Subgroups — C₁₃×#24780 #15711119

Order 3328.

1150 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2416	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2067	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2033	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1874	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1808	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#121	—	2	2	no	—
16	C₂×C₁₃×#121	C₂²	1	2	yes	—
17	C₂×C₁₃×#121	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
20	C₁₃×#466	—	2	4	no	—
21	C₁₃×#466	—	2	4	no	—
22	C₈×D₄×C₁₃	—	2	4	no	—
23	C₂×C₁₃×#107	—	2	4	no	—
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#107	C₂²	1	2	yes	—
26	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#102	C₂²	1	2	yes	—
30	C₂×C₁₃×#102	C₂²	1	2	yes	—
31	C₂×C₁₃×#102	C₂²	1	2	yes	—
32	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#396	—	2	2	no	—
36	C₁₃×#394	—	2	2	no	—
37	C₁₃×#390	C₂²	1	2	yes	—
38	C₁₃×#389	C₂²	1	2	yes	—
39	C₁₃×#386	—	2	2	no	—
40	C₁₃×#380	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₂²×D₄×C₁₃	—	2	2	no	—
44	C₂²×D₄×C₁₃	—	2	2	no	—
45	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₃	—	2	2	no	—
48	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂×C₁₃×D₈	—	2	2	no	—
51	C₂×C₁₃×D₈	—	2	2	no	—
52	C₂×C₁₃×D₈	—	2	2	no	—
53	C₂²×C₈×C₁₃	—	2	2	no	—
54	C₂²×C₈×C₁₃	—	2	2	no	—
55	C₂²×C₈×C₁₃	—	2	2	no	—
56	C₂²×C₈×C₁₃	—	2	2	no	—
57	C₂²×C₈×C₁₃	—	2	2	no	—
58	C₂²×C₈×C₁₃	D₄	1	4	yes	complemented
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×#121	—	2	4	no	—
64	C₁₃×#121	—	2	4	no	—
65	C₁₃×#121	—	2	4	no	—
66	C₁₃×#121	—	4	2	no	—
67	C₁₃×#121	—	4	8	no	—
68	C₄×D₄×C₁₃	—	2	2	no	—
69	C₄×D₄×C₁₃	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
74	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
82	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
84	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	C₁₃×#107	—	2	2	no	—
87	C₁₃×#107	—	2	2	no	—
88	C₁₃×#107	—	2	4	no	—
89	C₁₃×#107	D₄	1	4	yes	complemented
90	C₁₃×C₄⋊C₈	—	2	2	no	—
91	C₁₃×#102	—	2	4	no	—
92	C₁₃×#102	—	2	4	no	—
93	C₁₃×#102	—	4	2	no	—
94	C₁₃×C₂²⋊C₈	—	2	2	no	—
95	C₁₃×C₂²⋊C₈	—	2	2	no	—
96	C₄×C₈×C₁₃	—	2	2	no	—
97	C₁₃×#95	—	2	2	no	—
98	C₁₃×#95	—	2	2	no	—
99	#24780	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂⁴×C₁₃	—	2	2	no	—
101	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	2	2	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	—	2	2	no	—
110	C₂×D₄×C₁₃	—	2	2	no	—
111	C₂×D₄×C₁₃	—	4	4	no	—
112	C₂×D₄×C₁₃	—	4	4	no	—
113	C₂×D₄×C₁₃	—	4	4	no	—
114	C₂×D₄×C₁₃	—	4	4	no	—
115	C₂×D₄×C₁₃	—	4	4	no	—
116	C₂×D₄×C₁₃	—	8	2	no	—
117	C₂×D₄×C₁₃	D₈	1	4	yes	complemented
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	4	4	no	—
132	C₂²×C₄×C₁₃	—	4	4	no	—
133	C₂²×C₄×C₁₃	—	8	2	no	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	#41	1	2	yes	—
140	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
141	C₁₃×D₈	—	4	4	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	1	no	—
