Subgroups — C₁₃×#60808 #15747147

Order 3328.

2162 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3221	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3220	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3151	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3142	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3036	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3006	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2921	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	C₂²	1	2	yes	—
11	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
12	C₁₃×#540	—	2	4	no	—
13	C₁₃×#540	C₂²	1	8	yes	complemented
14	C₁₃×#537	—	2	2	no	—
15	C₁₃×#536	C₂²	1	4	yes	complemented
16	C₁₃×#535	C₂²	1	4	yes	complemented
17	C₁₃×#534	—	2	2	no	—
18	C₁₃×#532	C₂²	1	2	yes	—
19	C₁₃×#532	C₂²	1	2	yes	—
20	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
22	C₁₃×#525	—	2	4	no	—
23	C₂×C₁₃×#123	—	2	2	no	—
24	C₂×C₁₃×#121	—	2	2	no	—
25	C₂×C₁₃×#121	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
27	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
28	C₁₃×#496	C₂²	1	8	yes	complemented
29	C₁₃×#493	C₂²	1	4	yes	complemented
30	C₁₃×#492	C₂²	1	4	yes	complemented
31	C₁₃×#491	C₂²	1	4	yes	complemented
32	C₁₃×#490	C₂²	1	4	yes	complemented
33	C₁₃×#488	C₂²	1	8	yes	complemented
34	C₁₃×#463	C₂²	1	16	yes	complemented
35	C₁₃×#461	C₂²	1	8	yes	complemented
36	C₁₃×#459	C₂²	1	8	yes	complemented
37	C₁₃×#449	C₂²	1	16	yes	complemented
38	C₁₃×#448	C₂²	1	8	yes	complemented
39	C₁₃×#447	C₂²	1	8	yes	complemented
40	C₁₃×#433	C₂²	1	8	yes	complemented
41	C₁₃×#423	C₂²	1	2	yes	complemented
42	C₁₃×#417	C₂²	1	8	yes	complemented
43	C₁₃×#407	C₂²	1	2	yes	—
44	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
45	C₂×C₁₃×#41	—	2	2	no	—
46	C₂×C₁₃×#41	—	2	2	no	—
47	C₂×C₁₃×#41	—	4	8	no	—
48	C₂×C₁₃×#41	C₂³	1	4	yes	—
49	C₂×C₁₃×#41	C₂³	1	4	yes	—
50	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
51	C₂²×D₄×C₁₃	—	2	2	no	—
52	C₂²×D₄×C₁₃	—	2	2	no	—
53	C₂²×D₄×C₁₃	—	2	2	no	—
54	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
55	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₃	—	2	2	no	—
57	C₂³×C₄×C₁₃	—	2	2	no	—
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×AGL(1,ℤ/8)	—	4	16	no	—
60	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
61	C₂×C₁₃×D₈	C₂³	1	16	yes	—
62	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
63	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₁₃×#127	—	2	2	no	—
66	C₁₃×#127	C₂³	1	2	yes	—
67	C₁₃×#127	C₂³	1	2	yes	—
68	C₁₃×#127	C₂³	1	4	yes	—
69	C₁₃×#125	—	2	2	no	—
70	C₁₃×#125	C₂³	1	4	yes	—
71	C₁₃×#124	C₂³	1	4	yes	—
72	C₁₃×#124	C₂³	1	4	yes	—
73	C₁₃×#123	—	2	16	no	—
74	C₁₃×#123	—	2	8	no	—
75	C₁₃×C₂²⋊Q₈	—	2	8	no	—
76	C₁₃×#121	—	2	4	no	—
77	C₁₃×#121	—	2	4	no	—
78	C₁₃×#121	—	2	4	no	—
79	C₁₃×#121	—	2	8	no	—
80	C₁₃×#121	—	2	16	no	—
81	C₁₃×#121	C₂³	1	8	yes	—
82	C₁₃×#120	—	2	8	no	—
83	C₄×D₄×C₁₃	—	2	4	no	—
84	C₄×D₄×C₁₃	—	2	4	no	—
85	C₄×D₄×C₁₃	—	2	4	no	—
86	C₄×D₄×C₁₃	C₂³	1	8	yes	—
87	C₁₃×#117	D₄	1	4	yes	—
88	C₁₃×#117	C₂³	1	4	yes	—
89	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
