Subgroups — C₁₃×#36707 #15723046

Order 3328.

2782 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#537	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2847	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2692	C₂	1	8	yes	maximal, complemented
5	C₁₃×#2676	C₂	1	8	yes	maximal, complemented
6	C₁₃×#2618	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2539	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2436	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2406	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2404	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2313	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	2	yes	—
13	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#537	—	2	8	no	—
16	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
17	C₂×C₁₃×#123	C₂²	1	4	yes	—
18	C₂×C₁₃×C₂²⋊Q₈	—	2	8	no	—
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	—
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
21	C₂×C₁₃×#121	C₂²	1	2	yes	—
22	C₂×C₁₃×#121	C₂²	1	2	yes	—
23	C₂×C₁₃×#121	C₂²	1	4	yes	—
24	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
25	C₂×C₁₃×#120	C₂²	1	4	yes	—
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₁₃×#399	C₂²	1	4	yes	—
32	C₁₃×#398	C₂²	1	4	yes	complemented
33	C₁₃×#396	C₂²	1	8	yes	complemented
34	C₁₃×#395	C₂²	1	4	yes	complemented
35	C₁₃×#394	C₂²	1	4	yes	complemented
36	C₁₃×#394	C₂²	1	4	yes	complemented
37	C₁₃×#393	C₂²	1	4	yes	—
38	C₁₃×#393	C₂²	1	8	yes	complemented
39	C₁₃×#392	C₂²	1	4	yes	—
40	C₁₃×#392	C₂²	1	4	yes	—
41	C₁₃×#391	C₂²	1	4	yes	complemented
42	C₁₃×#390	C₂²	1	8	yes	—
43	C₁₃×#387	C₂²	1	8	yes	complemented
44	C₁₃×#386	C₂²	1	4	yes	—
45	C₁₃×#386	C₂²	1	8	yes	—
46	C₁₃×#386	C₂²	1	4	yes	—
47	C₁₃×#386	C₂²	1	8	yes	—
48	C₁₃×#385	C₂²	1	8	yes	complemented
49	C₁₃×#381	C₂²	1	2	yes	—
50	C₁₃×#380	C₂²	1	2	yes	—
51	C₁₃×#380	C₂²	1	4	yes	—
52	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
53	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
54	C₂×C₁₃×#41	—	2	8	no	—
55	C₂×C₁₃×#41	—	4	8	no	—
56	C₂²×Q₈×C₁₃	—	2	4	no	—
57	C₂²×Q₈×C₁₃	—	4	4	no	—
58	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
59	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
60	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
61	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
62	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
63	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
64	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₃	—	2	4	no	—
66	C₂³×C₄×C₁₃	—	4	4	no	—
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
72	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#124	—	4	8	no	—
76	C₁₃×#123	—	4	8	no	—
77	C₁₃×C₂²⋊Q₈	—	2	32	no	—
78	C₁₃×C₂²⋊Q₈	—	2	16	no	—
79	C₁₃×#121	—	2	8	no	—
80	C₁₃×#121	—	2	8	no	—
81	C₁₃×#121	—	2	16	no	—
82	C₁₃×#121	—	4	8	no	—
83	C₁₃×#120	—	4	8	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
86	C₂×C₁₃×C₄⋊C₄	D₄	1	8	yes	complemented
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
98	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
100	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
105	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
106	C₁₃×#95	C₂³	1	4	yes	—
107	C₁₃×#95	C₂³	1	8	yes	—
108	C₁₃×#95	C₂³	1	4	yes	—
109	C₁₃×#95	C₂³	1	4	yes	—
110	C₁₃×#95	C₂³	1	4	yes	—
111	C₁₃×#95	C₂³	1	8	yes	—
112	#36707	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂⁴×C₁₃	—	2	2	no	—
114	C₂⁴×C₁₃	—	2	4	no	—
115	C₂⁴×C₁₃	—	2	4	no	—
116	C₂⁴×C₁₃	—	4	2	no	—
117	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
118	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
