Subgroups — C₁₃×#61408 #15747747

Order 3328.

1858 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3507	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3402	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3400	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3396	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3395	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3393	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3156	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#3046	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3037	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2951	C₂	1	2	yes	maximal, complemented
13	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#137	C₂²	1	4	yes	—
15	C₂×C₁₃×#135	C₂²	1	2	yes	—
16	C₂×C₁₃×#135	C₂²	1	2	yes	—
17	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
18	C₁₃×#559	C₂²	1	4	yes	—
19	C₁₃×#557	C₂²	1	4	yes	—
20	C₁₃×#556	—	2	2	no	—
21	C₁₃×#556	C₂²	1	8	yes	—
22	C₁₃×#554	—	2	2	no	—
23	C₁₃×#552	—	2	4	no	—
24	C₁₃×#539	—	2	4	no	—
25	C₁₃×#536	C₂²	1	4	yes	—
26	C₁₃×#533	C₂²	1	1	yes	characteristic
27	C₁₃×#532	C₂²	1	2	yes	—
28	C₁₃×#529	—	2	4	no	—
29	C₁₃×#520	C₂²	1	4	yes	—
30	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
31	C₁₃×#497	C₂²	1	8	yes	—
32	C₁₃×#495	C₂²	1	2	yes	—
33	C₁₃×#495	C₂²	1	4	yes	—
34	C₁₃×#495	C₂²	1	2	yes	—
35	C₁₃×#494	C₂²	1	4	yes	—
36	C₁₃×#494	C₂²	1	1	yes	characteristic
37	C₁₃×#493	C₂²	1	1	yes	characteristic
38	C₁₃×#492	C₂²	1	2	yes	—
39	C₁₃×#464	C₂²	1	8	yes	—
40	C₁₃×#464	C₂²	1	8	yes	—
41	C₁₃×#463	C₂²	1	8	yes	—
42	C₁₃×#462	C₂²	1	4	yes	—
43	C₁₃×#462	C₂²	1	8	yes	—
44	C₁₃×#461	C₂²	1	8	yes	—
45	C₁₃×#460	C₂²	1	4	yes	—
46	C₁₃×#446	C₂²	1	2	yes	—
47	C₁₃×#446	C₂²	1	2	yes	—
48	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
49	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
50	C₁₃×#440	C₂²	1	8	yes	—
51	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
52	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
53	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
54	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
55	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
56	C₄×C₁₃×D₈	C₂²	1	4	yes	—
57	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
58	C₁₃×#424	C₂²	1	2	yes	—
59	C₁₃×#423	C₂²	1	1	yes	characteristic
60	C₁₃×#417	C₂²	1	4	yes	—
61	C₂×C₁₃×#103	C₂²	1	2	yes	—
62	C₁₃×#405	C₂²	1	2	yes	—
63	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
64	C₂×C₁₃×#41	C₂³	1	4	yes	—
65	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
66	C₁₃×#137	—	4	8	no	—
67	C₁₃×#135	—	2	8	no	—
68	C₁₃×#135	—	4	4	no	—
69	C₂×C₁₃×Q₁₆	—	2	4	no	—
70	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
71	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
72	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
73	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
74	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
75	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
76	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
77	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
78	C₂×C₁₃×D₈	C₂³	1	2	yes	—
79	C₂×C₁₃×D₈	C₂³	1	2	yes	—
80	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
84	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
85	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
86	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
87	C₁₃×#127	C₂³	1	2	yes	—
88	C₁₃×#126	—	2	8	no	—
89	C₁₃×#126	—	2	8	no	—
90	C₁₃×#125	—	2	4	no	—
91	C₁₃×#125	—	2	8	no	—
92	C₁₃×#125	D₄	1	2	yes	—
93	C₁₃×#124	—	2	4	no	—
94	C₁₃×#124	C₂³	1	8	yes	—
95	C₁₃×#124	C₂³	1	4	yes	—
96	C₁₃×#123	—	2	8	no	—
97	C₁₃×#123	—	2	8	no	—
98	C₁₃×C₂²⋊Q₈	—	2	8	no	—
99	C₁₃×C₂²⋊Q₈	—	2	4	no	—
100	C₁₃×C₂²⋊Q₈	—	2	4	no	—
101	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
102	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
103	C₁₃×#121	—	2	2	no	—
