Subgroups — C₁₃×#36716 #15723055

Order 3328.

2406 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#538	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2849	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2700	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2698	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2681	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2680	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2622	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2591	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2583	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2579	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2504	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2502	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2409	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2312	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#538	—	2	8	no	—
19	C₂×C₁₃×#126	C₂²	1	2	yes	—
20	C₂×C₁₃×#124	C₂²	1	2	yes	—
21	C₂×C₁₃×#123	C₂²	1	2	yes	—
22	C₂×C₁₃×#123	C₂²	1	4	yes	—
23	C₂×C₁₃×C₂²⋊Q₈	—	2	8	no	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
28	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#121	C₂²	1	2	yes	—
30	C₂×C₁₃×#120	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
32	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₁₃×#400	C₂²	1	2	yes	complemented
38	C₁₃×#398	C₂²	1	4	yes	complemented
39	C₁₃×#398	C₂²	1	4	yes	complemented
40	C₁₃×#398	C₂²	1	2	yes	complemented
41	C₁₃×#397	C₂²	1	4	yes	—
42	C₁₃×#397	C₂²	1	4	yes	—
43	C₁₃×#397	C₂²	1	4	yes	complemented
44	C₁₃×#396	C₂²	1	4	yes	complemented
45	C₁₃×#395	C₂²	1	2	yes	complemented
46	C₁₃×#395	C₂²	1	4	yes	complemented
47	C₁₃×#394	C₂²	1	4	yes	—
48	C₁₃×#394	C₂²	1	4	yes	—
49	C₁₃×#394	C₂²	1	2	yes	complemented
50	C₁₃×#393	C₂²	1	4	yes	complemented
51	C₁₃×#391	C₂²	1	2	yes	complemented
52	C₁₃×#391	C₂²	1	4	yes	complemented
53	C₁₃×#390	C₂²	1	2	yes	complemented
54	C₁₃×#389	C₂²	1	4	yes	complemented
55	C₁₃×#388	C₂²	1	4	yes	—
56	C₁₃×#388	C₂²	1	4	yes	—
57	C₁₃×#388	C₂²	1	4	yes	complemented
58	C₁₃×#387	C₂²	1	4	yes	complemented
59	C₁₃×#386	C₂²	1	2	yes	—
60	C₁₃×#386	C₂²	1	2	yes	—
61	C₁₃×#386	C₂²	1	2	yes	—
62	C₁₃×#386	C₂²	1	2	yes	—
63	C₁₃×#386	C₂²	1	4	yes	—
64	C₁₃×#385	C₂²	1	2	yes	—
65	C₁₃×#385	C₂²	1	2	yes	—
66	C₁₃×#385	C₂²	1	2	yes	—
67	C₁₃×#385	C₂²	1	2	yes	—
68	C₁₃×#385	C₂²	1	4	yes	—
69	C₁₃×#385	C₂²	1	4	yes	complemented
70	C₁₃×#384	C₂²	1	2	yes	complemented
71	C₁₃×#382	C₂²	1	2	yes	complemented
72	C₁₃×#381	C₂²	1	4	yes	—
73	C₁₃×#380	C₂²	1	2	yes	—
74	C₁₃×#379	C₂²	1	2	yes	—
75	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
76	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
77	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₁₃	—	2	4	no	—
79	C₂²×Q₈×C₁₃	—	4	4	no	—
80	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
81	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
83	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
84	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
86	C₂³×C₄×C₁₃	—	2	4	no	—
87	C₂³×C₄×C₁₃	—	4	4	no	—