119	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
120	C₁₃×#41	—	4	32	no	—
121	C₂×Q₈×C₁₃	—	2	8	no	—
122	C₂×Q₈×C₁₃	—	2	4	no	—
123	C₂×Q₈×C₁₃	—	2	8	no	—
124	C₂×Q₈×C₁₃	—	4	4	no	—
125	C₂×Q₈×C₁₃	—	4	4	no	—
126	C₂×Q₈×C₁₃	—	4	16	no	—
127	C₂×D₄×C₁₃	—	2	8	no	—
128	C₂×D₄×C₁₃	—	2	8	no	—
129	C₂×D₄×C₁₃	—	2	8	no	—
130	C₂×D₄×C₁₃	—	2	16	no	—
131	C₂×D₄×C₁₃	—	2	4	no	—
132	C₂×D₄×C₁₃	—	2	4	no	—
133	C₂×D₄×C₁₃	—	2	4	no	—
134	C₂×D₄×C₁₃	—	4	4	no	—
135	C₂×D₄×C₁₃	—	4	8	no	—
136	C₂×D₄×C₁₃	—	4	4	no	—
137	C₂×D₄×C₁₃	—	4	8	no	—
138	C₂×D₄×C₁₃	—	4	4	no	—
139	C₂²×C₄×C₁₃	—	2	2	no	—
140	C₂²×C₄×C₁₃	—	2	4	no	—
141	C₂²×C₄×C₁₃	—	2	4	no	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	—	2	2	no	—
144	C₂²×C₄×C₁₃	—	2	4	no	—
145	C₂²×C₄×C₁₃	—	2	8	no	—
146	C₂²×C₄×C₁₃	—	2	8	no	—
147	C₂²×C₄×C₁₃	—	2	8	no	—
148	C₂²×C₄×C₁₃	—	4	2	no	—
149	C₂²×C₄×C₁₃	—	4	4	no	—
150	C₂²×C₄×C₁₃	—	4	2	no	—
151	C₂²×C₄×C₁₃	—	4	2	no	—
152	C₂²×C₄×C₁₃	—	4	4	no	—
153	C₂²×C₄×C₁₃	—	4	4	no	—
154	C₂²×C₄×C₁₃	—	4	16	no	—
155	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
156	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
166	C₁₃×C₄⋊C₄	—	2	8	no	—
167	C₁₃×C₄⋊C₄	—	2	8	no	—
168	C₁₃×C₄⋊C₄	—	2	4	no	—
169	C₁₃×C₄⋊C₄	—	2	4	no	—
170	C₁₃×C₄⋊C₄	—	4	4	no	—
171	C₁₃×C₄⋊C₄	—	4	8	no	—
172	C₁₃×C₄⋊C₄	C₂×D₄	1	16	yes	—
173	C₁₃×C₂²⋊C₄	—	2	8	no	—
174	C₁₃×C₂²⋊C₄	—	2	8	no	—
175	C₁₃×C₂²⋊C₄	—	2	8	no	—
176	C₁₃×C₂²⋊C₄	—	2	8	no	—
177	C₁₃×C₂²⋊C₄	—	2	8	no	—
178	C₁₃×C₂²⋊C₄	—	2	16	no	—
179	C₁₃×C₂²⋊C₄	—	4	8	no	—
180	C₁₃×C₂²⋊C₄	—	4	8	no	—
181	C₁₃×C₂²⋊C₄	—	4	8	no	—
182	C₄²×C₁₃	—	4	4	no	—
183	C₂×#537	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
185	#2847	C₂×C₁₃	1	2	yes	complemented
186	#2692	C₂×C₁₃	1	8	yes	complemented
187	#2676	C₂×C₁₃	1	8	yes	complemented
188	#2618	C₂×C₁₃	1	2	yes	complemented
189	#2539	C₂×C₁₃	1	2	yes	complemented
190	#2436	C₂×C₁₃	1	2	yes	complemented
191	#2406	C₂×C₁₃	1	2	yes	complemented
192	#2404	C₂×C₁₃	1	2	yes	complemented
193	#2313	C₂×C₁₃	1	1	yes	characteristic, complemented
194	C₂³×C₁₃	—	2	2	no	—
195	C₂³×C₁₃	—	2	2	no	—
196	C₂³×C₁₃	—	2	8	no	—
197	C₂³×C₁₃	—	2	2	no	—
198	C₂³×C₁₃	—	2	4	no	—
199	C₂³×C₁₃	—	2	4	no	—
200	C₂³×C₁₃	—	2	2	no	—
201	C₂³×C₁₃	—	2	4	no	—
202	C₂³×C₁₃	—	2	8	no	—
203	C₂³×C₁₃	—	2	4	no	—
204	C₂³×C₁₃	—	2	4	no	—
205	C₂³×C₁₃	—	2	8	no	—
206	C₂³×C₁₃	—	4	16	no	—
207	C₂³×C₁₃	—	4	4	no	—
208	C₂³×C₁₃	—	4	4	no	—
209	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
210	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
211	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
212	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
213	Q₈×C₁₃	—	4	16	no	—
214	Q₈×C₁₃	—	4	8	no	—
215	D₄×C₁₃	—	4	8	no	—
216	D₄×C₁₃	—	4	16	no	—
217	D₄×C₁₃	—	8	4	no	—
218	D₄×C₁₃	—	8	4	no	—
219	D₄×C₁₃	—	8	16	no	—
220	C₂×C₄×C₁₃	—	2	8	no	—
221	C₂×C₄×C₁₃	—	2	8	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	8	no	—
231	C₂×C₄×C₁₃	—	2	8	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	8	no	—
237	C₂×C₄×C₁₃	—	4	4	no	—
238	C₂×C₄×C₁₃	—	4	4	no	—
239	C₂×C₄×C₁₃	—	4	16	no	—
240	C₂×C₄×C₁₃	—	4	16	no	—
241	C₂×C₄×C₁₃	—	4	4	no	—
242	C₂×C₄×C₁₃	—	4	4	no	—
243	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
244	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
245	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
246	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
247	C₂²×#41	C₂²×C₁₃	1	2	yes	—
248	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
249	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
250	#537	—	2	8	no	—
251	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
252	C₂×#123	C₂²×C₁₃	1	4	yes	—
253	C₂×C₂²⋊Q₈	—	2	8	no	—
254	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	—