104	C₁₃×#121	—	2	2	no	—
105	C₄×Q₈×C₁₃	—	2	4	no	—
106	C₄×Q₈×C₁₃	—	2	2	no	—
107	C₄×Q₈×C₁₃	—	2	2	no	—
108	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
109	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
110	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
111	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
112	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
113	C₄×D₄×C₁₃	—	2	4	no	—
114	C₄×D₄×C₁₃	—	2	8	no	—
115	C₄×D₄×C₁₃	—	2	2	no	—
116	C₄×D₄×C₁₃	—	2	2	no	—
117	C₄×D₄×C₁₃	C₂³	1	8	yes	—
118	C₁₃×#117	—	2	4	no	—
119	C₁₃×#117	—	2	8	no	—
120	C₁₃×#117	C₂³	1	2	yes	—
121	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₃	—	2	2	no	—
125	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
126	C₁₃×#107	C₂³	1	2	yes	—
127	C₁₃×#107	C₂³	1	2	yes	—
128	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
129	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
130	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
131	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
132	C₁₃×#103	C₂³	1	4	yes	—
133	C₁₃×#103	C₂³	1	4	yes	—
134	C₁₃×#103	C₂³	1	8	yes	—
135	C₁₃×#102	C₂³	1	8	yes	—
136	C₁₃×#97	C₂³	1	4	yes	—
137	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
140	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
141	C₄×C₈×C₁₃	C₂³	1	4	yes	—
142	#61408	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₁₃×#41	—	2	8	no	—
144	C₁₃×#41	—	2	8	no	—
145	C₂×Q₈×C₁₃	—	2	2	no	—
146	C₂×Q₈×C₁₃	—	2	4	no	—
147	C₂×Q₈×C₁₃	—	2	4	no	—
148	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
149	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
150	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
151	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
152	C₂×D₄×C₁₃	—	2	4	no	—
153	C₂×D₄×C₁₃	—	2	2	no	—
154	C₂×D₄×C₁₃	—	2	2	no	—
155	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	4	no	—
159	C₂²×C₄×C₁₃	—	2	8	no	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₁₃×Q₁₆	—	2	4	no	—
164	C₁₃×Q₁₆	—	2	4	no	—
165	C₁₃×Q₁₆	—	2	4	no	—
166	C₁₃×Q₁₆	—	4	2	no	—
167	C₁₃×Q₁₆	—	4	8	no	—
168	C₁₃×SD₁₆	—	2	8	no	—
169	C₁₃×SD₁₆	—	4	4	no	—
170	C₁₃×SD₁₆	—	4	8	no	—
171	C₁₃×D₈	—	2	4	no	—
172	C₁₃×D₈	—	4	2	no	—
173	C₁₃×M₁₆	—	2	4	no	—
174	C₂×C₈×C₁₃	—	2	2	no	—
175	C₂×C₈×C₁₃	#41	1	4	yes	—
176	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
179	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
181	C₁₃×C₄⋊C₄	—	2	2	no	—
182	C₁₃×C₄⋊C₄	—	2	8	no	—
183	C₁₃×C₄⋊C₄	—	2	4	no	—
184	C₁₃×C₄⋊C₄	—	2	4	no	—
185	C₁₃×C₄⋊C₄	—	2	8	no	—
186	C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₁₃×C₄⋊C₄	—	2	8	no	—
189	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
190	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
191	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
192	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
193	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
194	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
195	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
196	C₁₃×C₂²⋊C₄	—	2	4	no	—
197	C₁₃×C₂²⋊C₄	—	2	8	no	—
198	C₁₃×C₂²⋊C₄	—	2	8	no	—
199	C₁₃×C₂²⋊C₄	—	2	4	no	—
200	C₁₃×C₂²⋊C₄	—	2	8	no	—
201	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
202	C₄²×C₁₃	—	2	4	no	—
203	C₄²×C₁₃	—	2	4	no	—
204	C₄²×C₁₃	—	2	8	no	—
205	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
208	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
209	C₄²×C₁₃	C₂⁴	1	4	yes	—
210	#3507	C₂×C₁₃	1	2	yes	complemented
211	#3402	C₂×C₁₃	1	4	yes	complemented
212	#3400	C₂×C₁₃	1	4	yes	complemented
213	#3396	C₂×C₁₃	1	2	yes	complemented
214	#3395	C₂×C₁₃	1	2	yes	complemented
215	#3393	C₂×C₁₃	1	4	yes	complemented
216	#3156	C₂×C₁₃	1	2	yes	complemented
217	#3147	C₂×C₁₃	1	1	yes	characteristic
218	#3046	C₂×C₁₃	1	4	yes	complemented
219	#3037	C₂×C₁₃	1	2	yes	complemented
220	#2960	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#2951	C₂×C₁₃	1	2	yes	complemented
