Subgroups — C₁₃×#36731 #15723070

Order 3328.

2130 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2847	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2743	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2740	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2699	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2688	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2656	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2646	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2444	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2424	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2325	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#381	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#121	C₂²	1	2	yes	—
14	C₂×C₁₃×#121	C₂²	1	2	yes	—
15	C₂×C₁₃×#121	C₂²	1	2	yes	—
16	C₂×C₁₃×#121	C₂²	1	4	yes	—
17	C₂×C₁₃×#121	C₂²	1	4	yes	—
18	C₂×C₁₃×#120	C₂²	1	4	yes	—
19	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
20	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₁₃×#400	C₂²	1	4	yes	complemented
22	C₁₃×#400	C₂²	1	4	yes	complemented
23	C₁₃×#399	C₂²	1	4	yes	complemented
24	C₁₃×#398	C₂²	1	4	yes	complemented
25	C₁₃×#397	C₂²	1	4	yes	complemented
26	C₁₃×#397	C₂²	1	4	yes	complemented
27	C₁₃×#396	C₂²	1	4	yes	—
28	C₁₃×#394	C₂²	1	4	yes	—
29	C₁₃×#394	C₂²	1	4	yes	—
30	C₁₃×#394	C₂²	1	4	yes	complemented
31	C₁₃×#392	C₂²	1	4	yes	—
32	C₁₃×#392	C₂²	1	4	yes	complemented
33	C₁₃×#390	C₂²	1	4	yes	—
34	C₁₃×#388	C₂²	1	4	yes	—
35	C₁₃×#388	C₂²	1	4	yes	complemented
36	C₁₃×#388	C₂²	1	4	yes	complemented
37	C₁₃×#387	C₂²	1	4	yes	complemented
38	C₁₃×#387	C₂²	1	4	yes	complemented
39	C₁₃×#386	C₂²	1	4	yes	—
40	C₁₃×#386	C₂²	1	4	yes	—
41	C₁₃×#386	C₂²	1	4	yes	—
42	C₁₃×#386	C₂²	1	4	yes	—
43	C₁₃×#386	C₂²	1	4	yes	—
44	C₁₃×#386	C₂²	1	4	yes	complemented
45	C₁₃×#386	C₂²	1	4	yes	complemented
46	C₁₃×#385	C₂²	1	4	yes	—
47	C₁₃×#385	C₂²	1	4	yes	complemented
48	C₁₃×#381	C₂²	1	4	yes	—
49	C₁₃×#381	C₂²	1	4	yes	—
50	C₁₃×#381	C₂²	1	4	yes	complemented
51	C₁₃×#380	C₂²	1	2	yes	—
52	C₁₃×#380	C₂²	1	2	yes	—
53	C₁₃×#380	C₂²	1	2	yes	—
54	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#95	C₂²	1	2	yes	—
57	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
59	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
60	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
61	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
62	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
63	C₂³×C₄×C₁₃	—	2	4	no	—
64	C₂³×C₄×C₁₃	—	4	4	no	—
65	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
66	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
70	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₁₃×#121	—	2	8	no	—
73	C₁₃×#121	—	4	8	no	—
74	C₁₃×#121	—	4	4	no	—
75	C₁₃×#121	—	4	4	no	—
76	C₁₃×#121	—	4	8	no	—
77	C₁₃×#120	—	4	8	no	—
78	C₄×D₄×C₁₃	—	4	8	no	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
86	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
