Subgroups — C₁₃×#60799 #15747138

Order 3328.

2262 conjugacy classes of subgroups.

The subgroup lattice has 586 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×#124	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3215	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3213	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3211	C₂	1	8	yes	maximal, complemented
6	C₁₃×#3153	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3140	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3040	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3004	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3003	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
15	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	—
16	C₁₃×#533	C₂²	1	2	yes	complemented
17	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
18	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
19	C₁₃×#532	C₂²	1	2	yes	complemented
20	C₁₃×#529	—	2	2	no	—
21	C₁₃×#529	—	2	2	no	—
22	C₁₃×#529	C₂²	1	4	yes	complemented
23	C₂×C₁₃×#124	—	2	2	no	—
24	C₂×C₁₃×#124	—	2	2	no	—
25	C₂×C₁₃×#124	—	2	2	no	—
26	C₂×C₁₃×#124	C₂²	1	2	yes	—
27	C₂×C₁₃×#124	C₂²	1	2	yes	—
28	C₂×C₁₃×#124	C₂²	1	4	yes	—
29	C₂×C₁₃×#124	C₂²	1	4	yes	—
30	C₁₃×#525	—	2	2	no	—
31	C₁₃×#525	C₂²	1	2	yes	—
32	C₄×C₁₃×#41	—	2	2	no	—
33	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
34	C₂²×C₁₃×C₂²⋊C₄	—	2	2	no	—
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#497	C₂²	1	4	yes	complemented
37	C₁₃×#496	C₂²	1	4	yes	complemented
38	C₁₃×#495	C₂²	1	8	yes	complemented
39	C₁₃×#489	C₂²	1	8	yes	complemented
40	C₁₃×#488	C₂²	1	8	yes	complemented
41	C₁₃×#464	C₂²	1	16	yes	complemented
42	C₁₃×#463	C₂²	1	16	yes	complemented
43	C₁₃×#451	C₂²	1	8	yes	complemented
44	C₁₃×#450	C₂²	1	8	yes	—
45	C₁₃×#448	C₂²	1	8	yes	complemented
46	C₁₃×#447	C₂²	1	8	yes	—
47	C₁₃×#432	C₂²	1	4	yes	complemented
48	C₁₃×#431	C₂²	1	4	yes	complemented
49	C₁₃×#423	C₂²	1	2	yes	complemented
50	C₁₃×#419	C₂²	1	4	yes	complemented
51	C₁₃×#418	C₂²	1	4	yes	—
52	C₁₃×#407	C₂²	1	2	yes	—
53	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
54	C₂⁵×C₁₃	—	2	1	no	—
55	C₂×C₁₃×#41	—	2	2	no	—
56	C₂×C₁₃×#41	C₂³	1	2	yes	—
57	C₂²×Q₈×C₁₃	—	2	2	no	—
58	C₂²×Q₈×C₁₃	—	2	1	no	—
59	C₂²×Q₈×C₁₃	—	4	4	no	—
60	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
61	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
62	C₂²×D₄×C₁₃	—	2	2	no	—
63	C₂²×D₄×C₁₃	—	2	1	no	—
64	C₂²×D₄×C₁₃	—	4	4	no	—
65	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
66	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
67	C₂³×C₄×C₁₃	—	2	1	no	—
68	C₂³×C₄×C₁₃	D₄	1	2	yes	—
69	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×#137	—	4	8	no	—
71	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
72	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	complemented
73	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
74	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	complemented
75	C₂×C₁₃×D₈	C₂³	1	8	yes	—
76	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
