Subgroups — C₁₃×#24631 #15710970

Order 3328.

974 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2548	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2054	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2012	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1983	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×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
14	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#124	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#117	—	2	1	no	—
19	C₁₃×#459	—	2	4	no	—
20	C₄×C₁₃×SD₁₆	—	2	4	no	—
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#103	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	2	yes	—
27	C₂×C₁₃×#102	C₂²	1	2	yes	—
28	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#102	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#394	—	2	2	no	—
32	C₁₃×#390	—	2	1	no	—
33	C₁₃×#390	—	2	1	no	—
34	C₁₃×#390	C₂²	1	2	yes	—
35	C₁₃×#390	C₂²	1	2	yes	—
36	C₁₃×#388	—	2	2	no	—
37	C₁₃×#384	C₂²	1	1	yes	characteristic
38	C₁₃×#380	—	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	1	no	—
46	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
47	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	—	2	1	no	—
49	C₂×C₁₃×SD₁₆	—	2	2	no	—
50	C₂×C₁₃×SD₁₆	—	2	2	no	—
51	C₂×C₁₃×SD₁₆	—	2	2	no	—
52	C₂×C₁₃×D₈	—	2	4	no	—
53	C₂×C₁₃×D₈	—	4	2	no	—
54	C₂×C₁₃×D₈	—	4	2	no	—
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₁₃×#127	—	2	2	no	—
59	C₁₃×#127	—	2	2	no	—
60	C₁₃×#124	—	2	4	no	—
61	C₁₃×#124	—	4	2	no	—
62	C₄×Q₈×C₁₃	—	2	2	no	—
63	C₄×Q₈×C₁₃	—	2	2	no	—
64	C₄×D₄×C₁₃	—	2	2	no	—
65	C₄×D₄×C₁₃	D₄	1	4	yes	—
66	C₁₃×#117	—	4	4	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
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×C₄²×C₁₃	—	2	2	no	—
83	C₂×C₄²×C₁₃	—	2	1	no	—
84	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	C₁₃×#106	—	2	2	no	—
87	C₁₃×C₄⋊C₈	—	2	2	no	—
88	C₁₃×C₄⋊C₈	—	4	2	no	—
89	C₁₃×#103	—	2	2	no	—
90	C₁₃×#103	—	4	2	no	—
91	C₁₃×#102	—	2	2	no	—
92	C₁₃×#102	—	2	4	no	—
93	C₁₃×#102	—	2	4	no	—
94	C₁₃×#102	—	4	2	no	—
95	C₄×C₈×C₁₃	—	2	2	no	—
96	C₁₃×#95	—	2	2	no	—
97	C₁₃×#95	D₄	1	2	yes	—
98	#24631	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂⁴×C₁₃	—	2	1	no	—
100	C₂⁴×C₁₃	—	2	2	no	—
101	C₂×Q₈×C₁₃	—	2	1	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	#41	1	2	yes	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	1	no	—
109	C₂×D₄×C₁₃	—	2	1	no	—
110	C₂×D₄×C₁₃	—	2	1	no	—
111	C₂×D₄×C₁₃	—	2	2	no	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	—	2	2	no	—
114	C₂×D₄×C₁₃	—	2	1	no	—
115	C₂×D₄×C₁₃	—	2	1	no	—
116	C₂×D₄×C₁₃	—	2	2	no	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	4	2	no	—
119	C₂×D₄×C₁₃	—	4	2	no	—
120	C₂×D₄×C₁₃	—	4	2	no	—
121	C₂×D₄×C₁₃	—	4	2	no	—
122	C₂×D₄×C₁₃	—	8	1	no	—
123	C₂×D₄×C₁₃	—	8	1	no	—
124	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	4	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	4	2	no	—
131	C₂²×C₄×C₁₃	—	4	2	no	—
132	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₁₃×SD₁₆	—	2	8	no	—
138	C₁₃×D₈	—	4	8	no	—
139	C₂×C₈×C₁₃	—	2	1	no	—
140	C₂×C₈×C₁₃	—	2	1	no	—
141	C₂×C₈×C₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	—	2	1	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₂×C₈×C₁₃	#41	1	2	yes	—
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	4	2	no	—
156	C₁₃×C₄⋊C₄	—	4	2	no	—
157	C₁₃×C₄⋊C₄	—	8	1	no	—
158	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
159	C₁₃×C₂²⋊C₄	—	2	4	no	—
160	C₁₃×C₂²⋊C₄	—	4	4	no	—
161	C₁₃×C₂²⋊C₄	—	4	4	no	—
162	C₁₃×C₂²⋊C₄	—	4	4	no	—
163	C₁₃×C₂²⋊C₄	—	8	2	no	—