90	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
95	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
98	C₁₃×#103	C₂³	1	16	yes	—
99	C₁₃×#102	C₂³	1	16	yes	—
100	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
101	C₁₃×#97	C₂³	1	4	yes	—
102	C₄×C₈×C₁₃	C₂³	1	4	yes	—
103	#60808	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₂⁴×C₁₃	—	2	2	no	—
105	C₂⁴×C₁₃	—	2	2	no	—
106	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₁₃×#41	—	2	16	no	—
108	C₁₃×#41	—	4	8	no	—
109	C₁₃×#41	—	4	8	no	—
110	C₁₃×#41	—	4	8	no	—
111	C₂×Q₈×C₁₃	—	2	2	no	—
112	C₂×Q₈×C₁₃	—	4	4	no	—
113	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
114	C₂×D₄×C₁₃	—	2	4	no	—
115	C₂×D₄×C₁₃	—	2	4	no	—
116	C₂×D₄×C₁₃	—	2	8	no	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	—	2	4	no	—
120	C₂×D₄×C₁₃	—	2	4	no	—
121	C₂×D₄×C₁₃	—	2	8	no	—
122	C₂×D₄×C₁₃	—	2	8	no	—
123	C₂×D₄×C₁₃	—	4	4	no	—
124	C₂×D₄×C₁₃	—	4	8	no	—
125	C₂×D₄×C₁₃	—	8	4	no	—
126	C₂×D₄×C₁₃	—	8	4	no	—
127	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
128	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
129	C₂²×C₄×C₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	4	no	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	2	8	no	—
135	C₂²×C₄×C₁₃	—	4	8	no	—
136	C₂²×C₄×C₁₃	—	8	4	no	—
137	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₁₃×SD₁₆	—	4	16	no	—
144	C₁₃×D₈	—	4	16	no	—
145	C₁₃×M₁₆	—	2	8	no	—
146	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
147	C₁₃×C₄⋊C₄	—	2	8	no	—
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	2	4	no	—
150	C₁₃×C₄⋊C₄	—	2	4	no	—
151	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
152	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
153	C₁₃×C₂²⋊C₄	—	2	8	no	—
154	C₁₃×C₂²⋊C₄	—	2	8	no	—
155	C₁₃×C₂²⋊C₄	—	2	8	no	—
156	C₁₃×C₂²⋊C₄	—	2	8	no	—
157	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
158	C₄²×C₁₃	C₂×D₄	1	2	yes	—
159	C₄²×C₁₃	C₂×D₄	1	2	yes	—
160	C₄²×C₁₃	C₂⁴	1	2	yes	—
161	C₄²×C₁₃	C₂⁴	1	2	yes	—
162	C₂×#540	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#3449	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#3221	C₂×C₁₃	1	8	yes	complemented
165	#3220	C₂×C₁₃	1	8	yes	complemented
166	#3151	C₂×C₁₃	1	2	yes	complemented
167	#3142	C₂×C₁₃	1	2	yes	complemented
168	#3036	C₂×C₁₃	1	4	yes	complemented
169	#3006	C₂×C₁₃	1	4	yes	complemented
170	#2921	C₂×C₁₃	1	1	yes	characteristic, complemented
171	C₂³×C₁₃	—	2	2	no	—
172	C₂³×C₁₃	—	2	4	no	—
173	C₂³×C₁₃	—	2	4	no	—
174	C₂³×C₁₃	—	4	2	no	—
175	C₂³×C₁₃	—	4	4	no	—
176	C₂³×C₁₃	—	4	4	no	—
177	C₂³×C₁₃	—	4	4	no	—
178	C₂³×C₁₃	—	4	4	no	—
179	C₂³×C₁₃	—	8	4	no	—
180	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
181	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₁₃	—	2	8	no	—
183	Q₈×C₁₃	—	4	4	no	—
184	D₄×C₁₃	—	2	8	no	—
185	D₄×C₁₃	—	2	8	no	—
186	D₄×C₁₃	—	4	4	no	—
187	D₄×C₁₃	—	4	8	no	—
188	D₄×C₁₃	—	4	8	no	—
189	D₄×C₁₃	—	4	4	no	—
190	D₄×C₁₃	—	8	4	no	—
191	D₄×C₁₃	—	8	4	no	—
192	D₄×C₁₃	—	8	8	no	—
193	D₄×C₁₃	—	8	8	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	4	no	—
197	C₂×C₄×C₁₃	—	2	4	no	—
198	C₂×C₄×C₁₃	—	2	4	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	8	no	—
202	C₂×C₄×C₁₃	—	4	4	no	—
