Subgroups — C₁₃×#60798 #15747137

Order 3328.

2822 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3217	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3208	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3205	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3151	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3138	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3038	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3003	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×D₄×C₁₃	—	2	2	no	—
12	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
13	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
14	C₁₃×#533	C₂²	1	2	yes	complemented
15	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
16	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
17	C₁₃×#532	C₂²	1	2	yes	complemented
18	C₂×C₁₃×#127	—	2	2	no	—
19	C₂×C₁₃×#127	—	2	2	no	—
20	C₂×C₁₃×#127	—	2	2	no	—
21	C₂×C₁₃×#127	C₂²	1	2	yes	—
22	C₂×C₁₃×#127	C₂²	1	2	yes	—
23	C₂×C₁₃×#127	C₂²	1	4	yes	—
24	C₂×C₁₃×#127	C₂²	1	4	yes	—
25	C₁₃×#529	—	2	2	no	—
26	C₁₃×#529	—	2	2	no	—
27	C₁₃×#529	C₂²	1	4	yes	complemented
28	C₁₃×#525	—	2	2	no	—
29	C₁₃×#525	C₂²	1	2	yes	—
30	C₄×C₁₃×#41	—	2	2	no	—
31	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#496	C₂²	1	8	yes	complemented
34	C₁₃×#493	C₂²	1	4	yes	complemented
35	C₁₃×#492	C₂²	1	4	yes	complemented
36	C₁₃×#490	C₂²	1	8	yes	complemented
37	C₁₃×#486	C₂²	1	8	yes	complemented
38	C₁₃×#460	C₂²	1	16	yes	complemented
39	C₁₃×#459	C₂²	1	16	yes	complemented
40	C₁₃×#450	C₂²	1	16	yes	complemented
41	C₁₃×#447	C₂²	1	16	yes	complemented
42	C₁₃×#432	C₂²	1	4	yes	complemented
43	C₁₃×#431	C₂²	1	4	yes	complemented
44	C₁₃×#423	C₂²	1	2	yes	complemented
45	C₁₃×#418	C₂²	1	8	yes	complemented
46	C₁₃×#407	C₂²	1	2	yes	—
47	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
48	C₂⁵×C₁₃	—	2	2	no	—
49	C₂×C₁₃×#41	—	2	2	no	—
50	C₂×C₁₃×#41	C₂³	1	2	yes	—
51	C₂²×D₄×C₁₃	—	2	4	no	—
52	C₂²×D₄×C₁₃	—	2	2	no	—
53	C₂²×D₄×C₁₃	—	2	4	no	—
54	C₂²×D₄×C₁₃	—	2	4	no	—
55	C₂²×D₄×C₁₃	—	2	4	no	—
56	C₂²×D₄×C₁₃	—	2	4	no	—
57	C₂²×D₄×C₁₃	—	2	4	no	—
58	C₂²×D₄×C₁₃	—	2	4	no	—
59	C₂²×D₄×C₁₃	—	4	8	no	—
60	C₂²×D₄×C₁₃	—	4	16	no	—
61	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
62	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
63	C₂³×C₄×C₁₃	D₄	1	2	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×AGL(1,ℤ/8)	—	4	16	no	—
66	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	complemented
67	C₂×C₁₃×D₈	C₂³	1	16	yes	complemented
68	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
69	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
70	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
71	C₁₃×#127	—	2	2	no	—
72	C₁₃×#127	—	2	2	no	—
73	C₁₃×#127	—	2	4	no	—
74	C₁₃×#127	—	2	4	no	—
75	C₁₃×#127	—	2	4	no	—