77	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
78	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
79	C₁₃×#127	C₂³	1	1	yes	characteristic, complemented
80	C₁₃×#126	—	2	4	no	—
81	C₁₃×#125	—	2	2	no	—
82	C₁₃×#125	C₂³	1	2	yes	complemented
83	C₁₃×#124	—	2	2	no	—
84	C₁₃×#124	—	2	2	no	—
85	C₁₃×#124	—	2	4	no	—
86	C₁₃×#124	—	2	4	no	—
87	C₁₃×#124	—	2	4	no	—
88	C₁₃×#124	—	2	4	no	—
89	C₁₃×#124	—	2	4	no	—
90	C₁₃×#124	—	2	2	no	—
91	C₁₃×#124	C₂³	1	8	yes	—
92	C₁₃×#124	C₂³	1	4	yes	—
93	C₁₃×#124	C₂³	1	4	yes	—
94	C₁₃×#124	C₂³	1	2	yes	complemented
95	C₁₃×#123	—	2	4	no	—
96	C₁₃×#123	—	2	2	no	—
97	C₁₃×C₂²⋊Q₈	—	2	2	no	—
98	C₁₃×C₂²⋊Q₈	—	2	2	no	—
99	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
100	C₁₃×#121	—	2	2	no	—
101	C₁₃×#121	—	2	2	no	—
102	C₁₃×#121	C₂³	1	4	yes	—
103	C₁₃×#120	—	2	2	no	—
104	C₄×Q₈×C₁₃	—	2	2	no	—
105	C₄×Q₈×C₁₃	—	2	2	no	—
106	C₄×Q₈×C₁₃	C₂³	1	4	yes	complemented
107	C₄×D₄×C₁₃	—	2	4	no	—
108	C₄×D₄×C₁₃	—	2	4	no	—
109	C₄×D₄×C₁₃	—	2	4	no	—
110	C₄×D₄×C₁₃	—	2	2	no	—
111	C₄×D₄×C₁₃	—	2	2	no	—
112	C₄×D₄×C₁₃	C₂³	1	4	yes	complemented
113	C₁₃×#117	—	2	2	no	—
114	C₁₃×#117	—	2	4	no	—
115	C₁₃×#117	—	2	2	no	—
116	C₁₃×#117	C₂³	1	2	yes	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
123	C₂×C₄²×C₁₃	—	2	2	no	—
124	C₂×C₄²×C₁₃	D₄	1	2	yes	—
125	C₂×C₄²×C₁₃	D₄	1	2	yes	—
126	C₂×C₄²×C₁₃	D₄	1	2	yes	—
127	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
130	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
131	C₁₃×C₄⋊C₈	C₂³	1	8	yes	complemented
132	C₁₃×#103	C₂³	1	16	yes	complemented
133	C₁₃×#102	C₂³	1	16	yes	—
134	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
135	C₁₃×#97	C₂³	1	4	yes	complemented
136	C₄×C₈×C₁₃	C₂³	1	4	yes	complemented
137	#60799	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂⁴×C₁₃	—	2	4	no	—
139	C₂⁴×C₁₃	—	2	2	no	—
140	C₂⁴×C₁₃	—	4	4	no	—
141	C₂⁴×C₁₃	—	4	8	no	—
142	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₁₃×#41	—	2	8	no	—
144	C₁₃×#41	—	4	8	no	—
145	C₂×Q₈×C₁₃	—	2	2	no	—
146	C₂×Q₈×C₁₃	—	2	4	no	—
147	C₂×Q₈×C₁₃	—	2	2	no	—
148	C₂×Q₈×C₁₃	—	2	8	no	—
149	C₂×Q₈×C₁₃	—	4	8	no	—
150	C₂×Q₈×C₁₃	—	4	4	no	—
151	C₂×Q₈×C₁₃	—	4	8	no	—
152	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
153	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
154	C₂×D₄×C₁₃	—	2	2	no	—
155	C₂×D₄×C₁₃	—	2	4	no	—
156	C₂×D₄×C₁₃	—	2	2	no	—
157	C₂×D₄×C₁₃	—	2	4	no	—
158	C₂×D₄×C₁₃	—	2	2	no	—
159	C₂×D₄×C₁₃	—	2	8	no	—
160	C₂×D₄×C₁₃	—	4	8	no	—
161	C₂×D₄×C₁₃	—	4	4	no	—
162	C₂×D₄×C₁₃	—	4	8	no	—
163	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
164	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₁₃	—	2	4	no	—
166	C₂²×C₄×C₁₃	—	2	4	no	—
167	C₂²×C₄×C₁₃	—	2	2	no	—
168	C₂²×C₄×C₁₃	—	2	2	no	—
169	C₂²×C₄×C₁₃	—	2	4	no	—
170	C₂²×C₄×C₁₃	—	4	4	no	—
171	C₂²×C₄×C₁₃	—	4	4	no	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
177	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
179	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
182	C₁₃×Q₁₆	—	4	8	no	—
