Subgroups — C₁₃×#60046 #15746385

Order 3328.

1898 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2805	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2724	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2683	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2599	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2586	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2573	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2477	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2470	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2406	C₂	1	2	yes	maximal
10	C₁₃×#2374	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2360	C₂	1	4	yes	maximal, complemented
12	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2296	C₂	1	2	yes	maximal, complemented
14	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#123	C₂²	1	2	yes	—
16	C₂×C₁₃×#123	C₂²	1	2	yes	—
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
18	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
19	C₂×C₁₃×#117	C₂²	1	2	yes	—
20	C₂×C₁₃×#117	C₂²	1	2	yes	—
21	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#400	C₂²	1	4	yes	—
25	C₁₃×#400	C₂²	1	4	yes	—
26	C₁₃×#398	C₂²	1	2	yes	—
27	C₁₃×#397	C₂²	1	4	yes	—
28	C₁₃×#397	C₂²	1	2	yes	—
29	C₁₃×#396	C₂²	1	4	yes	—
30	C₁₃×#395	C₂²	1	4	yes	—
31	C₁₃×#395	C₂²	1	2	yes	—
32	C₁₃×#394	C₂²	1	4	yes	—
33	C₁₃×#393	C₂²	1	2	yes	—
34	C₁₃×#391	C₂²	1	1	yes	characteristic
35	C₁₃×#391	C₂²	1	1	yes	characteristic
36	C₁₃×#391	C₂²	1	4	yes	—
37	C₁₃×#390	C₂²	1	1	yes	characteristic
38	C₁₃×#390	C₂²	1	1	yes	characteristic
39	C₁₃×#389	C₂²	1	2	yes	—
40	C₁₃×#389	C₂²	1	2	yes	—
41	C₁₃×#389	C₂²	1	4	yes	—
42	C₁₃×#389	C₂²	1	2	yes	—
43	C₁₃×#389	C₂²	1	2	yes	—
44	C₁₃×#389	C₂²	1	4	yes	—
45	C₁₃×#388	C₂²	1	4	yes	—
46	C₁₃×#388	C₂²	1	4	yes	—
47	C₁₃×#388	C₂²	1	4	yes	—
48	C₁₃×#387	C₂²	1	4	yes	—
49	C₁₃×#387	C₂²	1	4	yes	—
50	C₁₃×#387	C₂²	1	4	yes	—
51	C₁₃×#387	C₂²	1	4	yes	—
52	C₁₃×#387	C₂²	1	4	yes	—
53	C₁₃×#386	C₂²	1	4	yes	—
54	C₁₃×#386	C₂²	1	2	yes	—
55	C₁₃×#386	C₂²	1	2	yes	—
56	C₁₃×#385	C₂²	1	4	yes	—
57	C₁₃×#385	C₂²	1	4	yes	—
58	C₁₃×#385	C₂²	1	4	yes	—
59	C₁₃×#385	C₂²	1	4	yes	—
60	C₁₃×#383	C₂²	1	2	yes	—
61	C₁₃×#381	C₂²	1	2	yes	—
62	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
63	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
64	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
65	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
66	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
67	C₂×C₁₃×#41	—	2	4	no	—
68	C₂×C₁₃×#41	—	4	2	no	—
69	C₂×C₁₃×#41	—	4	2	no	—
70	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
71	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
77	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
78	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
79	C₁₃×#123	—	2	8	no	—
80	C₁₃×#123	—	4	4	no	—
81	C₁₃×C₂²⋊Q₈	—	2	16	no	—
82	C₄×Q₈×C₁₃	—	4	4	no	—
83	C₁₃×#117	—	2	8	no	—
84	C₁₃×#117	—	4	2	no	—
85	C₁₃×#117	—	4	4	no	—
86	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	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	2	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
110	C₂×C₄²×C₁₃	—	4	2	no	—
111	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
112	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
113	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
114	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
