Subgroups — C₁₃×#24628 #15710967

Order 3328.

1034 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2541	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2055	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2014	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1982	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1926	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
14	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#127	C₂²	1	2	yes	—
16	C₂×C₁₃×#121	—	2	1	no	—
17	C₂×C₁₃×#121	—	2	1	no	—
18	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#460	—	2	4	no	—
21	C₄×C₁₃×SD₁₆	—	2	4	no	—
22	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#102	C₂²	1	2	yes	—
28	C₂×C₁₃×#102	C₂²	1	2	yes	—
29	C₂×C₁₃×#102	C₂²	1	2	yes	—
30	C₂×C₁₃×#102	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#392	—	2	2	no	—
33	C₁₃×#391	C₂²	1	2	yes	—
34	C₁₃×#390	C₂²	1	2	yes	—
35	C₁₃×#387	—	2	2	no	—
36	C₁₃×#384	C₂²	1	1	yes	characteristic
37	C₁₃×#382	—	2	1	no	—
38	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
40	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₃	—	2	1	no	—
45	C₂²×D₄×C₁₃	—	2	2	no	—
46	C₂²×D₄×C₁₃	—	2	2	no	—
47	C₂²×D₄×C₁₃	—	2	1	no	—
48	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
49	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	—	2	1	no	—
51	C₂×C₁₃×SD₁₆	—	2	2	no	—
52	C₂×C₁₃×SD₁₆	—	2	2	no	—
53	C₂×C₁₃×SD₁₆	—	2	4	no	—
54	C₂×C₁₃×SD₁₆	—	2	2	no	—
55	C₂×C₁₃×SD₁₆	—	4	2	no	—
56	C₂×C₁₃×SD₁₆	—	4	2	no	—
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₁₃×#127	—	2	4	no	—
61	C₁₃×#127	—	2	2	no	—
62	C₁₃×#127	—	2	2	no	—
63	C₁₃×#127	—	4	2	no	—
64	C₁₃×#121	—	4	4	no	—
65	C₁₃×#121	—	4	4	no	—
66	C₄×Q₈×C₁₃	—	2	2	no	—
67	C₄×Q₈×C₁₃	D₄	1	4	yes	complemented
68	C₄×D₄×C₁₃	—	2	2	no	—
69	C₄×D₄×C₁₃	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
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	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
81	C₂×C₄²×C₁₃	—	2	1	no	—
82	C₂×C₄²×C₁₃	—	2	2	no	—
83	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
84	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
85	C₁₃×#106	—	2	2	no	—
86	C₁₃×C₄⋊C₈	—	2	2	no	—
87	C₁₃×C₄⋊C₈	—	4	2	no	—
88	C₁₃×#103	—	2	2	no	—
89	C₁₃×#102	—	2	4	no	—
90	C₁₃×#102	—	2	2	no	—
91	C₁₃×#102	—	2	4	no	—
92	C₁₃×#102	—	4	2	no	—
93	C₁₃×#102	—	4	2	no	—
94	C₄×C₈×C₁₃	—	2	2	no	—
95	C₁₃×#95	—	2	2	no	—
96	C₁₃×#95	—	2	2	no	—
97	C₁₃×#95	—	2	2	no	—
98	C₁₃×#95	D₄	1	2	yes	—
99	#24628	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂⁴×C₁₃	—	2	1	no	—
101	C₂⁴×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	1	no	—
103	C₂×Q₈×C₁₃	—	2	1	no	—
104	C₂×Q₈×C₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₃	—	2	1	no	—
106	C₂×Q₈×C₁₃	—	2	1	no	—
107	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
108	C₂×D₄×C₁₃	—	2	1	no	—
109	C₂×D₄×C₁₃	—	2	2	no	—
110	C₂×D₄×C₁₃	—	2	1	no	—
111	C₂×D₄×C₁₃	—	2	1	no	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	—	2	2	no	—
114	C₂×D₄×C₁₃	—	2	2	no	—
115	C₂×D₄×C₁₃	—	2	1	no	—
116	C₂×D₄×C₁₃	—	2	1	no	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	—	4	4	no	—