203	C₂×C₄×C₁₃	—	4	4	no	—
204	C₂×C₄×C₁₃	—	4	8	no	—
205	C₂×C₄×C₁₃	—	8	8	no	—
206	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
207	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
208	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
209	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
211	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
212	C₈×C₁₃	—	2	8	no	—
213	C₂²×#41	C₂²×C₁₃	1	2	yes	—
214	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	8	yes	complemented
215	#540	—	2	4	no	—
216	#540	C₂²×C₁₃	1	8	yes	complemented
217	#537	—	2	2	no	—
218	#536	C₂²×C₁₃	1	4	yes	complemented
219	#535	C₂²×C₁₃	1	4	yes	complemented
220	#534	—	2	2	no	—
221	#532	C₂²×C₁₃	1	2	yes	—
222	#532	C₂²×C₁₃	1	2	yes	—
223	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
224	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
225	#525	—	2	4	no	—
226	C₂×#123	—	2	2	no	—
227	C₂×#121	—	2	2	no	—
228	C₂×#121	C₂²×C₁₃	1	2	yes	—
229	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
230	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
231	#496	C₂²×C₁₃	1	8	yes	complemented
232	#493	C₂²×C₁₃	1	4	yes	complemented
233	#492	C₂²×C₁₃	1	4	yes	complemented
234	#491	C₂²×C₁₃	1	4	yes	complemented
235	#490	C₂²×C₁₃	1	4	yes	complemented
236	#488	C₂²×C₁₃	1	8	yes	complemented
237	#463	C₂²×C₁₃	1	16	yes	complemented
238	#461	C₂²×C₁₃	1	8	yes	complemented
239	#459	C₂²×C₁₃	1	8	yes	complemented
240	#449	C₂²×C₁₃	1	16	yes	complemented
241	#448	C₂²×C₁₃	1	8	yes	complemented
242	#447	C₂²×C₁₃	1	8	yes	complemented
243	#433	C₂²×C₁₃	1	8	yes	complemented
244	#423	C₂²×C₁₃	1	2	yes	complemented
245	#417	C₂²×C₁₃	1	8	yes	complemented
246	#407	C₂²×C₁₃	1	2	yes	—
247	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
248	C₂²×C₁₃	—	2	2	no	—
249	C₂²×C₁₃	—	2	4	no	—
250	C₂²×C₁₃	—	2	2	no	—
251	C₂²×C₁₃	—	4	4	no	—
252	C₂²×C₁₃	—	4	4	no	—
253	C₂²×C₁₃	—	4	8	no	—
254	C₂²×C₁₃	—	4	4	no	—
255	C₂²×C₁₃	—	4	4	no	—
256	C₂²×C₁₃	—	8	2	no	—
257	C₂²×C₁₃	—	8	8	no	—
258	C₂²×C₁₃	—	8	8	no	—
259	C₂²×C₁₃	#535	1	2	yes	—
260	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
261	C₄×C₁₃	—	2	4	no	—
262	C₄×C₁₃	—	2	4	no	—
263	C₄×C₁₃	—	2	2	no	—
264	C₄×C₁₃	—	4	4	no	—
265	C₄×C₁₃	—	4	4	no	—
266	C₄×C₁₃	#535	1	2	yes	—
267	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
268	C₂×#41	—	2	2	no	—
269	C₂×#41	—	2	2	no	—
270	C₂×#41	—	4	8	no	—
271	C₂×#41	C₂³×C₁₃	1	4	yes	—
272	C₂×#41	C₂³×C₁₃	1	4	yes	—
273	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
274	C₂²×D₄	—	2	2	no	—
275	C₂²×D₄	—	2	2	no	—
276	C₂²×D₄	—	2	2	no	—
277	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
278	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
279	C₂³×C₄	—	2	2	no	—
280	C₂³×C₄	—	2	2	no	—
281	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
282	AGL(1,ℤ/8)	—	4	16	no	—
283	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
284	C₂×D₈	C₂³×C₁₃	1	16	yes	—
285	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
286	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
287	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
288	#127	—	2	2	no	—
289	#127	C₂³×C₁₃	1	4	yes	—
290	#127	C₂³×C₁₃	1	2	yes	—
