₁₃	1	2	yes	complemented
241	#2973	C₂×C₁₃	1	1	yes	characteristic, complemented
242	C₂³×C₁₃	—	2	2	no	—
243	C₂³×C₁₃	—	2	2	no	—
244	C₂³×C₁₃	—	2	4	no	—
245	C₂³×C₁₃	—	4	1	no	—
246	C₂³×C₁₃	—	4	1	no	—
247	C₂³×C₁₃	—	4	1	no	—
248	C₂³×C₁₃	—	4	1	no	—
249	C₂³×C₁₃	—	4	2	no	—
250	C₂³×C₁₃	—	4	2	no	—
251	C₂³×C₁₃	—	4	4	no	—
252	C₂³×C₁₃	—	4	2	no	—
253	C₂³×C₁₃	—	4	4	no	—
254	C₂³×C₁₃	—	8	2	no	—
255	C₂³×C₁₃	—	8	2	no	—
256	C₂³×C₁₃	—	8	2	no	—
257	C₂³×C₁₃	—	8	2	no	—
258	C₂³×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
259	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
260	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
261	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
262	Q₈×C₁₃	—	4	4	no	—
263	D₄×C₁₃	—	2	8	no	—
264	D₄×C₁₃	—	2	4	no	—
265	D₄×C₁₃	—	2	8	no	—
266	D₄×C₁₃	—	4	2	no	—
267	D₄×C₁₃	—	4	4	no	—
268	D₄×C₁₃	—	4	8	no	—
269	D₄×C₁₃	—	4	8	no	—
270	D₄×C₁₃	—	4	8	no	—
271	D₄×C₁₃	—	4	8	no	—
272	D₄×C₁₃	—	8	2	no	—
273	D₄×C₁₃	—	8	2	no	—
274	D₄×C₁₃	—	8	2	no	—
275	D₄×C₁₃	—	8	4	no	—
276	C₂×C₄×C₁₃	—	2	2	no	—
277	C₂×C₄×C₁₃	—	2	4	no	—
278	C₂×C₄×C₁₃	—	2	4	no	—
279	C₂×C₄×C₁₃	—	2	2	no	—
280	C₂×C₄×C₁₃	—	2	2	no	—
281	C₂×C₄×C₁₃	—	2	2	no	—
282	C₂×C₄×C₁₃	—	2	4	no	—
283	C₂×C₄×C₁₃	—	2	2	no	—
284	C₂×C₄×C₁₃	—	4	2	no	—
285	C₂×C₄×C₁₃	—	4	2	no	—
286	C₂×C₄×C₁₃	—	4	1	no	—
287	C₂×C₄×C₁₃	—	4	1	no	—
288	C₂×C₄×C₁₃	—	4	1	no	—
289	C₂×C₄×C₁₃	—	4	8	no	—
290	C₂×C₄×C₁₃	—	4	2	no	—
291	C₂×C₄×C₁₃	—	4	2	no	—
292	C₂×C₄×C₁₃	—	4	4	no	—
293	C₂×C₄×C₁₃	—	4	2	no	—
294	C₂×C₄×C₁₃	—	4	4	no	—
295	C₂×C₄×C₁₃	—	8	4	no	—
296	C₂×C₄×C₁₃	—	8	4	no	—
297	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
298	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
300	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
301	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
302	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
303	C₈×C₁₃	—	2	8	no	—
304	C₂×H(5,𝔽₂)	—	2	1	no	—
305	#553	—	2	4	no	—
306	#553	C₂²×C₁₃	1	8	yes	complemented
307	#547	C₂²×C₁₃	1	4	yes	complemented
308	#546	—	2	4	no	—
309	D₄²	C₂²×C₁₃	1	4	yes	complemented
310	#537	—	2	1	no	—
311	#534	—	2	1	no	—
312	#534	—	2	1	no	—
313	#532	C₂²×C₁₃	1	2	yes	—
314	C₂×#126	—	2	1	no	—
315	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
316	C₂×#123	—	2	1	no	—
317	C₂×#121	—	2	1	no	—
318	C₂×#121	C₂²×C₁₃	1	2	yes	—
319	C₂×#121	C₂²×C₁₃	1	2	yes	—
320	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
321	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
322	C₂×C₄×D₄	—	2	1	no	—
323	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
325	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
326	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
327	#501	C₂²×C₁₃	1	4	yes	complemented
328	#490	C₂²×C₁₃	1	4	yes	complemented
329	#482	C₂²×C₁₃	1	8	yes	complemented
330	#481	C₂²×C₁₃	1	8	yes	complemented
331	#481	C₂²×C₁₃	1	4	yes	complemented
332	#481	C₂²×C₁₃	1	4	yes	complemented
333	#481	C₂²×C₁₃	1	4	yes	complemented
334	#480	C₂²×C₁₃	1	4	yes	complemented
335	#480	C₂²×C₁₃	1	4	yes	complemented