120	C₂×D₄×C₁₃	—	4	4	no	—
121	C₂×D₄×C₁₃	—	4	4	no	—
122	C₂×D₄×C₁₃	—	4	2	no	—
123	C₂×D₄×C₁₃	—	4	2	no	—
124	C₂×D₄×C₁₃	—	4	4	no	—
125	C₂×D₄×C₁₃	—	4	2	no	—
126	C₂×D₄×C₁₃	—	4	2	no	—
127	C₂×D₄×C₁₃	—	8	2	no	—
128	C₂×D₄×C₁₃	—	8	1	no	—
129	C₂×D₄×C₁₃	—	8	1	no	—
130	C₂×D₄×C₁₃	—	8	2	no	—
131	C₂×D₄×C₁₃	#41	1	2	yes	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	4	2	no	—
137	C₂²×C₄×C₁₃	—	4	2	no	—
138	C₂²×C₄×C₁₃	—	4	2	no	—
139	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
144	C₁₃×SD₁₆	—	2	8	no	—
145	C₁₃×SD₁₆	—	4	8	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	2	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	—	2	2	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₂×C₈×C₁₃	#41	1	2	yes	—
155	C₁₃×C₄⋊C₄	—	2	4	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	2	1	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	4	2	no	—
163	C₁₃×C₄⋊C₄	—	8	1	no	—
164	C₁₃×C₄⋊C₄	SD₁₆	1	4	yes	complemented
165	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
166	C₁₃×C₂²⋊C₄	—	4	4	no	—
167	C₁₃×C₂²⋊C₄	—	4	2	no	—
168	C₁₃×C₂²⋊C₄	—	4	4	no	—
169	C₄²×C₁₃	—	2	4	no	—
170	C₄²×C₁₃	—	2	2	no	—
171	C₄²×C₁₃	—	2	2	no	—
172	C₄²×C₁₃	—	8	2	no	—
173	C₄²×C₁₃	C₂×D₄	1	2	yes	—
174	C₄²×C₁₃	#41	1	2	yes	—
175	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#2541	C₂×C₁₃	1	1	yes	characteristic
178	#2355	C₂×C₁₃	1	1	yes	characteristic, complemented
179	#2055	C₂×C₁₃	1	2	yes	complemented
180	#2014	C₂×C₁₃	1	2	yes	complemented
181	#1982	C₂×C₁₃	1	2	yes	complemented
182	#1957	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#1926	C₂×C₁₃	1	2	yes	complemented
185	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
186	C₂³×C₁₃	—	2	2	no	—
187	C₂³×C₁₃	—	4	1	no	—
188	C₂³×C₁₃	—	4	1	no	—
189	C₂³×C₁₃	—	4	1	no	—
190	C₂³×C₁₃	—	4	1	no	—
191	C₂³×C₁₃	—	4	1	no	—
192	C₂³×C₁₃	—	4	1	no	—
193	C₂³×C₁₃	—	4	2	no	—
194	C₂³×C₁₃	—	4	2	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	C₂²×D₄	1	1	yes	characteristic
201	Q₈×C₁₃	—	2	2	no	—
202	Q₈×C₁₃	—	2	2	no	—
203	Q₈×C₁₃	—	4	1	no	—
204	Q₈×C₁₃	—	4	1	no	—
205	D₄×C₁₃	—	2	2	no	—
206	D₄×C₁₃	—	2	2	no	—
207	D₄×C₁₃	—	4	2	no	—
208	D₄×C₁₃	—	4	1	no	—
209	D₄×C₁₃	—	4	2	no	—
210	D₄×C₁₃	—	4	2	no	—
211	D₄×C₁₃	—	4	1	no	—
212	D₄×C₁₃	—	4	2	no	—
213	D₄×C₁₃	—	8	8	no	—
214	D₄×C₁₃	—	8	4	no	—
215	D₄×C₁₃	—	8	8	no	—
216	D₄×C₁₃	—	8	4	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	4	1	no	—
227	C₂×C₄×C₁₃	—	4	1	no	—
228	C₂×C₄×C₁₃	—	4	1	no	—
229	C₂×C₄×C₁₃	—	4	1	no	—
230	C₂×C₄×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	—	4	1	no	—
233	C₂×C₄×C₁₃	—	4	1	no	—
234	C₂×C₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	—	4	2	no	—
236	C₂×C₄×C₁₃	—	8	4	no	—
237	C₂×C₄×C₁₃	#121	1	2	yes	—
238	C₂×C₄×C₁₃	#121	1	2	yes	—
239	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
240	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
241	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
242	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
246	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