255	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
256	C₂×#121	C₂²×C₁₃	1	2	yes	—
257	C₂×#121	C₂²×C₁₃	1	2	yes	—
258	C₂×#121	C₂²×C₁₃	1	4	yes	—
259	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
260	C₂×#120	C₂²×C₁₃	1	4	yes	—
261	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
262	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
263	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
264	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
265	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
266	#399	C₂²×C₁₃	1	4	yes	—
267	#398	C₂²×C₁₃	1	4	yes	complemented
268	#396	C₂²×C₁₃	1	8	yes	complemented
269	#395	C₂²×C₁₃	1	4	yes	complemented
270	#394	C₂²×C₁₃	1	4	yes	complemented
271	#394	C₂²×C₁₃	1	4	yes	complemented
272	#393	C₂²×C₁₃	1	4	yes	—
273	#393	C₂²×C₁₃	1	8	yes	complemented
274	#392	C₂²×C₁₃	1	4	yes	—
275	#392	C₂²×C₁₃	1	4	yes	—
276	#391	C₂²×C₁₃	1	4	yes	complemented
277	#390	C₂²×C₁₃	1	8	yes	—
278	#387	C₂²×C₁₃	1	8	yes	complemented
279	#386	C₂²×C₁₃	1	4	yes	—
280	#386	C₂²×C₁₃	1	8	yes	—
281	#386	C₂²×C₁₃	1	4	yes	—
282	#386	C₂²×C₁₃	1	8	yes	—
283	#385	C₂²×C₁₃	1	8	yes	complemented
284	#381	C₂²×C₁₃	1	2	yes	—
285	#380	C₂²×C₁₃	1	2	yes	—
286	#380	C₂²×C₁₃	1	4	yes	—
287	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
288	C₂²×C₁₃	—	2	2	no	—
289	C₂²×C₁₃	—	2	2	no	—
290	C₂²×C₁₃	—	2	8	no	—
291	C₂²×C₁₃	—	2	4	no	—
292	C₂²×C₁₃	—	2	8	no	—
293	C₂²×C₁₃	—	4	16	no	—
294	C₂²×C₁₃	—	4	2	no	—
295	C₂²×C₁₃	—	4	2	no	—
296	C₂²×C₁₃	—	4	4	no	—
297	C₂²×C₁₃	—	4	4	no	—
298	C₂²×C₁₃	—	4	4	no	—
299	C₂²×C₁₃	—	4	4	no	—
300	C₂²×C₁₃	—	4	8	no	—
301	C₂²×C₁₃	—	4	8	no	—
302	C₂²×C₁₃	#535	1	4	yes	—
303	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
304	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
305	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
306	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
307	C₄×C₁₃	—	2	4	no	—
308	C₄×C₁₃	—	2	4	no	—
309	C₄×C₁₃	—	2	4	no	—
310	C₄×C₁₃	—	2	4	no	—
311	C₄×C₁₃	—	4	2	no	—
312	C₄×C₁₃	—	4	4	no	—
313	C₄×C₁₃	—	4	2	no	—
314	C₄×C₁₃	—	4	8	no	—
315	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
316	C₂×#41	—	2	8	no	—
317	C₂×#41	—	4	8	no	—
318	C₂²×Q₈	—	2	4	no	—
319	C₂²×Q₈	—	4	4	no	—
320	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
321	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
322	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
323	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
324	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
325	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
326	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
327	C₂³×C₄	—	2	4	no	—
328	C₂³×C₄	—	4	4	no	—
329	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
330	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
331	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
332	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
333	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
334	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
335	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
336	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
337	#124	—	4	8	no	—
338	#123	—	4	8	no	—
339	C₂²⋊Q₈	—	2	32	no	—
340	C₂²⋊Q₈	—	2	16	no	—
341	#121	—	2	8	no	—
342	#121	—	2	8	no	—
343	#121	—	2	16	no	—
344	#121	—	4	8	no	—
345	#120	—	4	8	no	—
346	C₂×C₄⋊C₄	—	2	4	no	—
347	C₂×C₄⋊C₄	—	2	4	no	—
348	C₂×C₄⋊C₄	D₄×C₁₃	1	8	yes	complemented
349	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
350	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
351	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
354	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
