Subgroups — C₁₃×#3565 #13112623

Order 1664.

930 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#563	C₂	1	2	yes	maximal, complemented
2	C₁₃×#562	C₂	1	2	yes	maximal, complemented
3	C₁₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#556	C₂	1	2	yes	maximal, complemented
5	C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#552	C₂	1	2	yes	maximal, complemented
11	C₁₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#542	C₂	1	2	yes	maximal, complemented
18	C₁₃×#542	C₂	1	2	yes	maximal, complemented
19	C₁₃×#541	C₂	1	2	yes	maximal, complemented
20	C₁₃×#539	C₂	1	2	yes	maximal, complemented
21	C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
27	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
28	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
30	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
31	C₁₃×#126	C₂²	1	2	yes	—
32	C₁₃×#126	C₂²	1	1	yes	characteristic
33	C₁₃×#126	C₂²	1	1	yes	characteristic
34	C₁₃×#126	C₂²	1	2	yes	—
35	C₁₃×#126	C₂²	1	2	yes	—
36	C₁₃×#126	C₂²	1	2	yes	—
37	C₁₃×#126	C₂²	1	2	yes	—
38	C₁₃×#126	C₂²	1	2	yes	—
39	C₁₃×#126	C₂²	1	2	yes	—
40	C₁₃×#126	C₂²	1	2	yes	—
41	C₁₃×#126	C₂²	1	2	yes	—
42	C₁₃×#125	C₂²	1	1	yes	characteristic
43	C₁₃×#125	C₂²	1	1	yes	characteristic
44	C₁₃×#125	C₂²	1	1	yes	characteristic
45	C₁₃×#125	C₂²	1	1	yes	characteristic
46	C₁₃×#125	C₂²	1	2	yes	—
47	C₁₃×#125	C₂²	1	2	yes	—
48	C₁₃×#125	C₂²	1	2	yes	—
49	C₁₃×#125	C₂²	1	2	yes	—
50	C₁₃×#125	C₂²	1	2	yes	—
51	C₁₃×#125	C₂²	1	1	yes	characteristic
52	C₁₃×#125	C₂²	1	2	yes	—
53	C₁₃×#125	C₂²	1	1	yes	characteristic
54	C₁₃×#124	C₂²	1	1	yes	characteristic
55	C₁₃×#124	C₂²	1	1	yes	characteristic
56	C₁₃×#124	C₂²	1	2	yes	—
57	C₁₃×#124	C₂²	1	2	yes	—
58	C₁₃×#124	C₂²	1	2	yes	—
59	C₁₃×#124	C₂²	1	2	yes	—
60	C₁₃×#124	C₂²	1	2	yes	—
61	C₁₃×#123	C₂²	1	1	yes	characteristic
62	C₁₃×#123	C₂²	1	1	yes	characteristic
63	C₁₃×#123	C₂²	1	2	yes	—
64	C₁₃×#123	C₂²	1	2	yes	—
65	C₁₃×#123	C₂²	1	2	yes	—
66	C₁₃×#123	C₂²	1	2	yes	—
67	C₁₃×#123	C₂²	1	2	yes	—
68	C₁₃×#123	C₂²	1	2	yes	—
69	C₁₃×#123	C₂²	1	2	yes	—
70	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
71	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
72	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
73	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
74	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
75	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
76	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
77	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
78	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
79	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
80	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
81	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
82	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
83	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
84	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
85	C₁₃×#121	C₂²	1	1	yes	characteristic
86	C₁₃×#121	C₂²	1	1	yes	characteristic
87	C₁₃×#121	C₂²	1	2	yes	—
88	C₁₃×#121	C₂²	1	1	yes	characteristic
89	C₁₃×#121	C₂²	1	1	yes	characteristic
90	C₁₃×#121	C₂²	1	2	yes	—
91	C₁₃×#121	C₂²	1	2	yes	—
92	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
93	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
94	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
95	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
96	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
97	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
98	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
99	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
100	C₄×D₄×C₁₃	C₂²	1	2	yes	—
101	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
102	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
103	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
104	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
105	C₄×D₄×C₁₃	C₂²	1	2	yes	—
106	C₄×D₄×C₁₃	C₂²	1	2	yes	—
107	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
108	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
109	C₁₃×#117	C₂²	1	1	yes	characteristic
110	C₁₃×#117	C₂²	1	1	yes	characteristic
111	C₁₃×#117	C₂²	1	2	yes	—
112	C₁₃×#117	C₂²	1	1	yes	characteristic
113	C₁₃×#117	C₂²	1	1	yes	characteristic
114	C₁₃×#117	C₂²	1	2	yes	—
115	C₁₃×#117	C₂²	1	2	yes	—
116	C₁₃×#117	C₂²	1	2	yes	—
117	C₁₃×#117	C₂²	1	1	yes	characteristic
118	C₁₃×#117	C₂²	1	1	yes	characteristic
119	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
121	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
122	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
