Subgroups — C₁₃×#25034 #15711373

Order 3328.

962 conjugacy classes of subgroups.

The subgroup lattice has 508 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
2	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2422	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2071	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2033	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1862	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1808	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₃×C₂²⋊C₄	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	C₂×C₁₃×#123	—	2	2	no	—
15	C₂×C₁₃×#121	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
17	C₁₃×#466	—	2	4	no	—
18	C₄×C₁₃×D₈	—	2	4	no	—
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#107	C₂²	1	2	yes	—
23	C₂×C₁₃×#102	C₂²	1	2	yes	—
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#397	—	2	2	no	—
30	C₁₃×#394	—	2	2	no	—
31	C₁₃×#390	C₂²	1	2	yes	—
32	C₁₃×#389	C₂²	1	2	yes	—
33	C₁₃×#385	—	2	2	no	—
34	C₁₃×#384	C₂²	1	2	yes	—
35	C₁₃×#380	C₂²	1	2	yes	—
36	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	1	yes	characteristic
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₂²×D₄×C₁₃	—	2	2	no	—
42	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃	—	2	2	no	—
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂×C₁₃×D₈	—	2	2	no	—
46	C₂×C₁₃×D₈	—	2	2	no	—
47	C₂×C₁₃×D₈	D₄	1	4	yes	—
48	C₂²×C₈×C₁₃	—	2	2	no	—
49	C₂²×C₈×C₁₃	—	2	2	no	—
50	C₂²×C₈×C₁₃	—	2	2	no	—
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₁₃×#123	—	4	8	no	—
56	C₁₃×#121	—	2	4	no	—
57	C₁₃×#121	—	4	2	no	—
58	C₄×D₄×C₁₃	—	2	4	no	—
59	C₄×D₄×C₁₃	—	4	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
72	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#107	—	2	2	no	—
76	C₁₃×#107	—	2	2	no	—
77	C₁₃×#107	—	2	2	no	—
78	C₁₃×#107	—	4	2	no	—
79	C₁₃×#102	—	2	4	no	—
80	C₁₃×#102	—	2	4	no	—
81	C₁₃×#102	—	2	4	no	—
82	C₁₃×C₂²⋊C₈	—	2	2	no	—
83	C₄×C₈×C₁₃	—	2	2	no	—
84	C₄×C₈×C₁₃	—	2	2	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	D₄	1	1	yes	characteristic
88	C₁₃×#95	D₄	1	1	yes	characteristic
89	#25034	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	—	2	2	no	—
91	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
92	C₂×D₄×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	—	2	2	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	4	4	no	—
98	C₂×D₄×C₁₃	—	4	4	no	—
99	C₂×D₄×C₁₃	—	8	2	no	—
100	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	4	4	no	—
111	C₂²×C₄×C₁₃	—	4	4	no	—
112	C₂²×C₄×C₁₃	—	8	2	no	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₁₃×D₈	—	2	8	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	—	4	4	no	—
129	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₁₃	#41	1	2	yes	—
131	C₂×C₈×C₁₃	#41	1	2	yes	—
132	C₂×C₈×C₁₃	#41	1	2	yes	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	4	4	no	—
140	C₁₃×C₄⋊C₄	—	4	4	no	—
141	C₁₃×C₄⋊C₄	—	8	2	no	—
142	C₁₃×C₂²⋊C₄	—	2	2	no	—
143	C₁₃×C₂²⋊C₄	—	4	4	no	—
144	C₁₃×C₂²⋊C₄	—	4	4	no	—
145	C₁₃×C₂²⋊C₄	—	4	4	no	—
146	C₁₃×C₂²⋊C₄	—	4	4	no	—
147	C₁₃×C₂²⋊C₄	—	4	4	no	—
148	C₁₃×C₂²⋊C₄	D₈	1	4	yes	complemented