222	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₂³×C₁₃	—	2	4	no	—
224	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
225	Q₈×C₁₃	—	2	4	no	—
226	Q₈×C₁₃	—	2	4	no	—
227	Q₈×C₁₃	—	2	4	no	—
228	Q₈×C₁₃	—	2	4	no	—
229	Q₈×C₁₃	—	2	4	no	—
230	Q₈×C₁₃	—	4	2	no	—
231	Q₈×C₁₃	—	4	4	no	—
232	D₄×C₁₃	—	2	4	no	—
233	D₄×C₁₃	—	2	4	no	—
234	D₄×C₁₃	—	4	8	no	—
235	D₄×C₁₃	—	4	4	no	—
236	D₄×C₁₃	—	8	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	4	1	no	—
242	C₂×C₄×C₁₃	—	4	4	no	—
243	C₂×C₄×C₁₃	—	4	8	no	—
244	C₂×C₄×C₁₃	—	8	8	no	—
245	C₂×C₄×C₁₃	—	8	2	no	—
246	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
248	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
251	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
254	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
255	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
256	C₈×C₁₃	—	2	1	no	—
257	C₈×C₁₃	—	2	1	no	—
258	C₈×C₁₃	—	2	4	no	—
259	C₈×C₁₃	C₂×#41	1	2	yes	—
260	C₈×C₁₃	C₂×#41	1	2	yes	—
261	C₂×#137	C₂²×C₁₃	1	4	yes	—
262	C₂×#135	C₂²×C₁₃	1	2	yes	—
263	C₂×#135	C₂²×C₁₃	1	2	yes	—
264	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
265	#559	C₂²×C₁₃	1	4	yes	—
266	#557	C₂²×C₁₃	1	4	yes	—
267	#556	—	2	2	no	—
268	#556	C₂²×C₁₃	1	8	yes	—
269	#554	—	2	2	no	—
270	#552	—	2	4	no	—
271	#539	—	2	4	no	—
272	#536	C₂²×C₁₃	1	4	yes	—
273	#533	C₂²×C₁₃	1	1	yes	characteristic
274	#532	C₂²×C₁₃	1	2	yes	—
275	#529	—	2	4	no	—
276	#520	C₂²×C₁₃	1	4	yes	—
277	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
278	#497	C₂²×C₁₃	1	8	yes	—
279	#495	C₂²×C₁₃	1	2	yes	—
280	#495	C₂²×C₁₃	1	4	yes	—
281	#495	C₂²×C₁₃	1	2	yes	—
282	#494	C₂²×C₁₃	1	4	yes	—
283	#494	C₂²×C₁₃	1	1	yes	characteristic
284	#493	C₂²×C₁₃	1	1	yes	characteristic
285	#492	C₂²×C₁₃	1	2	yes	—
286	#464	C₂²×C₁₃	1	8	yes	—
287	#464	C₂²×C₁₃	1	8	yes	—
288	#463	C₂²×C₁₃	1	8	yes	—
289	#462	C₂²×C₁₃	1	4	yes	—
290	#462	C₂²×C₁₃	1	8	yes	—
291	#461	C₂²×C₁₃	1	8	yes	—
292	#460	C₂²×C₁₃	1	4	yes	—
293	#446	C₂²×C₁₃	1	2	yes	—
294	#446	C₂²×C₁₃	1	2	yes	—
295	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
296	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
297	#440	C₂²×C₁₃	1	8	yes	—
298	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
299	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
300	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
301	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
302	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
303	C₄×D₈	C₂²×C₁₃	1	4	yes	—
304	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
305	#424	C₂²×C₁₃	1	2	yes	—
306	#423	C₂²×C₁₃	1	1	yes	characteristic
307	#417	C₂²×C₁₃	1	4	yes	—
308	C₂×#103	C₂²×C₁₃	1	2	yes	—
309	#405	C₂²×C₁₃	1	2	yes	—
310	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
311	C₂²×C₁₃	—	2	1	no	—
312	C₂²×C₁₃	—	2	1	no	—
313	C₂²×C₁₃	—	4	4	no	—
314	C₂²×C₁₃	—	4	4	no	—
315	C₂²×C₁₃	—	4	4	no	—
316	C₂²×C₁₃	#550	1	2	yes	—
317	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
318	C₄×C₁₃	—	2	1	no	—
319	C₄×C₁₃	—	2	1	no	—
320	C₄×C₁₃	—	2	4	no	—
321	C₄×C₁₃	—	2	1	no	—
322	C₄×C₁₃	—	2	4	no	—
323	C₄×C₁₃	—	4	4	no	—
324	C₄×C₁₃	—	4	4	no	—
325	C₄×C₁₃	—	4	4	no	—
326	C₄×C₁₃	#550	1	2	yes	—
327	C₄×C₁₃	#578	1	2	yes	—
328	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
329	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
330	C₂×#41	C₂³×C₁₃	1	4	yes	—
331	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
332	#137	—	4	8	no	—
333	#135	—	2	8	no	—
334	#135	—	4	4	no	—
335	C₂×Q₁₆	—	2	4	no	—
336	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
337	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
338	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
339	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
340	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
341	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
