Subgroups — C₁₃×#2688 #13111746

Order 1664.

626 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#392	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#392	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#381	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#121	—	2	4	no	—
26	C₁₃×#121	—	2	4	no	—
27	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₁₃×#95	C₂²	1	1	yes	characteristic
44	C₁₃×#95	C₂²	1	1	yes	characteristic
45	C₁₃×#95	C₂²	1	1	yes	characteristic
46	C₁₃×#95	C₂²	1	1	yes	characteristic
47	C₁₃×#95	C₂²	1	1	yes	characteristic
48	C₁₃×#95	C₂²	1	1	yes	characteristic
49	C₁₃×#95	C₂²	1	1	yes	characteristic
50	C₁₃×#95	C₂²	1	1	yes	characteristic
51	C₁₃×#95	C₂²	1	1	yes	characteristic
52	C₁₃×#95	C₂²	1	1	yes	characteristic
53	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
54	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
55	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
56	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
57	C₂×D₄×C₁₃	—	2	2	no	—
58	C₂×D₄×C₁₃	—	2	2	no	—
59	C₂×D₄×C₁₃	—	2	2	no	—
60	C₂×D₄×C₁₃	—	2	2	no	—
61	C₂×D₄×C₁₃	—	2	2	no	—
62	C₂×D₄×C₁₃	—	2	2	no	—
63	C₂×D₄×C₁₃	—	2	2	no	—
64	C₂×D₄×C₁₃	—	2	2	no	—
65	C₂×D₄×C₁₃	—	4	1	no	—
66	C₂×D₄×C₁₃	—	4	1	no	—
67	C₂×D₄×C₁₃	—	4	1	no	—
68	C₂×D₄×C₁₃	—	4	1	no	—
69	C₂×D₄×C₁₃	—	4	1	no	—
70	C₂×D₄×C₁₃	—	4	1	no	—
71	C₂×D₄×C₁₃	—	4	1	no	—
72	C₂×D₄×C₁₃	—	4	1	no	—
73	C₂×D₄×C₁₃	—	4	1	no	—
74	C₂×D₄×C₁₃	D₄	1	4	yes	complemented
75	C₂²×C₄×C₁₃	—	2	2	no	—
76	C₂²×C₄×C₁₃	—	2	2	no	—
77	C₂²×C₄×C₁₃	—	2	2	no	—
78	C₂²×C₄×C₁₃	—	4	1	no	—
79	C₂²×C₄×C₁₃	—	4	1	no	—
80	C₂²×C₄×C₁₃	—	4	1	no	—
81	C₂²×C₄×C₁₃	—	4	1	no	—
82	C₂²×C₄×C₁₃	—	4	1	no	—
83	C₂²×C₄×C₁₃	—	4	1	no	—
84	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₁₃×C₄⋊C₄	—	2	2	no	—
96	C₁₃×C₄⋊C₄	—	2	2	no	—
97	C₁₃×C₄⋊C₄	—	4	1	no	—
98	C₁₃×C₂²⋊C₄	—	2	2	no	—
99	C₁₃×C₂²⋊C₄	—	2	2	no	—
100	C₁₃×C₂²⋊C₄	—	2	2	no	—
101	C₁₃×C₂²⋊C₄	—	2	2	no	—
102	C₁₃×C₂²⋊C₄	—	2	2	no	—
103	C₁₃×C₂²⋊C₄	—	4	1	no	—
104	C₁₃×C₂²⋊C₄	—	4	1	no	—
105	C₁₃×C₂²⋊C₄	—	4	1	no	—
106	C₁₃×C₂²⋊C₄	—	4	1	no	—
107	C₁₃×C₂²⋊C₄	—	4	1	no	—
108	C₁₃×C₂²⋊C₄	—	4	1	no	—
109	C₁₃×C₂²⋊C₄	—	4	1	no	—
110	C₁₃×C₂²⋊C₄	—	4	1	no	—
111	#2688	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂³×C₁₃	—	2	1	no	—
113	C₂³×C₁₃	—	2	1	no	—
114	C₂³×C₁₃	—	2	1	no	—
115	C₂³×C₁₃	—	2	1	no	—
116	C₂³×C₁₃	—	2	1	no	—
117	C₂³×C₁₃	—	2	1	no	—
118	C₂³×C₁₃	—	2	1	no	—
119	C₂³×C₁₃	—	2	1	no	—
120	C₂³×C₁₃	—	2	1	no	—
121	C₂³×C₁₃	—	2	1	no	—
122	C₂³×C₁₃	—	2	1	no	—
123	C₂³×C₁₃	—	2	1	no	—
124	C₂³×C₁₃	—	2	1	no	—
125	C₂³×C₁₃	—	2	1	no	—
126	C₂³×C₁₃	—	2	1	no	—
127	C₂³×C₁₃	—	2	1	no	—
128	C₂³×C₁₃	—	2	1	no	—
129	C₂³×C₁₃	—	2	1	no	—
130	C₂³×C₁₃	—	2	1	no	—
131	C₂³×C₁₃	—	2	1	no	—
132	C₂³×C₁₃	—	2	1	no	—
133	C₂³×C₁₃	—	2	1	no	—
134	C₂³×C₁₃	—	2	1	no	—
135	C₂³×C₁₃	—	2	1	no	—
136	C₂³×C₁₃	—	2	1	no	—
137	C₂³×C₁₃	C₂×D₄	1	2	yes	—
138	C₂³×C₁₃	C₂×D₄	1	2	yes	—
139	C₂³×C₁₃	#41	1	2	yes	—
140	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
141	D₄×C₁₃	—	4	4	no	—
142	D₄×C₁₃	—	4	4	no	—
143	D₄×C₁₃	—	4	4	no	—
144	D₄×C₁₃	—	4	4	no	—
145	D₄×C₁₃	—	4	4	no	—
146	D₄×C₁₃	—	4	4	no	—
147	C₂×C₄×C₁₃	—	2	1	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	1	no	—
150	C₂×C₄×C₁₃	—	2	1	no	—
151	C₂×C₄×C₁₃	—	2	1	no	—
152	C₂×C₄×C₁₃	—	2	1	no	—
153	C₂×C₄×C₁₃	—	2	1	no	—
154	C₂×C₄×C₁₃	—	2	1	no	—
155	C₂×C₄×C₁₃	—	2	1	no	—
156	C₂×C₄×C₁₃	—	2	1	no	—
157	C₂×C₄×C₁₃	—	2	1	no	—
158	C₂×C₄×C₁₃	—	2	1	no	—
159	C₂×C₄×C₁₃	—	2	1	no	—
160	C₂×C₄×C₁₃	—	2	1	no	—
161	C₂×C₄×C₁₃	—	2	1	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	4	4	no	—
179	C₂×C₄×C₁₃	—	4	4	no	—
180	C₂×C₄×C₁₃	—	4	4	no	—
181	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
182	C₂×C₄×C₁₃	#41	1	2	yes	—