336	#478	C₂²×C₁₃	1	8	yes	complemented
337	#476	C₂²×C₁₃	1	4	yes	complemented
338	#469	C₂²×C₁₃	1	8	yes	complemented
339	#466	C₂²×C₁₃	1	8	yes	complemented
340	#459	C₂²×C₁₃	1	4	yes	complemented
341	#447	C₂²×C₁₃	1	4	yes	complemented
342	#447	C₂²×C₁₃	1	4	yes	complemented
343	#447	C₂²×C₁₃	1	4	yes	complemented
344	#442	C₂²×C₁₃	1	8	yes	complemented
345	#435	C₂²×C₁₃	1	8	yes	complemented
346	#432	C₂²×C₁₃	1	2	yes	complemented
347	#428	C₂²×C₁₃	1	4	yes	complemented
348	C₂×#106	C₂²×C₁₃	1	4	yes	complemented
349	#418	C₂²×C₁₃	1	4	yes	complemented
350	C₂×#102	C₂²×C₁₃	1	4	yes	complemented
351	#407	C₂²×C₁₃	1	2	yes	complemented
352	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
353	C₂²×C₁₃	—	2	1	no	—
354	C₂²×C₁₃	—	2	2	no	—
355	C₂²×C₁₃	—	2	1	no	—
356	C₂²×C₁₃	—	2	2	no	—
357	C₂²×C₁₃	—	2	2	no	—
358	C₂²×C₁₃	—	2	2	no	—
359	C₂²×C₁₃	—	2	2	no	—
360	C₂²×C₁₃	—	4	4	no	—
361	C₂²×C₁₃	—	4	2	no	—
362	C₂²×C₁₃	—	4	4	no	—
363	C₂²×C₁₃	—	4	2	no	—
364	C₂²×C₁₃	—	4	4	no	—
365	C₂²×C₁₃	—	4	4	no	—
366	C₂²×C₁₃	—	4	2	no	—
367	C₂²×C₁₃	—	8	2	no	—
368	C₂²×C₁₃	—	8	4	no	—
369	C₂²×C₁₃	—	16	4	no	—
370	C₂²×C₁₃	—	16	4	no	—
371	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
372	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
373	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
374	C₄×C₁₃	—	2	2	no	—
375	C₄×C₁₃	—	2	1	no	—
376	C₄×C₁₃	—	2	2	no	—
377	C₄×C₁₃	—	2	2	no	—
378	C₄×C₁₃	—	2	2	no	—
379	C₄×C₁₃	—	4	2	no	—
380	C₄×C₁₃	—	4	2	no	—
381	C₄×C₁₃	—	4	4	no	—
382	C₄×C₁₃	—	4	2	no	—
383	C₄×C₁₃	#585	1	2	yes	—
384	H(5,𝔽₂)	—	4	8	no	—
385	C₂×#41	—	2	4	no	—
386	C₂×#41	—	2	2	no	—
387	C₂²×D₄	—	2	1	no	—
388	C₂²×D₄	—	2	2	no	—
389	C₂²×D₄	—	2	2	no	—
390	C₂²×D₄	—	2	1	no	—
391	C₂²×D₄	—	2	4	no	—
392	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
393	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
394	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
395	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
396	C₂³×C₄	—	2	1	no	—
397	C₂³×C₄	—	2	1	no	—
398	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
399	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
400	C₂×D₈	C₂³×C₁₃	1	8	yes	—
401	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
402	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
403	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
404	#127	C₂³×C₁₃	1	2	yes	—
405	#126	—	2	8	no	—
406	#125	—	2	2	no	—
407	#125	C₂³×C₁₃	1	4	yes	—
408	#124	—	2	2	no	—
409	#123	—	2	8	no	—
410	#123	—	2	4	no	—
411	#123	—	2	4	no	—
412	C₂²⋊Q₈	—	2	4	no	—
413	#121	—	2	8	no	—
414	#121	—	2	2	no	—
415	#121	—	2	2	no	—
416	#121	—	2	2	no	—
417	#121	—	2	2	no	—
418	#121	—	2	2	no	—
419	#121	—	2	2	no	—
420	#121	—	2	2	no	—
421	#121	—	2	4	no	—
422	#121	C₂³×C₁₃	1	4	yes	—
423	#121	C₂³×C₁₃	1	4	yes	—
424	#121	C₂³×C₁₃	1	4	yes	—
425	#121	C₂³×C₁₃	1	4	yes	—
426	#121	C₂³×C₁₃	1	4	yes	—
427	#120	—	2	4	no	—
428	#120	—	2	4	no	—
429	C₄×D₄	—	2	8	no	—
430	C₄×D₄	—	2	2	no	—
431	C₄×D₄	—	2	2	no	—
432	C₄×D₄	D₄×C₁₃	1	4	yes	—
433	C₄×D₄	C₂³×C₁₃	1	4	yes	—
434	C₄×D₄	C₂³×C₁₃	1	4	yes	—
435	C₄×D₄	C₂³×C₁₃	1	4	yes	—