183	C₁₃×SD₁₆	—	4	8	no	—
184	C₁₃×SD₁₆	—	4	8	no	—
185	C₁₃×D₈	—	4	8	no	—
186	C₁₃×M₁₆	—	2	8	no	—
187	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
188	C₁₃×C₄⋊C₄	—	2	2	no	—
189	C₁₃×C₄⋊C₄	—	2	2	no	—
190	C₁₃×C₄⋊C₄	—	2	4	no	—
191	C₁₃×C₄⋊C₄	—	2	4	no	—
192	C₁₃×C₄⋊C₄	—	2	4	no	—
193	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
194	C₁₃×C₂²⋊C₄	—	2	4	no	—
195	C₁₃×C₂²⋊C₄	—	2	2	no	—
196	C₁₃×C₂²⋊C₄	—	2	8	no	—
197	C₁₃×C₂²⋊C₄	—	2	8	no	—
198	C₁₃×C₂²⋊C₄	—	2	8	no	—
199	C₁₃×C₂²⋊C₄	—	2	8	no	—
200	C₁₃×C₂²⋊C₄	—	2	4	no	—
201	C₁₃×C₂²⋊C₄	—	2	4	no	—
202	C₁₃×C₂²⋊C₄	—	2	4	no	—
203	C₄²×C₁₃	—	2	4	no	—
204	C₄²×C₁₃	—	2	2	no	—
205	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₁₃	C₂×D₄	1	2	yes	—
207	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₁₃	C₂×D₄	1	2	yes	—
209	C₄²×C₁₃	C₂×D₄	1	2	yes	—
210	C₄²×C₁₃	C₂×D₄	1	2	yes	—
211	C₄²×C₁₃	C₂×D₄	1	2	yes	—
212	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
213	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
214	C₄²×C₁₃	C₂⁴	1	2	yes	—
215	#3444	C₂×C₁₃	1	1	yes	characteristic, complemented
216	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#3215	C₂×C₁₃	1	4	yes	complemented
218	#3213	C₂×C₁₃	1	4	yes	complemented
219	#3211	C₂×C₁₃	1	8	yes	complemented
220	#3153	C₂×C₁₃	1	2	yes	complemented
221	#3140	C₂×C₁₃	1	2	yes	complemented
222	#3040	C₂×C₁₃	1	4	yes	complemented
223	#3004	C₂×C₁₃	1	2	yes	complemented
224	#3003	C₂×C₁₃	1	2	yes	complemented
225	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₂³×C₁₃	—	2	2	no	—
227	C₂³×C₁₃	—	2	4	no	—
228	C₂³×C₁₃	—	2	4	no	—
229	C₂³×C₁₃	—	2	2	no	—
230	C₂³×C₁₃	—	4	8	no	—
231	C₂³×C₁₃	—	4	8	no	—
232	C₂³×C₁₃	—	4	8	no	—
233	C₂³×C₁₃	—	4	4	no	—
234	C₂³×C₁₃	—	4	8	no	—
235	C₂³×C₁₃	—	8	16	no	—
236	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
237	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
238	Q₈×C₁₃	—	2	4	no	—
239	Q₈×C₁₃	—	2	8	no	—
240	Q₈×C₁₃	—	4	8	no	—
241	Q₈×C₁₃	—	4	4	no	—
242	Q₈×C₁₃	—	4	4	no	—
243	D₄×C₁₃	—	2	4	no	—
244	D₄×C₁₃	—	2	8	no	—
245	D₄×C₁₃	—	4	8	no	—
246	D₄×C₁₃	—	4	4	no	—
247	D₄×C₁₃	—	4	4	no	—
248	D₄×C₁₃	—	4	8	no	—
249	D₄×C₁₃	—	4	4	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	4	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	4	no	—
258	C₂×C₄×C₁₃	—	4	2	no	—
259	C₂×C₄×C₁₃	—	4	2	no	—
260	C₂×C₄×C₁₃	—	4	2	no	—
261	C₂×C₄×C₁₃	—	4	2	no	—
262	C₂×C₄×C₁₃	—	4	8	no	—
263	C₂×C₄×C₁₃	—	4	8	no	—
264	C₂×C₄×C₁₃	—	4	4	no	—
265	C₂×C₄×C₁₃	—	4	4	no	—
266	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
268	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
269	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
270	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
271	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
273	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
274	C₈×C₁₃	—	2	8	no	—
275	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
276	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
278	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	—
279	#533	C₂²×C₁₃	1	2	yes	complemented