355	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
356	C₂×C₂²⋊C₄	—	2	4	no	—
357	C₂×C₂²⋊C₄	—	2	4	no	—
358	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
360	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
361	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
362	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
363	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
364	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
365	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
366	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
367	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
368	#95	C₂³×C₁₃	1	4	yes	—
369	#95	C₂³×C₁₃	1	8	yes	—
370	#95	C₂³×C₁₃	1	4	yes	—
371	#95	C₂³×C₁₃	1	4	yes	—
372	#95	C₂³×C₁₃	1	4	yes	—
373	#95	C₂³×C₁₃	1	8	yes	—
374	C₂×C₁₃	—	2	4	no	—
375	C₂×C₁₃	—	4	4	no	—
376	C₂×C₁₃	—	8	4	no	—
377	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
378	C₂×C₁₃	#3484	1	1	yes	characteristic
379	C₂×C₁₃	#3486	1	1	yes	characteristic
380	C₂×C₁₃	#3536	1	4	yes	—
381	C₂⁴	—	2	2	no	—
382	C₂⁴	—	2	4	no	—
383	C₂⁴	—	2	4	no	—
384	C₂⁴	—	4	2	no	—
385	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
386	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
387	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
388	#41	—	4	32	no	—
389	C₂×Q₈	—	2	8	no	—
390	C₂×Q₈	—	2	4	no	—
391	C₂×Q₈	—	2	8	no	—
392	C₂×Q₈	—	4	4	no	—
393	C₂×Q₈	—	4	4	no	—
394	C₂×Q₈	—	4	16	no	—
395	C₂×D₄	—	2	8	no	—
396	C₂×D₄	—	2	8	no	—
397	C₂×D₄	—	2	8	no	—
398	C₂×D₄	—	2	16	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	4	4	no	—
403	C₂×D₄	—	4	8	no	—
404	C₂×D₄	—	4	4	no	—
405	C₂×D₄	—	4	8	no	—
406	C₂×D₄	—	4	4	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	8	no	—
414	C₂²×C₄	—	2	8	no	—
415	C₂²×C₄	—	2	8	no	—
416	C₂²×C₄	—	4	2	no	—
417	C₂²×C₄	—	4	4	no	—
418	C₂²×C₄	—	4	2	no	—
419	C₂²×C₄	—	4	2	no	—
420	C₂²×C₄	—	4	4	no	—
421	C₂²×C₄	—	4	4	no	—
422	C₂²×C₄	—	4	16	no	—
423	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
424	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
425	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
426	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
427	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
428	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
429	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
430	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
431	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
432	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
433	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
434	C₄⋊C₄	—	2	8	no	—
435	C₄⋊C₄	—	2	8	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	—	4	4	no	—
439	C₄⋊C₄	—	4	8	no	—
440	C₄⋊C₄	C₂×D₄×C₁₃	1	16	yes	—
441	C₂²⋊C₄	—	2	8	no	—
442	C₂²⋊C₄	—	2	8	no	—
443	C₂²⋊C₄	—	2	8	no	—
444	C₂²⋊C₄	—	2	8	no	—
445	C₂²⋊C₄	—	2	8	no	—
446	C₂²⋊C₄	—	2	16	no	—
447	C₂²⋊C₄	—	4	8	no	—
448	C₂²⋊C₄	—	4	8	no	—
449	C₂²⋊C₄	—	4	8	no	—
450	C₄²	—	4	4	no	—
451	C₁₃	#36707	1	1	yes	characteristic, direct product factor, Sylow
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	8	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	4	no	—
457	C₂³	—	2	4	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	4	no	—
460	C₂³	—	2	8	no	—
461	C₂³	—	2	4	no	—
462	C₂³	—	2	4	no	—
463	C₂³	—	2	8	no	—
464	C₂³	—	4	16	no	—
465	C₂³	—	4	4	no	—
466	C₂³	—	4	4	no	—
467	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
468	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
469	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
470	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