88	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
90	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₁₃×#126	—	2	8	no	—
97	C₁₃×#124	—	2	8	no	—
98	C₁₃×#123	—	2	8	no	—
99	C₁₃×#123	—	4	8	no	—
100	C₁₃×C₂²⋊Q₈	—	2	4	no	—
101	C₁₃×C₂²⋊Q₈	—	2	16	no	—
102	C₁₃×C₂²⋊Q₈	—	2	16	no	—
103	C₁₃×C₂²⋊Q₈	—	4	8	no	—
104	C₁₃×#121	—	2	4	no	—
105	C₁₃×#121	—	2	8	no	—
106	C₁₃×#120	—	2	8	no	—
107	C₄×D₄×C₁₃	—	2	8	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
125	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
126	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
131	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
134	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
144	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
145	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
146	C₁₃×#95	C₂³	1	2	yes	—
147	C₁₃×#95	C₂³	1	2	yes	—
148	C₁₃×#95	C₂³	1	4	yes	—
149	C₁₃×#95	C₂³	1	4	yes	—
150	C₁₃×#95	C₂³	1	4	yes	—
151	C₁₃×#95	C₂³	1	4	yes	—
152	C₁₃×#95	C₂³	1	4	yes	—
153	C₁₃×#95	C₂³	1	4	yes	—
154	C₁₃×#95	C₂³	1	4	yes	—
155	C₁₃×#95	C₂³	1	4	yes	—
156	C₁₃×#95	C₂³	1	4	yes	—
157	#36716	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂⁴×C₁₃	—	2	4	no	—
159	C₂⁴×C₁₃	—	4	2	no	—
160	C₂⁴×C₁₃	—	4	2	no	—
161	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
162	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
163	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
164	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
165	C₂×Q₈×C₁₃	—	2	8	no	—
166	C₂×Q₈×C₁₃	—	2	2	no	—
167	C₂×Q₈×C₁₃	—	2	8	no	—
168	C₂×Q₈×C₁₃	—	4	4	no	—
169	C₂×Q₈×C₁₃	—	4	2	no	—
170	C₂×Q₈×C₁₃	—	4	16	no	—
171	C₂×D₄×C₁₃	—	2	4	no	—
172	C₂×D₄×C₁₃	—	2	8	no	—
173	C₂×D₄×C₁₃	—	2	4	no	—
174	C₂×D₄×C₁₃	—	2	4	no	—
175	C₂×D₄×C₁₃	—	2	2	no	—
176	C₂×D₄×C₁₃	—	4	4	no	—
177	C₂×D₄×C₁₃	—	4	2	no	—
178	C₂×D₄×C₁₃	—	4	4	no	—
179	C₂²×C₄×C₁₃	—	2	2	no	—
180	C₂²×C₄×C₁₃	—	2	4	no	—
181	C₂²×C₄×C₁₃	—	2	2	no	—
182	C₂²×C₄×C₁₃	—	2	2	no	—
183	C₂²×C₄×C₁₃	—	2	2	no	—
184	C₂²×C₄×C₁₃	—	2	8	no	—
185	C₂²×C₄×C₁₃	—	2	8	no	—
186	C₂²×C₄×C₁₃	—	2	4	no	—
187	C₂²×C₄×C₁₃	—	4	4	no	—
188	C₂²×C₄×C₁₃	—	4	2	no	—
189	C₂²×C₄×C₁₃	—	4	2	no	—
190	C₂²×C₄×C₁₃	—	4	2	no	—
191	C₂²×C₄×C₁₃	—	4	2	no	—
192	C₂²×C₄×C₁₃	—	4	2	no	—
193	C₂²×C₄×C₁₃	—	4	4	no	—
194	C₂²×C₄×C₁₃	—	4	16	no	—
195	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
196	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
197	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
209	C₁₃×C₄⋊C₄	—	2	4	no	—
210	C₁₃×C₄⋊C₄	—	2	4	no	—
211	C₁₃×C₄⋊C₄	—	2	8	no	—
212	C₁₃×C₄⋊C₄	—	2	4	no	—
213	C₁₃×C₄⋊C₄	—	2	4	no	—
214	C₁₃×C₄⋊C₄	—	2	4	no	—
215	C₁₃×C₄⋊C₄	—	2	4	no	—
216	C₁₃×C₄⋊C₄	—	2	2	no	—
217	C₁₃×C₄⋊C₄	—	2	2	no	—
218	C₁₃×C₄⋊C₄	—	2	8	no	—
219	C₁₃×C₄⋊C₄	—	4	4	no	—
220	C₁₃×C₄⋊C₄	—	4	4	no	—
221	C₁₃×C₄⋊C₄	—	4	4	no	—
222	C₁₃×C₄⋊C₄	—	4	4	no	—
223	C₁₃×C₂²⋊C₄	—	2	8	no	—
224	C₁₃×C₂²⋊C₄	—	2	4	no	—
225	C₁₃×C₂²⋊C₄	—	2	4	no	—
226	C₁₃×C₂²⋊C₄	—	2	4	no	—
227	C₁₃×C₂²⋊C₄	—	2	4	no	—
228	C₁₃×C₂²⋊C₄	—	2	4	no	—
229	C₁₃×C₂²⋊C₄	—	2	4	no	—
230	C₁₃×C₂²⋊C₄	—	2	4	no	—
231	C₁₃×C₂²⋊C₄	—	2	8	no	—
232	C₁₃×C₂²⋊C₄	—	4	4	no	—
233	C₁₃×C₂²⋊C₄	—	4	4	no	—
234	C₁₃×C₂²⋊C₄	—	4	4	no	—