149	C₄²×C₁₃	—	2	1	no	—
150	C₄²×C₁₃	—	2	1	no	—
151	C₄²×C₁₃	—	2	1	no	—
152	C₄²×C₁₃	—	2	1	no	—
153	C₂×#466	C₂×C₁₃	1	1	yes	characteristic
154	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#2422	C₂×C₁₃	1	2	yes	complemented
156	#2071	C₂×C₁₃	1	2	yes	complemented
157	#2033	C₂×C₁₃	1	2	yes	complemented
158	#1970	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#1862	C₂×C₁₃	1	2	yes	complemented
161	#1845	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#1808	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₈×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₂³×C₁₃	—	2	1	no	—
165	C₂³×C₁₃	—	2	1	no	—
166	C₂³×C₁₃	—	2	1	no	—
167	C₂³×C₁₃	—	2	1	no	—
168	C₂³×C₁₃	—	2	1	no	—
169	C₂³×C₁₃	—	2	1	no	—
170	C₂³×C₁₃	—	2	4	no	—
171	C₂³×C₁₃	—	4	2	no	—
172	C₂³×C₁₃	—	4	2	no	—
173	C₂³×C₁₃	—	4	2	no	—
174	C₂³×C₁₃	—	4	2	no	—
175	C₂³×C₁₃	—	4	2	no	—
176	C₂³×C₁₃	—	4	2	no	—
177	C₂³×C₁₃	C₂×D₈	1	2	yes	—
178	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
179	D₄×C₁₃	—	2	4	no	—
180	D₄×C₁₃	—	2	4	no	—
181	D₄×C₁₃	—	4	2	no	—
182	D₄×C₁₃	—	4	2	no	—
183	D₄×C₁₃	—	8	8	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	—	4	2	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	8	8	no	—
210	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
211	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
212	C₂×C₄×C₁₃	#135	1	2	yes	—
213	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
219	C₈×C₁₃	—	2	2	no	—
220	C₈×C₁₃	—	4	1	no	—
221	C₈×C₁₃	—	4	1	no	—
222	C₈×C₁₃	#123	1	4	yes	complemented
223	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
224	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×#123	—	2	2	no	—
226	C₂×#121	C₂²×C₁₃	1	2	yes	—
227	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
228	#466	—	2	4	no	—
229	C₄×D₈	—	2	4	no	—
230	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
231	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×#107	C₂²×C₁₃	1	2	yes	—
234	C₂×#102	C₂²×C₁₃	1	2	yes	—
235	C₂×#102	C₂²×C₁₃	1	2	yes	—
236	C₂×#102	C₂²×C₁₃	1	2	yes	—
237	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
238	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
240	#397	—	2	2	no	—
241	#394	—	2	2	no	—
242	#390	C₂²×C₁₃	1	2	yes	—
243	#389	C₂²×C₁₃	1	2	yes	—
244	#385	—	2	2	no	—
245	#384	C₂²×C₁₃	1	2	yes	—
246	#380	C₂²×C₁₃	1	2	yes	—
247	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
248	#340	C₂²×C₁₃	1	2	yes	—
249	#340	C₂²×C₁₃	1	2	yes	—
250	#336	C₂²×C₁₃	1	1	yes	characteristic
251	#336	C₂²×C₁₃	1	1	yes	characteristic
252	C₂²×C₁₃	—	2	2	no	—
253	C₂²×C₁₃	—	2	2	no	—
254	C₂²×C₁₃	—	2	2	no	—
255	C₂²×C₁₃	—	4	1	no	—
256	C₂²×C₁₃	—	4	1	no	—
257	C₂²×C₁₃	—	4	1	no	—
258	C₂²×C₁₃	—	4	1	no	—
259	C₂²×C₁₃	—	4	4	no	—
260	C₂²×C₁₃	—	4	4	no	—
261	C₂²×C₁₃	—	4	4	no	—
262	C₂²×C₁₃	—	8	2	no	—
263	C₂²×C₁₃	—	8	2	no	—
264	C₂²×C₁₃	—	8	2	no	—
265	C₂²×C₁₃	—	8	2	no	—
266	C₂²×C₁₃	#532	1	1	yes	characteristic
267	C₂²×C₁₃	D₄²	1	1	yes	characteristic
268	C₂²×C₁₃	#547	1	1	yes	characteristic
269	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
270	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
271	C₂²×C₁₃	#576	1	1	yes	characteristic