76	C₁₃×#127	—	2	4	no	—
77	C₁₃×#127	—	2	4	no	—
78	C₁₃×#127	C₂³	1	8	yes	—
79	C₁₃×#127	C₂³	1	4	yes	—
80	C₁₃×#127	C₂³	1	4	yes	—
81	C₁₃×#127	C₂³	1	1	yes	characteristic, complemented
82	C₁₃×#126	—	2	4	no	—
83	C₁₃×#125	—	2	2	no	—
84	C₁₃×#125	C₂³	1	2	yes	complemented
85	C₁₃×#124	—	2	2	no	—
86	C₁₃×#124	C₂³	1	2	yes	complemented
87	C₁₃×#123	—	2	4	no	—
88	C₁₃×#123	—	2	2	no	—
89	C₁₃×C₂²⋊Q₈	—	2	2	no	—
90	C₁₃×C₂²⋊Q₈	—	2	2	no	—
91	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
92	C₁₃×#121	—	2	2	no	—
93	C₁₃×#121	—	2	2	no	—
94	C₁₃×#121	C₂³	1	4	yes	—
95	C₁₃×#120	—	2	2	no	—
96	C₄×Q₈×C₁₃	—	2	2	no	—
97	C₄×Q₈×C₁₃	—	2	2	no	—
98	C₄×Q₈×C₁₃	C₂³	1	4	yes	complemented
99	C₄×D₄×C₁₃	—	2	4	no	—
100	C₄×D₄×C₁₃	—	2	4	no	—
101	C₄×D₄×C₁₃	—	2	4	no	—
102	C₄×D₄×C₁₃	—	2	2	no	—
103	C₄×D₄×C₁₃	—	2	2	no	—
104	C₄×D₄×C₁₃	C₂³	1	4	yes	complemented
105	C₁₃×#117	—	2	2	no	—
106	C₁₃×#117	—	2	4	no	—
107	C₁₃×#117	—	2	2	no	—
108	C₁₃×#117	C₂³	1	2	yes	—
109	C₂×C₄²×C₁₃	—	2	2	no	—
110	C₂×C₄²×C₁₃	D₄	1	2	yes	—
111	C₂×C₄²×C₁₃	D₄	1	2	yes	—
112	C₂×C₄²×C₁₃	D₄	1	2	yes	—
113	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
117	C₁₃×C₄⋊C₈	C₂³	1	8	yes	complemented
118	C₁₃×#102	C₂³	1	32	yes	complemented
119	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
120	C₁₃×#97	C₂³	1	4	yes	complemented
121	C₄×C₈×C₁₃	C₂³	1	4	yes	complemented
122	#60798	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₂⁴×C₁₃	—	2	4	no	—
124	C₂⁴×C₁₃	—	2	8	no	—
125	C₂⁴×C₁₃	—	4	8	no	—
126	C₂⁴×C₁₃	—	4	16	no	—
127	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₁₃×#41	—	2	8	no	—
129	C₁₃×#41	—	4	8	no	—
130	C₂×Q₈×C₁₃	—	2	2	no	—
131	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
132	C₂×D₄×C₁₃	—	2	2	no	—
133	C₂×D₄×C₁₃	—	2	4	no	—
134	C₂×D₄×C₁₃	—	2	2	no	—
135	C₂×D₄×C₁₃	—	2	8	no	—
136	C₂×D₄×C₁₃	—	2	4	no	—
137	C₂×D₄×C₁₃	—	2	8	no	—
138	C₂×D₄×C₁₃	—	2	8	no	—
139	C₂×D₄×C₁₃	—	2	8	no	—
140	C₂×D₄×C₁₃	—	2	8	no	—
141	C₂×D₄×C₁₃	—	2	16	no	—
142	C₂×D₄×C₁₃	—	4	16	no	—
143	C₂×D₄×C₁₃	—	4	8	no	—
144	C₂×D₄×C₁₃	—	4	16	no	—
145	C₂×D₄×C₁₃	—	4	16	no	—
146	C₂×D₄×C₁₃	—	4	16	no	—
147	C₂×D₄×C₁₃	—	4	16	no	—
148	C₂×D₄×C₁₃	—	4	16	no	—
149	C₂×D₄×C₁₃	—	4	16	no	—
150	C₂×D₄×C₁₃	—	4	16	no	—
151	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
152	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₁₃	—	2	8	no	—
154	C₂²×C₄×C₁₃	—	2	4	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	—	2	4	no	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
167	C₁₃×SD₁₆	—	4	16	no	—
168	C₁₃×D₈	—	4	16	no	—
169	C₁₃×M₁₆	—	2	8	no	—
170	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
171	C₁₃×C₄⋊C₄	—	2	2	no	—
172	C₁₃×C₄⋊C₄	—	2	2	no	—
173	C₁₃×C₄⋊C₄	—	2	4	no	—
174	C₁₃×C₄⋊C₄	—	2	4	no	—
175	C₁₃×C₄⋊C₄	—	2	4	no	—
176	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
177	C₁₃×C₂²⋊C₄	—	2	4	no	—
178	C₁₃×C₂²⋊C₄	—	2	2	no	—
