Subgroups — C₁₃×#3546 #13112604

Order 1664.

1150 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#560	C₂	1	4	yes	maximal, complemented
2	C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#553	C₂	1	2	yes	maximal, complemented
4	C₁₃×#550	C₂	1	2	yes	maximal, complemented
5	C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#546	C₂	1	2	yes	maximal, complemented
8	C₁₃×#546	C₂	1	2	yes	maximal, complemented
9	D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#542	C₂	1	2	yes	maximal, complemented
11	C₁₃×#538	C₂	1	4	yes	maximal, complemented
12	C₁₃×#537	C₂	1	2	yes	maximal, complemented
13	C₁₃×#535	C₂	1	2	yes	maximal, complemented
14	C₁₃×#535	C₂	1	2	yes	maximal, complemented
15	C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#41	C₂²	1	2	yes	complemented
19	C₂×C₁₃×#41	C₂²	1	2	yes	complemented
20	C₂×C₁₃×#41	C₂²	1	2	yes	complemented
21	C₂×C₁₃×#41	C₂²	1	2	yes	complemented
22	C₂²×D₄×C₁₃	C₂²	1	2	yes	—
23	C₂²×D₄×C₁₃	C₂²	1	2	yes	—
24	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×#127	C₂²	1	1	yes	characteristic
27	C₁₃×#127	C₂²	1	1	yes	characteristic
28	C₁₃×#127	C₂²	1	2	yes	complemented
29	C₁₃×#127	C₂²	1	4	yes	complemented
30	C₁₃×#126	C₂²	1	2	yes	complemented
31	C₁₃×#126	C₂²	1	4	yes	complemented
32	C₁₃×#126	C₂²	1	4	yes	complemented
33	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#124	C₂²	1	1	yes	characteristic
35	C₁₃×#124	C₂²	1	2	yes	—
36	C₁₃×#124	C₂²	1	2	yes	complemented
37	C₁₃×#124	C₂²	1	2	yes	complemented
38	C₁₃×#124	C₂²	1	4	yes	complemented
39	C₁₃×#123	C₂²	1	2	yes	complemented
40	C₁₃×#123	C₂²	1	4	yes	complemented
41	C₁₃×#123	C₂²	1	4	yes	complemented
42	C₁₃×#123	C₂²	1	4	yes	complemented
43	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
45	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
46	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
47	C₁₃×#121	C₂²	1	1	yes	characteristic
48	C₁₃×#121	C₂²	1	1	yes	characteristic
49	C₁₃×#121	C₂²	1	2	yes	—
50	C₁₃×#121	C₂²	1	2	yes	—
51	C₁₃×#121	C₂²	1	2	yes	—
52	C₁₃×#121	C₂²	1	2	yes	complemented
53	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#121	C₂²	1	2	yes	complemented
55	C₁₃×#121	C₂²	1	2	yes	complemented
56	C₁₃×#121	C₂²	1	4	yes	complemented
57	C₁₃×#121	C₂²	1	2	yes	complemented
58	C₁₃×#121	C₂²	1	4	yes	complemented
59	C₁₃×#121	C₂²	1	4	yes	complemented
60	C₁₃×#121	C₂²	1	4	yes	complemented
61	C₁₃×#121	C₂²	1	4	yes	complemented
62	C₁₃×#121	C₂²	1	4	yes	complemented
63	C₁₃×#120	C₂²	1	4	yes	—
64	C₁₃×#120	C₂²	1	4	yes	complemented
65	C₁₃×#120	C₂²	1	4	yes	complemented
66	C₁₃×#120	C₂²	1	4	yes	complemented
67	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
68	C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
69	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
70	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
71	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
72	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
73	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
74	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
75	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
76	C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
77	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
78	C₁₃×#117	C₂²	1	2	yes	complemented
79	C₁₃×#117	C₂²	1	2	yes	complemented
80	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
81	C₂×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
82	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
83	C₂⁴×C₁₃	C₂³	1	4	yes	—
84	C₁₃×#41	—	4	4	no	—