247	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
248	C₈×C₁₃	—	2	2	no	—
249	C₈×C₁₃	—	4	1	no	—
250	C₈×C₁₃	—	4	2	no	—
251	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
252	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
253	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
254	C₂×#127	C₂²×C₁₃	1	2	yes	—
255	C₂×#121	—	2	1	no	—
256	C₂×#121	—	2	1	no	—
257	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
258	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
259	#460	—	2	4	no	—
260	C₄×SD₁₆	—	2	4	no	—
261	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
264	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×#102	C₂²×C₁₃	1	2	yes	—
267	C₂×#102	C₂²×C₁₃	1	2	yes	—
268	C₂×#102	C₂²×C₁₃	1	2	yes	—
269	C₂×#102	C₂²×C₁₃	1	2	yes	—
270	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
271	#392	—	2	2	no	—
272	#391	C₂²×C₁₃	1	2	yes	—
273	#390	C₂²×C₁₃	1	2	yes	—
274	#387	—	2	2	no	—
275	#384	C₂²×C₁₃	1	1	yes	characteristic
276	#382	—	2	1	no	—
277	C₄×C₄⋊C₄	—	2	1	no	—
278	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
279	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
280	#340	C₂²×C₁₃	1	2	yes	—
281	#336	C₂²×C₁₃	1	2	yes	—
282	C₂²×C₁₃	—	4	2	no	—
283	C₂²×C₁₃	—	4	2	no	—
284	C₂²×C₁₃	—	4	2	no	—
285	C₂²×C₁₃	—	8	1	no	—
286	C₂²×C₁₃	—	8	1	no	—
287	C₂²×C₁₃	—	8	1	no	—
288	C₂²×C₁₃	—	8	1	no	—
289	C₂²×C₁₃	—	8	2	no	—
290	C₂²×C₁₃	—	8	2	no	—
291	C₂²×C₁₃	—	8	2	no	—
292	C₂²×C₁₃	—	8	2	no	—
293	C₂²×C₁₃	—	8	2	no	—
294	C₂²×C₁₃	—	8	2	no	—
295	C₂²×C₁₃	—	8	2	no	—
296	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
297	C₂²×C₁₃	#546	1	1	yes	characteristic
298	C₂²×C₁₃	#550	1	1	yes	characteristic
299	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
300	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
301	C₂²×C₁₃	#576	1	1	yes	characteristic
302	C₂²×C₁₃	#577	1	1	yes	characteristic
303	C₄×C₁₃	—	2	4	no	—
304	C₄×C₁₃	—	2	2	no	—
305	C₄×C₁₃	—	4	2	no	—
306	C₄×C₁₃	—	4	2	no	—
307	C₄×C₁₃	—	4	2	no	—
308	C₄×C₁₃	—	8	2	no	—
309	C₄×C₁₃	—	8	1	no	—
310	C₄×C₁₃	#460	1	4	yes	—
311	C₄×C₁₃	#525	1	1	yes	characteristic
312	C₄×C₁₃	#535	1	1	yes	characteristic
313	C₄×C₁₃	#553	1	1	yes	characteristic
314	C₄×C₁₃	#555	1	1	yes	characteristic
315	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
316	C₂²×D₄	—	2	1	no	—
317	C₂²×D₄	—	2	2	no	—
318	C₂²×D₄	—	2	2	no	—
319	C₂²×D₄	—	2	1	no	—
320	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
321	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
322	C₂³×C₄	—	2	1	no	—
323	C₂×SD₁₆	—	2	2	no	—
324	C₂×SD₁₆	—	2	2	no	—
325	C₂×SD₁₆	—	2	4	no	—
326	C₂×SD₁₆	—	2	2	no	—
327	C₂×SD₁₆	—	4	2	no	—
328	C₂×SD₁₆	—	4	2	no	—
329	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
330	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
331	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
332	#127	—	2	4	no	—
333	#127	—	2	2	no	—
334	#127	—	2	2	no	—
335	#127	—	4	2	no	—
336	#121	—	4	4	no	—
337	#121	—	4	4	no	—
338	C₄×Q₈	—	2	2	no	—
339	C₄×Q₈	D₄×C₁₃	1	4	yes	complemented
340	C₄×D₄	—	2	2	no	—
341	C₄×D₄	—	2	2	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