115	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
116	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
118	C₁₃×#95	C₂³	1	4	yes	—
119	C₁₃×#95	C₂³	1	4	yes	—
120	C₁₃×#95	C₂³	1	4	yes	—
121	C₁₃×#95	C₂³	1	4	yes	—
122	C₁₃×#95	C₂³	1	4	yes	—
123	C₁₃×#95	C₂³	1	4	yes	—
124	C₁₃×#95	C₂³	1	4	yes	—
125	C₁₃×#95	C₂³	1	4	yes	—
126	C₁₃×#95	C₂³	1	4	yes	—
127	C₁₃×#95	C₂³	1	2	yes	—
128	C₁₃×#95	C₂³	1	2	yes	—
129	C₁₃×#95	C₂³	1	4	yes	—
130	C₁₃×#95	C₂³	1	4	yes	—
131	C₁₃×#95	C₂³	1	4	yes	—
132	#60046	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
134	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₁₃×#41	—	4	16	no	—
136	C₂×Q₈×C₁₃	—	2	8	no	—
137	C₂×Q₈×C₁₃	—	2	2	no	—
138	C₂×Q₈×C₁₃	—	4	2	no	—
139	C₂×Q₈×C₁₃	—	4	1	no	—
140	C₂×Q₈×C₁₃	—	4	1	no	—
141	C₂×D₄×C₁₃	—	2	4	no	—
142	C₂×D₄×C₁₃	—	2	4	no	—
143	C₂×D₄×C₁₃	—	4	1	no	—
144	C₂×D₄×C₁₃	—	4	1	no	—
145	C₂×D₄×C₁₃	—	4	2	no	—
146	C₂×D₄×C₁₃	#41	1	4	yes	—
147	C₂²×C₄×C₁₃	—	2	4	no	—
148	C₂²×C₄×C₁₃	—	2	2	no	—
149	C₂²×C₄×C₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₃	—	2	2	no	—
151	C₂²×C₄×C₁₃	—	2	2	no	—
152	C₂²×C₄×C₁₃	—	2	4	no	—
153	C₂²×C₄×C₁₃	—	2	4	no	—
154	C₂²×C₄×C₁₃	—	2	4	no	—
155	C₂²×C₄×C₁₃	—	2	8	no	—
156	C₂²×C₄×C₁₃	—	2	4	no	—
157	C₂²×C₄×C₁₃	—	4	2	no	—
158	C₂²×C₄×C₁₃	—	4	2	no	—
159	C₂²×C₄×C₁₃	—	4	2	no	—
160	C₂²×C₄×C₁₃	—	4	2	no	—
161	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
172	C₁₃×C₄⋊C₄	—	2	4	no	—
173	C₁₃×C₄⋊C₄	—	2	8	no	—
174	C₁₃×C₄⋊C₄	—	2	8	no	—
175	C₁₃×C₄⋊C₄	—	2	8	no	—
176	C₁₃×C₄⋊C₄	—	2	8	no	—
177	C₁₃×C₄⋊C₄	—	2	8	no	—
178	C₁₃×C₄⋊C₄	—	4	4	no	—
179	C₁₃×C₄⋊C₄	—	4	2	no	—
180	C₁₃×C₄⋊C₄	—	4	2	no	—
181	C₁₃×C₄⋊C₄	—	4	1	no	—
182	C₁₃×C₄⋊C₄	—	4	1	no	—
183	C₁₃×C₄⋊C₄	—	4	2	no	—
184	C₁₃×C₄⋊C₄	—	4	4	no	—
185	C₁₃×C₄⋊C₄	#41	1	8	yes	complemented
186	C₁₃×C₂²⋊C₄	—	2	4	no	—
187	C₁₃×C₂²⋊C₄	—	2	8	no	—
188	C₁₃×C₂²⋊C₄	—	2	8	no	—
189	C₁₃×C₂²⋊C₄	—	2	8	no	—
190	C₁₃×C₂²⋊C₄	—	2	8	no	—
191	C₁₃×C₂²⋊C₄	—	2	8	no	—
192	C₁₃×C₂²⋊C₄	—	2	8	no	—
193	C₁₃×C₂²⋊C₄	—	4	2	no	—
194	C₁₃×C₂²⋊C₄	—	4	2	no	—
195	C₄²×C₁₃	—	2	8	no	—
196	C₄²×C₁₃	—	2	4	no	—
197	C₄²×C₁₃	—	4	1	no	—
198	C₄²×C₁₃	—	4	2	no	—
199	C₄²×C₁₃	—	4	1	no	—
200	C₄²×C₁₃	—	4	4	no	—
201	C₄²×C₁₃	—	4	4	no	—
202	#2805	C₂×C₁₃	1	2	yes	complemented
203	#2724	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#2683	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#2599	C₂×C₁₃	1	2	yes	complemented
206	#2586	C₂×C₁₃	1	2	yes	complemented
207	#2573	C₂×C₁₃	1	4	yes	complemented
208	#2477	C₂×C₁₃	1	4	yes	complemented
209	#2470	C₂×C₁₃	1	4	yes	complemented
210	#2406	C₂×C₁₃	1	2	yes	—
211	#2374	C₂×C₁₃	1	2	yes	complemented
212	#2360	C₂×C₁₃	1	4	yes	complemented
213	#2297	C₂×C₁₃	1	1	yes	characteristic
214	#2296	C₂×C₁₃	1	2	yes	complemented
215	C₂³×C₁₃	—	2	4	no	—
216	C₂³×C₁₃	—	2	2	no	—
217	C₂³×C₁₃	—	2	1	no	—
218	C₂³×C₁₃	—	2	1	no	—
219	C₂³×C₁₃	—	2	2	no	—
220	C₂³×C₁₃	—	2	2	no	—
221	C₂³×C₁₃	—	2	4	no	—
222	C₂³×C₁₃	—	2	2	no	—
223	C₂³×C₁₃	C₂×#41	1	4	yes	—
224	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
225	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
226	Q₈×C₁₃	—	4	8	no	—
227	Q₈×C₁₃	—	4	4	no	—
228	D₄×C₁₃	—	4	4	no	—
229	D₄×C₁₃	—	4	8	no	—
230	C₂×C₄×C₁₃	—	2	16	no	—
231	C₂×C₄×C₁₃	—	2	8	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	4	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	2	1	no	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	1	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	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	4	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	4	no	—