436	#117	—	2	2	no	—
437	#117	C₂³×C₁₃	1	4	yes	—
438	C₂×C₄⋊C₄	—	2	1	no	—
439	C₂×C₄⋊C₄	—	2	2	no	—
440	C₂×C₄⋊C₄	—	2	1	no	—
441	C₂×C₄⋊C₄	—	2	1	no	—
442	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
446	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
448	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	—	2	2	no	—
453	C₂×C₂²⋊C₄	—	2	2	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
456	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
457	C₂×C₄²	—	2	1	no	—
458	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
459	#107	C₂³×C₁₃	1	8	yes	—
460	#106	C₂³×C₁₃	1	8	yes	—
461	#106	C₂³×C₁₃	1	8	yes	—
462	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
463	#102	C₂³×C₁₃	1	8	yes	—
464	#102	C₂³×C₁₃	1	8	yes	—
465	#102	C₂³×C₁₃	1	8	yes	—
466	#102	C₂³×C₁₃	1	8	yes	—
467	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
468	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
469	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
470	#97	C₂³×C₁₃	1	4	yes	—
471	C₂×C₁₃	—	2	2	no	—
472	C₂×C₁₃	—	2	4	no	—
473	C₂×C₁₃	—	4	2	no	—
474	C₂×C₁₃	—	8	2	no	—
475	C₂×C₁₃	—	8	4	no	—
476	C₂×C₁₃	#3485	1	1	yes	characteristic
477	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
478	C₂×C₁₃	#3585	1	1	yes	characteristic
479	C₂⁴	—	2	1	no	—
480	C₂⁴	—	2	2	no	—
481	C₂⁴	—	2	2	no	—
482	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
483	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
484	#41	—	4	8	no	—
485	#41	—	4	16	no	—
486	C₂×Q₈	—	2	2	no	—
487	C₂×D₄	—	2	4	no	—
488	C₂×D₄	—	2	4	no	—
489	C₂×D₄	—	2	4	no	—
490	C₂×D₄	—	2	4	no	—
491	C₂×D₄	—	2	4	no	—
492	C₂×D₄	—	2	4	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	2	no	—
495	C₂×D₄	—	2	2	no	—
496	C₂×D₄	—	2	2	no	—
497	C₂×D₄	—	2	2	no	—
498	C₂×D₄	—	4	2	no	—
499	C₂×D₄	—	4	4	no	—
500	C₂×D₄	—	4	4	no	—
501	C₂×D₄	—	4	16	no	—
502	C₂×D₄	—	4	8	no	—
503	C₂×D₄	—	4	8	no	—
504	C₂×D₄	—	4	4	no	—
505	C₂×D₄	—	8	2	no	—
506	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
507	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
508	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	4	no	—
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	—	4	2	no	—
519	C₂²×C₄	—	8	2	no	—
520	C₂²×C₄	—	8	2	no	—
521	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
522	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
523	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
524	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
525	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
526	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
530	D₈	—	4	8	no	—
531	M₁₆	—	4	4	no	—
532	C₂×C₈	—	4	4	no	—
533	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	4	no	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	2	no	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
544	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
545	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
546	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