280	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
281	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
282	#532	C₂²×C₁₃	1	2	yes	complemented
283	#529	—	2	2	no	—
284	#529	—	2	2	no	—
285	#529	C₂²×C₁₃	1	4	yes	complemented
286	C₂×#124	—	2	2	no	—
287	C₂×#124	—	2	2	no	—
288	C₂×#124	—	2	2	no	—
289	C₂×#124	C₂²×C₁₃	1	2	yes	—
290	C₂×#124	C₂²×C₁₃	1	4	yes	—
291	C₂×#124	C₂²×C₁₃	1	4	yes	—
292	C₂×#124	C₂²×C₁₃	1	2	yes	—
293	#525	—	2	2	no	—
294	#525	C₂²×C₁₃	1	2	yes	—
295	C₄×#41	—	2	2	no	—
296	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
297	C₂²×C₂²⋊C₄	—	2	2	no	—
298	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
299	#497	C₂²×C₁₃	1	4	yes	complemented
300	#496	C₂²×C₁₃	1	4	yes	complemented
301	#495	C₂²×C₁₃	1	8	yes	complemented
302	#489	C₂²×C₁₃	1	8	yes	complemented
303	#488	C₂²×C₁₃	1	8	yes	complemented
304	#464	C₂²×C₁₃	1	16	yes	complemented
305	#463	C₂²×C₁₃	1	16	yes	complemented
306	#451	C₂²×C₁₃	1	8	yes	complemented
307	#450	C₂²×C₁₃	1	8	yes	—
308	#448	C₂²×C₁₃	1	8	yes	complemented
309	#447	C₂²×C₁₃	1	8	yes	—
310	#432	C₂²×C₁₃	1	4	yes	complemented
311	#431	C₂²×C₁₃	1	4	yes	complemented
312	#423	C₂²×C₁₃	1	2	yes	complemented
313	#419	C₂²×C₁₃	1	4	yes	complemented
314	#418	C₂²×C₁₃	1	4	yes	—
315	#407	C₂²×C₁₃	1	2	yes	—
316	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
317	C₂²×C₁₃	—	2	8	no	—
318	C₂²×C₁₃	—	2	2	no	—
319	C₂²×C₁₃	—	2	2	no	—
320	C₂²×C₁₃	—	2	2	no	—
321	C₂²×C₁₃	—	4	2	no	—
322	C₂²×C₁₃	—	4	4	no	—
323	C₂²×C₁₃	—	4	4	no	—
324	C₂²×C₁₃	—	4	8	no	—
325	C₂²×C₁₃	—	8	8	no	—
326	C₂²×C₁₃	—	8	16	no	—
327	C₂²×C₁₃	#535	1	2	yes	—
328	C₂²×C₁₃	#575	1	4	yes	—
329	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
330	C₄×C₁₃	—	2	2	no	—
331	C₄×C₁₃	—	2	2	no	—
332	C₄×C₁₃	—	2	2	no	—
333	C₄×C₁₃	—	2	2	no	—
334	C₄×C₁₃	—	2	2	no	—
335	C₄×C₁₃	—	4	4	no	—
336	C₄×C₁₃	—	4	2	no	—
337	C₄×C₁₃	—	4	4	no	—
338	C₄×C₁₃	#535	1	2	yes	—
339	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
340	C₂⁵	—	2	1	no	—
341	C₂×#41	—	2	2	no	—
342	C₂×#41	C₂³×C₁₃	1	2	yes	—
343	C₂²×Q₈	—	2	2	no	—
344	C₂²×Q₈	—	2	1	no	—
345	C₂²×Q₈	—	4	4	no	—
346	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
347	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
348	C₂²×D₄	—	2	2	no	—
349	C₂²×D₄	—	2	1	no	—
350	C₂²×D₄	—	4	4	no	—
351	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
352	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
353	C₂³×C₄	—	2	1	no	—
354	C₂³×C₄	D₄×C₁₃	1	2	yes	—
355	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
356	#137	—	4	8	no	—
357	AGL(1,ℤ/8)	—	4	8	no	—
358	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	complemented
359	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
360	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	complemented
361	C₂×D₈	C₂³×C₁₃	1	8	yes	—
362	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
363	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
364	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
365	#127	C₂³×C₁₃	1	1	yes	characteristic, complemented