258	C₂×C₄×C₁₃	—	4	8	no	—
259	C₂×C₄×C₁₃	—	4	8	no	—
260	C₂×C₄×C₁₃	—	8	4	no	—
261	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
262	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
263	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
264	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
265	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
266	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×#123	C₂²×C₁₃	1	2	yes	—
268	C₂×#123	C₂²×C₁₃	1	2	yes	—
269	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
270	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
271	C₂×#117	C₂²×C₁₃	1	2	yes	—
272	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×#117	C₂²×C₁₃	1	2	yes	—
274	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
275	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
276	#400	C₂²×C₁₃	1	4	yes	—
277	#400	C₂²×C₁₃	1	4	yes	—
278	#398	C₂²×C₁₃	1	2	yes	—
279	#397	C₂²×C₁₃	1	4	yes	—
280	#397	C₂²×C₁₃	1	2	yes	—
281	#396	C₂²×C₁₃	1	4	yes	—
282	#395	C₂²×C₁₃	1	2	yes	—
283	#395	C₂²×C₁₃	1	4	yes	—
284	#394	C₂²×C₁₃	1	4	yes	—
285	#393	C₂²×C₁₃	1	2	yes	—
286	#391	C₂²×C₁₃	1	1	yes	characteristic
287	#391	C₂²×C₁₃	1	4	yes	—
288	#391	C₂²×C₁₃	1	1	yes	characteristic
289	#390	C₂²×C₁₃	1	1	yes	characteristic
290	#390	C₂²×C₁₃	1	1	yes	characteristic
291	#389	C₂²×C₁₃	1	2	yes	—
292	#389	C₂²×C₁₃	1	4	yes	—
293	#389	C₂²×C₁₃	1	2	yes	—
294	#389	C₂²×C₁₃	1	4	yes	—
295	#389	C₂²×C₁₃	1	2	yes	—
296	#389	C₂²×C₁₃	1	2	yes	—
297	#388	C₂²×C₁₃	1	4	yes	—
298	#388	C₂²×C₁₃	1	4	yes	—
299	#388	C₂²×C₁₃	1	4	yes	—
300	#387	C₂²×C₁₃	1	4	yes	—
301	#387	C₂²×C₁₃	1	4	yes	—
302	#387	C₂²×C₁₃	1	4	yes	—
303	#387	C₂²×C₁₃	1	4	yes	—
304	#387	C₂²×C₁₃	1	4	yes	—
305	#386	C₂²×C₁₃	1	2	yes	—
306	#386	C₂²×C₁₃	1	2	yes	—
307	#386	C₂²×C₁₃	1	4	yes	—
308	#385	C₂²×C₁₃	1	4	yes	—
309	#385	C₂²×C₁₃	1	4	yes	—
310	#385	C₂²×C₁₃	1	4	yes	—
311	#385	C₂²×C₁₃	1	4	yes	—
312	#383	C₂²×C₁₃	1	2	yes	—
313	#381	C₂²×C₁₃	1	2	yes	—
314	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
315	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
316	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
317	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
318	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
319	C₂²×C₁₃	—	2	8	no	—
320	C₂²×C₁₃	—	2	2	no	—
321	C₂²×C₁₃	—	2	4	no	—
322	C₂²×C₁₃	—	2	4	no	—
323	C₂²×C₁₃	—	4	2	no	—
324	C₂²×C₁₃	—	4	1	no	—
325	C₂²×C₁₃	—	4	2	no	—
326	C₂²×C₁₃	—	4	4	no	—
327	C₂²×C₁₃	—	4	1	no	—
328	C₂²×C₁₃	—	4	2	no	—
329	C₂²×C₁₃	C₂²×#41	1	2	yes	—
330	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
331	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
332	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
333	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
334	C₄×C₁₃	—	2	8	no	—
335	C₄×C₁₃	—	2	2	no	—
336	C₄×C₁₃	—	2	2	no	—
337	C₄×C₁₃	—	2	4	no	—
338	C₄×C₁₃	—	2	4	no	—
339	C₄×C₁₃	—	4	2	no	—
340	C₄×C₁₃	—	4	4	no	—
341	C₄×C₁₃	—	4	2	no	—
342	C₄×C₁₃	—	4	4	no	—
343	C₄×C₁₃	—	4	4	no	—
344	C₄×C₁₃	—	4	2	no	—
345	C₂×#41	—	2	4	no	—
346	C₂×#41	—	4	2	no	—
347	C₂×#41	—	4	2	no	—
348	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
349	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
350	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