547	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
548	C₂²⋊C₄	—	2	4	no	—
549	C₂²⋊C₄	—	2	4	no	—
550	C₂²⋊C₄	—	2	4	no	—
551	C₂²⋊C₄	—	2	4	no	—
552	C₂²⋊C₄	—	2	4	no	—
553	C₂²⋊C₄	—	2	4	no	—
554	C₂²⋊C₄	—	2	4	no	—
555	C₂²⋊C₄	—	2	4	no	—
556	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
557	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
558	C₄²	—	2	4	no	—
559	C₄²	C₂×D₄×C₁₃	1	2	yes	—
560	C₄²	C₂⁴×C₁₃	1	2	yes	—
561	C₁₃	#61707	1	1	yes	characteristic, direct product factor, Sylow
562	C₂³	—	2	2	no	—
563	C₂³	—	2	2	no	—
564	C₂³	—	2	4	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	4	1	no	—
568	C₂³	—	4	1	no	—
569	C₂³	—	4	2	no	—
570	C₂³	—	4	2	no	—
571	C₂³	—	4	4	no	—
572	C₂³	—	4	2	no	—
573	C₂³	—	4	4	no	—
574	C₂³	—	8	2	no	—
575	C₂³	—	8	2	no	—
576	C₂³	—	8	2	no	—
577	C₂³	—	8	2	no	—
578	C₂³	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
579	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
580	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
581	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
582	Q₈	—	4	4	no	—
583	D₄	—	2	8	no	—
584	D₄	—	2	4	no	—
585	D₄	—	2	8	no	—
586	D₄	—	4	4	no	—
587	D₄	—	4	2	no	—
588	D₄	—	4	8	no	—
589	D₄	—	4	8	no	—
590	D₄	—	4	8	no	—
591	D₄	—	4	8	no	—
592	D₄	—	8	2	no	—
593	D₄	—	8	2	no	—
594	D₄	—	8	2	no	—
595	D₄	—	8	4	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	4	2	no	—
605	C₂×C₄	—	4	2	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	8	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	4	4	no	—
613	C₂×C₄	—	4	2	no	—
614	C₂×C₄	—	4	4	no	—
615	C₂×C₄	—	8	4	no	—
616	C₂×C₄	—	8	4	no	—
617	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
618	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
619	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
620	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
621	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
622	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
623	C₈	—	2	8	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	2	2	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	4	4	no	—
632	C₂²	—	4	4	no	—
633	C₂²	—	4	2	no	—
634	C₂²	—	4	2	no	—
635	C₂²	—	4	4	no	—
636	C₂²	—	4	2	no	—
637	C₂²	—	4	4	no	—
638	C₂²	—	8	2	no	—
639	C₂²	—	8	4	no	—
640	C₂²	—	16	4	no	—
641	C₂²	—	16	4	no	—
642	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
643	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
644	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
645	C₄	—	2	2	no	—
646	C₄	—	2	2	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	4	4	no	—
651	C₄	—	4	2	no	—
652	C₄	—	4	2	no	—
653	C₄	—	4	2	no	—
654	C₄	C₁₃×#585	1	2	yes	—
655	C₂	—	2	2	no	—
656	C₂	—	2	4	no	—
657	C₂	—	4	2	no	—
658	C₂	—	8	2	no	—
659	C₂	—	8	4	no	—
660	C₂	C₁₃×#3485	1	1	yes	characteristic
661	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
662	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×#553	C₂	semidirect
3. C₁₃×#3345	C₂	semidirect
4. C₁₃×#3318	C₂	semidirect
5. C₁₃×#3234	C₂	semidirect
6. C₁₃×#3192	C₂	semidirect