291	#127	C₂³×C₁₃	1	2	yes	—
292	#125	—	2	2	no	—
293	#125	C₂³×C₁₃	1	4	yes	—
294	#124	C₂³×C₁₃	1	4	yes	—
295	#124	C₂³×C₁₃	1	4	yes	—
296	#123	—	2	16	no	—
297	#123	—	2	8	no	—
298	C₂²⋊Q₈	—	2	8	no	—
299	#121	—	2	4	no	—
300	#121	—	2	4	no	—
301	#121	—	2	4	no	—
302	#121	—	2	8	no	—
303	#121	—	2	16	no	—
304	#121	C₂³×C₁₃	1	8	yes	—
305	#120	—	2	8	no	—
306	C₄×D₄	—	2	4	no	—
307	C₄×D₄	—	2	4	no	—
308	C₄×D₄	—	2	4	no	—
309	C₄×D₄	C₂³×C₁₃	1	8	yes	—
310	#117	D₄×C₁₃	1	4	yes	—
311	#117	C₂³×C₁₃	1	4	yes	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
314	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
318	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
320	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
321	#103	C₂³×C₁₃	1	16	yes	—
322	#102	C₂³×C₁₃	1	16	yes	—
323	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
324	#97	C₂³×C₁₃	1	4	yes	—
325	C₄×C₈	C₂³×C₁₃	1	4	yes	—
326	C₂×C₁₃	—	2	2	no	—
327	C₂×C₁₃	—	4	2	no	—
328	C₂×C₁₃	—	8	4	no	—
329	C₂×C₁₃	—	8	4	no	—
330	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
331	C₂×C₁₃	#3585	1	2	yes	—
332	C₂⁴	—	2	2	no	—
333	C₂⁴	—	2	2	no	—
334	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
335	#41	—	2	16	no	—
336	#41	—	4	8	no	—
337	#41	—	4	8	no	—
338	#41	—	4	8	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	4	4	no	—
341	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	2	8	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	8	no	—
350	C₂×D₄	—	2	8	no	—
351	C₂×D₄	—	4	4	no	—
352	C₂×D₄	—	4	8	no	—
353	C₂×D₄	—	8	4	no	—
354	C₂×D₄	—	8	4	no	—
355	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
356	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	4	8	no	—
364	C₂²×C₄	—	8	4	no	—
365	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
369	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
370	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
371	SD₁₆	—	4	16	no	—
372	D₈	—	4	16	no	—
373	M₁₆	—	2	8	no	—
374	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
380	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	2	8	no	—
383	C₂²⋊C₄	—	2	8	no	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
386	C₄²	C₂×D₄×C₁₃	1	2	yes	—
387	C₄²	C₂×D₄×C₁₃	1	2	yes	—
388	C₄²	C₂⁴×C₁₃	1	2	yes	—
389	C₄²	C₂⁴×C₁₃	1	2	yes	—
390	C₁₃	#60808	1	1	yes	characteristic, direct product factor, Sylow
391	C₂³	—	2	2	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	2	4	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	4	no	—
396	C₂³	—	4	4	no	—
397	C₂³	—	4	4	no	—
398	C₂³	—	4	4	no	—
399	C₂³	—	8	4	no	—
400	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
401	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
402	Q₈	—	2	8	no	—
403	Q₈	—	4	4	no	—
404	D₄	—	2	8	no	—
405	D₄	—	2	8	no	—
406	D₄	—	4	4	no	—
407	D₄	—	4	8	no	—
408	D₄	—	4	8	no	—
409	D₄	—	4	4	no	—
410	D₄	—	8	8	no	—
411	D₄	—	8	4	no	—
412	D₄	—	8	4	no	—
413	D₄	—	8	8	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	8	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	8	no	—
425	C₂×C₄	—	8	8	no	—
426	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
427	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