179	C₁₃×C₂²⋊C₄	—	2	4	no	—
180	C₁₃×C₂²⋊C₄	—	2	4	no	—
181	C₁₃×C₂²⋊C₄	—	2	4	no	—
182	C₄²×C₁₃	—	2	4	no	—
183	C₄²×C₁₃	—	2	2	no	—
184	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₁₃	C₂×D₄	1	2	yes	—
186	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₁₃	C₂×D₄	1	2	yes	—
188	C₄²×C₁₃	C₂×D₄	1	2	yes	—
189	C₄²×C₁₃	C₂×D₄	1	2	yes	—
190	C₄²×C₁₃	C₂×D₄	1	2	yes	—
191	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
192	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
193	C₄²×C₁₃	C₂⁴	1	2	yes	—
194	#3444	C₂×C₁₃	1	1	yes	characteristic, complemented
195	C₂²×#127	C₂×C₁₃	1	1	yes	characteristic, complemented
196	#3217	C₂×C₁₃	1	8	yes	complemented
197	#3208	C₂×C₁₃	1	4	yes	complemented
198	#3205	C₂×C₁₃	1	4	yes	complemented
199	#3151	C₂×C₁₃	1	2	yes	complemented
200	#3138	C₂×C₁₃	1	2	yes	complemented
201	#3038	C₂×C₁₃	1	4	yes	complemented
202	#3003	C₂×C₁₃	1	4	yes	complemented
203	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
204	C₂³×C₁₃	—	2	2	no	—
205	C₂³×C₁₃	—	2	4	no	—
206	C₂³×C₁₃	—	2	2	no	—
207	C₂³×C₁₃	—	2	8	no	—
208	C₂³×C₁₃	—	4	16	no	—
209	C₂³×C₁₃	—	4	16	no	—
210	C₂³×C₁₃	—	4	16	no	—
211	C₂³×C₁₃	—	4	8	no	—
212	C₂³×C₁₃	—	4	16	no	—
213	C₂³×C₁₃	—	8	32	no	—
214	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
215	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
216	Q₈×C₁₃	—	2	4	no	—
217	Q₈×C₁₃	—	4	4	no	—
218	D₄×C₁₃	—	2	4	no	—
219	D₄×C₁₃	—	2	16	no	—
220	D₄×C₁₃	—	4	16	no	—
221	D₄×C₁₃	—	4	16	no	—
222	D₄×C₁₃	—	4	16	no	—
223	D₄×C₁₃	—	4	4	no	—
224	D₄×C₁₃	—	4	8	no	—
225	D₄×C₁₃	—	4	8	no	—
226	D₄×C₁₃	—	4	16	no	—
227	D₄×C₁₃	—	4	16	no	—
228	D₄×C₁₃	—	4	4	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	4	no	—
233	C₂×C₄×C₁₃	—	2	4	no	—
234	C₂×C₄×C₁₃	—	2	4	no	—
235	C₂×C₄×C₁₃	—	2	4	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	4	4	no	—
240	C₂×C₄×C₁₃	—	4	8	no	—
241	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	8	yes	complemented
242	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
243	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
244	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
245	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
249	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
250	C₈×C₁₃	—	2	8	no	—
251	C₂³×D₄	—	2	2	no	—
252	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
253	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	8	yes	complemented
254	#533	C₂²×C₁₃	1	2	yes	complemented
255	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
256	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
257	#532	C₂²×C₁₃	1	2	yes	complemented
258	C₂×#127	—	2	2	no	—
259	C₂×#127	—	2	2	no	—
260	C₂×#127	—	2	2	no	—
261	C₂×#127	C₂²×C₁₃	1	2	yes	—
262	C₂×#127	C₂²×C₁₃	1	4	yes	—
263	C₂×#127	C₂²×C₁₃	1	4	yes	—
264	C₂×#127	C₂²×C₁₃	1	2	yes	—