123	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
126	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
127	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
128	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
129	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₁₃	C₂³	1	2	yes	—
132	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
133	C₂×D₄×C₁₃	C₂³	1	2	yes	—
134	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
135	C₂×D₄×C₁₃	C₂³	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
142	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
143	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
144	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
145	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
146	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
171	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
176	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
177	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
182	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
183	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
184	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
187	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
188	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
192	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
200	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
201	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
206	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
209	C₄²×C₁₃	C₂³	1	1	yes	characteristic
210	C₄²×C₁₃	C₂³	1	1	yes	characteristic
211	C₄²×C₁₃	C₂³	1	1	yes	characteristic
212	C₄²×C₁₃	C₂³	1	1	yes	characteristic
213	C₄²×C₁₃	C₂³	1	2	yes	—
214	C₄²×C₁₃	C₂³	1	2	yes	—
215	C₄²×C₁₃	C₂³	1	2	yes	—
216	C₄²×C₁₃	C₂³	1	2	yes	—
217	C₄²×C₁₃	C₂³	1	1	yes	characteristic
218	C₄²×C₁₃	C₂³	1	1	yes	characteristic
219	C₄²×C₁₃	C₂³	1	2	yes	—
220	C₄²×C₁₃	C₂³	1	2	yes	—
221	C₄²×C₁₃	C₂³	1	2	yes	—
222	#3565	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
225	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
226	C₂³×C₁₃	C₂⁴	1	2	yes	—
227	Q₈×C₁₃	—	2	2	no	—
228	Q₈×C₁₃	—	4	1	no	—
229	Q₈×C₁₃	—	4	2	no	—
230	Q₈×C₁₃	—	4	2	no	—
231	Q₈×C₁₃	—	4	2	no	—
232	Q₈×C₁₃	—	4	2	no	—
233	D₄×C₁₃	—	2	2	no	—
234	D₄×C₁₃	—	4	1	no	—
235	D₄×C₁₃	—	4	1	no	—
236	D₄×C₁₃	—	4	2	no	—
237	D₄×C₁₃	—	4	2	no	—
238	D₄×C₁₃	—	4	1	no	—
239	D₄×C₁₃	—	4	2	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	4	2	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	2	no	—
246	C₂×C₄×C₁₃	—	4	2	no	—
247	C₂×C₄×C₁₃	—	4	2	no	—
248	C₂×C₄×C₁₃	—	4	2	no	—
249	C₂×C₄×C₁₃	—	4	1	no	—
250	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
261	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
263	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
264	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
265	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
267	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
269	#563	C₂×C₁₃	1	2	yes	complemented
270	#562	C₂×C₁₃	1	2	yes	complemented
271	#557	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#556	C₂×C₁₃	1	2	yes	complemented
273	#556	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#555	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#554	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#553	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#553	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#552	C₂×C₁₃	1	2	yes	complemented
279	#552	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#552	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#544	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#544	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#542	C₂×C₁₃	1	1	yes	characteristic, complemented
284	#542	C₂×C₁₃	1	1	yes	characteristic, complemented
285	#542	C₂×C₁₃	1	2	yes	complemented
286	#542	C₂×C₁₃	1	2	yes	complemented
287	#541	C₂×C₁₃	1	2	yes	complemented
288	#539	C₂×C₁₃	1	2	yes	complemented
289	#533	C₂×C₁₃	1	1	yes	characteristic, complemented
290	#529	C₂×C₁₃	1	1	yes	characteristic, complemented
291	#529	C₂×C₁₃	1	1	yes	characteristic, complemented
292	C₂²×C₁₃	—	2	1	no	—
293	C₂²×C₁₃	—	2	1	no	—
294	C₂²×C₁₃	—	2	1	no	—
295	C₂²×C₁₃	—	2	2	no	—
296	C₂²×C₁₃	—	2	1	no	—
297	C₂²×C₁₃	—	2	1	no	—
298	C₂²×C₁₃	—	2	2	no	—
299	C₂²×C₁₃	—	2	1	no	—
300	C₂²×C₁₃	—	2	1	no	—
301	C₂²×C₁₃	—	2	2	no	—
302	C₂²×C₁₃	—	2	1	no	—
303	C₂²×C₁₃	—	2	1	no	—
304	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
305	C₄×C₁₃	—	2	1	no	—
306	C₄×C₁₃	—	2	1	no	—
307	C₄×C₁₃	—	2	1	no	—
308	C₄×C₁₃	—	2	2	no	—
309	C₄×C₁₃	—	2	1	no	—
310	C₄×C₁₃	—	2	1	no	—
311	C₄×C₁₃	—	2	2	no	—
312	C₄×C₁₃	—	2	1	no	—