144	C₂×C₈×C₁₃	—	2	8	no	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₂×C₈×C₁₃	—	2	1	no	—
147	C₂×C₈×C₁₃	—	2	1	no	—
148	C₂×C₈×C₁₃	—	2	1	no	—
149	C₂×C₈×C₁₃	—	2	1	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	—	4	4	no	—
152	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
154	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
155	C₂×C₈×C₁₃	#41	1	2	yes	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	4	4	no	—
163	C₁₃×C₄⋊C₄	—	4	4	no	—
164	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
165	C₁₃×C₂²⋊C₄	—	2	2	no	—
166	C₁₃×C₂²⋊C₄	—	2	2	no	—
167	C₁₃×C₂²⋊C₄	—	4	4	no	—
168	C₁₃×C₂²⋊C₄	—	4	4	no	—
169	C₁₃×C₂²⋊C₄	—	4	4	no	—
170	C₁₃×C₂²⋊C₄	—	4	4	no	—
171	C₁₃×C₂²⋊C₄	—	8	2	no	—
172	C₄²×C₁₃	—	2	1	no	—
173	C₄²×C₁₃	—	2	1	no	—
174	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
175	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
177	C₂²×#107	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#2416	C₂×C₁₃	1	2	yes	complemented
179	#2067	C₂×C₁₃	1	2	yes	complemented
180	#2033	C₂×C₁₃	1	2	yes	complemented
181	#1970	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#1874	C₂×C₁₃	1	2	yes	complemented
184	#1808	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂³×C₁₃	—	2	1	no	—
186	C₂³×C₁₃	—	2	1	no	—
187	C₂³×C₁₃	—	2	1	no	—
188	C₂³×C₁₃	—	2	1	no	—
189	C₂³×C₁₃	—	2	1	no	—
190	C₂³×C₁₃	—	2	1	no	—
191	C₂³×C₁₃	—	2	1	no	—
192	C₂³×C₁₃	—	2	1	no	—
193	C₂³×C₁₃	—	2	1	no	—
194	C₂³×C₁₃	—	2	1	no	—
195	C₂³×C₁₃	—	4	2	no	—
196	C₂³×C₁₃	—	4	2	no	—
197	C₂³×C₁₃	—	4	2	no	—
198	C₂³×C₁₃	—	4	2	no	—
199	C₂³×C₁₃	—	4	2	no	—
200	C₂³×C₁₃	—	4	2	no	—
201	C₂³×C₁₃	—	4	2	no	—
202	C₂³×C₁₃	#121	1	2	yes	—
203	C₂³×C₁₃	C₂×D₈	1	2	yes	—
204	C₂³×C₁₃	C₂×D₈	1	2	yes	—
205	C₂³×C₁₃	#135	1	2	yes	—
206	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	D₄×C₁₃	—	2	8	no	—
208	D₄×C₁₃	—	4	2	no	—
209	D₄×C₁₃	—	4	2	no	—
210	D₄×C₁₃	—	4	2	no	—
211	D₄×C₁₃	—	4	2	no	—
212	D₄×C₁₃	—	8	8	no	—
213	D₄×C₁₃	—	8	8	no	—
214	C₂×C₄×C₁₃	—	2	1	no	—
215	C₂×C₄×C₁₃	—	2	1	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	4	2	no	—
230	C₂×C₄×C₁₃	—	4	2	no	—
231	C₂×C₄×C₁₃	—	4	1	no	—
232	C₂×C₄×C₁₃	—	4	1	no	—
233	C₂×C₄×C₁₃	—	4	1	no	—
234	C₂×C₄×C₁₃	—	4	1	no	—
235	C₂×C₄×C₁₃	—	4	2	no	—
236	C₂×C₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	4	2	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	—	4	2	no	—
240	C₂×C₄×C₁₃	—	4	2	no	—
241	C₂×C₄×C₁₃	—	8	8	no	—
242	C₂×C₄×C₁₃	#121	1	2	yes	—
243	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
244	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
249	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
250	C₈×C₁₃	—	2	2	no	—
251	C₈×C₁₃	—	4	1	no	—
252	C₈×C₁₃	—	4	1	no	—
253	C₈×C₁₃	#121	1	4	yes	complemented
254	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
255	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
256	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×#121	—	2	2	no	—