164	C₁₃×C₂²⋊C₄	—	8	2	no	—
165	C₁₃×C₂²⋊C₄	—	8	2	no	—
166	C₄²×C₁₃	—	2	2	no	—
167	C₄²×C₁₃	—	2	2	no	—
168	C₄²×C₁₃	—	4	4	no	—
169	C₄²×C₁₃	—	4	2	no	—
170	C₄²×C₁₃	C₂×D₄	1	2	yes	—
171	C₄²×C₁₃	#41	1	2	yes	—
172	C₂×#459	C₂×C₁₃	1	1	yes	characteristic
173	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#2548	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#2354	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#2054	C₂×C₁₃	1	2	yes	complemented
177	#2012	C₂×C₁₃	1	2	yes	complemented
178	#1983	C₂×C₁₃	1	2	yes	complemented
179	#1957	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
181	#1926	C₂×C₁₃	1	2	yes	complemented
182	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
183	C₂³×C₁₃	—	2	2	no	—
184	C₂³×C₁₃	—	4	1	no	—
185	C₂³×C₁₃	—	4	1	no	—
186	C₂³×C₁₃	—	4	1	no	—
187	C₂³×C₁₃	—	4	1	no	—
188	C₂³×C₁₃	—	4	1	no	—
189	C₂³×C₁₃	—	4	1	no	—
190	C₂³×C₁₃	—	4	2	no	—
191	C₂³×C₁₃	—	4	2	no	—
192	C₂³×C₁₃	—	4	2	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	C₂²×D₄	1	1	yes	characteristic
198	Q₈×C₁₃	—	2	2	no	—
199	Q₈×C₁₃	—	2	2	no	—
200	Q₈×C₁₃	—	4	1	no	—
201	Q₈×C₁₃	—	4	1	no	—
202	D₄×C₁₃	—	2	2	no	—
203	D₄×C₁₃	—	2	2	no	—
204	D₄×C₁₃	—	4	2	no	—
205	D₄×C₁₃	—	4	2	no	—
206	D₄×C₁₃	—	4	1	no	—
207	D₄×C₁₃	—	4	2	no	—
208	D₄×C₁₃	—	4	1	no	—
209	D₄×C₁₃	—	4	2	no	—
210	D₄×C₁₃	—	8	4	no	—
211	D₄×C₁₃	—	8	4	no	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	2	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	—	4	1	no	—
223	C₂×C₄×C₁₃	—	4	1	no	—
224	C₂×C₄×C₁₃	—	4	1	no	—
225	C₂×C₄×C₁₃	—	4	1	no	—
226	C₂×C₄×C₁₃	—	4	8	no	—
227	C₂×C₄×C₁₃	—	4	1	no	—
228	C₂×C₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	—	4	2	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	#121	1	2	yes	—
234	C₂×C₄×C₁₃	#121	1	2	yes	—
235	C₂×C₄×C₁₃	#135	1	2	yes	—
236	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
237	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
241	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
242	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
243	C₈×C₁₃	—	2	2	no	—
244	C₈×C₁₃	—	4	1	no	—
245	C₈×C₁₃	—	4	2	no	—
246	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
247	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
248	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
249	C₂×#124	C₂²×C₁₃	1	2	yes	—
250	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
251	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
252	C₂×#117	—	2	1	no	—
253	#459	—	2	4	no	—
254	C₄×SD₁₆	—	2	4	no	—
255	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
258	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
259	C₂×#103	C₂²×C₁₃	1	2	yes	—
260	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×#102	C₂²×C₁₃	1	2	yes	—
262	C₂×#102	C₂²×C₁₃	1	2	yes	—
263	C₂×#102	C₂²×C₁₃	1	2	yes	—
264	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
265	#394	—	2	2	no	—
266	#390	—	2	1	no	—
267	#390	—	2	1	no	—
268	#390	C₂²×C₁₃	1	2	yes	—
269	#390	C₂²×C₁₃	1	2	yes	—
270	#388	—	2	2	no	—
271	#384	C₂²×C₁₃	1	1	yes	characteristic
272	#380	—	2	1	no	—
273	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
274	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
275	#340	C₂²×C₁₃	1	2	yes	—
276	#336	C₂²×C₁₃	1	2	yes	—
277	C₂²×C₁₃	—	4	2	no	—
278	C₂²×C₁₃	—	4	2	no	—
279	C₂²×C₁₃	—	4	2	no	—
280	C₂²×C₁₃	—	8	1	no	—
281	C₂²×C₁₃	—	8	1	no	—
282	C₂²×C₁₃	—	8	1	no	—
283	C₂²×C₁₃	—	8	1	no	—
284	C₂²×C₁₃	—	8	2	no	—
285	C₂²×C₁₃	—	8	2	no	—
286	C₂²×C₁₃	—	8	2	no	—
287	C₂²×C₁₃	—	8	2	no	—
288	C₂²×C₁₃	—	8	2	no	—
289	C₂²×C₁₃	—	8	2	no	—
290	C₂²×C₁₃	—	8	2	no	—
291	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