471	Q₈	—	4	16	no	—
472	Q₈	—	4	8	no	—
473	D₄	—	4	8	no	—
474	D₄	—	4	16	no	—
475	D₄	—	8	4	no	—
476	D₄	—	8	4	no	—
477	D₄	—	8	16	no	—
478	C₂×C₄	—	2	8	no	—
479	C₂×C₄	—	2	8	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	8	no	—
489	C₂×C₄	—	2	8	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	8	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	—	4	4	no	—
497	C₂×C₄	—	4	16	no	—
498	C₂×C₄	—	4	16	no	—
499	C₂×C₄	—	4	4	no	—
500	C₂×C₄	—	4	4	no	—
501	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
502	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
503	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
504	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
505	C₂²	—	2	8	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	8	no	—
509	C₂²	—	2	4	no	—
510	C₂²	—	4	16	no	—
511	C₂²	—	4	4	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	4	8	no	—
515	C₂²	—	4	8	no	—
516	C₂²	—	4	4	no	—
517	C₂²	—	4	4	no	—
518	C₂²	—	4	4	no	—
519	C₂²	C₁₃×#535	1	4	yes	—
520	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
521	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
522	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
523	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
524	C₄	—	2	4	no	—
525	C₄	—	2	4	no	—
526	C₄	—	2	4	no	—
527	C₄	—	2	4	no	—
528	C₄	—	4	8	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	4	no	—
531	C₄	—	4	2	no	—
532	C₂	—	2	4	no	—
533	C₂	—	4	4	no	—
534	C₂	—	8	4	no	—
535	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
536	C₂	C₁₃×#3484	1	1	yes	characteristic
537	C₂	C₁₃×#3486	1	1	yes	characteristic
538	C₂	C₁₃×#3536	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
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
1. C₂×C₁₃×#537	C₂	semidirect
2. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
3. C₁₃×#2847	C₂	semidirect
4. C₁₃×#2692	C₂	semidirect
5. C₁₃×#2676	C₂	semidirect
6. C₁₃×#2618	C₂	semidirect
7. C₁₃×#2539	C₂	semidirect
8. C₁₃×#2436	C₂	semidirect
9. C₁₃×#2406	C₂	semidirect
10. C₁₃×#2404	C₂	semidirect
11. C₁₃×#2313	C₂	semidirect
16. C₂×C₁₃×#124	C₂²	semidirect
20. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
24. C₂×C₁₃×#121	C₂²	semidirect
32. C₁₃×#398	C₂²	semidirect
33. C₁₃×#396	C₂²	semidirect
34. C₁₃×#395	C₂²	semidirect
35. C₁₃×#394	C₂²	semidirect
36. C₁₃×#394	C₂²	semidirect
38. C₁₃×#393	C₂²	semidirect
41. C₁₃×#391	C₂²	semidirect
43. C₁₃×#387	C₂²	semidirect
48. C₁₃×#385	C₂²	semidirect
86. C₂×C₁₃×C₄⋊C₄	D₄	semidirect
112. #36707	C₁₃	direct (N × H)
183. C₂×#537	C₂×C₁₃	semidirect
184. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
185. #2847	C₂×C₁₃	semidirect
186. #2692	C₂×C₁₃	semidirect
187. #2676	C₂×C₁₃	semidirect
188. #2618	C₂×C₁₃	semidirect
189. #2539	C₂×C₁₃	semidirect
190. #2436	C₂×C₁₃	semidirect
191. #2406	C₂×C₁₃	semidirect
192. #2404	C₂×C₁₃	semidirect
193. #2313	C₂×C₁₃	semidirect
251. C₂×#124	C₂²×C₁₃	semidirect
255. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
259. C₂×#121	C₂²×C₁₃	semidirect
267. #398	C₂²×C₁₃	semidirect
268. #396	C₂²×C₁₃	semidirect
269. #395	C₂²×C₁₃	semidirect
270. #394	C₂²×C₁₃	semidirect
271. #394	C₂²×C₁₃	semidirect
273. #393	C₂²×C₁₃	semidirect
276. #391	C₂²×C₁₃	semidirect
278. #387	C₂²×C₁₃	semidirect
283. #385	C₂²×C₁₃	semidirect
348. C₂×C₄⋊C₄	D₄×C₁₃	semidirect
451. C₁₃	#36707	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×#537	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₁₃×#2847	2
C₁₃×#2692	2
C₁₃×#2676	2
C₁₃×#2618	2
C₁₃×#2539	2
C₁₃×#2436	2
C₁₃×#2406	2
C₁₃×#2404	2
C₁₃×#2313	2
#36707	13

Subgroups — C13×#36707 #15723046

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36707 #15723046