272	C₂²×C₁₃	#578	1	1	yes	characteristic
273	C₄×C₁₃	—	2	2	no	—
274	C₄×C₁₃	—	2	2	no	—
275	C₄×C₁₃	—	2	2	no	—
276	C₄×C₁₃	—	4	1	no	—
277	C₄×C₁₃	—	4	1	no	—
278	C₄×C₁₃	—	8	2	no	—
279	C₄×C₁₃	—	8	2	no	—
280	C₄×C₁₃	—	8	2	no	—
281	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
282	C₄×C₁₃	#542	1	1	yes	characteristic
283	C₄×C₁₃	#547	1	1	yes	characteristic
284	C₄×C₁₃	#553	1	1	yes	characteristic
285	C₂²×D₄	—	2	2	no	—
286	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
287	C₂³×C₄	—	2	2	no	—
288	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
289	C₂×D₈	—	2	2	no	—
290	C₂×D₈	—	2	2	no	—
291	C₂×D₈	D₄×C₁₃	1	4	yes	—
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	—	2	2	no	—
294	C₂²×C₈	—	2	2	no	—
295	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
298	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
299	#123	—	4	8	no	—
300	#121	—	2	4	no	—
301	#121	—	4	2	no	—
302	C₄×D₄	—	2	4	no	—
303	C₄×D₄	—	4	2	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
308	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
309	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
317	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
318	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
319	#107	—	2	2	no	—
320	#107	—	2	2	no	—
321	#107	—	2	2	no	—
322	#107	—	4	2	no	—
323	#102	—	2	4	no	—
324	#102	—	2	4	no	—
325	#102	—	2	4	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	C₄×C₈	—	2	2	no	—
328	C₄×C₈	—	2	2	no	—
329	#95	—	2	2	no	—
330	#95	—	2	2	no	—
331	#95	D₄×C₁₃	1	1	yes	characteristic
332	#95	D₄×C₁₃	1	1	yes	characteristic
333	C₂×C₁₃	—	4	2	no	—
334	C₂×C₁₃	—	8	4	no	—
335	C₂×C₁₃	#2422	1	1	yes	characteristic
336	C₂×C₁₃	#3169	1	1	yes	characteristic
337	C₂×C₁₃	#3175	1	1	yes	characteristic
338	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
339	C₂×C₁₃	#3283	1	1	yes	characteristic
340	C₂×C₁₃	#3334	1	1	yes	characteristic
341	C₂×C₁₃	#3339	1	1	yes	characteristic
342	C₂⁴	—	2	2	no	—
343	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	4	4	no	—
350	C₂×D₄	—	4	4	no	—
351	C₂×D₄	—	8	2	no	—
352	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	4	4	no	—
363	C₂²×C₄	—	4	4	no	—
364	C₂²×C₄	—	8	2	no	—
365	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
370	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
371	D₈	—	2	8	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	4	4	no	—
381	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
382	C₂×C₈	C₁₃×#41	1	2	yes	—
383	C₂×C₈	C₁₃×#41	1	2	yes	—
384	C₂×C₈	C₁₃×#41	1	2	yes	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	4	4	no	—
392	C₄⋊C₄	—	4	4	no	—
393	C₄⋊C₄	—	8	2	no	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	4	4	no	—
396	C₂²⋊C₄	—	4	4	no	—
397	C₂²⋊C₄	—	4	4	no	—
398	C₂²⋊C₄	—	4	4	no	—
399	C₂²⋊C₄	—	4	4	no	—
400	C₂²⋊C₄	C₁₃×D₈	1	4	yes	complemented
401	C₄²	—	2	1	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	2	1	no	—
405	C₁₃	#25034	1	1	yes	characteristic, direct product factor, Sylow
406	C₂³	—	2	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	C₂×C₁₃×D₈	1	2	yes	—
420	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