88	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
89	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
90	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
91	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
92	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
100	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
101	C₁₃×#95	C₂³	1	4	yes	—
102	C₁₃×#95	C₂³	1	4	yes	—
103	C₁₃×#95	C₂³	1	4	yes	—
104	C₁₃×#95	C₂³	1	4	yes	—
105	C₁₃×#95	C₂³	1	4	yes	—
106	C₁₃×#95	C₂³	1	4	yes	—
107	C₁₃×#95	C₂³	1	4	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	4	yes	—
112	#36731	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	1	no	—
117	C₂⁴×C₁₃	—	4	1	no	—
118	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
119	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
120	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₂×D₄×C₁₃	—	2	8	no	—
122	C₂×D₄×C₁₃	—	2	8	no	—
123	C₂×D₄×C₁₃	—	2	8	no	—
124	C₂×D₄×C₁₃	—	2	8	no	—
125	C₂×D₄×C₁₃	—	2	8	no	—
126	C₂×D₄×C₁₃	—	2	4	no	—
127	C₂×D₄×C₁₃	—	4	4	no	—
128	C₂×D₄×C₁₃	—	4	4	no	—
129	C₂×D₄×C₁₃	—	4	2	no	—
130	C₂×D₄×C₁₃	—	4	2	no	—
131	C₂×D₄×C₁₃	—	4	4	no	—
132	C₂×D₄×C₁₃	—	4	4	no	—
133	C₂×D₄×C₁₃	—	4	4	no	—
134	C₂×D₄×C₁₃	—	4	4	no	—
135	C₂×D₄×C₁₃	—	4	4	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₃	—	2	4	no	—
140	C₂²×C₄×C₁₃	—	2	4	no	—
141	C₂²×C₄×C₁₃	—	2	4	no	—
142	C₂²×C₄×C₁₃	—	2	4	no	—
143	C₂²×C₄×C₁₃	—	4	2	no	—
144	C₂²×C₄×C₁₃	—	4	2	no	—
145	C₂²×C₄×C₁₃	—	4	2	no	—
146	C₂²×C₄×C₁₃	—	4	2	no	—
147	C₂²×C₄×C₁₃	—	4	2	no	—
148	C₂²×C₄×C₁₃	—	4	2	no	—
149	C₂²×C₄×C₁₃	—	4	4	no	—
150	C₂²×C₄×C₁₃	—	4	4	no	—
151	C₂²×C₄×C₁₃	—	4	2	no	—
152	C₂²×C₄×C₁₃	—	4	4	no	—
153	C₂²×C₄×C₁₃	—	4	2	no	—
154	C₂²×C₄×C₁₃	—	4	16	no	—
155	C₂²×C₄×C₁₃	#41	1	4	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
164	C₁₃×C₄⋊C₄	—	2	4	no	—
165	C₁₃×C₄⋊C₄	—	4	4	no	—
166	C₁₃×C₄⋊C₄	—	4	4	no	—
167	C₁₃×C₄⋊C₄	—	4	2	no	—
168	C₁₃×C₄⋊C₄	—	4	2	no	—
169	C₁₃×C₄⋊C₄	—	4	4	no	—
170	C₁₃×C₄⋊C₄	—	4	4	no	—
171	C₁₃×C₂²⋊C₄	—	2	8	no	—
172	C₁₃×C₂²⋊C₄	—	2	8	no	—
173	C₁₃×C₂²⋊C₄	—	2	8	no	—
174	C₁₃×C₂²⋊C₄	—	4	4	no	—
175	C₁₃×C₂²⋊C₄	—	4	4	no	—
176	C₁₃×C₂²⋊C₄	—	4	4	no	—
177	C₁₃×C₂²⋊C₄	—	4	4	no	—
178	C₁₃×C₂²⋊C₄	—	4	4	no	—
179	C₁₃×C₂²⋊C₄	—	4	4	no	—
180	C₁₃×C₂²⋊C₄	—	4	4	no	—
181	C₁₃×C₂²⋊C₄	—	4	4	no	—
182	C₁₃×C₂²⋊C₄	—	4	4	no	—
183	C₁₃×C₂²⋊C₄	—	4	4	no	—
184	C₄²×C₁₃	—	4	4	no	—
185	#2847	C₂×C₁₃	1	2	yes	complemented
186	#2743	C₂×C₁₃	1	4	yes	complemented
187	#2740	C₂×C₁₃	1	4	yes	complemented
188	#2699	C₂×C₁₃	1	4	yes	complemented
189	#2688	C₂×C₁₃	1	4	yes	complemented
190	#2656	C₂×C₁₃	1	1	yes	characteristic, complemented
191	#2646	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#2444	C₂×C₁₃	1	4	yes	complemented
193	#2424	C₂×C₁₃	1	4	yes	complemented
194	#2325	C₂×C₁₃	1	2	yes	complemented
195	C₂×#381	C₂×C₁₃	1	1	yes	characteristic, complemented
196	C₂³×C₁₃	—	2	2	no	—
197	C₂³×C₁₃	—	2	1	no	—
198	C₂³×C₁₃	—	2	1	no	—
199	C₂³×C₁₃	—	2	8	no	—
200	C₂³×C₁₃	—	2	2	no	—