235	C₁₃×C₂²⋊C₄	—	4	4	no	—
236	C₁₃×C₂²⋊C₄	—	4	4	no	—
237	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
238	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
239	C₄²×C₁₃	—	2	4	no	—
240	C₄²×C₁₃	—	4	2	no	—
241	C₄²×C₁₃	—	4	2	no	—
242	C₂×#538	C₂×C₁₃	1	1	yes	characteristic
243	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#2849	C₂×C₁₃	1	2	yes	complemented
245	#2700	C₂×C₁₃	1	4	yes	complemented
246	#2698	C₂×C₁₃	1	4	yes	complemented
247	#2681	C₂×C₁₃	1	4	yes	complemented
248	#2680	C₂×C₁₃	1	4	yes	complemented
249	#2622	C₂×C₁₃	1	2	yes	complemented
250	#2591	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#2583	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#2579	C₂×C₁₃	1	2	yes	complemented
253	#2504	C₂×C₁₃	1	1	yes	characteristic, complemented
254	#2502	C₂×C₁₃	1	1	yes	characteristic, complemented
255	#2409	C₂×C₁₃	1	2	yes	complemented
256	#2312	C₂×C₁₃	1	1	yes	characteristic, complemented
257	C₂³×C₁₃	—	2	2	no	—
258	C₂³×C₁₃	—	2	2	no	—
259	C₂³×C₁₃	—	2	8	no	—
260	C₂³×C₁₃	—	2	4	no	—
261	C₂³×C₁₃	—	2	4	no	—
262	C₂³×C₁₃	—	2	4	no	—
263	C₂³×C₁₃	—	2	2	no	—
264	C₂³×C₁₃	—	2	4	no	—
265	C₂³×C₁₃	—	2	4	no	—
266	C₂³×C₁₃	—	2	4	no	—
267	C₂³×C₁₃	—	4	4	no	—
268	C₂³×C₁₃	—	4	4	no	—
269	C₂³×C₁₃	—	4	16	no	—
270	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
271	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
272	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
273	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
274	Q₈×C₁₃	—	4	16	no	—
275	Q₈×C₁₃	—	8	2	no	—
276	D₄×C₁₃	—	4	8	no	—
277	D₄×C₁₃	—	8	2	no	—
278	D₄×C₁₃	—	8	4	no	—
279	D₄×C₁₃	—	8	4	no	—
280	C₂×C₄×C₁₃	—	2	8	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	—	2	2	no	—
285	C₂×C₄×C₁₃	—	2	2	no	—
286	C₂×C₄×C₁₃	—	2	2	no	—
287	C₂×C₄×C₁₃	—	2	2	no	—
288	C₂×C₄×C₁₃	—	2	2	no	—
289	C₂×C₄×C₁₃	—	2	2	no	—
290	C₂×C₄×C₁₃	—	2	2	no	—
291	C₂×C₄×C₁₃	—	2	2	no	—
292	C₂×C₄×C₁₃	—	2	4	no	—
293	C₂×C₄×C₁₃	—	2	4	no	—
294	C₂×C₄×C₁₃	—	2	4	no	—
295	C₂×C₄×C₁₃	—	2	4	no	—
296	C₂×C₄×C₁₃	—	2	4	no	—
297	C₂×C₄×C₁₃	—	2	4	no	—
298	C₂×C₄×C₁₃	—	2	4	no	—
299	C₂×C₄×C₁₃	—	2	4	no	—
300	C₂×C₄×C₁₃	—	2	4	no	—
301	C₂×C₄×C₁₃	—	2	4	no	—
302	C₂×C₄×C₁₃	—	2	4	no	—
303	C₂×C₄×C₁₃	—	2	4	no	—
304	C₂×C₄×C₁₃	—	4	4	no	—
305	C₂×C₄×C₁₃	—	4	4	no	—
306	C₂×C₄×C₁₃	—	4	16	no	—
307	C₂×C₄×C₁₃	—	4	4	no	—
308	C₂×C₄×C₁₃	—	4	4	no	—
309	C₂×C₄×C₁₃	—	4	4	no	—
310	C₂×C₄×C₁₃	—	8	4	no	—
311	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
312	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
313	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
314	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
315	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
316	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
317	#538	—	2	8	no	—
318	C₂×#126	C₂²×C₁₃	1	2	yes	—
319	C₂×#124	C₂²×C₁₃	1	2	yes	—
320	C₂×#123	C₂²×C₁₃	1	2	yes	—
321	C₂×#123	C₂²×C₁₃	1	4	yes	—
322	C₂×C₂²⋊Q₈	—	2	8	no	—
323	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
325	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
326	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