346	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
348	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
349	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
350	C₂×C₂²⋊C₄	—	2	1	no	—
351	C₂×C₂²⋊C₄	—	2	2	no	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₄²	—	2	1	no	—
354	C₂×C₄²	—	2	2	no	—
355	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
356	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
357	#106	—	2	2	no	—
358	C₄⋊C₈	—	2	2	no	—
359	C₄⋊C₈	—	4	2	no	—
360	#103	—	2	2	no	—
361	#102	—	2	4	no	—
362	#102	—	2	2	no	—
363	#102	—	2	4	no	—
364	#102	—	4	2	no	—
365	#102	—	4	2	no	—
366	C₄×C₈	—	2	2	no	—
367	#95	—	2	2	no	—
368	#95	—	2	2	no	—
369	#95	—	2	2	no	—
370	#95	D₄×C₁₃	1	2	yes	—
371	C₂×C₁₃	—	8	2	no	—
372	C₂×C₁₃	—	16	2	no	—
373	C₂×C₁₃	#2414	1	1	yes	characteristic
374	C₂×C₁₃	C₂×#460	1	1	yes	characteristic
375	C₂×C₁₃	#3045	1	1	yes	characteristic
376	C₂×C₁₃	#3295	1	1	yes	characteristic
377	C₂×C₁₃	#3324	1	1	yes	characteristic
378	C₂×C₁₃	#3392	1	1	yes	characteristic
379	C₂×C₁₃	#3399	1	1	yes	characteristic
380	C₂⁴	—	2	1	no	—
381	C₂⁴	—	2	2	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	4	4	no	—
400	C₂×D₄	—	4	4	no	—
401	C₂×D₄	—	4	4	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂×D₄	—	4	2	no	—
404	C₂×D₄	—	4	4	no	—
405	C₂×D₄	—	4	2	no	—
406	C₂×D₄	—	4	2	no	—
407	C₂×D₄	—	8	2	no	—
408	C₂×D₄	—	8	1	no	—
409	C₂×D₄	—	8	1	no	—
410	C₂×D₄	—	8	2	no	—
411	C₂×D₄	C₁₃×#41	1	2	yes	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	4	2	no	—
417	C₂²×C₄	—	4	2	no	—
418	C₂²×C₄	—	4	2	no	—
419	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
420	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
422	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
424	SD₁₆	—	2	8	no	—
425	SD₁₆	—	4	8	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	C₁₃×#41	1	2	yes	—
435	C₄⋊C₄	—	2	4	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	4	2	no	—
443	C₄⋊C₄	—	8	1	no	—
444	C₄⋊C₄	C₁₃×SD₁₆	1	4	yes	complemented
445	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
446	C₂²⋊C₄	—	4	4	no	—
447	C₂²⋊C₄	—	4	2	no	—
448	C₂²⋊C₄	—	4	4	no	—
449	C₄²	—	2	4	no	—
450	C₄²	—	2	2	no	—
451	C₄²	—	2	2	no	—
452	C₄²	—	8	2	no	—
453	C₄²	C₂×D₄×C₁₃	1	2	yes	—
454	C₄²	C₁₃×#41	1	2	yes	—
455	C₁₃	#24628	1	1	yes	characteristic, direct product factor, Sylow
456	C₂³	—	2	2	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	4	1	no	—
460	C₂³	—	4	1	no	—
461	C₂³	—	4	1	no	—
462	C₂³	—	4	1	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	2	no	—
465	C₂³	—	4	2	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	4	2	no	—
470	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
471	Q₈	—	2	2	no	—
472	Q₈	—	2	2	no	—
473	Q₈	—	4	1	no	—
474	Q₈	—	4	1	no	—
475	D₄	—	2	2	no	—
476	D₄	—	2	2	no	—
477	D₄	—	4	2	no	—
478	D₄	—	4	1	no	—
479	D₄	—	4	2	no	—
480	D₄	—	4	2	no	—
481	D₄	—	4	1	no	—
482	D₄	—	4	2	no	—
483	D₄	—	8	8	no	—
484	D₄	—	8	4	no	—
485	D₄	—	8	8	no	—
486	D₄	—	8	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	8	4	no	—
507	C₂×C₄	C₁₃×#121	1	2	yes	—