351	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
352	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
353	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
354	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
355	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
356	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
357	#123	—	2	8	no	—
358	#123	—	4	4	no	—
359	C₂²⋊Q₈	—	2	16	no	—
360	C₄×Q₈	—	4	4	no	—
361	#117	—	2	8	no	—
362	#117	—	4	2	no	—
363	#117	—	4	4	no	—
364	C₂×C₄⋊C₄	—	4	4	no	—
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
367	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
370	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
371	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
373	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
378	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
382	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
388	C₂×C₄²	—	4	2	no	—
389	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
390	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
391	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
392	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
393	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
394	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
396	#95	C₂³×C₁₃	1	4	yes	—
397	#95	C₂³×C₁₃	1	4	yes	—
398	#95	C₂³×C₁₃	1	4	yes	—
399	#95	C₂³×C₁₃	1	4	yes	—
400	#95	C₂³×C₁₃	1	4	yes	—
401	#95	C₂³×C₁₃	1	4	yes	—
402	#95	C₂³×C₁₃	1	4	yes	—
403	#95	C₂³×C₁₃	1	4	yes	—
404	#95	C₂³×C₁₃	1	4	yes	—
405	#95	C₂³×C₁₃	1	2	yes	—
406	#95	C₂³×C₁₃	1	2	yes	—
407	#95	C₂³×C₁₃	1	4	yes	—
408	#95	C₂³×C₁₃	1	4	yes	—
409	#95	C₂³×C₁₃	1	4	yes	—
410	C₂×C₁₃	—	4	4	no	—
411	C₂×C₁₃	—	4	2	no	—
412	C₂×C₁₃	#3481	1	1	yes	characteristic
413	C₂×C₁₃	#3482	1	2	yes	—
414	C₂×C₁₃	#3490	1	1	yes	characteristic
415	C₂×C₁₃	#3492	1	2	yes	—
416	C₂×C₁₃	#3550	1	1	yes	characteristic
417	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
418	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
419	#41	—	4	16	no	—
420	C₂×Q₈	—	2	8	no	—
421	C₂×Q₈	—	2	2	no	—
422	C₂×Q₈	—	4	2	no	—
423	C₂×Q₈	—	4	1	no	—
424	C₂×Q₈	—	4	1	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	4	1	no	—
428	C₂×D₄	—	4	1	no	—
429	C₂×D₄	—	4	2	no	—
430	C₂×D₄	C₁₃×#41	1	4	yes	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	8	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	—	4	2	no	—
444	C₂²×C₄	—	4	2	no	—
445	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
446	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
447	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
448	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
449	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
450	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
451	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
452	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
453	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
454	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
455	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	8	no	—
458	C₄⋊C₄	—	2	8	no	—
459	C₄⋊C₄	—	2	8	no	—
460	C₄⋊C₄	—	2	8	no	—
461	C₄⋊C₄	—	2	8	no	—
462	C₄⋊C₄	—	4	4	no	—
463	C₄⋊C₄	—	4	2	no	—
464	C₄⋊C₄	—	4	2	no	—
465	C₄⋊C₄	—	4	1	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	—	4	2	no	—
468	C₄⋊C₄	—	4	4	no	—
469	C₄⋊C₄	C₁₃×#41	1	8	yes	complemented