421	D₄	—	2	4	no	—
422	D₄	—	2	4	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	2	no	—
425	D₄	—	8	8	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	8	8	no	—
452	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
453	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
454	C₂×C₄	C₁₃×#135	1	2	yes	—
455	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
456	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
457	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
458	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
459	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
460	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	4	1	no	—
463	C₈	—	4	1	no	—
464	C₈	C₁₃×#123	1	4	yes	complemented
465	C₂²	—	2	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	4	1	no	—
469	C₂²	—	4	1	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	4	no	—
473	C₂²	—	4	4	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	—	8	2	no	—
479	C₂²	C₁₃×#532	1	1	yes	characteristic
480	C₂²	D₄²×C₁₃	1	1	yes	characteristic
481	C₂²	C₁₃×#547	1	1	yes	characteristic
482	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
483	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
484	C₂²	C₁₃×#576	1	1	yes	characteristic
485	C₂²	C₁₃×#578	1	1	yes	characteristic
486	C₄	—	2	2	no	—
487	C₄	—	2	2	no	—
488	C₄	—	2	2	no	—
489	C₄	—	4	1	no	—
490	C₄	—	4	1	no	—
491	C₄	—	8	2	no	—
492	C₄	—	8	2	no	—
493	C₄	—	8	2	no	—
494	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
495	C₄	C₁₃×#542	1	1	yes	characteristic
496	C₄	C₁₃×#547	1	1	yes	characteristic
497	C₄	C₁₃×#553	1	1	yes	characteristic
498	C₂	—	4	2	no	—
499	C₂	—	8	4	no	—
500	C₂	C₁₃×#2422	1	1	yes	characteristic
501	C₂	C₁₃×#3169	1	1	yes	characteristic
502	C₂	C₁₃×#3175	1	1	yes	characteristic
503	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
504	C₂	C₁₃×#3283	1	1	yes	characteristic
505	C₂	C₁₃×#3334	1	1	yes	characteristic
506	C₂	C₁₃×#3339	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#466	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₁₃×D₈	C₂	semidirect
3. C₁₃×#2422	C₂	semidirect
4. C₁₃×#2071	C₂	semidirect
5. C₁₃×#2033	C₂	semidirect
6. C₁₃×#1970	C₂	semidirect
7. C₁₃×#1942	C₂	semidirect
8. C₁₃×#1862	C₂	semidirect
9. C₁₃×#1845	C₂	semidirect
10. C₁₃×#1808	C₂	semidirect
11. C₈×C₁₃×C₂²⋊C₄	C₂	semidirect
89. #25034	C₁₃	direct (N × H)
148. C₁₃×C₂²⋊C₄	D₈	semidirect
154. C₂×C₄×D₈	C₂×C₁₃	semidirect
155. #2422	C₂×C₁₃	semidirect
156. #2071	C₂×C₁₃	semidirect
157. #2033	C₂×C₁₃	semidirect
158. #1970	C₂×C₁₃	semidirect
159. #1942	C₂×C₁₃	semidirect
160. #1862	C₂×C₁₃	semidirect
161. #1845	C₂×C₁₃	semidirect
162. #1808	C₂×C₁₃	semidirect
163. C₈×C₂²⋊C₄	C₂×C₁₃	semidirect
222. C₈×C₁₃	#123	semidirect
400. C₂²⋊C₄	C₁₃×D₈	semidirect
405. C₁₃	#25034	direct (N × H)
464. C₈	C₁₃×#123	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×C₄×C₁₃×D₈	2
C₁₃×#2422	2
C₁₃×#2071	2
C₁₃×#2033	2
C₁₃×#1970	2
C₁₃×#1942	2
C₁₃×#1862	2
C₁₃×#1845	2
C₁₃×#1808	2
C₈×C₁₃×C₂²⋊C₄	2
#25034	13

Subgroups — C13×#25034 #15711373

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25034 #15711373