7. C₁₃×#3186	C₂	semidirect
8. C₁₃×#3109	C₂	semidirect
9. C₁₃×#3094	C₂	semidirect
10. C₂×C₁₃×#481	C₂	semidirect
11. C₁₃×#2973	C₂	semidirect
14. C₁₃×#553	C₂²	semidirect
15. C₁₃×#547	C₂²	semidirect
17. D₄²×C₁₃	C₂²	semidirect
23. C₂×C₁₃×#125	C₂²	semidirect
28. C₂×C₁₃×#121	C₂²	semidirect
29. C₂×C₁₃×#121	C₂²	semidirect
32. C₂×C₄×D₄×C₁₃	C₂²	semidirect
33. C₂×C₁₃×#117	C₂²	semidirect
34. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
35. C₁₃×#501	C₂²	semidirect
36. C₁₃×#490	C₂²	semidirect
37. C₁₃×#482	C₂²	semidirect
38. C₁₃×#481	C₂²	semidirect
39. C₁₃×#481	C₂²	semidirect
40. C₁₃×#481	C₂²	semidirect
41. C₁₃×#481	C₂²	semidirect
42. C₁₃×#480	C₂²	semidirect
43. C₁₃×#480	C₂²	semidirect
44. C₁₃×#478	C₂²	semidirect
45. C₁₃×#476	C₂²	semidirect
46. C₁₃×#469	C₂²	semidirect
47. C₁₃×#466	C₂²	semidirect
48. C₁₃×#459	C₂²	semidirect
49. C₁₃×#447	C₂²	semidirect
50. C₁₃×#447	C₂²	semidirect
51. C₁₃×#447	C₂²	semidirect
52. C₁₃×#442	C₂²	semidirect
53. C₁₃×#435	C₂²	semidirect
54. C₁₃×#432	C₂²	semidirect
55. C₁₃×#428	C₂²	semidirect
56. C₂×C₁₃×#106	C₂²	semidirect
57. C₁₃×#418	C₂²	semidirect
58. C₂×C₁₃×#102	C₂²	semidirect
59. C₁₃×#407	C₂²	semidirect
60. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
148. #61707	C₁₃	direct (N × H)
231. #3496	C₂×C₁₃	semidirect
232. C₂×#553	C₂×C₁₃	semidirect
233. #3345	C₂×C₁₃	semidirect
234. #3318	C₂×C₁₃	semidirect
235. #3234	C₂×C₁₃	semidirect
236. #3192	C₂×C₁₃	semidirect
237. #3186	C₂×C₁₃	semidirect
238. #3109	C₂×C₁₃	semidirect
239. #3094	C₂×C₁₃	semidirect
240. C₂×#481	C₂×C₁₃	semidirect
241. #2973	C₂×C₁₃	semidirect
306. #553	C₂²×C₁₃	semidirect
307. #547	C₂²×C₁₃	semidirect
309. D₄²	C₂²×C₁₃	semidirect
315. C₂×#125	C₂²×C₁₃	semidirect
320. C₂×#121	C₂²×C₁₃	semidirect
321. C₂×#121	C₂²×C₁₃	semidirect
324. C₂×C₄×D₄	C₂²×C₁₃	semidirect
325. C₂×#117	C₂²×C₁₃	semidirect
326. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
327. #501	C₂²×C₁₃	semidirect
328. #490	C₂²×C₁₃	semidirect
329. #482	C₂²×C₁₃	semidirect
330. #481	C₂²×C₁₃	semidirect
331. #481	C₂²×C₁₃	semidirect
332. #481	C₂²×C₁₃	semidirect
333. #481	C₂²×C₁₃	semidirect
334. #480	C₂²×C₁₃	semidirect
335. #480	C₂²×C₁₃	semidirect
336. #478	C₂²×C₁₃	semidirect
337. #476	C₂²×C₁₃	semidirect
338. #469	C₂²×C₁₃	semidirect
339. #466	C₂²×C₁₃	semidirect
340. #459	C₂²×C₁₃	semidirect
341. #447	C₂²×C₁₃	semidirect
342. #447	C₂²×C₁₃	semidirect
343. #447	C₂²×C₁₃	semidirect
344. #442	C₂²×C₁₃	semidirect
345. #435	C₂²×C₁₃	semidirect
346. #432	C₂²×C₁₃	semidirect
347. #428	C₂²×C₁₃	semidirect
348. C₂×#106	C₂²×C₁₃	semidirect
349. #418	C₂²×C₁₃	semidirect
350. C₂×#102	C₂²×C₁₃	semidirect
351. #407	C₂²×C₁₃	semidirect
352. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
561. C₁₃	#61707	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×#3496	2
C₂×C₁₃×#553	2
C₁₃×#3345	2
C₁₃×#3318	2
C₁₃×#3234	2
C₁₃×#3192	2
C₁₃×#3186	2
C₁₃×#3109	2
C₁₃×#3094	2
C₂×C₁₃×#481	2
C₁₃×#2973	2
#61707	13

Subgroups — C13×#61707 #15748046

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61707 #15748046