85	C₁₃×#41	—	4	4	no	—
86	C₁₃×#41	—	4	4	no	—
87	C₁₃×#41	—	4	4	no	—
88	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
90	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
91	C₂×D₄×C₁₃	—	4	4	no	—
92	C₂×D₄×C₁₃	—	4	4	no	—
93	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂×D₄×C₁₃	C₂³	1	2	yes	—
96	C₂×D₄×C₁₃	C₂³	1	2	yes	—
97	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×D₄×C₁₃	C₂³	1	2	yes	—
99	C₂×D₄×C₁₃	C₂³	1	2	yes	—
100	C₂×D₄×C₁₃	C₂³	1	2	yes	—
101	C₂×D₄×C₁₃	C₂³	1	4	yes	—
102	C₂×D₄×C₁₃	C₂³	1	4	yes	—
103	C₂×D₄×C₁₃	C₂³	1	4	yes	—
104	C₂×D₄×C₁₃	C₂³	1	2	yes	—
105	C₂×D₄×C₁₃	C₂³	1	4	yes	—
106	C₂×D₄×C₁₃	C₂³	1	2	yes	—
107	C₂×D₄×C₁₃	C₂³	1	4	yes	—
108	C₂×D₄×C₁₃	C₂³	1	4	yes	—
109	C₂×D₄×C₁₃	C₂³	1	2	yes	—
110	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
117	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
118	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
119	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
122	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
123	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
126	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
131	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
133	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
134	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
137	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
144	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
145	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₄²×C₁₃	C₂³	1	1	yes	characteristic
149	C₄²×C₁₃	C₂³	1	1	yes	characteristic
150	C₄²×C₁₃	C₂³	1	1	yes	characteristic
151	C₄²×C₁₃	C₂³	1	1	yes	characteristic
152	C₄²×C₁₃	C₂³	1	2	yes	—
153	C₄²×C₁₃	C₂³	1	4	yes	—
154	#3546	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂³×C₁₃	—	4	4	no	—
156	C₂³×C₁₃	—	4	4	no	—
157	C₂³×C₁₃	—	4	4	no	—
158	C₂³×C₁₃	C₂⁴	1	2	yes	—
159	C₂³×C₁₃	C₂⁴	1	2	yes	—
160	C₂³×C₁₃	C₂⁴	1	4	yes	—
161	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
162	C₂³×C₁₃	C₂⁴	1	2	yes	—
163	Q₈×C₁₃	—	2	2	no	—
164	Q₈×C₁₃	—	2	4	no	—
165	Q₈×C₁₃	—	4	2	no	—
166	D₄×C₁₃	—	2	2	no	—
167	D₄×C₁₃	—	2	2	no	—
168	D₄×C₁₃	—	2	4	no	—
169	D₄×C₁₃	—	2	4	no	—
170	D₄×C₁₃	—	2	2	no	—
171	D₄×C₁₃	—	4	4	no	—
172	D₄×C₁₃	—	4	4	no	—
173	D₄×C₁₃	—	4	2	no	—
174	D₄×C₁₃	—	4	2	no	—
175	D₄×C₁₃	—	4	2	no	—
176	D₄×C₁₃	—	4	4	no	—
177	D₄×C₁₃	—	4	2	no	—
178	D₄×C₁₃	—	4	2	no	—
179	D₄×C₁₃	—	4	2	no	—
180	D₄×C₁₃	—	4	4	no	—
181	D₄×C₁₃	—	4	4	no	—
182	D₄×C₁₃	—	4	4	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	4	no	—
190	C₂×C₄×C₁₃	—	4	4	no	—
191	C₂×C₄×C₁₃	—	4	4	no	—
192	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
193	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
198	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
199	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
200	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
201	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
202	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
204	#560	C₂×C₁₃	1	4	yes	complemented
205	#556	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#553	C₂×C₁₃	1	2	yes	complemented
207	#550	C₂×C₁₃	1	2	yes	complemented
208	#550	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#547	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#546	C₂×C₁₃	1	2	yes	complemented
211	#546	C₂×C₁₃	1	2	yes	complemented
212	D₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#542	C₂×C₁₃	1	2	yes	complemented
214	#538	C₂×C₁₃	1	4	yes	complemented
215	#537	C₂×C₁₃	1	2	yes	complemented