292	C₂²×C₁₃	#546	1	1	yes	characteristic
293	C₂²×C₁₃	#550	1	1	yes	characteristic
294	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
295	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
296	C₂²×C₁₃	#576	1	1	yes	characteristic
297	C₂²×C₁₃	#577	1	1	yes	characteristic
298	C₄×C₁₃	—	2	2	no	—
299	C₄×C₁₃	—	4	2	no	—
300	C₄×C₁₃	—	4	2	no	—
301	C₄×C₁₃	—	4	2	no	—
302	C₄×C₁₃	—	4	2	no	—
303	C₄×C₁₃	—	8	2	no	—
304	C₄×C₁₃	—	8	1	no	—
305	C₄×C₁₃	#463	1	4	yes	—
306	C₄×C₁₃	#525	1	1	yes	characteristic
307	C₄×C₁₃	#535	1	1	yes	characteristic
308	C₄×C₁₃	#553	1	1	yes	characteristic
309	C₄×C₁₃	#555	1	1	yes	characteristic
310	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
311	C₂²×D₄	—	2	1	no	—
312	C₂²×D₄	—	2	1	no	—
313	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
314	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
315	C₂³×C₄	—	2	1	no	—
316	C₂×SD₁₆	—	2	2	no	—
317	C₂×SD₁₆	—	2	2	no	—
318	C₂×SD₁₆	—	2	2	no	—
319	C₂×D₈	—	2	4	no	—
320	C₂×D₈	—	4	2	no	—
321	C₂×D₈	—	4	2	no	—
322	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
323	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
324	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
325	#127	—	2	2	no	—
326	#127	—	2	2	no	—
327	#124	—	2	4	no	—
328	#124	—	4	2	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×Q₈	—	2	2	no	—
331	C₄×D₄	—	2	2	no	—
332	C₄×D₄	D₄×C₁₃	1	4	yes	—
333	#117	—	4	4	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
338	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
341	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	—	2	2	no	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₄²	—	2	2	no	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
352	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
353	#106	—	2	2	no	—
354	C₄⋊C₈	—	2	2	no	—
355	C₄⋊C₈	—	4	2	no	—
356	#103	—	2	2	no	—
357	#103	—	4	2	no	—
358	#102	—	2	2	no	—
359	#102	—	2	4	no	—
360	#102	—	2	4	no	—
361	#102	—	4	2	no	—
362	C₄×C₈	—	2	2	no	—
363	#95	—	2	2	no	—
364	#95	D₄×C₁₃	1	2	yes	—
365	C₂×C₁₃	—	8	2	no	—
366	C₂×C₁₃	—	16	2	no	—
367	C₂×C₁₃	#2414	1	1	yes	characteristic
368	C₂×C₁₃	C₂×#463	1	1	yes	characteristic
369	C₂×C₁₃	#3045	1	1	yes	characteristic
370	C₂×C₁₃	#3305	1	1	yes	characteristic
371	C₂×C₁₃	#3332	1	1	yes	characteristic
372	C₂×C₁₃	#3394	1	1	yes	characteristic
373	C₂×C₁₃	#3399	1	1	yes	characteristic
374	C₂⁴	—	2	1	no	—
375	C₂⁴	—	2	2	no	—
376	C₂×Q₈	—	2	1	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	C₁₃×#41	1	2	yes	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	4	2	no	—
394	C₂×D₄	—	4	2	no	—
395	C₂×D₄	—	4	2	no	—
396	C₂×D₄	—	4	2	no	—
397	C₂×D₄	—	8	1	no	—
398	C₂×D₄	—	8	1	no	—
399	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	4	2	no	—
406	C₂²×C₄	—	4	2	no	—
407	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
408	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
409	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
411	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
412	SD₁₆	—	2	8	no	—
413	D₈	—	4	8	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	C₁₃×#41	1	2	yes	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	4	2	no	—
431	C₄⋊C₄	—	4	2	no	—
432	C₄⋊C₄	—	8	1	no	—
433	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₂²⋊C₄	—	4	4	no	—
436	C₂²⋊C₄	—	4	4	no	—
437	C₂²⋊C₄	—	4	4	no	—
438	C₂²⋊C₄	—	8	2	no	—
439	C₂²⋊C₄	—	8	2	no	—
440	C₂²⋊C₄	—	8	2	no	—
441	C₄²	—	2	2	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	4	4	no	—
444	C₄²	—	4	2	no	—
445	C₄²	C₂×D₄×C₁₃	1	2	yes	—
446	C₄²	C₁₃×#41	1	2	yes	—