313	C₄×C₁₃	—	2	2	no	—
314	C₄×C₁₃	—	2	2	no	—
315	C₄×C₁₃	—	2	2	no	—
316	C₄×C₁₃	—	2	1	no	—
317	C₄×C₁₃	—	2	1	no	—
318	C₄×C₁₃	—	2	2	no	—
319	C₄×C₁₃	—	2	1	no	—
320	C₄×C₁₃	—	2	1	no	—
321	C₄×C₁₃	—	2	2	no	—
322	C₄×C₁₃	—	2	1	no	—
323	C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
324	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
325	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
326	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
327	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
328	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
329	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
330	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
331	#126	C₂²×C₁₃	1	2	yes	—
332	#126	C₂²×C₁₃	1	1	yes	characteristic
333	#126	C₂²×C₁₃	1	1	yes	characteristic
334	#126	C₂²×C₁₃	1	2	yes	—
335	#126	C₂²×C₁₃	1	2	yes	—
336	#126	C₂²×C₁₃	1	2	yes	—
337	#126	C₂²×C₁₃	1	2	yes	—
338	#126	C₂²×C₁₃	1	2	yes	—
339	#126	C₂²×C₁₃	1	2	yes	—
340	#126	C₂²×C₁₃	1	2	yes	—
341	#126	C₂²×C₁₃	1	2	yes	—
342	#125	C₂²×C₁₃	1	1	yes	characteristic
343	#125	C₂²×C₁₃	1	1	yes	characteristic
344	#125	C₂²×C₁₃	1	1	yes	characteristic
345	#125	C₂²×C₁₃	1	1	yes	characteristic
346	#125	C₂²×C₁₃	1	2	yes	—
347	#125	C₂²×C₁₃	1	2	yes	—
348	#125	C₂²×C₁₃	1	2	yes	—
349	#125	C₂²×C₁₃	1	2	yes	—
350	#125	C₂²×C₁₃	1	2	yes	—
351	#125	C₂²×C₁₃	1	1	yes	characteristic
352	#125	C₂²×C₁₃	1	2	yes	—
353	#125	C₂²×C₁₃	1	1	yes	characteristic
354	#124	C₂²×C₁₃	1	1	yes	characteristic
355	#124	C₂²×C₁₃	1	1	yes	characteristic
356	#124	C₂²×C₁₃	1	2	yes	—
357	#124	C₂²×C₁₃	1	2	yes	—
358	#124	C₂²×C₁₃	1	2	yes	—
359	#124	C₂²×C₁₃	1	2	yes	—
360	#124	C₂²×C₁₃	1	2	yes	—
361	#123	C₂²×C₁₃	1	1	yes	characteristic
362	#123	C₂²×C₁₃	1	1	yes	characteristic
363	#123	C₂²×C₁₃	1	2	yes	—
364	#123	C₂²×C₁₃	1	2	yes	—
365	#123	C₂²×C₁₃	1	2	yes	—
366	#123	C₂²×C₁₃	1	2	yes	—
367	#123	C₂²×C₁₃	1	2	yes	—
368	#123	C₂²×C₁₃	1	2	yes	—
369	#123	C₂²×C₁₃	1	2	yes	—
370	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
371	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
372	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
373	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
374	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
375	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
376	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
377	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
378	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
379	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
380	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
381	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
382	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
383	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
384	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
385	#121	C₂²×C₁₃	1	1	yes	characteristic
386	#121	C₂²×C₁₃	1	1	yes	characteristic
387	#121	C₂²×C₁₃	1	2	yes	—
388	#121	C₂²×C₁₃	1	1	yes	characteristic
389	#121	C₂²×C₁₃	1	1	yes	characteristic
390	#121	C₂²×C₁₃	1	2	yes	—
391	#121	C₂²×C₁₃	1	2	yes	—
392	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
393	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
394	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
395	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
396	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
397	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
398	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
399	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
400	C₄×D₄	C₂²×C₁₃	1	2	yes	—
401	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
402	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
403	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
404	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
405	C₄×D₄	C₂²×C₁₃	1	2	yes	—
406	C₄×D₄	C₂²×C₁₃	1	2	yes	—
407	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
408	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
409	#117	C₂²×C₁₃	1	1	yes	characteristic
410	#117	C₂²×C₁₃	1	1	yes	characteristic
411	#117	C₂²×C₁₃	1	2	yes	—
412	#117	C₂²×C₁₃	1	1	yes	characteristic
413	#117	C₂²×C₁₃	1	1	yes	characteristic
414	#117	C₂²×C₁₃	1	2	yes	—
415	#117	C₂²×C₁₃	1	2	yes	—
416	#117	C₂²×C₁₃	1	2	yes	—
417	#117	C₂²×C₁₃	1	1	yes	characteristic
418	#117	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
420	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
422	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
423	C₂×C₁₃	—	4	1	no	—
424	C₂×C₁₃	—	4	1	no	—
425	C₂×C₁₃	—	4	1	no	—
426	C₂×C₁₃	—	4	2	no	—
427	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