216	#535	C₂×C₁₃	1	2	yes	complemented
217	#535	C₂×C₁₃	1	2	yes	complemented
218	#532	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#532	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#529	C₂×C₁₃	1	1	yes	characteristic, complemented
221	C₂²×C₁₃	—	2	1	no	—
222	C₂²×C₁₃	—	2	1	no	—
223	C₂²×C₁₃	—	2	2	no	—
224	C₂²×C₁₃	—	2	2	no	—
225	C₂²×C₁₃	—	2	2	no	—
226	C₂²×C₁₃	—	2	2	no	—
227	C₂²×C₁₃	—	2	4	no	—
228	C₂²×C₁₃	—	2	4	no	—
229	C₂²×C₁₃	—	2	2	no	—
230	C₂²×C₁₃	—	2	2	no	—
231	C₂²×C₁₃	—	2	1	no	—
232	C₂²×C₁₃	—	2	2	no	—
233	C₂²×C₁₃	—	2	4	no	—
234	C₂²×C₁₃	—	2	2	no	—
235	C₂²×C₁₃	—	2	2	no	—
236	C₂²×C₁₃	—	8	8	no	—
237	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
238	C₄×C₁₃	—	2	1	no	—
239	C₄×C₁₃	—	2	2	no	—
240	C₄×C₁₃	—	2	2	no	—
241	C₄×C₁₃	—	2	2	no	—
242	C₄×C₁₃	—	2	1	no	—
243	C₄×C₁₃	—	2	4	no	—
244	C₄×C₁₃	—	2	2	no	—
245	C₄×C₁₃	—	2	1	no	—
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	—	2	2	no	—
248	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
249	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
250	C₂×#41	C₂²×C₁₃	1	2	yes	complemented
251	C₂×#41	C₂²×C₁₃	1	2	yes	complemented
252	C₂×#41	C₂²×C₁₃	1	2	yes	complemented
253	C₂×#41	C₂²×C₁₃	1	2	yes	complemented
254	C₂²×D₄	C₂²×C₁₃	1	2	yes	—
255	C₂²×D₄	C₂²×C₁₃	1	2	yes	—
256	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
257	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
258	#127	C₂²×C₁₃	1	1	yes	characteristic
259	#127	C₂²×C₁₃	1	1	yes	characteristic
260	#127	C₂²×C₁₃	1	2	yes	complemented
261	#127	C₂²×C₁₃	1	4	yes	complemented
262	#126	C₂²×C₁₃	1	2	yes	complemented
263	#126	C₂²×C₁₃	1	4	yes	complemented
264	#126	C₂²×C₁₃	1	4	yes	complemented
265	#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
266	#124	C₂²×C₁₃	1	1	yes	characteristic
267	#124	C₂²×C₁₃	1	2	yes	—
268	#124	C₂²×C₁₃	1	2	yes	complemented
269	#124	C₂²×C₁₃	1	2	yes	complemented
270	#124	C₂²×C₁₃	1	4	yes	complemented
271	#123	C₂²×C₁₃	1	2	yes	complemented
272	#123	C₂²×C₁₃	1	4	yes	complemented
273	#123	C₂²×C₁₃	1	4	yes	complemented
274	#123	C₂²×C₁₃	1	4	yes	complemented
275	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
276	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
277	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
278	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
279	#121	C₂²×C₁₃	1	1	yes	characteristic
280	#121	C₂²×C₁₃	1	1	yes	characteristic
281	#121	C₂²×C₁₃	1	2	yes	—
282	#121	C₂²×C₁₃	1	2	yes	—
283	#121	C₂²×C₁₃	1	2	yes	—
284	#121	C₂²×C₁₃	1	2	yes	complemented
285	#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
286	#121	C₂²×C₁₃	1	2	yes	complemented
287	#121	C₂²×C₁₃	1	2	yes	complemented
288	#121	C₂²×C₁₃	1	4	yes	complemented
289	#121	C₂²×C₁₃	1	2	yes	complemented
290	#121	C₂²×C₁₃	1	4	yes	complemented
291	#121	C₂²×C₁₃	1	4	yes	complemented
292	#121	C₂²×C₁₃	1	4	yes	complemented
293	#121	C₂²×C₁₃	1	4	yes	complemented
294	#121	C₂²×C₁₃	1	4	yes	complemented
295	#120	C₂²×C₁₃	1	4	yes	—
296	#120	C₂²×C₁₃	1	4	yes	complemented
297	#120	C₂²×C₁₃	1	4	yes	complemented
298	#120	C₂²×C₁₃	1	4	yes	complemented
299	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
300	C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
301	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
302	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
303	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
304	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
305	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
306	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