508	C₂×C₄	C₁₃×#121	1	2	yes	—
509	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
510	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
511	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
512	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
513	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
514	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
515	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
516	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
517	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
518	C₈	—	2	2	no	—
519	C₈	—	4	1	no	—
520	C₈	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	8	1	no	—
525	C₂²	—	8	1	no	—
526	C₂²	—	8	1	no	—
527	C₂²	—	8	1	no	—
528	C₂²	—	8	2	no	—
529	C₂²	—	8	2	no	—
530	C₂²	—	8	2	no	—
531	C₂²	—	8	2	no	—
532	C₂²	—	8	2	no	—
533	C₂²	—	8	2	no	—
534	C₂²	—	8	2	no	—
535	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
536	C₂²	C₁₃×#546	1	1	yes	characteristic
537	C₂²	C₁₃×#550	1	1	yes	characteristic
538	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
539	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
540	C₂²	C₁₃×#576	1	1	yes	characteristic
541	C₂²	C₁₃×#577	1	1	yes	characteristic
542	C₄	—	2	4	no	—
543	C₄	—	2	2	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	2	no	—
547	C₄	—	8	1	no	—
548	C₄	—	8	2	no	—
549	C₄	C₁₃×#460	1	4	yes	—
550	C₄	C₁₃×#525	1	1	yes	characteristic
551	C₄	C₁₃×#535	1	1	yes	characteristic
552	C₄	C₁₃×#553	1	1	yes	characteristic
553	C₄	C₁₃×#555	1	1	yes	characteristic
554	C₂	—	8	2	no	—
555	C₂	—	16	2	no	—
556	C₂	C₁₃×#2414	1	1	yes	characteristic
557	C₂	C₂×C₁₃×#460	1	1	yes	characteristic
558	C₂	C₁₃×#3045	1	1	yes	characteristic
559	C₂	C₁₃×#3295	1	1	yes	characteristic
560	C₂	C₁₃×#3324	1	1	yes	characteristic
561	C₂	C₁₃×#3392	1	1	yes	characteristic
562	C₂	C₁₃×#3399	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2541	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#460	C₂	semidirect
2. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
4. C₁₃×#2355	C₂	semidirect
5. C₁₃×#2055	C₂	semidirect
6. C₁₃×#2014	C₂	semidirect
7. C₁₃×#1982	C₂	semidirect
8. C₁₃×#1957	C₂	semidirect
9. C₁₃×#1939	C₂	semidirect
10. C₁₃×#1926	C₂	semidirect
11. C₁₃×#1802	C₂	semidirect
67. C₄×Q₈×C₁₃	D₄	semidirect
99. #24628	C₁₃	direct (N × H)
164. C₁₃×C₄⋊C₄	SD₁₆	semidirect
175. C₂×#460	C₂×C₁₃	semidirect
176. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
178. #2355	C₂×C₁₃	semidirect
179. #2055	C₂×C₁₃	semidirect
180. #2014	C₂×C₁₃	semidirect
181. #1982	C₂×C₁₃	semidirect
182. #1957	C₂×C₁₃	semidirect
183. #1939	C₂×C₁₃	semidirect
184. #1926	C₂×C₁₃	semidirect
185. #1802	C₂×C₁₃	semidirect
339. C₄×Q₈	D₄×C₁₃	semidirect
444. C₄⋊C₄	C₁₃×SD₁₆	semidirect
455. C₁₃	#24628	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×#460	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2541	2
C₁₃×#2355	2
C₁₃×#2055	2
C₁₃×#2014	2
C₁₃×#1982	2
C₁₃×#1957	2
C₁₃×#1939	2
C₁₃×#1926	2
C₁₃×#1802	2
#24628	13

Subgroups — C13×#24628 #15710967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24628 #15710967