327	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×#121	C₂²×C₁₃	1	2	yes	—
329	C₂×#120	C₂²×C₁₃	1	2	yes	—
330	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
331	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
332	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
333	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
334	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
335	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
336	#400	C₂²×C₁₃	1	2	yes	complemented
337	#398	C₂²×C₁₃	1	4	yes	complemented
338	#398	C₂²×C₁₃	1	2	yes	complemented
339	#398	C₂²×C₁₃	1	4	yes	complemented
340	#397	C₂²×C₁₃	1	4	yes	—
341	#397	C₂²×C₁₃	1	4	yes	—
342	#397	C₂²×C₁₃	1	4	yes	complemented
343	#396	C₂²×C₁₃	1	4	yes	complemented
344	#395	C₂²×C₁₃	1	2	yes	complemented
345	#395	C₂²×C₁₃	1	4	yes	complemented
346	#394	C₂²×C₁₃	1	4	yes	—
347	#394	C₂²×C₁₃	1	4	yes	—
348	#394	C₂²×C₁₃	1	2	yes	complemented
349	#393	C₂²×C₁₃	1	4	yes	complemented
350	#391	C₂²×C₁₃	1	4	yes	complemented
351	#391	C₂²×C₁₃	1	2	yes	complemented
352	#390	C₂²×C₁₃	1	2	yes	complemented
353	#389	C₂²×C₁₃	1	4	yes	complemented
354	#388	C₂²×C₁₃	1	4	yes	—
355	#388	C₂²×C₁₃	1	4	yes	—
356	#388	C₂²×C₁₃	1	4	yes	complemented
357	#387	C₂²×C₁₃	1	4	yes	complemented
358	#386	C₂²×C₁₃	1	2	yes	—
359	#386	C₂²×C₁₃	1	2	yes	—
360	#386	C₂²×C₁₃	1	2	yes	—
361	#386	C₂²×C₁₃	1	4	yes	—
362	#386	C₂²×C₁₃	1	2	yes	—
363	#385	C₂²×C₁₃	1	2	yes	—
364	#385	C₂²×C₁₃	1	2	yes	—
365	#385	C₂²×C₁₃	1	2	yes	—
366	#385	C₂²×C₁₃	1	4	yes	—
367	#385	C₂²×C₁₃	1	2	yes	—
368	#385	C₂²×C₁₃	1	4	yes	complemented
369	#384	C₂²×C₁₃	1	2	yes	complemented
370	#382	C₂²×C₁₃	1	2	yes	complemented
371	#381	C₂²×C₁₃	1	4	yes	—
372	#380	C₂²×C₁₃	1	2	yes	—
373	#379	C₂²×C₁₃	1	2	yes	—
374	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
375	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
376	C₂²×C₁₃	—	2	2	no	—
377	C₂²×C₁₃	—	2	2	no	—
378	C₂²×C₁₃	—	2	8	no	—
379	C₂²×C₁₃	—	2	4	no	—
380	C₂²×C₁₃	—	2	4	no	—
381	C₂²×C₁₃	—	2	4	no	—
382	C₂²×C₁₃	—	4	16	no	—
383	C₂²×C₁₃	—	4	8	no	—
384	C₂²×C₁₃	—	4	2	no	—
385	C₂²×C₁₃	—	4	2	no	—
386	C₂²×C₁₃	—	4	2	no	—
387	C₂²×C₁₃	—	4	8	no	—
388	C₂²×C₁₃	#536	1	4	yes	—
389	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
390	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
391	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
392	C₂²×C₁₃	#585	1	2	yes	—
393	C₄×C₁₃	—	2	4	no	—
394	C₄×C₁₃	—	2	4	no	—
395	C₄×C₁₃	—	2	2	no	—
396	C₄×C₁₃	—	2	2	no	—
397	C₄×C₁₃	—	4	2	no	—
398	C₄×C₁₃	—	4	2	no	—
399	C₄×C₁₃	—	4	2	no	—
400	C₄×C₁₃	—	4	2	no	—
401	C₄×C₁₃	—	4	2	no	—
402	C₄×C₁₃	—	4	2	no	—
403	C₄×C₁₃	—	4	4	no	—
404	C₄×C₁₃	—	4	4	no	—
405	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
406	C₂²×Q₈	—	2	4	no	—
407	C₂²×Q₈	—	4	4	no	—
408	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
409	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
410	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
411	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
412	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
413	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
414	C₂³×C₄	—	2	4	no	—