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	8	no	—
472	C₂²⋊C₄	—	2	8	no	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	—	2	8	no	—
476	C₂²⋊C₄	—	2	8	no	—
477	C₂²⋊C₄	—	4	2	no	—
478	C₂²⋊C₄	—	4	2	no	—
479	C₄²	—	2	8	no	—
480	C₄²	—	2	4	no	—
481	C₄²	—	4	1	no	—
482	C₄²	—	4	2	no	—
483	C₄²	—	4	1	no	—
484	C₄²	—	4	4	no	—
485	C₄²	—	4	4	no	—
486	C₁₃	#60046	1	1	yes	characteristic, direct product factor, Sylow
487	C₂³	—	2	4	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	1	no	—
490	C₂³	—	2	1	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	4	no	—
494	C₂³	—	2	2	no	—
495	C₂³	C₂×C₁₃×#41	1	4	yes	—
496	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
497	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
498	Q₈	—	4	8	no	—
499	Q₈	—	4	4	no	—
500	D₄	—	4	4	no	—
501	D₄	—	4	8	no	—
502	C₂×C₄	—	2	16	no	—
503	C₂×C₄	—	2	8	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	4	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	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	4	8	no	—
531	C₂×C₄	—	4	8	no	—
532	C₂×C₄	—	8	4	no	—
533	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
534	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
535	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
536	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
537	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
538	C₂²	—	2	8	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	4	no	—
541	C₂²	—	2	4	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	4	no	—
548	C₂²	C₂²×C₁₃×#41	1	2	yes	—
549	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
550	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
551	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
552	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
553	C₄	—	2	8	no	—
554	C₄	—	2	2	no	—
555	C₄	—	2	2	no	—
556	C₄	—	2	4	no	—
557	C₄	—	2	4	no	—
558	C₄	—	4	2	no	—
559	C₄	—	4	2	no	—
560	C₄	—	4	4	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	4	no	—
563	C₄	—	4	4	no	—
564	C₂	—	4	4	no	—
565	C₂	—	4	2	no	—
566	C₂	C₁₃×#3481	1	1	yes	characteristic
567	C₂	C₁₃×#3482	1	2	yes	—
568	C₂	C₁₃×#3490	1	1	yes	characteristic
569	C₂	C₁₃×#3492	1	2	yes	—
570	C₂	C₁₃×#3550	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
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×#2805	C₂	semidirect
2. C₁₃×#2724	C₂	semidirect
3. C₁₃×#2683	C₂	semidirect
4. C₁₃×#2599	C₂	semidirect
5. C₁₃×#2586	C₂	semidirect
6. C₁₃×#2573	C₂	semidirect
7. C₁₃×#2477	C₂	semidirect
8. C₁₃×#2470	C₂	semidirect
10. C₁₃×#2374	C₂	semidirect
11. C₁₃×#2360	C₂	semidirect
13. C₁₃×#2296	C₂	semidirect
132. #60046	C₁₃	direct (N × H)
185. C₁₃×C₄⋊C₄	#41	semidirect
202. #2805	C₂×C₁₃	semidirect
203. #2724	C₂×C₁₃	semidirect
204. #2683	C₂×C₁₃	semidirect
205. #2599	C₂×C₁₃	semidirect
206. #2586	C₂×C₁₃	semidirect
207. #2573	C₂×C₁₃	semidirect
208. #2477	C₂×C₁₃	semidirect
209. #2470	C₂×C₁₃	semidirect
211. #2374	C₂×C₁₃	semidirect
212. #2360	C₂×C₁₃	semidirect
214. #2296	C₂×C₁₃	semidirect
469. C₄⋊C₄	C₁₃×#41	semidirect
486. C₁₃	#60046	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×#2805	2
C₁₃×#2724	2
C₁₃×#2683	2
C₁₃×#2599	2
C₁₃×#2586	2
C₁₃×#2573	2
C₁₃×#2477	2
C₁₃×#2470	2
C₁₃×#2406	2
C₁₃×#2374	2
C₁₃×#2360	2
C₁₃×#2297	2
C₁₃×#2296	2
#60046	13

Subgroups — C13×#60046 #15746385

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60046 #15746385