183	C₂×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₂×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
185	#400	C₂×C₁₃	1	1	yes	characteristic, complemented
186	#397	C₂×C₁₃	1	1	yes	characteristic, complemented
187	#397	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#394	C₂×C₁₃	1	1	yes	characteristic, complemented
189	#392	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#392	C₂×C₁₃	1	1	yes	characteristic, complemented
191	#386	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#386	C₂×C₁₃	1	1	yes	characteristic, complemented
193	#386	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#386	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#386	C₂×C₁₃	1	1	yes	characteristic, complemented
196	#385	C₂×C₁₃	1	1	yes	characteristic, complemented
197	#381	C₂×C₁₃	1	1	yes	characteristic, complemented
198	C₂²×C₁₃	—	2	2	no	—
199	C₂²×C₁₃	—	2	2	no	—
200	C₂²×C₁₃	—	2	2	no	—
201	C₂²×C₁₃	—	2	2	no	—
202	C₂²×C₁₃	—	2	2	no	—
203	C₂²×C₁₃	—	2	2	no	—
204	C₂²×C₁₃	—	2	2	no	—
205	C₂²×C₁₃	—	2	2	no	—
206	C₂²×C₁₃	—	2	2	no	—
207	C₂²×C₁₃	—	4	1	no	—
208	C₂²×C₁₃	—	4	1	no	—
209	C₂²×C₁₃	—	4	1	no	—
210	C₂²×C₁₃	—	4	1	no	—
211	C₂²×C₁₃	—	4	1	no	—
212	C₂²×C₁₃	—	4	1	no	—
213	C₂²×C₁₃	—	4	1	no	—
214	C₂²×C₁₃	—	4	1	no	—
215	C₂²×C₁₃	—	4	1	no	—
216	C₂²×C₁₃	—	4	1	no	—
217	C₂²×C₁₃	—	4	1	no	—
218	C₂²×C₁₃	—	4	1	no	—
219	C₂²×C₁₃	—	4	1	no	—
220	C₂²×C₁₃	—	4	1	no	—
221	C₂²×C₁₃	—	4	1	no	—
222	C₂²×C₁₃	—	4	1	no	—
223	C₂²×C₁₃	—	4	1	no	—
224	C₂²×C₁₃	—	4	1	no	—
225	C₂²×C₁₃	—	4	1	no	—
226	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
228	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
229	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
230	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
231	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
232	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
233	C₄×C₁₃	—	2	2	no	—
234	C₄×C₁₃	—	2	2	no	—
235	C₄×C₁₃	—	4	1	no	—
236	C₄×C₁₃	—	4	1	no	—
237	C₄×C₁₃	—	4	1	no	—
238	C₄×C₁₃	—	4	1	no	—
239	C₄×C₁₃	—	4	1	no	—
240	C₄×C₁₃	—	4	1	no	—
241	C₄×C₁₃	—	4	1	no	—
242	C₄×C₁₃	—	4	1	no	—
243	C₄×C₁₃	—	4	1	no	—
244	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
245	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
246	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
247	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
248	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
249	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
250	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic
251	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic
252	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic
253	#121	—	2	4	no	—
254	#121	—	2	4	no	—
255	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
258	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
271	#95	C₂²×C₁₃	1	1	yes	characteristic
272	#95	C₂²×C₁₃	1	1	yes	characteristic
273	#95	C₂²×C₁₃	1	1	yes	characteristic
274	#95	C₂²×C₁₃	1	1	yes	characteristic
275	#95	C₂²×C₁₃	1	1	yes	characteristic
276	#95	C₂²×C₁₃	1	1	yes	characteristic
277	#95	C₂²×C₁₃	1	1	yes	characteristic
278	#95	C₂²×C₁₃	1	1	yes	characteristic
279	#95	C₂²×C₁₃	1	1	yes	characteristic
280	#95	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×C₁₃	—	4	2	no	—
282	C₂×C₁₃	—	4	2	no	—
283	C₂×C₁₃	—	4	2	no	—
284	C₂×C₁₃	—	8	1	no	—
285	C₂×C₁₃	#534	1	1	yes	characteristic
286	C₂×C₁₃	#538	1	1	yes	characteristic
287	C₂×C₁₃	#540	1	1	yes	characteristic
288	C₂×C₁₃	#546	1	1	yes	characteristic
289	C₂×C₁₃	#546	1	1	yes	characteristic
290	C₂×C₁₃	#553	1	1	yes	characteristic
291	C₂×C₁₃	#560	1	1	yes	characteristic
292	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
293	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