265	#529	—	2	2	no	—
266	#529	—	2	2	no	—
267	#529	C₂²×C₁₃	1	4	yes	complemented
268	#525	—	2	2	no	—
269	#525	C₂²×C₁₃	1	2	yes	—
270	C₄×#41	—	2	2	no	—
271	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
272	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
273	#496	C₂²×C₁₃	1	8	yes	complemented
274	#493	C₂²×C₁₃	1	4	yes	complemented
275	#492	C₂²×C₁₃	1	4	yes	complemented
276	#490	C₂²×C₁₃	1	8	yes	complemented
277	#486	C₂²×C₁₃	1	8	yes	complemented
278	#460	C₂²×C₁₃	1	16	yes	complemented
279	#459	C₂²×C₁₃	1	16	yes	complemented
280	#450	C₂²×C₁₃	1	16	yes	complemented
281	#447	C₂²×C₁₃	1	16	yes	complemented
282	#432	C₂²×C₁₃	1	4	yes	complemented
283	#431	C₂²×C₁₃	1	4	yes	complemented
284	#423	C₂²×C₁₃	1	2	yes	complemented
285	#418	C₂²×C₁₃	1	8	yes	complemented
286	#407	C₂²×C₁₃	1	2	yes	—
287	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
288	C₂²×C₁₃	—	2	8	no	—
289	C₂²×C₁₃	—	2	2	no	—
290	C₂²×C₁₃	—	2	2	no	—
291	C₂²×C₁₃	—	2	2	no	—
292	C₂²×C₁₃	—	4	2	no	—
293	C₂²×C₁₃	—	4	8	no	—
294	C₂²×C₁₃	—	4	4	no	—
295	C₂²×C₁₃	—	4	16	no	—
296	C₂²×C₁₃	—	8	16	no	—
297	C₂²×C₁₃	—	8	32	no	—
298	C₂²×C₁₃	#535	1	2	yes	—
299	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
300	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
301	C₄×C₁₃	—	2	2	no	—
302	C₄×C₁₃	—	2	2	no	—
303	C₄×C₁₃	—	2	2	no	—
304	C₄×C₁₃	—	4	2	no	—
305	C₄×C₁₃	—	4	4	no	—
306	C₄×C₁₃	#535	1	2	yes	—
307	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
308	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
309	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
310	C₂⁵	—	2	2	no	—
311	C₂×#41	—	2	2	no	—
312	C₂×#41	C₂³×C₁₃	1	2	yes	—
313	C₂²×D₄	—	2	4	no	—
314	C₂²×D₄	—	2	2	no	—
315	C₂²×D₄	—	2	4	no	—
316	C₂²×D₄	—	2	4	no	—
317	C₂²×D₄	—	2	4	no	—
318	C₂²×D₄	—	2	4	no	—
319	C₂²×D₄	—	2	4	no	—
320	C₂²×D₄	—	2	4	no	—
321	C₂²×D₄	—	4	8	no	—
322	C₂²×D₄	—	4	16	no	—
323	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
324	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
325	C₂³×C₄	D₄×C₁₃	1	2	yes	—
326	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
327	AGL(1,ℤ/8)	—	4	16	no	—
328	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	complemented
329	C₂×D₈	C₂³×C₁₃	1	16	yes	complemented
330	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
331	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
332	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
333	#127	—	2	2	no	—
334	#127	—	2	4	no	—
335	#127	—	2	2	no	—
336	#127	—	2	4	no	—
337	#127	—	2	4	no	—
338	#127	—	2	4	no	—
339	#127	—	2	4	no	—
340	#127	C₂³×C₁₃	1	8	yes	—
341	#127	C₂³×C₁₃	1	4	yes	—
342	#127	C₂³×C₁₃	1	4	yes	—
343	#127	C₂³×C₁₃	1	1	yes	characteristic, complemented
344	#126	—	2	4	no	—
345	#125	—	2	2	no	—
346	#125	C₂³×C₁₃	1	2	yes	complemented
347	#124	—	2	2	no	—
348	#124	C₂³×C₁₃	1	2	yes	complemented