258	C₂×#121	C₂²×C₁₃	1	2	yes	—
259	C₂×#121	C₂²×C₁₃	1	2	yes	—
260	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
261	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
262	#466	—	2	4	no	—
263	#466	—	2	4	no	—
264	C₈×D₄	—	2	4	no	—
265	C₂×#107	—	2	4	no	—
266	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×#107	C₂²×C₁₃	1	2	yes	—
269	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×#102	C₂²×C₁₃	1	2	yes	—
272	C₂×#102	C₂²×C₁₃	1	2	yes	—
273	C₂×#102	C₂²×C₁₃	1	2	yes	—
274	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
277	#396	—	2	2	no	—
278	#394	—	2	2	no	—
279	#390	C₂²×C₁₃	1	2	yes	—
280	#389	C₂²×C₁₃	1	2	yes	—
281	#386	—	2	2	no	—
282	#380	C₂²×C₁₃	1	2	yes	—
283	#340	C₂²×C₁₃	1	2	yes	—
284	#340	C₂²×C₁₃	1	2	yes	—
285	C₂²×C₁₃	—	2	2	no	—
286	C₂²×C₁₃	—	2	2	no	—
287	C₂²×C₁₃	—	2	2	no	—
288	C₂²×C₁₃	—	2	2	no	—
289	C₂²×C₁₃	—	2	2	no	—
290	C₂²×C₁₃	—	2	2	no	—
291	C₂²×C₁₃	—	2	2	no	—
292	C₂²×C₁₃	—	2	2	no	—
293	C₂²×C₁₃	—	2	2	no	—
294	C₂²×C₁₃	—	4	1	no	—
295	C₂²×C₁₃	—	4	1	no	—
296	C₂²×C₁₃	—	4	1	no	—
297	C₂²×C₁₃	—	4	1	no	—
298	C₂²×C₁₃	—	8	2	no	—
299	C₂²×C₁₃	—	8	2	no	—
300	C₂²×C₁₃	—	8	2	no	—
301	C₂²×C₁₃	—	8	2	no	—
302	C₂²×C₁₃	—	8	2	no	—
303	C₂²×C₁₃	—	8	2	no	—
304	C₂²×C₁₃	—	8	2	no	—
305	C₂²×C₁₃	#466	1	4	yes	complemented
306	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
307	C₂²×C₁₃	D₄²	1	1	yes	characteristic
308	C₂²×C₁₃	#547	1	1	yes	characteristic
309	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
310	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
311	C₂²×C₁₃	#576	1	1	yes	characteristic
312	C₂²×C₁₃	#578	1	1	yes	characteristic
313	C₄×C₁₃	—	2	2	no	—
314	C₄×C₁₃	—	2	2	no	—
315	C₄×C₁₃	—	4	1	no	—
316	C₄×C₁₃	—	4	4	no	—
317	C₄×C₁₃	—	4	1	no	—
318	C₄×C₁₃	—	8	2	no	—
319	C₄×C₁₃	—	8	2	no	—
320	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
321	C₄×C₁₃	#537	1	1	yes	characteristic
322	C₄×C₁₃	#548	1	1	yes	characteristic
323	C₄×C₁₃	#553	1	1	yes	characteristic
324	C₂²×D₄	—	2	2	no	—
325	C₂²×D₄	—	2	2	no	—
326	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
327	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
328	C₂³×C₄	—	2	2	no	—
329	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
330	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
331	C₂×D₈	—	2	2	no	—
332	C₂×D₈	—	2	2	no	—
333	C₂×D₈	—	2	2	no	—
334	C₂²×C₈	—	2	2	no	—
335	C₂²×C₈	—	2	2	no	—
336	C₂²×C₈	—	2	2	no	—
337	C₂²×C₈	—	2	2	no	—
338	C₂²×C₈	—	2	2	no	—
339	C₂²×C₈	D₄×C₁₃	1	4	yes	complemented
340	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
342	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
343	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
344	#121	—	2	4	no	—
345	#121	—	2	4	no	—
346	#121	—	2	4	no	—
347	#121	—	4	2	no	—
348	#121	—	4	8	no	—
349	C₄×D₄	—	2	2	no	—
350	C₄×D₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	4	no	—
352	C₂×C₄⋊C₄	—	2	2	no	—
353	C₂×C₄⋊C₄	—	2	2	no	—
354	C₂×C₄⋊C₄	—	4	2	no	—
355	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