307	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
308	C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
309	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
310	#117	C₂²×C₁₃	1	2	yes	complemented
311	#117	C₂²×C₁₃	1	2	yes	complemented
312	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
313	C₂×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
314	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
315	C₂×C₁₃	—	4	1	no	—
316	C₂×C₁₃	—	4	2	no	—
317	C₂×C₁₃	—	4	4	no	—
318	C₂×C₁₃	—	4	2	no	—
319	C₂×C₁₃	—	4	2	no	—
320	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
321	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
322	C₂×C₁₃	#585	1	1	yes	characteristic
323	C₂⁴	C₂³×C₁₃	1	4	yes	—
324	#41	—	4	4	no	—
325	#41	—	4	4	no	—
326	#41	—	4	4	no	—
327	#41	—	4	4	no	—
328	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
329	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
330	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
331	C₂×D₄	—	4	4	no	—
332	C₂×D₄	—	4	4	no	—
333	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
334	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
335	C₂×D₄	C₂³×C₁₃	1	2	yes	—
336	C₂×D₄	C₂³×C₁₃	1	2	yes	—
337	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
338	C₂×D₄	C₂³×C₁₃	1	2	yes	—
339	C₂×D₄	C₂³×C₁₃	1	2	yes	—
340	C₂×D₄	C₂³×C₁₃	1	2	yes	—
341	C₂×D₄	C₂³×C₁₃	1	4	yes	—
342	C₂×D₄	C₂³×C₁₃	1	4	yes	—
343	C₂×D₄	C₂³×C₁₃	1	4	yes	—
344	C₂×D₄	C₂³×C₁₃	1	2	yes	—
345	C₂×D₄	C₂³×C₁₃	1	4	yes	—
346	C₂×D₄	C₂³×C₁₃	1	2	yes	—
347	C₂×D₄	C₂³×C₁₃	1	4	yes	—
348	C₂×D₄	C₂³×C₁₃	1	4	yes	—
349	C₂×D₄	C₂³×C₁₃	1	2	yes	—
350	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
351	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
352	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
353	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
354	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
355	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
356	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
357	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
358	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
359	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
360	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
361	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
362	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
363	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
364	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
365	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
366	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
367	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
368	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
369	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
370	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
371	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
372	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
373	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
374	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
375	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
376	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
377	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
378	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
379	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
380	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
381	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