349	#123	—	2	4	no	—
350	#123	—	2	2	no	—
351	C₂²⋊Q₈	—	2	2	no	—
352	C₂²⋊Q₈	—	2	2	no	—
353	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
354	#121	—	2	2	no	—
355	#121	—	2	2	no	—
356	#121	C₂³×C₁₃	1	4	yes	—
357	#120	—	2	2	no	—
358	C₄×Q₈	—	2	2	no	—
359	C₄×Q₈	—	2	2	no	—
360	C₄×Q₈	C₂³×C₁₃	1	4	yes	complemented
361	C₄×D₄	—	2	4	no	—
362	C₄×D₄	—	2	4	no	—
363	C₄×D₄	—	2	4	no	—
364	C₄×D₄	—	2	2	no	—
365	C₄×D₄	—	2	2	no	—
366	C₄×D₄	C₂³×C₁₃	1	4	yes	complemented
367	#117	—	2	2	no	—
368	#117	—	2	4	no	—
369	#117	—	2	2	no	—
370	#117	C₂³×C₁₃	1	2	yes	—
371	C₂×C₄²	—	2	2	no	—
372	C₂×C₄²	D₄×C₁₃	1	2	yes	—
373	C₂×C₄²	D₄×C₁₃	1	2	yes	—
374	C₂×C₄²	D₄×C₁₃	1	2	yes	—
375	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
376	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
377	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
378	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
379	C₄⋊C₈	C₂³×C₁₃	1	8	yes	complemented
380	#102	C₂³×C₁₃	1	32	yes	complemented
381	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
382	#97	C₂³×C₁₃	1	4	yes	complemented
383	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
384	C₂×C₁₃	—	2	2	no	—
385	C₂×C₁₃	—	2	4	no	—
386	C₂×C₁₃	—	8	2	no	—
387	C₂×C₁₃	—	8	8	no	—
388	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
389	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	2	yes	—
390	C₂⁴	—	2	4	no	—
391	C₂⁴	—	2	8	no	—
392	C₂⁴	—	4	8	no	—
393	C₂⁴	—	4	16	no	—
394	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
395	#41	—	2	8	no	—
396	#41	—	4	8	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	8	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	8	no	—
405	C₂×D₄	—	2	8	no	—
406	C₂×D₄	—	2	8	no	—
407	C₂×D₄	—	2	8	no	—
408	C₂×D₄	—	2	16	no	—
409	C₂×D₄	—	4	16	no	—
410	C₂×D₄	—	4	8	no	—
411	C₂×D₄	—	4	16	no	—
412	C₂×D₄	—	4	16	no	—
413	C₂×D₄	—	4	16	no	—
414	C₂×D₄	—	4	16	no	—
415	C₂×D₄	—	4	16	no	—
416	C₂×D₄	—	4	16	no	—
417	C₂×D₄	—	4	16	no	—
418	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
419	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
420	C₂²×C₄	—	2	8	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
425	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
427	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
428	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
429	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
430	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
431	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
432	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
433	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
434	SD₁₆	—	4	16	no	—
435	D₈	—	4	16	no	—
436	M₁₆	—	2	8	no	—
437	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₄²	—	2	4	no	—
450	C₄²	—	2	2	no	—
451	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