357	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	—	2	2	no	—
363	C₂×C₂²⋊C₄	—	2	2	no	—
364	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
367	#107	—	2	2	no	—
368	#107	—	2	2	no	—
369	#107	—	2	4	no	—
370	#107	D₄×C₁₃	1	4	yes	complemented
371	C₄⋊C₈	—	2	2	no	—
372	#102	—	2	4	no	—
373	#102	—	2	4	no	—
374	#102	—	4	2	no	—
375	C₂²⋊C₈	—	2	2	no	—
376	C₂²⋊C₈	—	2	2	no	—
377	C₄×C₈	—	2	2	no	—
378	#95	—	2	2	no	—
379	#95	—	2	2	no	—
380	C₂×C₁₃	—	2	4	no	—
381	C₂×C₁₃	—	4	2	no	—
382	C₂×C₁₃	—	16	2	no	—
383	C₂×C₁₃	#2416	1	1	yes	characteristic
384	C₂×C₁₃	C₂×#466	1	1	yes	characteristic
385	C₂×C₁₃	#3061	1	1	yes	characteristic
386	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
387	C₂×C₁₃	#3285	1	1	yes	characteristic
388	C₂×C₁₃	#3334	1	1	yes	characteristic
389	C₂×C₁₃	#3339	1	1	yes	characteristic
390	C₂⁴	—	2	2	no	—
391	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
392	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	4	4	no	—
402	C₂×D₄	—	4	4	no	—
403	C₂×D₄	—	4	4	no	—
404	C₂×D₄	—	4	4	no	—
405	C₂×D₄	—	4	4	no	—
406	C₂×D₄	—	8	2	no	—
407	C₂×D₄	C₁₃×D₈	1	4	yes	complemented
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	4	4	no	—
422	C₂²×C₄	—	4	4	no	—
423	C₂²×C₄	—	8	2	no	—
424	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
428	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₁₃×#41	1	2	yes	—
430	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
431	D₈	—	4	4	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	8	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	4	4	no	—
442	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
443	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
444	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
445	C₂×C₈	C₁₃×#41	1	2	yes	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	4	4	no	—
453	C₄⋊C₄	—	4	4	no	—
454	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	2	2	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	—	8	2	no	—
462	C₄²	—	2	1	no	—
463	C₄²	—	2	1	no	—
464	C₁₃	#24780	1	1	yes	characteristic, direct product factor, Sylow
465	C₂³	—	2	1	no	—
466	C₂³	—	2	1	no	—
467	C₂³	—	2	1	no	—
468	C₂³	—	2	1	no	—
469	C₂³	—	2	1	no	—
470	C₂³	—	2	1	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	2	1	no	—
473	C₂³	—	2	1	no	—
474	C₂³	—	2	1	no	—
475	C₂³	—	4	2	no	—
476	C₂³	—	4	2	no	—
477	C₂³	—	4	2	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	C₁₃×#121	1	2	yes	—
483	C₂³	C₂×C₁₃×D₈	1	2	yes	—
484	C₂³	C₂×C₁₃×D₈	1	2	yes	—
485	C₂³	C₁₃×#135	1	2	yes	—
486	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
487	D₄	—	2	8	no	—
488	D₄	—	4	2	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	2	no	—
491	D₄	—	4	2	no	—
492	D₄	—	8	8	no	—
493	D₄	—	8	8	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	8	8	no	—
522	C₂×C₄	C₁₃×#121	1	2	yes	—
523	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
524	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