366	#126	—	2	4	no	—
367	#125	—	2	2	no	—
368	#125	C₂³×C₁₃	1	2	yes	complemented
369	#124	—	2	2	no	—
370	#124	—	2	4	no	—
371	#124	—	2	2	no	—
372	#124	—	2	4	no	—
373	#124	—	2	4	no	—
374	#124	—	2	4	no	—
375	#124	—	2	4	no	—
376	#124	—	2	2	no	—
377	#124	C₂³×C₁₃	1	8	yes	—
378	#124	C₂³×C₁₃	1	4	yes	—
379	#124	C₂³×C₁₃	1	4	yes	—
380	#124	C₂³×C₁₃	1	2	yes	complemented
381	#123	—	2	4	no	—
382	#123	—	2	2	no	—
383	C₂²⋊Q₈	—	2	2	no	—
384	C₂²⋊Q₈	—	2	2	no	—
385	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
386	#121	—	2	2	no	—
387	#121	—	2	2	no	—
388	#121	C₂³×C₁₃	1	4	yes	—
389	#120	—	2	2	no	—
390	C₄×Q₈	—	2	2	no	—
391	C₄×Q₈	—	2	2	no	—
392	C₄×Q₈	C₂³×C₁₃	1	4	yes	complemented
393	C₄×D₄	—	2	4	no	—
394	C₄×D₄	—	2	4	no	—
395	C₄×D₄	—	2	4	no	—
396	C₄×D₄	—	2	2	no	—
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	C₂³×C₁₃	1	4	yes	complemented
399	#117	—	2	2	no	—
400	#117	—	2	4	no	—
401	#117	—	2	2	no	—
402	#117	C₂³×C₁₃	1	2	yes	—
403	C₂×C₂²⋊C₄	—	2	4	no	—
404	C₂×C₂²⋊C₄	—	2	4	no	—
405	C₂×C₂²⋊C₄	—	2	4	no	—
406	C₂×C₂²⋊C₄	—	2	4	no	—
407	C₂×C₂²⋊C₄	—	2	4	no	—
408	C₂×C₂²⋊C₄	—	2	4	no	—
409	C₂×C₄²	—	2	2	no	—
410	C₂×C₄²	D₄×C₁₃	1	2	yes	—
411	C₂×C₄²	D₄×C₁₃	1	2	yes	—
412	C₂×C₄²	D₄×C₁₃	1	2	yes	—
413	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
414	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
415	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
416	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
417	C₄⋊C₈	C₂³×C₁₃	1	8	yes	complemented
418	#103	C₂³×C₁₃	1	16	yes	complemented
419	#102	C₂³×C₁₃	1	16	yes	—
420	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
421	#97	C₂³×C₁₃	1	4	yes	complemented
422	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
423	C₂×C₁₃	—	2	2	no	—
424	C₂×C₁₃	—	2	4	no	—
425	C₂×C₁₃	—	8	2	no	—
426	C₂×C₁₃	—	8	4	no	—
427	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
428	C₂×C₁₃	C₂×#575	1	2	yes	—
429	C₂⁴	—	2	4	no	—
430	C₂⁴	—	2	2	no	—
431	C₂⁴	—	4	4	no	—
432	C₂⁴	—	4	8	no	—
433	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
434	#41	—	2	8	no	—
435	#41	—	4	8	no	—
436	C₂×Q₈	—	2	2	no	—
437	C₂×Q₈	—	2	4	no	—
438	C₂×Q₈	—	2	2	no	—
439	C₂×Q₈	—	2	8	no	—
440	C₂×Q₈	—	4	8	no	—
441	C₂×Q₈	—	4	4	no	—
442	C₂×Q₈	—	4	8	no	—
443	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
444	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	4	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	8	no	—
451	C₂×D₄	—	4	8	no	—
452	C₂×D₄	—	4	4	no	—
453	C₂×D₄	—	4	8	no	—
454	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
455	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
456	C₂²×C₄	—	2	4	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	4	4	no	—
462	C₂²×C₄	—	4	4	no	—
463	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
464	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
466	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
467	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
468	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