452	C₄²	C₂×D₄×C₁₃	1	2	yes	—
453	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
454	C₄²	C₂×D₄×C₁₃	1	2	yes	—
455	C₄²	C₂×D₄×C₁₃	1	2	yes	—
456	C₄²	C₂×D₄×C₁₃	1	2	yes	—
457	C₄²	C₂×D₄×C₁₃	1	2	yes	—
458	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
459	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
460	C₄²	C₂⁴×C₁₃	1	2	yes	—
461	C₁₃	#60798	1	1	yes	characteristic, direct product factor, Sylow
462	C₂³	—	2	2	no	—
463	C₂³	—	2	4	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	8	no	—
466	C₂³	—	4	16	no	—
467	C₂³	—	4	16	no	—
468	C₂³	—	4	16	no	—
469	C₂³	—	4	8	no	—
470	C₂³	—	4	16	no	—
471	C₂³	—	8	32	no	—
472	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
473	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
474	Q₈	—	2	4	no	—
475	Q₈	—	4	4	no	—
476	D₄	—	2	4	no	—
477	D₄	—	2	16	no	—
478	D₄	—	4	16	no	—
479	D₄	—	4	16	no	—
480	D₄	—	4	16	no	—
481	D₄	—	4	4	no	—
482	D₄	—	4	8	no	—
483	D₄	—	4	8	no	—
484	D₄	—	4	16	no	—
485	D₄	—	4	16	no	—
486	D₄	—	4	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	4	4	no	—
498	C₂×C₄	—	4	8	no	—
499	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	8	yes	complemented
500	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
501	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
502	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
503	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
504	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
505	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
506	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
507	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
508	C₈	—	2	8	no	—
509	C₂²	—	2	8	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	4	4	no	—
514	C₂²	—	4	16	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	8	no	—
517	C₂²	—	8	16	no	—
518	C₂²	—	8	32	no	—
519	C₂²	C₁₃×#535	1	2	yes	—
520	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
521	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	4	4	no	—
526	C₄	—	4	2	no	—
527	C₄	C₁₃×#535	1	2	yes	—
528	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
529	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
530	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
531	C₂	—	2	2	no	—
532	C₂	—	2	4	no	—
533	C₂	—	8	8	no	—
534	C₂	—	8	2	no	—
535	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
536	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	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 ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3444	C₂	semidirect
2. C₂²×C₁₃×#127	C₂	semidirect
3. C₁₃×#3217	C₂	semidirect
4. C₁₃×#3208	C₂	semidirect
5. C₁₃×#3205	C₂	semidirect
6. C₁₃×#3151	C₂	semidirect
7. C₁₃×#3138	C₂	semidirect
8. C₁₃×#3038	C₂	semidirect
9. C₁₃×#3003	C₂	semidirect