382	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
383	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
384	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
385	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
386	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
387	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
388	C₄²	C₂³×C₁₃	1	1	yes	characteristic
389	C₄²	C₂³×C₁₃	1	1	yes	characteristic
390	C₄²	C₂³×C₁₃	1	1	yes	characteristic
391	C₄²	C₂³×C₁₃	1	1	yes	characteristic
392	C₄²	C₂³×C₁₃	1	2	yes	—
393	C₄²	C₂³×C₁₃	1	4	yes	—
394	C₁₃	#3546	1	1	yes	characteristic, direct product factor, Sylow
395	C₂³	—	4	4	no	—
396	C₂³	—	4	4	no	—
397	C₂³	—	4	4	no	—
398	C₂³	C₂⁴×C₁₃	1	2	yes	—
399	C₂³	C₂⁴×C₁₃	1	2	yes	—
400	C₂³	C₂⁴×C₁₃	1	4	yes	—
401	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
402	C₂³	C₂⁴×C₁₃	1	2	yes	—
403	Q₈	—	2	2	no	—
404	Q₈	—	2	4	no	—
405	Q₈	—	4	2	no	—
406	D₄	—	2	2	no	—
407	D₄	—	2	2	no	—
408	D₄	—	2	4	no	—
409	D₄	—	2	4	no	—
410	D₄	—	2	2	no	—
411	D₄	—	4	4	no	—
412	D₄	—	4	4	no	—
413	D₄	—	4	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	4	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	4	no	—
421	D₄	—	4	4	no	—
422	D₄	—	4	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	—	4	4	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
433	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
434	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
435	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
436	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
437	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
438	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
439	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
440	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
441	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
442	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
443	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	2	4	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	8	8	no	—
460	C₂²	C₂⁵×C₁₃	1	1	yes	characteristic
461	C₄	—	2	1	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	4	no	—
467	C₄	—	2	2	no	—
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	2	no	—
471	C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
472	C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
473	C₂	—	4	2	no	—
474	C₂	—	4	2	no	—
475	C₂	—	4	4	no	—
476	C₂	—	4	1	no	—
477	C₂	—	4	2	no	—
478	C₂	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
479	C₂	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
480	C₂	C₁₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#560	C₂	semidirect
2. C₁₃×#556	C₂	semidirect
3. C₁₃×#553	C₂	semidirect
4. C₁₃×#550	C₂	semidirect
5. C₁₃×#550	C₂	semidirect
6. C₁₃×#547	C₂	semidirect
7. C₁₃×#546	C₂	semidirect
8. C₁₃×#546	C₂	semidirect
9. D₄²×C₁₃	C₂	semidirect
10. C₁₃×#542	C₂	semidirect
11. C₁₃×#538	C₂	semidirect
12. C₁₃×#537	C₂	semidirect
13. C₁₃×#535	C₂	semidirect
14. C₁₃×#535	C₂	semidirect
15. C₁₃×#532	C₂	semidirect
16. C₁₃×#532	C₂	semidirect
17. C₁₃×#529	C₂	semidirect
18. C₂×C₁₃×#41	C₂²	semidirect
19. C₂×C₁₃×#41	C₂²	semidirect
20. C₂×C₁₃×#41	C₂²	semidirect
21. C₂×C₁₃×#41	C₂²	semidirect
24. C₁₃×C₄⋊Q₈	C₂²	semidirect
25. C₁₃×C₄⋊Q₈	C₂²	semidirect
28. C₁₃×#127	C₂²	semidirect
29. C₁₃×#127	C₂²	semidirect
30. C₁₃×#126	C₂²	semidirect
31. C₁₃×#126	C₂²	semidirect
32. C₁₃×#126	C₂²	semidirect
33. C₁₃×#125	C₂²	semidirect
36. C₁₃×#124	C₂²	semidirect
37. C₁₃×#124	C₂²	semidirect
38. C₁₃×#124	C₂²	semidirect
39. C₁₃×#123	C₂²	semidirect