342	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
343	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
344	C₂×D₈	C₂³×C₁₃	1	2	yes	—
345	C₂×D₈	C₂³×C₁₃	1	2	yes	—
346	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
347	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
348	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
349	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
350	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
351	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
352	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
353	#127	C₂³×C₁₃	1	2	yes	—
354	#126	—	2	8	no	—
355	#126	—	2	8	no	—
356	#125	—	2	4	no	—
357	#125	—	2	8	no	—
358	#125	D₄×C₁₃	1	2	yes	—
359	#124	—	2	4	no	—
360	#124	C₂³×C₁₃	1	4	yes	—
361	#124	C₂³×C₁₃	1	8	yes	—
362	#123	—	2	8	no	—
363	#123	—	2	8	no	—
364	C₂²⋊Q₈	—	2	8	no	—
365	C₂²⋊Q₈	—	2	4	no	—
366	C₂²⋊Q₈	—	2	4	no	—
367	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
368	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
369	#121	—	2	2	no	—
370	#121	—	2	2	no	—
371	C₄×Q₈	—	2	4	no	—
372	C₄×Q₈	—	2	2	no	—
373	C₄×Q₈	—	2	2	no	—
374	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
375	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
376	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
377	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
378	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
379	C₄×D₄	—	2	4	no	—
380	C₄×D₄	—	2	8	no	—
381	C₄×D₄	—	2	2	no	—
382	C₄×D₄	—	2	2	no	—
383	C₄×D₄	C₂³×C₁₃	1	8	yes	—
384	#117	—	2	4	no	—
385	#117	—	2	8	no	—
386	#117	C₂³×C₁₃	1	2	yes	—
387	C₂×C₄⋊C₄	—	2	2	no	—
388	C₂×C₄⋊C₄	—	2	4	no	—
389	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
390	C₂×C₄²	—	2	2	no	—
391	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
392	#107	C₂³×C₁₃	1	2	yes	—
393	#107	C₂³×C₁₃	1	2	yes	—
394	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
395	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
396	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
397	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
398	#103	C₂³×C₁₃	1	4	yes	—
399	#103	C₂³×C₁₃	1	4	yes	—
400	#103	C₂³×C₁₃	1	8	yes	—
401	#102	C₂³×C₁₃	1	8	yes	—
402	#97	C₂³×C₁₃	1	4	yes	—
403	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
404	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
405	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
406	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
407	C₄×C₈	C₂³×C₁₃	1	4	yes	—
408	C₂×C₁₃	—	2	2	no	—
409	C₂×C₁₃	—	8	4	no	—
410	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
411	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
412	C₂×C₁₃	#3584	1	1	yes	characteristic
413	#41	—	2	8	no	—
414	#41	—	2	8	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	4	no	—
417	C₂×Q₈	—	2	4	no	—
418	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
419	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
420	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
421	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	8	no	—
430	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
432	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
433	Q₁₆	—	2	4	no	—
434	Q₁₆	—	2	4	no	—
435	Q₁₆	—	2	4	no	—
436	Q₁₆	—	4	2	no	—
437	Q₁₆	—	4	8	no	—
438	SD₁₆	—	2	8	no	—
439	SD₁₆	—	4	4	no	—
440	SD₁₆	—	4	8	no	—
441	D₈	—	2	4	no	—
442	D₈	—	4	2	no	—
443	M₁₆	—	2	4	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	C₁₃×#41	1	4	yes	—
446	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
447	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
448	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
449	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
450	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	8	no	—
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	8	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	8	no	—