469	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
470	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
471	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
472	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
473	Q₁₆	—	4	8	no	—
474	SD₁₆	—	4	8	no	—
475	SD₁₆	—	4	8	no	—
476	D₈	—	4	8	no	—
477	M₁₆	—	2	8	no	—
478	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	4	no	—
482	C₄⋊C₄	—	2	4	no	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
485	C₂²⋊C₄	—	2	4	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	8	no	—
488	C₂²⋊C₄	—	2	8	no	—
489	C₂²⋊C₄	—	2	8	no	—
490	C₂²⋊C₄	—	2	8	no	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₄²	—	2	4	no	—
495	C₄²	—	2	2	no	—
496	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
497	C₄²	C₂×D₄×C₁₃	1	2	yes	—
498	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
499	C₄²	C₂×D₄×C₁₃	1	2	yes	—
500	C₄²	C₂×D₄×C₁₃	1	2	yes	—
501	C₄²	C₂×D₄×C₁₃	1	2	yes	—
502	C₄²	C₂×D₄×C₁₃	1	2	yes	—
503	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
504	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
505	C₄²	C₂⁴×C₁₃	1	2	yes	—
506	C₁₃	#60799	1	1	yes	characteristic, direct product factor, Sylow
507	C₂³	—	2	2	no	—
508	C₂³	—	2	4	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	4	8	no	—
512	C₂³	—	4	8	no	—
513	C₂³	—	4	8	no	—
514	C₂³	—	4	4	no	—
515	C₂³	—	4	8	no	—
516	C₂³	—	8	16	no	—
517	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
518	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
519	Q₈	—	2	4	no	—
520	Q₈	—	2	8	no	—
521	Q₈	—	4	8	no	—
522	Q₈	—	4	4	no	—
523	Q₈	—	4	4	no	—
524	D₄	—	2	4	no	—
525	D₄	—	2	8	no	—
526	D₄	—	4	8	no	—
527	D₄	—	4	4	no	—
528	D₄	—	4	4	no	—
529	D₄	—	4	8	no	—
530	D₄	—	4	4	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	8	no	—
544	C₂×C₄	—	4	8	no	—
545	C₂×C₄	—	4	4	no	—
546	C₂×C₄	—	4	4	no	—
547	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
548	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
549	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
550	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
551	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
552	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
553	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
554	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
555	C₈	—	2	8	no	—
556	C₂²	—	2	8	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	4	4	no	—
561	C₂²	—	4	8	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	4	no	—
564	C₂²	—	8	8	no	—
565	C₂²	—	8	16	no	—
566	C₂²	C₁₃×#535	1	2	yes	—
567	C₂²	C₁₃×#575	1	4	yes	—
568	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
569	C₄	—	2	2	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	4	4	no	—
575	C₄	—	4	4	no	—
576	C₄	—	4	2	no	—
577	C₄	C₁₃×#535	1	2	yes	—
578	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
579	C₂	—	2	2	no	—
580	C₂	—	2	4	no	—
581	C₂	—	8	4	no	—
582	C₂	—	8	2	no	—
583	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