428	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
429	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
430	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
431	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
432	C₈	—	2	8	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	8	no	—
439	C₂²	—	4	4	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	8	2	no	—
442	C₂²	—	8	8	no	—
443	C₂²	—	8	8	no	—
444	C₂²	C₁₃×#535	1	2	yes	—
445	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
446	C₄	—	2	4	no	—
447	C₄	—	2	4	no	—
448	C₄	—	2	2	no	—
449	C₄	—	4	4	no	—
450	C₄	—	4	4	no	—
451	C₄	C₁₃×#535	1	2	yes	—
452	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
453	C₂	—	2	2	no	—
454	C₂	—	4	2	no	—
455	C₂	—	8	4	no	—
456	C₂	—	8	4	no	—
457	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
458	C₂	C₁₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#540	C₂	semidirect
2. C₁₃×#3449	C₂	semidirect
3. C₁₃×#3221	C₂	semidirect
4. C₁₃×#3220	C₂	semidirect
5. C₁₃×#3151	C₂	semidirect
6. C₁₃×#3142	C₂	semidirect
7. C₁₃×#3036	C₂	semidirect
8. C₁₃×#3006	C₂	semidirect
9. C₁₃×#2921	C₂	semidirect
11. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
13. C₁₃×#540	C₂²	semidirect
15. C₁₃×#536	C₂²	semidirect
16. C₁₃×#535	C₂²	semidirect
20. C₂×C₁₃×#127	C₂²	semidirect
21. C₂×C₁₃×#125	C₂²	semidirect
26. C₂×C₄×D₄×C₁₃	C₂²	semidirect
28. C₁₃×#496	C₂²	semidirect
29. C₁₃×#493	C₂²	semidirect
30. C₁₃×#492	C₂²	semidirect
31. C₁₃×#491	C₂²	semidirect
32. C₁₃×#490	C₂²	semidirect
33. C₁₃×#488	C₂²	semidirect
34. C₁₃×#463	C₂²	semidirect
35. C₁₃×#461	C₂²	semidirect
36. C₁₃×#459	C₂²	semidirect
37. C₁₃×#449	C₂²	semidirect
38. C₁₃×#448	C₂²	semidirect
39. C₁₃×#447	C₂²	semidirect
40. C₁₃×#433	C₂²	semidirect
41. C₁₃×#423	C₂²	semidirect
42. C₁₃×#417	C₂²	semidirect
44. C₄×C₁₃×M₁₆	C₂²	semidirect
103. #60808	C₁₃	direct (N × H)
162. C₂×#540	C₂×C₁₃	semidirect
163. #3449	C₂×C₁₃	semidirect
164. #3221	C₂×C₁₃	semidirect
165. #3220	C₂×C₁₃	semidirect
166. #3151	C₂×C₁₃	semidirect
167. #3142	C₂×C₁₃	semidirect
168. #3036	C₂×C₁₃	semidirect
169. #3006	C₂×C₁₃	semidirect
170. #2921	C₂×C₁₃	semidirect
214. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
216. #540	C₂²×C₁₃	semidirect
218. #536	C₂²×C₁₃	semidirect
219. #535	C₂²×C₁₃	semidirect
223. C₂×#127	C₂²×C₁₃	semidirect
224. C₂×#125	C₂²×C₁₃	semidirect
229. C₂×C₄×D₄	C₂²×C₁₃	semidirect
231. #496	C₂²×C₁₃	semidirect
232. #493	C₂²×C₁₃	semidirect
233. #492	C₂²×C₁₃	semidirect
234. #491	C₂²×C₁₃	semidirect
235. #490	C₂²×C₁₃	semidirect
236. #488	C₂²×C₁₃	semidirect
237. #463	C₂²×C₁₃	semidirect
238. #461	C₂²×C₁₃	semidirect
239. #459	C₂²×C₁₃	semidirect
240. #449	C₂²×C₁₃	semidirect
241. #448	C₂²×C₁₃	semidirect
242. #447	C₂²×C₁₃	semidirect
243. #433	C₂²×C₁₃	semidirect
244. #423	C₂²×C₁₃	semidirect
245. #417	C₂²×C₁₃	semidirect
247. C₄×M₁₆	C₂²×C₁₃	semidirect
390. C₁₃	#60808	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×#540	2
C₁₃×#3449	2
C₁₃×#3221	2
C₁₃×#3220	2
C₁₃×#3151	2
C₁₃×#3142	2
C₁₃×#3036	2
C₁₃×#3006	2
C₁₃×#2921	2
#60808	13

Subgroups — C13×#60808 #15747147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60808 #15747147