415	C₂³×C₄	—	4	4	no	—
416	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
417	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
418	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
419	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
420	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
421	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
422	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
423	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
424	#126	—	2	8	no	—
425	#124	—	2	8	no	—
426	#123	—	2	8	no	—
427	#123	—	4	8	no	—
428	C₂²⋊Q₈	—	2	4	no	—
429	C₂²⋊Q₈	—	2	16	no	—
430	C₂²⋊Q₈	—	2	16	no	—
431	C₂²⋊Q₈	—	4	8	no	—
432	#121	—	2	4	no	—
433	#121	—	2	8	no	—
434	#120	—	2	8	no	—
435	C₄×D₄	—	2	8	no	—
436	C₂×C₄⋊C₄	—	2	4	no	—
437	C₂×C₄⋊C₄	—	2	4	no	—
438	C₂×C₄⋊C₄	—	2	4	no	—
439	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
440	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
441	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
442	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
444	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
449	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
450	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
451	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
452	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
453	C₂×C₂²⋊C₄	—	2	4	no	—
454	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
471	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
472	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
473	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
474	#95	C₂³×C₁₃	1	2	yes	—
475	#95	C₂³×C₁₃	1	2	yes	—
476	#95	C₂³×C₁₃	1	4	yes	—
477	#95	C₂³×C₁₃	1	4	yes	—
478	#95	C₂³×C₁₃	1	4	yes	—
479	#95	C₂³×C₁₃	1	4	yes	—
480	#95	C₂³×C₁₃	1	4	yes	—
481	#95	C₂³×C₁₃	1	4	yes	—
482	#95	C₂³×C₁₃	1	4	yes	—
483	#95	C₂³×C₁₃	1	4	yes	—
484	#95	C₂³×C₁₃	1	4	yes	—
485	C₂×C₁₃	—	2	4	no	—
486	C₂×C₁₃	—	4	4	no	—
487	C₂×C₁₃	—	8	2	no	—
488	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
489	C₂×C₁₃	#3484	1	1	yes	characteristic
490	C₂×C₁₃	#3485	1	1	yes	characteristic
491	C₂×C₁₃	#3541	1	4	yes	—
492	C₂⁴	—	2	4	no	—
493	C₂⁴	—	4	2	no	—
494	C₂⁴	—	4	2	no	—
495	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
496	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
497	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
498	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
499	C₂×Q₈	—	2	8	no	—
500	C₂×Q₈	—	2	2	no	—
501	C₂×Q₈	—	2	8	no	—
502	C₂×Q₈	—	4	4	no	—
503	C₂×Q₈	—	4	2	no	—
504	C₂×Q₈	—	4	16	no	—
505	C₂×D₄	—	2	4	no	—
506	C₂×D₄	—	2	8	no	—
507	C₂×D₄	—	2	4	no	—
508	C₂×D₄	—	2	4	no	—
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	4	4	no	—
511	C₂×D₄	—	4	2	no	—
512	C₂×D₄	—	4	4	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	4	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	8	no	—
519	C₂²×C₄	—	2	8	no	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	—	4	4	no	—
522	C₂²×C₄	—	4	2	no	—
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	—	4	2	no	—
525	C₂²×C₄	—	4	2	no	—