201	C₂³×C₁₃	—	2	2	no	—
202	C₂³×C₁₃	—	2	2	no	—
203	C₂³×C₁₃	—	2	2	no	—
204	C₂³×C₁₃	—	2	2	no	—
205	C₂³×C₁₃	—	2	2	no	—
206	C₂³×C₁₃	—	2	4	no	—
207	C₂³×C₁₃	—	2	4	no	—
208	C₂³×C₁₃	—	2	4	no	—
209	C₂³×C₁₃	—	2	4	no	—
210	C₂³×C₁₃	—	2	4	no	—
211	C₂³×C₁₃	—	2	4	no	—
212	C₂³×C₁₃	—	2	4	no	—
213	C₂³×C₁₃	—	4	8	no	—
214	C₂³×C₁₃	—	4	8	no	—
215	C₂³×C₁₃	—	4	4	no	—
216	C₂³×C₁₃	—	4	4	no	—
217	C₂³×C₁₃	C₂×#41	1	2	yes	—
218	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
219	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
220	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
221	D₄×C₁₃	—	4	16	no	—
222	D₄×C₁₃	—	8	4	no	—
223	D₄×C₁₃	—	8	8	no	—
224	D₄×C₁₃	—	8	8	no	—
225	D₄×C₁₃	—	8	8	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	1	no	—
230	C₂×C₄×C₁₃	—	2	1	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	4	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	4	no	—
243	C₂×C₄×C₁₃	—	2	4	no	—
244	C₂×C₄×C₁₃	—	2	4	no	—
245	C₂×C₄×C₁₃	—	2	4	no	—
246	C₂×C₄×C₁₃	—	2	4	no	—
247	C₂×C₄×C₁₃	—	4	4	no	—
248	C₂×C₄×C₁₃	—	4	8	no	—
249	C₂×C₄×C₁₃	—	4	8	no	—
250	C₂×C₄×C₁₃	—	4	4	no	—
251	C₂×C₄×C₁₃	—	8	4	no	—
252	C₂×C₄×C₁₃	—	8	4	no	—
253	C₂×C₄×C₁₃	—	8	8	no	—
254	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
255	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×#121	C₂²×C₁₃	1	2	yes	—
257	C₂×#121	C₂²×C₁₃	1	2	yes	—
258	C₂×#121	C₂²×C₁₃	1	2	yes	—
259	C₂×#121	C₂²×C₁₃	1	4	yes	—
260	C₂×#121	C₂²×C₁₃	1	4	yes	—
261	C₂×#120	C₂²×C₁₃	1	4	yes	—
262	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
263	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
264	#400	C₂²×C₁₃	1	4	yes	complemented
265	#400	C₂²×C₁₃	1	4	yes	complemented
266	#399	C₂²×C₁₃	1	4	yes	complemented
267	#398	C₂²×C₁₃	1	4	yes	complemented
268	#397	C₂²×C₁₃	1	4	yes	complemented
269	#397	C₂²×C₁₃	1	4	yes	complemented
270	#396	C₂²×C₁₃	1	4	yes	—
271	#394	C₂²×C₁₃	1	4	yes	—
272	#394	C₂²×C₁₃	1	4	yes	—
273	#394	C₂²×C₁₃	1	4	yes	complemented
274	#392	C₂²×C₁₃	1	4	yes	—
275	#392	C₂²×C₁₃	1	4	yes	complemented
276	#390	C₂²×C₁₃	1	4	yes	—
277	#388	C₂²×C₁₃	1	4	yes	—
278	#388	C₂²×C₁₃	1	4	yes	complemented
279	#388	C₂²×C₁₃	1	4	yes	complemented
280	#387	C₂²×C₁₃	1	4	yes	complemented
281	#387	C₂²×C₁₃	1	4	yes	complemented
282	#386	C₂²×C₁₃	1	4	yes	—
283	#386	C₂²×C₁₃	1	4	yes	—
284	#386	C₂²×C₁₃	1	4	yes	—
285	#386	C₂²×C₁₃	1	4	yes	—
286	#386	C₂²×C₁₃	1	4	yes	—
287	#386	C₂²×C₁₃	1	4	yes	complemented
288	#386	C₂²×C₁₃	1	4	yes	complemented
289	#385	C₂²×C₁₃	1	4	yes	—
290	#385	C₂²×C₁₃	1	4	yes	complemented
291	#381	C₂²×C₁₃	1	4	yes	—
292	#381	C₂²×C₁₃	1	4	yes	—
293	#381	C₂²×C₁₃	1	4	yes	complemented
294	#380	C₂²×C₁₃	1	2	yes	—
295	#380	C₂²×C₁₃	1	2	yes	—
296	#380	C₂²×C₁₃	1	2	yes	—
297	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×#95	C₂²×C₁₃	1	2	yes	—
300	C₂²×C₁₃	—	2	2	no	—
301	C₂²×C₁₃	—	2	2	no	—
302	C₂²×C₁₃	—	2	4	no	—
303	C₂²×C₁₃	—	2	4	no	—
304	C₂²×C₁₃	—	2	4	no	—
305	C₂²×C₁₃	—	2	4	no	—
306	C₂²×C₁₃	—	2	4	no	—
307	C₂²×C₁₃	—	4	16	no	—