428	C₂×C₁₃	#585	1	1	yes	characteristic
429	C₂×C₁₃	#585	1	1	yes	characteristic
430	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
431	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
432	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
433	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
434	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
435	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
436	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
437	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
438	C₂×D₄	C₂³×C₁₃	1	2	yes	—
439	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
440	C₂×D₄	C₂³×C₁₃	1	2	yes	—
441	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
442	C₂×D₄	C₂³×C₁₃	1	2	yes	—
443	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
444	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
445	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
446	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
447	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
448	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
449	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
450	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
451	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
452	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
453	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
454	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
455	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
456	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
457	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
458	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
459	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
460	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
461	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
462	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
463	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
464	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
465	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
466	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
467	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
468	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
469	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
470	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
471	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
472	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
473	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
474	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
475	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
476	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
477	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
478	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
479	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
480	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
481	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
482	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
483	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
484	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
485	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
486	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
487	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
488	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
489	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
490	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
491	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
492	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
493	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
494	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
495	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
496	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
497	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
498	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
499	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
500	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
501	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
502	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
503	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
504	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
505	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
506	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
507	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
508	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
509	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
510	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
511	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
512	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
513	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
514	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
515	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
516	C₄²	C₂³×C₁₃	1	1	yes	characteristic
517	C₄²	C₂³×C₁₃	1	1	yes	characteristic
518	C₄²	C₂³×C₁₃	1	1	yes	characteristic
519	C₄²	C₂³×C₁₃	1	1	yes	characteristic
520	C₄²	C₂³×C₁₃	1	2	yes	—
521	C₄²	C₂³×C₁₃	1	2	yes	—
522	C₄²	C₂³×C₁₃	1	2	yes	—
523	C₄²	C₂³×C₁₃	1	2	yes	—
524	C₄²	C₂³×C₁₃	1	1	yes	characteristic
525	C₄²	C₂³×C₁₃	1	1	yes	characteristic
526	C₄²	C₂³×C₁₃	1	2	yes	—
527	C₄²	C₂³×C₁₃	1	2	yes	—
528	C₄²	C₂³×C₁₃	1	2	yes	—
529	C₁₃	#3565	1	1	yes	characteristic, direct product factor, Sylow
530	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
531	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
532	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
533	C₂³	C₂⁴×C₁₃	1	2	yes	—
534	Q₈	—	2	2	no	—
535	Q₈	—	4	1	no	—
536	Q₈	—	4	2	no	—
537	Q₈	—	4	2	no	—
538	Q₈	—	4	2	no	—
539	Q₈	—	4	2	no	—
540	D₄	—	2	2	no	—
541	D₄	—	4	1	no	—
542	D₄	—	4	1	no	—
543	D₄	—	4	2	no	—
544	D₄	—	4	2	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
558	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
559	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
560	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
561	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
562	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
563	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
564	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
565	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
566	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
567	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
568	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
569	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
570	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
571	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
572	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
573	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
574	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
575	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	2	1	no	—
587	C₂²	—	2	1	no	—
588	C₂²	C₂⁵×C₁₃	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	2	no	—
600	C₄	—	2	1	no	—
601	C₄	—	2	1	no	—
602	C₄	—	2	2	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	1	no	—
607	C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
608	C₂	—	4	1	no	—
609	C₂	—	4	1	no	—
610	C₂	—	4	1	no	—
611	C₂	—	4	2	no	—
612	C₂	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
613	C₂	C₁₃×#585	1	1	yes	characteristic
614	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×#563	C₂	semidirect
2. C₁₃×#562	C₂	semidirect
3. C₁₃×#557	C₂	semidirect
4. C₁₃×#556	C₂	semidirect
5. C₁₃×#556	C₂	semidirect
6. C₁₃×#555	C₂	semidirect
7. C₁₃×#554	C₂	semidirect
8. C₁₃×#553	C₂	semidirect
9. C₁₃×#553	C₂	semidirect
10. C₁₃×#552	C₂	semidirect
11. C₁₃×#552	C₂	semidirect
12. C₁₃×#552	C₂	semidirect
13. C₁₃×#544	C₂	semidirect
14. C₁₃×#544	C₂	semidirect
15. C₁₃×#542	C₂	semidirect
16. C₁₃×#542	C₂	semidirect
17. C₁₃×#542	C₂	semidirect
18. C₁₃×#542	C₂	semidirect
19. C₁₃×#541	C₂	semidirect
20. C₁₃×#539	C₂	semidirect
21. C₁₃×#533	C₂	semidirect
22. C₁₃×#529	C₂	semidirect
23. C₁₃×#529	C₂	semidirect
222. #3565	C₁₃	direct (N × H)
269. #563	C₂×C₁₃	semidirect
270. #562	C₂×C₁₃	semidirect
271. #557	C₂×C₁₃	semidirect
272. #556	C₂×C₁₃	semidirect
273. #556	C₂×C₁₃	semidirect
274. #555	C₂×C₁₃	semidirect
275. #554	C₂×C₁₃	semidirect
276. #553	C₂×C₁₃	semidirect
277. #553	C₂×C₁₃	semidirect
278. #552	C₂×C₁₃	semidirect
279. #552	C₂×C₁₃	semidirect
280. #552	C₂×C₁₃	semidirect
281. #544	C₂×C₁₃	semidirect
282. #544	C₂×C₁₃	semidirect
283. #542	C₂×C₁₃	semidirect
284. #542	C₂×C₁₃	semidirect
285. #542	C₂×C₁₃	semidirect
286. #542	C₂×C₁₃	semidirect
287. #541	C₂×C₁₃	semidirect
288. #539	C₂×C₁₃	semidirect
289. #533	C₂×C₁₃	semidirect
290. #529	C₂×C₁₃	semidirect
291. #529	C₂×C₁₃	semidirect
529. C₁₃	#3565	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×#563	2
C₁₃×#562	2
C₁₃×#557	2
C₁₃×#556	2
C₁₃×#555	2
C₁₃×#554	2
C₁₃×#553	2
C₁₃×#552	2
C₁₃×#544	2
C₁₃×#542	2
C₁₃×#541	2
C₁₃×#539	2
C₁₃×#533	2
C₁₃×#529	2
#3565	13

Subgroups — C13×#3565 #13112623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3565 #13112623