10. C₁₃×#2920	C₂	semidirect
13. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
14. C₁₃×#533	C₂²	semidirect
15. C₁₃×#533	C₂²	semidirect
16. C₁₃×#532	C₂²	semidirect
17. C₁₃×#532	C₂²	semidirect
27. C₁₃×#529	C₂²	semidirect
31. C₄×C₁₃×#41	C₂²	semidirect
33. C₁₃×#496	C₂²	semidirect
34. C₁₃×#493	C₂²	semidirect
35. C₁₃×#492	C₂²	semidirect
36. C₁₃×#490	C₂²	semidirect
37. C₁₃×#486	C₂²	semidirect
38. C₁₃×#460	C₂²	semidirect
39. C₁₃×#459	C₂²	semidirect
40. C₁₃×#450	C₂²	semidirect
41. C₁₃×#447	C₂²	semidirect
42. C₁₃×#432	C₂²	semidirect
43. C₁₃×#431	C₂²	semidirect
44. C₁₃×#423	C₂²	semidirect
45. C₁₃×#418	C₂²	semidirect
47. C₄×C₁₃×M₁₆	C₂²	semidirect
66. C₂×C₁₃×SD₁₆	C₂³	semidirect
67. C₂×C₁₃×D₈	C₂³	semidirect
69. C₁₃×C₄⋊Q₈	C₂³	semidirect
70. C₁₃×C₄⋊Q₈	C₂³	semidirect
81. C₁₃×#127	C₂³	semidirect
84. C₁₃×#125	C₂³	semidirect
86. C₁₃×#124	C₂³	semidirect
98. C₄×Q₈×C₁₃	C₂³	semidirect
104. C₄×D₄×C₁₃	C₂³	semidirect
117. C₁₃×C₄⋊C₈	C₂³	semidirect
118. C₁₃×#102	C₂³	semidirect
120. C₁₃×#97	C₂³	semidirect
121. C₄×C₈×C₁₃	C₂³	semidirect
122. #60798	C₁₃	direct (N × H)
194. #3444	C₂×C₁₃	semidirect
195. C₂²×#127	C₂×C₁₃	semidirect
196. #3217	C₂×C₁₃	semidirect
197. #3208	C₂×C₁₃	semidirect
198. #3205	C₂×C₁₃	semidirect
199. #3151	C₂×C₁₃	semidirect
200. #3138	C₂×C₁₃	semidirect
201. #3038	C₂×C₁₃	semidirect
202. #3003	C₂×C₁₃	semidirect
203. #2920	C₂×C₁₃	semidirect
241. C₂×C₄×C₁₃	AGL(1,ℤ/8)	semidirect
253. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
254. #533	C₂²×C₁₃	semidirect
255. #533	C₂²×C₁₃	semidirect
256. #532	C₂²×C₁₃	semidirect
257. #532	C₂²×C₁₃	semidirect
267. #529	C₂²×C₁₃	semidirect
271. C₄×#41	C₂²×C₁₃	semidirect
273. #496	C₂²×C₁₃	semidirect
274. #493	C₂²×C₁₃	semidirect
275. #492	C₂²×C₁₃	semidirect
276. #490	C₂²×C₁₃	semidirect
277. #486	C₂²×C₁₃	semidirect
278. #460	C₂²×C₁₃	semidirect
279. #459	C₂²×C₁₃	semidirect
280. #450	C₂²×C₁₃	semidirect
281. #447	C₂²×C₁₃	semidirect
282. #432	C₂²×C₁₃	semidirect
283. #431	C₂²×C₁₃	semidirect
284. #423	C₂²×C₁₃	semidirect
285. #418	C₂²×C₁₃	semidirect
287. C₄×M₁₆	C₂²×C₁₃	semidirect
328. C₂×SD₁₆	C₂³×C₁₃	semidirect
329. C₂×D₈	C₂³×C₁₃	semidirect
331. C₄⋊Q₈	C₂³×C₁₃	semidirect
332. C₄⋊Q₈	C₂³×C₁₃	semidirect
343. #127	C₂³×C₁₃	semidirect
346. #125	C₂³×C₁₃	semidirect
348. #124	C₂³×C₁₃	semidirect
360. C₄×Q₈	C₂³×C₁₃	semidirect
366. C₄×D₄	C₂³×C₁₃	semidirect
379. C₄⋊C₈	C₂³×C₁₃	semidirect
380. #102	C₂³×C₁₃	semidirect
382. #97	C₂³×C₁₃	semidirect
383. C₄×C₈	C₂³×C₁₃	semidirect
461. C₁₃	#60798	direct (N × H)
499. 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×#3444	2
C₂²×C₁₃×#127	2
C₁₃×#3217	2
C₁₃×#3208	2
C₁₃×#3205	2
C₁₃×#3151	2
C₁₃×#3138	2
C₁₃×#3038	2
C₁₃×#3003	2
C₁₃×#2920	2
#60798	13

Subgroups — C13×#60798 #15747137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60798 #15747137