308	C₂²×C₁₃	—	4	2	no	—
309	C₂²×C₁₃	—	4	2	no	—
310	C₂²×C₁₃	—	4	2	no	—
311	C₂²×C₁₃	—	4	2	no	—
312	C₂²×C₁₃	—	4	4	no	—
313	C₂²×C₁₃	—	4	4	no	—
314	C₂²×C₁₃	—	4	4	no	—
315	C₂²×C₁₃	—	4	4	no	—
316	C₂²×C₁₃	—	4	4	no	—
317	C₂²×C₁₃	—	4	4	no	—
318	C₂²×C₁₃	—	4	4	no	—
319	C₂²×C₁₃	#540	1	4	yes	—
320	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
321	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
322	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
323	C₂²×C₁₃	#585	1	1	yes	characteristic
324	C₂²×C₁₃	#585	1	1	yes	characteristic
325	C₄×C₁₃	—	2	4	no	—
326	C₄×C₁₃	—	4	4	no	—
327	C₄×C₁₃	—	4	1	no	—
328	C₄×C₁₃	—	4	1	no	—
329	C₄×C₁₃	—	4	4	no	—
330	C₄×C₁₃	—	4	4	no	—
331	C₄×C₁₃	—	4	4	no	—
332	C₄×C₁₃	—	4	4	no	—
333	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
334	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
335	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
336	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
337	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
338	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
339	C₂³×C₄	—	2	4	no	—
340	C₂³×C₄	—	4	4	no	—
341	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
342	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
343	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
344	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
345	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
346	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
347	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
348	#121	—	2	8	no	—
349	#121	—	4	8	no	—
350	#121	—	4	4	no	—
351	#121	—	4	4	no	—
352	#121	—	4	8	no	—
353	#120	—	4	8	no	—
354	C₄×D₄	—	4	8	no	—
355	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
356	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
357	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
359	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
360	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
361	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
362	C₂×C₂²⋊C₄	—	4	4	no	—
363	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
364	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
365	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
366	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
367	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
368	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
369	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
376	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
377	#95	C₂³×C₁₃	1	4	yes	—
378	#95	C₂³×C₁₃	1	4	yes	—
379	#95	C₂³×C₁₃	1	4	yes	—
380	#95	C₂³×C₁₃	1	4	yes	—
381	#95	C₂³×C₁₃	1	4	yes	—
382	#95	C₂³×C₁₃	1	4	yes	—
383	#95	C₂³×C₁₃	1	4	yes	—
384	#95	C₂³×C₁₃	1	4	yes	—
385	#95	C₂³×C₁₃	1	4	yes	—
386	#95	C₂³×C₁₃	1	4	yes	—
387	#95	C₂³×C₁₃	1	4	yes	—
388	C₂×C₁₃	—	2	4	no	—
389	C₂×C₁₃	—	4	4	no	—
390	C₂×C₁₃	—	8	4	no	—
391	C₂×C₁₃	C₂×#540	1	1	yes	characteristic