40. C₁₃×#123	C₂²	semidirect
41. C₁₃×#123	C₂²	semidirect
42. C₁₃×#123	C₂²	semidirect
43. C₁₃×C₂²⋊Q₈	C₂²	semidirect
44. C₁₃×C₂²⋊Q₈	C₂²	semidirect
45. C₁₃×C₂²⋊Q₈	C₂²	semidirect
46. C₁₃×C₂²⋊Q₈	C₂²	semidirect
52. C₁₃×#121	C₂²	semidirect
53. C₁₃×#121	C₂²	semidirect
54. C₁₃×#121	C₂²	semidirect
55. C₁₃×#121	C₂²	semidirect
56. C₁₃×#121	C₂²	semidirect
57. C₁₃×#121	C₂²	semidirect
58. C₁₃×#121	C₂²	semidirect
59. C₁₃×#121	C₂²	semidirect
60. C₁₃×#121	C₂²	semidirect
61. C₁₃×#121	C₂²	semidirect
62. C₁₃×#121	C₂²	semidirect
64. C₁₃×#120	C₂²	semidirect
65. C₁₃×#120	C₂²	semidirect
66. C₁₃×#120	C₂²	semidirect
67. C₄×Q₈×C₁₃	C₂²	semidirect
68. C₄×Q₈×C₁₃	C₂²	semidirect
71. C₄×D₄×C₁₃	C₂²	semidirect
72. C₄×D₄×C₁₃	C₂²	semidirect
73. C₄×D₄×C₁₃	C₂²	semidirect
74. C₄×D₄×C₁₃	C₂²	semidirect
75. C₄×D₄×C₁₃	C₂²	semidirect
76. C₄×D₄×C₁₃	C₂²	semidirect
77. C₄×D₄×C₁₃	C₂²	semidirect
78. C₁₃×#117	C₂²	semidirect
79. C₁₃×#117	C₂²	semidirect
80. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
81. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
82. C₂×C₄²×C₁₃	C₂²	semidirect
154. #3546	C₁₃	direct (N × H)
204. #560	C₂×C₁₃	semidirect
205. #556	C₂×C₁₃	semidirect
206. #553	C₂×C₁₃	semidirect
207. #550	C₂×C₁₃	semidirect
208. #550	C₂×C₁₃	semidirect
209. #547	C₂×C₁₃	semidirect
210. #546	C₂×C₁₃	semidirect
211. #546	C₂×C₁₃	semidirect
212. D₄²	C₂×C₁₃	semidirect
213. #542	C₂×C₁₃	semidirect
214. #538	C₂×C₁₃	semidirect
215. #537	C₂×C₁₃	semidirect
216. #535	C₂×C₁₃	semidirect
217. #535	C₂×C₁₃	semidirect
218. #532	C₂×C₁₃	semidirect
219. #532	C₂×C₁₃	semidirect
220. #529	C₂×C₁₃	semidirect
250. C₂×#41	C₂²×C₁₃	semidirect
251. C₂×#41	C₂²×C₁₃	semidirect
252. C₂×#41	C₂²×C₁₃	semidirect
253. C₂×#41	C₂²×C₁₃	semidirect
256. C₄⋊Q₈	C₂²×C₁₃	semidirect
257. C₄⋊Q₈	C₂²×C₁₃	semidirect
260. #127	C₂²×C₁₃	semidirect
261. #127	C₂²×C₁₃	semidirect
262. #126	C₂²×C₁₃	semidirect
263. #126	C₂²×C₁₃	semidirect
264. #126	C₂²×C₁₃	semidirect
265. #125	C₂²×C₁₃	semidirect
268. #124	C₂²×C₁₃	semidirect
269. #124	C₂²×C₁₃	semidirect
270. #124	C₂²×C₁₃	semidirect
271. #123	C₂²×C₁₃	semidirect
272. #123	C₂²×C₁₃	semidirect
273. #123	C₂²×C₁₃	semidirect
274. #123	C₂²×C₁₃	semidirect
275. C₂²⋊Q₈	C₂²×C₁₃	semidirect
276. C₂²⋊Q₈	C₂²×C₁₃	semidirect
277. C₂²⋊Q₈	C₂²×C₁₃	semidirect
278. C₂²⋊Q₈	C₂²×C₁₃	semidirect
284. #121	C₂²×C₁₃	semidirect
285. #121	C₂²×C₁₃	semidirect
286. #121	C₂²×C₁₃	semidirect
287. #121	C₂²×C₁₃	semidirect
288. #121	C₂²×C₁₃	semidirect
289. #121	C₂²×C₁₃	semidirect
290. #121	C₂²×C₁₃	semidirect
291. #121	C₂²×C₁₃	semidirect
292. #121	C₂²×C₁₃	semidirect
293. #121	C₂²×C₁₃	semidirect
294. #121	C₂²×C₁₃	semidirect
296. #120	C₂²×C₁₃	semidirect
297. #120	C₂²×C₁₃	semidirect
298. #120	C₂²×C₁₃	semidirect
299. C₄×Q₈	C₂²×C₁₃	semidirect
300. C₄×Q₈	C₂²×C₁₃	semidirect
303. C₄×D₄	C₂²×C₁₃	semidirect
304. C₄×D₄	C₂²×C₁₃	semidirect
305. C₄×D₄	C₂²×C₁₃	semidirect
306. C₄×D₄	C₂²×C₁₃	semidirect
307. C₄×D₄	C₂²×C₁₃	semidirect
308. C₄×D₄	C₂²×C₁₃	semidirect
309. C₄×D₄	C₂²×C₁₃	semidirect
310. #117	C₂²×C₁₃	semidirect
311. #117	C₂²×C₁₃	semidirect
312. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
313. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
314. C₂×C₄²	C₂²×C₁₃	semidirect
394. C₁₃	#3546	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×#560	2
C₁₃×#556	2
C₁₃×#553	2
C₁₃×#550	2
C₁₃×#547	2
C₁₃×#546	2
D₄²×C₁₃	2
C₁₃×#542	2
C₁₃×#538	2
C₁₃×#537	2
C₁₃×#535	2
C₁₃×#532	2
C₁₃×#529	2
#3546	13

Subgroups — C13×#3546 #13112604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3546 #13112604