584	C₂	C₂×C₁₃×#575	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×#124	C₂	semidirect
3. C₁₃×#3215	C₂	semidirect
4. C₁₃×#3213	C₂	semidirect
5. C₁₃×#3211	C₂	semidirect
6. C₁₃×#3153	C₂	semidirect
7. C₁₃×#3140	C₂	semidirect
8. C₁₃×#3040	C₂	semidirect
9. C₁₃×#3004	C₂	semidirect
10. C₁₃×#3003	C₂	semidirect
11. C₁₃×#2920	C₂	semidirect
14. C₂×C₁₃×#137	C₂²	semidirect
16. C₁₃×#533	C₂²	semidirect
17. C₁₃×#533	C₂²	semidirect
18. C₁₃×#532	C₂²	semidirect
19. C₁₃×#532	C₂²	semidirect
22. C₁₃×#529	C₂²	semidirect
33. C₄×C₁₃×#41	C₂²	semidirect
36. C₁₃×#497	C₂²	semidirect
37. C₁₃×#496	C₂²	semidirect
38. C₁₃×#495	C₂²	semidirect
39. C₁₃×#489	C₂²	semidirect
40. C₁₃×#488	C₂²	semidirect
41. C₁₃×#464	C₂²	semidirect
42. C₁₃×#463	C₂²	semidirect
43. C₁₃×#451	C₂²	semidirect
45. C₁₃×#448	C₂²	semidirect
47. C₁₃×#432	C₂²	semidirect
48. C₁₃×#431	C₂²	semidirect
49. C₁₃×#423	C₂²	semidirect
50. C₁₃×#419	C₂²	semidirect
53. C₄×C₁₃×M₁₆	C₂²	semidirect
72. C₂×C₁₃×Q₁₆	C₂³	semidirect
74. C₂×C₁₃×SD₁₆	C₂³	semidirect
77. C₁₃×C₄⋊Q₈	C₂³	semidirect
78. C₁₃×C₄⋊Q₈	C₂³	semidirect
79. C₁₃×#127	C₂³	semidirect
82. C₁₃×#125	C₂³	semidirect
94. C₁₃×#124	C₂³	semidirect
106. C₄×Q₈×C₁₃	C₂³	semidirect
112. C₄×D₄×C₁₃	C₂³	semidirect
131. C₁₃×C₄⋊C₈	C₂³	semidirect
132. C₁₃×#103	C₂³	semidirect
135. C₁₃×#97	C₂³	semidirect
136. C₄×C₈×C₁₃	C₂³	semidirect
137. #60799	C₁₃	direct (N × H)
215. #3444	C₂×C₁₃	semidirect
216. C₂²×#124	C₂×C₁₃	semidirect
217. #3215	C₂×C₁₃	semidirect
218. #3213	C₂×C₁₃	semidirect
219. #3211	C₂×C₁₃	semidirect
220. #3153	C₂×C₁₃	semidirect
221. #3140	C₂×C₁₃	semidirect
222. #3040	C₂×C₁₃	semidirect
223. #3004	C₂×C₁₃	semidirect
224. #3003	C₂×C₁₃	semidirect
225. #2920	C₂×C₁₃	semidirect
277. C₂×#137	C₂²×C₁₃	semidirect
279. #533	C₂²×C₁₃	semidirect
280. #533	C₂²×C₁₃	semidirect
281. #532	C₂²×C₁₃	semidirect
282. #532	C₂²×C₁₃	semidirect
285. #529	C₂²×C₁₃	semidirect
296. C₄×#41	C₂²×C₁₃	semidirect
299. #497	C₂²×C₁₃	semidirect
300. #496	C₂²×C₁₃	semidirect
301. #495	C₂²×C₁₃	semidirect
302. #489	C₂²×C₁₃	semidirect
303. #488	C₂²×C₁₃	semidirect
304. #464	C₂²×C₁₃	semidirect
305. #463	C₂²×C₁₃	semidirect
306. #451	C₂²×C₁₃	semidirect
308. #448	C₂²×C₁₃	semidirect
310. #432	C₂²×C₁₃	semidirect
311. #431	C₂²×C₁₃	semidirect
312. #423	C₂²×C₁₃	semidirect
313. #419	C₂²×C₁₃	semidirect
316. C₄×M₁₆	C₂²×C₁₃	semidirect
358. C₂×Q₁₆	C₂³×C₁₃	semidirect
360. C₂×SD₁₆	C₂³×C₁₃	semidirect
363. C₄⋊Q₈	C₂³×C₁₃	semidirect
364. C₄⋊Q₈	C₂³×C₁₃	semidirect
365. #127	C₂³×C₁₃	semidirect
368. #125	C₂³×C₁₃	semidirect
380. #124	C₂³×C₁₃	semidirect
392. C₄×Q₈	C₂³×C₁₃	semidirect
398. C₄×D₄	C₂³×C₁₃	semidirect
417. C₄⋊C₈	C₂³×C₁₃	semidirect
418. #103	C₂³×C₁₃	semidirect
421. #97	C₂³×C₁₃	semidirect
422. C₄×C₈	C₂³×C₁₃	semidirect
506. C₁₃	#60799	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×#3444	2
C₂²×C₁₃×#124	2
C₁₃×#3215	2
C₁₃×#3213	2
C₁₃×#3211	2
C₁₃×#3153	2
C₁₃×#3140	2
C₁₃×#3040	2
C₁₃×#3004	2
C₁₃×#3003	2
C₁₃×#2920	2
#60799	13

Subgroups — C13×#60799 #15747138

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60799 #15747138