392	C₂×C₁₃	#3490	1	1	yes	characteristic
393	C₂×C₁₃	#3493	1	1	yes	characteristic
394	C₂×C₁₃	#3534	1	2	yes	—
395	C₂×C₁₃	#3534	1	2	yes	—
396	C₂⁴	—	2	2	no	—
397	C₂⁴	—	2	4	no	—
398	C₂⁴	—	2	4	no	—
399	C₂⁴	—	4	1	no	—
400	C₂⁴	—	4	1	no	—
401	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
402	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
403	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
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	8	no	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	4	4	no	—
411	C₂×D₄	—	4	4	no	—
412	C₂×D₄	—	4	2	no	—
413	C₂×D₄	—	4	2	no	—
414	C₂×D₄	—	4	4	no	—
415	C₂×D₄	—	4	4	no	—
416	C₂×D₄	—	4	4	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	—	4	4	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	4	2	no	—
427	C₂²×C₄	—	4	2	no	—
428	C₂²×C₄	—	4	2	no	—
429	C₂²×C₄	—	4	2	no	—
430	C₂²×C₄	—	4	2	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	4	4	no	—
433	C₂²×C₄	—	4	4	no	—
434	C₂²×C₄	—	4	2	no	—
435	C₂²×C₄	—	4	4	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	4	16	no	—
438	C₂²×C₄	C₁₃×#41	1	4	yes	—
439	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
440	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
441	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
442	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
443	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
444	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
445	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
446	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	4	4	no	—
449	C₄⋊C₄	—	4	2	no	—
450	C₄⋊C₄	—	4	2	no	—
451	C₄⋊C₄	—	4	4	no	—
452	C₄⋊C₄	—	4	4	no	—
453	C₄⋊C₄	—	4	4	no	—
454	C₂²⋊C₄	—	2	8	no	—
455	C₂²⋊C₄	—	2	8	no	—
456	C₂²⋊C₄	—	2	8	no	—
457	C₂²⋊C₄	—	4	4	no	—
458	C₂²⋊C₄	—	4	4	no	—
459	C₂²⋊C₄	—	4	4	no	—
460	C₂²⋊C₄	—	4	4	no	—
461	C₂²⋊C₄	—	4	4	no	—
462	C₂²⋊C₄	—	4	4	no	—
463	C₂²⋊C₄	—	4	4	no	—
464	C₂²⋊C₄	—	4	4	no	—
465	C₂²⋊C₄	—	4	4	no	—
466	C₂²⋊C₄	—	4	4	no	—
467	C₄²	—	4	4	no	—
468	C₁₃	#36731	1	1	yes	characteristic, direct product factor, Sylow
469	C₂³	—	2	2	no	—
470	C₂³	—	2	1	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	2	8	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	2	4	no	—
481	C₂³	—	2	4	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	2	4	no	—
486	C₂³	—	4	8	no	—
487	C₂³	—	4	8	no	—
488	C₂³	—	4	4	no	—
489	C₂³	—	4	4	no	—
490	C₂³	C₂×C₁₃×#41	1	2	yes	—
491	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
492	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
493	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
494	D₄	—	4	16	no	—
495	D₄	—	8	4	no	—
496	D₄	—	8	8	no	—
497	D₄	—	8	8	no	—
498	D₄	—	8	8	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	4	4	no	—
521	C₂×C₄	—	4	8	no	—
522	C₂×C₄	—	4	8	no	—
523	C₂×C₄	—	4	4	no	—
524	C₂×C₄	—	8	4	no	—
525	C₂×C₄	—	8	4	no	—
526	C₂×C₄	—	8	8	no	—
527	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
528	C₂²	—	2	4	no	—