526	C₂²×C₄	—	4	2	no	—
527	C₂²×C₄	—	4	4	no	—
528	C₂²×C₄	—	4	16	no	—
529	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
530	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
531	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
532	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
533	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
534	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
535	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
536	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
537	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
538	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
539	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
541	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	—	2	4	no	—
545	C₄⋊C₄	—	2	8	no	—
546	C₄⋊C₄	—	2	4	no	—
547	C₄⋊C₄	—	2	4	no	—
548	C₄⋊C₄	—	2	4	no	—
549	C₄⋊C₄	—	2	4	no	—
550	C₄⋊C₄	—	2	2	no	—
551	C₄⋊C₄	—	2	2	no	—
552	C₄⋊C₄	—	2	8	no	—
553	C₄⋊C₄	—	4	4	no	—
554	C₄⋊C₄	—	4	4	no	—
555	C₄⋊C₄	—	4	4	no	—
556	C₄⋊C₄	—	4	4	no	—
557	C₂²⋊C₄	—	2	8	no	—
558	C₂²⋊C₄	—	2	4	no	—
559	C₂²⋊C₄	—	2	4	no	—
560	C₂²⋊C₄	—	2	4	no	—
561	C₂²⋊C₄	—	2	4	no	—
562	C₂²⋊C₄	—	2	4	no	—
563	C₂²⋊C₄	—	2	4	no	—
564	C₂²⋊C₄	—	2	4	no	—
565	C₂²⋊C₄	—	2	8	no	—
566	C₂²⋊C₄	—	4	4	no	—
567	C₂²⋊C₄	—	4	4	no	—
568	C₂²⋊C₄	—	4	4	no	—
569	C₂²⋊C₄	—	4	4	no	—
570	C₂²⋊C₄	—	4	4	no	—
571	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
572	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
573	C₄²	—	2	4	no	—
574	C₄²	—	4	2	no	—
575	C₄²	—	4	2	no	—
576	C₁₃	#36716	1	1	yes	characteristic, direct product factor, Sylow
577	C₂³	—	2	2	no	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	8	no	—
580	C₂³	—	2	4	no	—
581	C₂³	—	2	4	no	—
582	C₂³	—	2	4	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	4	no	—
585	C₂³	—	2	4	no	—
586	C₂³	—	2	4	no	—
587	C₂³	—	4	4	no	—
588	C₂³	—	4	4	no	—
589	C₂³	—	4	16	no	—
590	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
591	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
592	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
593	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
594	Q₈	—	4	16	no	—
595	Q₈	—	8	2	no	—
596	D₄	—	4	8	no	—
597	D₄	—	8	2	no	—
598	D₄	—	8	4	no	—
599	D₄	—	8	4	no	—
600	C₂×C₄	—	2	8	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	4	4	no	—
625	C₂×C₄	—	4	4	no	—
626	C₂×C₄	—	4	16	no	—
627	C₂×C₄	—	4	4	no	—
628	C₂×C₄	—	4	4	no	—
629	C₂×C₄	—	4	4	no	—
630	C₂×C₄	—	8	4	no	—
631	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
632	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
633	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
634	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
635	C₂²	—	2	8	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	4	no	—
639	C₂²	—	2	4	no	—
640	C₂²	—	2	4	no	—
641	C₂²	—	4	16	no	—
642	C₂²	—	4	8	no	—
643	C₂²	—	4	8	no	—
644	C₂²	—	4	2	no	—
645	C₂²	—	4	2	no	—
646	C₂²	—	4	2	no	—
647	C₂²	C₁₃×#536	1	4	yes	—
648	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
649	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