459	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
460	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
461	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
462	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
463	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
464	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
465	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	8	no	—
468	C₂²⋊C₄	—	2	8	no	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	2	8	no	—
471	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
472	C₄²	—	2	4	no	—
473	C₄²	—	2	4	no	—
474	C₄²	—	2	8	no	—
475	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
478	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
479	C₄²	C₂⁴×C₁₃	1	4	yes	—
480	C₁₃	#61408	1	1	yes	characteristic, direct product factor, Sylow
481	C₂³	—	2	4	no	—
482	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
483	Q₈	—	2	4	no	—
484	Q₈	—	2	4	no	—
485	Q₈	—	2	4	no	—
486	Q₈	—	2	4	no	—
487	Q₈	—	2	4	no	—
488	Q₈	—	4	2	no	—
489	Q₈	—	4	4	no	—
490	D₄	—	2	4	no	—
491	D₄	—	2	4	no	—
492	D₄	—	4	8	no	—
493	D₄	—	4	4	no	—
494	D₄	—	8	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	4	no	—
501	C₂×C₄	—	4	8	no	—
502	C₂×C₄	—	8	8	no	—
503	C₂×C₄	—	8	2	no	—
504	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
505	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
506	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
507	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
508	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
509	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
510	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
511	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
512	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
513	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
514	C₈	—	2	1	no	—
515	C₈	—	2	1	no	—
516	C₈	—	2	4	no	—
517	C₈	C₂×C₁₃×#41	1	2	yes	—
518	C₈	C₂×C₁₃×#41	1	2	yes	—
519	C₂²	—	2	1	no	—
520	C₂²	—	2	1	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	4	4	no	—
523	C₂²	—	4	4	no	—
524	C₂²	C₁₃×#550	1	2	yes	—
525	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
526	C₄	—	2	1	no	—
527	C₄	—	2	4	no	—
528	C₄	—	2	1	no	—
529	C₄	—	2	1	no	—
530	C₄	—	2	4	no	—
531	C₄	—	4	4	no	—
532	C₄	—	4	4	no	—
533	C₄	—	4	4	no	—
534	C₄	C₁₃×#550	1	2	yes	—
535	C₄	C₁₃×#578	1	2	yes	—
536	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
537	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
538	C₂	—	2	2	no	—
539	C₂	—	8	4	no	—
540	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
541	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
542	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3147	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3507	C₂	semidirect
2. C₁₃×#3402	C₂	semidirect
3. C₁₃×#3400	C₂	semidirect
4. C₁₃×#3396	C₂	semidirect
5. C₁₃×#3395	C₂	semidirect
6. C₁₃×#3393	C₂	semidirect
7. C₁₃×#3156	C₂	semidirect
9. C₁₃×#3046	C₂	semidirect
10. C₁₃×#3037	C₂	semidirect
11. C₁₃×#2960	C₂	semidirect
12. C₁₃×#2951	C₂	semidirect
13. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
142. #61408	C₁₃	direct (N × H)
210. #3507	C₂×C₁₃	semidirect
211. #3402	C₂×C₁₃	semidirect
212. #3400	C₂×C₁₃	semidirect
213. #3396	C₂×C₁₃	semidirect
214. #3395	C₂×C₁₃	semidirect
215. #3393	C₂×C₁₃	semidirect
216. #3156	C₂×C₁₃	semidirect
218. #3046	C₂×C₁₃	semidirect
219. #3037	C₂×C₁₃	semidirect
220. #2960	C₂×C₁₃	semidirect
221. #2951	C₂×C₁₃	semidirect
222. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
480. C₁₃	#61408	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3507	2
C₁₃×#3402	2
C₁₃×#3400	2
C₁₃×#3396	2
C₁₃×#3395	2
C₁₃×#3393	2
C₁₃×#3156	2
C₁₃×#3147	2
C₁₃×#3046	2
C₁₃×#3037	2
C₁₃×#2960	2
C₁₃×#2951	2
C₂×C₄×C₁₃×Q₁₆	2
#61408	13

Subgroups — C13×#61408 #15747747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61408 #15747747