529	C₂²	—	2	4	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	4	no	—
533	C₂²	—	2	4	no	—
534	C₂²	—	2	4	no	—
535	C₂²	—	4	16	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	4	4	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	4	4	no	—
544	C₂²	—	4	4	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	4	4	no	—
547	C₂²	C₁₃×#540	1	4	yes	—
548	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
549	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
550	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
551	C₂²	C₁₃×#585	1	1	yes	characteristic
552	C₂²	C₁₃×#585	1	1	yes	characteristic
553	C₄	—	2	4	no	—
554	C₄	—	4	4	no	—
555	C₄	—	4	4	no	—
556	C₄	—	4	4	no	—
557	C₄	—	4	4	no	—
558	C₄	—	4	4	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₂	—	2	4	no	—
562	C₂	—	4	4	no	—
563	C₂	—	8	4	no	—
564	C₂	C₂×C₁₃×#540	1	1	yes	characteristic
565	C₂	C₁₃×#3490	1	1	yes	characteristic
566	C₂	C₁₃×#3493	1	1	yes	characteristic
567	C₂	C₁₃×#3534	1	2	yes	—
568	C₂	C₁₃×#3534	1	2	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. C₁₃×#2847	C₂	semidirect
2. C₁₃×#2743	C₂	semidirect
3. C₁₃×#2740	C₂	semidirect
4. C₁₃×#2699	C₂	semidirect
5. C₁₃×#2688	C₂	semidirect
6. C₁₃×#2656	C₂	semidirect
7. C₁₃×#2646	C₂	semidirect
8. C₁₃×#2444	C₂	semidirect
9. C₁₃×#2424	C₂	semidirect
10. C₁₃×#2325	C₂	semidirect
11. C₂×C₁₃×#381	C₂	semidirect
21. C₁₃×#400	C₂²	semidirect
22. C₁₃×#400	C₂²	semidirect
23. C₁₃×#399	C₂²	semidirect
24. C₁₃×#398	C₂²	semidirect
25. C₁₃×#397	C₂²	semidirect
26. C₁₃×#397	C₂²	semidirect
30. C₁₃×#394	C₂²	semidirect
32. C₁₃×#392	C₂²	semidirect
35. C₁₃×#388	C₂²	semidirect
36. C₁₃×#388	C₂²	semidirect
37. C₁₃×#387	C₂²	semidirect
38. C₁₃×#387	C₂²	semidirect
44. C₁₃×#386	C₂²	semidirect
45. C₁₃×#386	C₂²	semidirect
47. C₁₃×#385	C₂²	semidirect
50. C₁₃×#381	C₂²	semidirect
112. #36731	C₁₃	direct (N × H)
185. #2847	C₂×C₁₃	semidirect
186. #2743	C₂×C₁₃	semidirect
187. #2740	C₂×C₁₃	semidirect
188. #2699	C₂×C₁₃	semidirect
189. #2688	C₂×C₁₃	semidirect
190. #2656	C₂×C₁₃	semidirect
191. #2646	C₂×C₁₃	semidirect
192. #2444	C₂×C₁₃	semidirect
193. #2424	C₂×C₁₃	semidirect
194. #2325	C₂×C₁₃	semidirect
195. C₂×#381	C₂×C₁₃	semidirect
264. #400	C₂²×C₁₃	semidirect
265. #400	C₂²×C₁₃	semidirect
266. #399	C₂²×C₁₃	semidirect
267. #398	C₂²×C₁₃	semidirect
268. #397	C₂²×C₁₃	semidirect
269. #397	C₂²×C₁₃	semidirect
273. #394	C₂²×C₁₃	semidirect
275. #392	C₂²×C₁₃	semidirect
278. #388	C₂²×C₁₃	semidirect
279. #388	C₂²×C₁₃	semidirect
280. #387	C₂²×C₁₃	semidirect
281. #387	C₂²×C₁₃	semidirect
287. #386	C₂²×C₁₃	semidirect
288. #386	C₂²×C₁₃	semidirect
290. #385	C₂²×C₁₃	semidirect
293. #381	C₂²×C₁₃	semidirect
468. C₁₃	#36731	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×#2847	2
C₁₃×#2743	2
C₁₃×#2740	2
C₁₃×#2699	2
C₁₃×#2688	2
C₁₃×#2656	2
C₁₃×#2646	2
C₁₃×#2444	2
C₁₃×#2424	2
C₁₃×#2325	2
C₂×C₁₃×#381	2
#36731	13

Subgroups — C13×#36731 #15723070

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36731 #15723070