650	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
651	C₂²	C₁₃×#585	1	2	yes	—
652	C₄	—	2	4	no	—
653	C₄	—	2	4	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	4	4	no	—
657	C₄	—	4	4	no	—
658	C₄	—	4	2	no	—
659	C₄	—	4	2	no	—
660	C₄	—	4	2	no	—
661	C₄	—	4	2	no	—
662	C₄	—	4	2	no	—
663	C₄	—	4	2	no	—
664	C₂	—	2	4	no	—
665	C₂	—	4	4	no	—
666	C₂	—	8	2	no	—
667	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
668	C₂	C₁₃×#3484	1	1	yes	characteristic
669	C₂	C₁₃×#3485	1	1	yes	characteristic
670	C₂	C₁₃×#3541	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#538	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
3. C₁₃×#2849	C₂	semidirect
4. C₁₃×#2700	C₂	semidirect
5. C₁₃×#2698	C₂	semidirect
6. C₁₃×#2681	C₂	semidirect
7. C₁₃×#2680	C₂	semidirect
8. C₁₃×#2622	C₂	semidirect
9. C₁₃×#2591	C₂	semidirect
10. C₁₃×#2583	C₂	semidirect
11. C₁₃×#2579	C₂	semidirect
12. C₁₃×#2504	C₂	semidirect
13. C₁₃×#2502	C₂	semidirect
14. C₁₃×#2409	C₂	semidirect
15. C₁₃×#2312	C₂	semidirect
27. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
37. C₁₃×#400	C₂²	semidirect
38. C₁₃×#398	C₂²	semidirect
39. C₁₃×#398	C₂²	semidirect
40. C₁₃×#398	C₂²	semidirect
43. C₁₃×#397	C₂²	semidirect
44. C₁₃×#396	C₂²	semidirect
45. C₁₃×#395	C₂²	semidirect
46. C₁₃×#395	C₂²	semidirect
49. C₁₃×#394	C₂²	semidirect
50. C₁₃×#393	C₂²	semidirect
51. C₁₃×#391	C₂²	semidirect
52. C₁₃×#391	C₂²	semidirect
53. C₁₃×#390	C₂²	semidirect
54. C₁₃×#389	C₂²	semidirect
57. C₁₃×#388	C₂²	semidirect
58. C₁₃×#387	C₂²	semidirect
69. C₁₃×#385	C₂²	semidirect
70. C₁₃×#384	C₂²	semidirect
71. C₁₃×#382	C₂²	semidirect
157. #36716	C₁₃	direct (N × H)
243. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
244. #2849	C₂×C₁₃	semidirect
245. #2700	C₂×C₁₃	semidirect
246. #2698	C₂×C₁₃	semidirect
247. #2681	C₂×C₁₃	semidirect
248. #2680	C₂×C₁₃	semidirect
249. #2622	C₂×C₁₃	semidirect
250. #2591	C₂×C₁₃	semidirect
251. #2583	C₂×C₁₃	semidirect
252. #2579	C₂×C₁₃	semidirect
253. #2504	C₂×C₁₃	semidirect
254. #2502	C₂×C₁₃	semidirect
255. #2409	C₂×C₁₃	semidirect
256. #2312	C₂×C₁₃	semidirect
326. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
336. #400	C₂²×C₁₃	semidirect
337. #398	C₂²×C₁₃	semidirect
338. #398	C₂²×C₁₃	semidirect
339. #398	C₂²×C₁₃	semidirect
342. #397	C₂²×C₁₃	semidirect
343. #396	C₂²×C₁₃	semidirect
344. #395	C₂²×C₁₃	semidirect
345. #395	C₂²×C₁₃	semidirect
348. #394	C₂²×C₁₃	semidirect
349. #393	C₂²×C₁₃	semidirect
350. #391	C₂²×C₁₃	semidirect
351. #391	C₂²×C₁₃	semidirect
352. #390	C₂²×C₁₃	semidirect
353. #389	C₂²×C₁₃	semidirect
356. #388	C₂²×C₁₃	semidirect
357. #387	C₂²×C₁₃	semidirect
368. #385	C₂²×C₁₃	semidirect
369. #384	C₂²×C₁₃	semidirect
370. #382	C₂²×C₁₃	semidirect
576. C₁₃	#36716	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#538	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₁₃×#2849	2
C₁₃×#2700	2
C₁₃×#2698	2
C₁₃×#2681	2
C₁₃×#2680	2
C₁₃×#2622	2
C₁₃×#2591	2
C₁₃×#2583	2
C₁₃×#2579	2
C₁₃×#2504	2
C₁₃×#2502	2
C₁₃×#2409	2
C₁₃×#2312	2
#36716	13

Subgroups — C13×#36716 #15723055

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36716 #15723055