294	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
295	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	D₄×C₁₃	1	4	yes	complemented
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	4	1	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
324	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
325	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
326	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
327	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
328	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
329	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
330	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
331	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
332	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
333	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₂²⋊C₄	—	4	1	no	—
348	C₂²⋊C₄	—	4	1	no	—
349	C₂²⋊C₄	—	4	1	no	—
350	C₁₃	#2688	1	1	yes	characteristic, direct product factor, Sylow
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	C₂×D₄×C₁₃	1	2	yes	—
377	C₂³	C₂×D₄×C₁₃	1	2	yes	—
378	C₂³	C₁₃×#41	1	2	yes	—
379	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
380	D₄	—	4	4	no	—
381	D₄	—	4	4	no	—
382	D₄	—	4	4	no	—
383	D₄	—	4	4	no	—
384	D₄	—	4	4	no	—
385	D₄	—	4	4	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
421	C₂×C₄	C₁₃×#41	1	2	yes	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	4	1	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	1	no	—
450	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
451	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
452	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
453	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
454	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
455	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
456	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	4	1	no	—
460	C₄	—	4	1	no	—
461	C₄	—	4	1	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	1	no	—
464	C₄	—	4	1	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	1	no	—
467	C₄	—	4	1	no	—
468	C₂	—	4	2	no	—
469	C₂	—	4	2	no	—
470	C₂	—	4	2	no	—
471	C₂	—	8	1	no	—
472	C₂	C₁₃×#534	1	1	yes	characteristic
473	C₂	C₁₃×#538	1	1	yes	characteristic
474	C₂	C₁₃×#540	1	1	yes	characteristic
475	C₂	C₁₃×#546	1	1	yes	characteristic
476	C₂	C₁₃×#546	1	1	yes	characteristic
477	C₂	C₁₃×#553	1	1	yes	characteristic
478	C₂	C₁₃×#560	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×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×#121	C₂	semidirect
2. C₂×C₁₃×#121	C₂	semidirect
3. C₁₃×#400	C₂	semidirect
4. C₁₃×#397	C₂	semidirect
5. C₁₃×#397	C₂	semidirect
6. C₁₃×#394	C₂	semidirect
7. C₁₃×#392	C₂	semidirect
8. C₁₃×#392	C₂	semidirect
9. C₁₃×#386	C₂	semidirect
10. C₁₃×#386	C₂	semidirect
11. C₁₃×#386	C₂	semidirect
12. C₁₃×#386	C₂	semidirect
13. C₁₃×#386	C₂	semidirect
14. C₁₃×#385	C₂	semidirect
15. C₁₃×#381	C₂	semidirect
74. C₂×D₄×C₁₃	D₄	semidirect
111. #2688	C₁₃	direct (N × H)
183. C₂×#121	C₂×C₁₃	semidirect
184. C₂×#121	C₂×C₁₃	semidirect
185. #400	C₂×C₁₃	semidirect
186. #397	C₂×C₁₃	semidirect
187. #397	C₂×C₁₃	semidirect
188. #394	C₂×C₁₃	semidirect
189. #392	C₂×C₁₃	semidirect
190. #392	C₂×C₁₃	semidirect
191. #386	C₂×C₁₃	semidirect
192. #386	C₂×C₁₃	semidirect
193. #386	C₂×C₁₃	semidirect
194. #386	C₂×C₁₃	semidirect
195. #386	C₂×C₁₃	semidirect
196. #385	C₂×C₁₃	semidirect
197. #381	C₂×C₁₃	semidirect
313. C₂×D₄	D₄×C₁₃	semidirect
350. C₁₃	#2688	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×#121	2
C₁₃×#400	2
C₁₃×#397	2
C₁₃×#394	2
C₁₃×#392	2
C₁₃×#386	2
C₁₃×#385	2
C₁₃×#381	2
#2688	13

Subgroups — C13×#2688 #13111746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2688 #13111746