447	C₁₃	#24631	1	1	yes	characteristic, direct product factor, Sylow
448	C₂³	—	2	2	no	—
449	C₂³	—	4	1	no	—
450	C₂³	—	4	1	no	—
451	C₂³	—	4	1	no	—
452	C₂³	—	4	1	no	—
453	C₂³	—	4	1	no	—
454	C₂³	—	4	1	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	4	2	no	—
462	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
463	Q₈	—	2	2	no	—
464	Q₈	—	2	2	no	—
465	Q₈	—	4	1	no	—
466	Q₈	—	4	1	no	—
467	D₄	—	2	2	no	—
468	D₄	—	2	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	1	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	1	no	—
474	D₄	—	4	2	no	—
475	D₄	—	8	4	no	—
476	D₄	—	8	4	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	8	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	C₁₃×#121	1	2	yes	—
499	C₂×C₄	C₁₃×#121	1	2	yes	—
500	C₂×C₄	C₁₃×#135	1	2	yes	—
501	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
502	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
503	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
504	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
505	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
506	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
507	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
508	C₈	—	2	2	no	—
509	C₈	—	4	1	no	—
510	C₈	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	8	1	no	—
515	C₂²	—	8	1	no	—
516	C₂²	—	8	1	no	—
517	C₂²	—	8	1	no	—
518	C₂²	—	8	2	no	—
519	C₂²	—	8	2	no	—
520	C₂²	—	8	2	no	—
521	C₂²	—	8	2	no	—
522	C₂²	—	8	2	no	—
523	C₂²	—	8	2	no	—
524	C₂²	—	8	2	no	—
525	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
526	C₂²	C₁₃×#546	1	1	yes	characteristic
527	C₂²	C₁₃×#550	1	1	yes	characteristic
528	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
529	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
530	C₂²	C₁₃×#576	1	1	yes	characteristic
531	C₂²	C₁₃×#577	1	1	yes	characteristic
532	C₄	—	2	2	no	—
533	C₄	—	4	2	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	2	no	—
537	C₄	—	8	1	no	—
538	C₄	—	8	2	no	—
539	C₄	C₁₃×#463	1	4	yes	—
540	C₄	C₁₃×#525	1	1	yes	characteristic
541	C₄	C₁₃×#535	1	1	yes	characteristic
542	C₄	C₁₃×#553	1	1	yes	characteristic
543	C₄	C₁₃×#555	1	1	yes	characteristic
544	C₂	—	8	2	no	—
545	C₂	—	16	2	no	—
546	C₂	C₁₃×#2414	1	1	yes	characteristic
547	C₂	C₂×C₁₃×#463	1	1	yes	characteristic
548	C₂	C₁₃×#3045	1	1	yes	characteristic
549	C₂	C₁₃×#3305	1	1	yes	characteristic
550	C₂	C₁₃×#3332	1	1	yes	characteristic
551	C₂	C₁₃×#3394	1	1	yes	characteristic
552	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	C₂×C₁₃×#459	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
2. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
3. C₁₃×#2548	C₂	semidirect
4. C₁₃×#2354	C₂	semidirect
5. C₁₃×#2054	C₂	semidirect
6. C₁₃×#2012	C₂	semidirect
7. C₁₃×#1983	C₂	semidirect
8. C₁₃×#1957	C₂	semidirect
9. C₁₃×#1939	C₂	semidirect
10. C₁₃×#1926	C₂	semidirect
11. C₁₃×#1803	C₂	semidirect
98. #24631	C₁₃	direct (N × H)
173. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
174. #2548	C₂×C₁₃	semidirect
175. #2354	C₂×C₁₃	semidirect
176. #2054	C₂×C₁₃	semidirect
177. #2012	C₂×C₁₃	semidirect
178. #1983	C₂×C₁₃	semidirect
179. #1957	C₂×C₁₃	semidirect
180. #1939	C₂×C₁₃	semidirect
181. #1926	C₂×C₁₃	semidirect
182. #1803	C₂×C₁₃	semidirect
447. C₁₃	#24631	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×#459	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2548	2
C₁₃×#2354	2
C₁₃×#2054	2
C₁₃×#2012	2
C₁₃×#1983	2
C₁₃×#1957	2
C₁₃×#1939	2
C₁₃×#1926	2
C₁₃×#1803	2
#24631	13

Subgroups — C13×#24631 #15710970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24631 #15710970