525	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
526	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
527	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
528	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
529	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
530	C₈	—	2	2	no	—
531	C₈	—	4	1	no	—
532	C₈	—	4	1	no	—
533	C₈	C₁₃×#121	1	4	yes	complemented
534	C₂²	—	2	2	no	—
535	C₂²	—	2	2	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	8	2	no	—
548	C₂²	—	8	2	no	—
549	C₂²	—	8	2	no	—
550	C₂²	—	8	2	no	—
551	C₂²	—	8	2	no	—
552	C₂²	—	8	2	no	—
553	C₂²	—	8	2	no	—
554	C₂²	C₁₃×#466	1	4	yes	complemented
555	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
556	C₂²	D₄²×C₁₃	1	1	yes	characteristic
557	C₂²	C₁₃×#547	1	1	yes	characteristic
558	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
559	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
560	C₂²	C₁₃×#576	1	1	yes	characteristic
561	C₂²	C₁₃×#578	1	1	yes	characteristic
562	C₄	—	2	2	no	—
563	C₄	—	2	2	no	—
564	C₄	—	4	4	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	8	2	no	—
568	C₄	—	8	2	no	—
569	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
570	C₄	C₁₃×#537	1	1	yes	characteristic
571	C₄	C₁₃×#548	1	1	yes	characteristic
572	C₄	C₁₃×#553	1	1	yes	characteristic
573	C₂	—	2	4	no	—
574	C₂	—	4	2	no	—
575	C₂	—	16	2	no	—
576	C₂	C₁₃×#2416	1	1	yes	characteristic
577	C₂	C₂×C₁₃×#466	1	1	yes	characteristic
578	C₂	C₁₃×#3061	1	1	yes	characteristic
579	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
580	C₂	C₁₃×#3285	1	1	yes	characteristic
581	C₂	C₁₃×#3334	1	1	yes	characteristic
582	C₂	C₁₃×#3339	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#466	C₂	semidirect
2. C₂×C₁₃×#466	C₂	semidirect
3. C₂×C₈×D₄×C₁₃	C₂	semidirect
4. C₂²×C₁₃×#107	C₂	semidirect
5. C₁₃×#2416	C₂	semidirect
6. C₁₃×#2067	C₂	semidirect
7. C₁₃×#2033	C₂	semidirect
8. C₁₃×#1970	C₂	semidirect
9. C₁₃×#1942	C₂	semidirect
10. C₁₃×#1874	C₂	semidirect
11. C₁₃×#1808	C₂	semidirect
58. C₂²×C₈×C₁₃	D₄	semidirect
89. C₁₃×#107	D₄	semidirect
99. #24780	C₁₃	direct (N × H)
117. C₂×D₄×C₁₃	D₈	semidirect
174. C₂×#466	C₂×C₁₃	semidirect
175. C₂×#466	C₂×C₁₃	semidirect
176. C₂×C₈×D₄	C₂×C₁₃	semidirect
177. C₂²×#107	C₂×C₁₃	semidirect
178. #2416	C₂×C₁₃	semidirect
179. #2067	C₂×C₁₃	semidirect
180. #2033	C₂×C₁₃	semidirect
181. #1970	C₂×C₁₃	semidirect
182. #1942	C₂×C₁₃	semidirect
183. #1874	C₂×C₁₃	semidirect
184. #1808	C₂×C₁₃	semidirect
253. C₈×C₁₃	#121	semidirect
305. C₂²×C₁₃	#466	semidirect
339. C₂²×C₈	D₄×C₁₃	semidirect
370. #107	D₄×C₁₃	semidirect
407. C₂×D₄	C₁₃×D₈	semidirect
464. C₁₃	#24780	direct (N × H)
533. C₈	C₁₃×#121	semidirect
554. C₂²	C₁₃×#466	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#466	2
C₂×C₈×D₄×C₁₃	2
C₂²×C₁₃×#107	2
C₁₃×#2416	2
C₁₃×#2067	2
C₁₃×#2033	2
C₁₃×#1970	2
C₁₃×#1942	2
C₁₃×#1874	2
C₁₃×#1808	2
#24780	13

Subgroups — C13×#24780 #15711119

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24780 #15711119