Subgroups — C₁₃×#17548 #15703887

Order 3328.

1102 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3520	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2275	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1509	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1508	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1506	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1504	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1503	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1501	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1500	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#328	C₂	1	2	yes	maximal, complemented
12	C₁₃×#556	C₄	1	1	yes	characteristic, complemented
13	C₁₃×#554	—	2	1	no	—
14	C₁₃×#552	C₄	1	2	yes	complemented
15	C₁₃×#551	—	2	2	no	—
16	D₄×Q₈×C₁₃	C₄	1	1	yes	characteristic, complemented
17	C₁₃×#548	C₄	1	2	yes	complemented
18	C₁₃×#547	C₄	1	1	yes	characteristic, complemented
19	C₁₃×#547	C₄	1	1	yes	characteristic, complemented
20	C₁₃×#546	—	2	1	no	—
21	C₁₃×#542	—	2	1	no	—
22	C₁₃×#539	—	2	2	no	—
23	C₁₃×#533	C₂²	1	1	yes	characteristic
24	C₁₃×#529	C₂²	1	1	yes	characteristic
25	C₁₃×#525	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₁₃×#520	—	2	1	no	—
28	C₂×C₄×D₄×C₁₃	—	2	1	no	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#436	—	2	1	no	—
31	C₁₃×#435	—	2	2	no	—
32	C₈×D₄×C₁₃	—	2	1	no	—
33	C₁₃×#432	C₂²	1	1	yes	characteristic
34	C₁₃×#431	C₂²	1	1	yes	characteristic
35	C₁₃×#407	C₂²	1	2	yes	—
36	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
37	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
38	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
40	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
41	C₁₃×#376	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#95	C₂²	1	2	yes	—
43	C₁₃×#328	C₂²	1	1	yes	characteristic
44	C₁₃×#328	C₂²	1	2	yes	—
45	C₁₃×#328	C₂²	1	2	yes	—
46	C₁₃×#328	C₂²	1	2	yes	—
47	C₁₃×#328	C₂²	1	1	yes	characteristic
48	C₁₃×#328	C₂²	1	2	yes	—
49	C₁₃×#328	C₂²	1	2	yes	—
50	C₁₃×#327	C₂²	1	1	yes	characteristic
51	C₁₃×#327	C₂²	1	1	yes	characteristic
52	C₁₃×#327	C₂²	1	2	yes	—
53	C₂×C₁₃×#41	—	2	1	no	—
54	C₂×C₁₃×#41	C₂×C₄	1	2	yes	complemented
55	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	complemented
56	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	—	2	2	no	—
58	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
59	C₂×C₁₃×M₁₆	—	2	2	no	—
60	C₂²×C₈×C₁₃	—	2	2	no	—
61	C₁₃×C₄⋊Q₈	—	2	1	no	—
62	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
63	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
64	C₁₃×#126	—	2	2	no	—
65	C₁₃×#126	—	2	2	no	—
66	C₁₃×#126	—	2	1	no	—
67	C₁₃×#125	—	2	2	no	—
68	C₁₃×#125	—	2	1	no	—
69	C₁₃×#125	C₂×C₄	1	1	yes	characteristic, complemented
70	C₁₃×#124	—	2	1	no	—
71	C₁₃×#124	—	2	2	no	—
72	C₁₃×#124	C₂×C₄	1	1	yes	characteristic, complemented
73	C₁₃×#123	—	2	2	no	—
74	C₁₃×#123	—	2	2	no	—
75	C₁₃×#123	—	2	1	no	—
76	C₁₃×#123	—	2	2	no	—
77	C₁₃×#123	—	2	2	no	—
78	C₁₃×C₂²⋊Q₈	—	2	2	no	—
79	C₁₃×C₂²⋊Q₈	—	2	2	no	—
80	C₁₃×C₂²⋊Q₈	—	2	1	no	—
81	C₁₃×C₂²⋊Q₈	—	2	2	no	—
82	C₁₃×C₂²⋊Q₈	—	2	1	no	—
83	C₁₃×C₂²⋊Q₈	—	2	2	no	—
84	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	complemented
85	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	complemented
86	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	complemented
87	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
88	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
89	C₁₃×#121	—	2	2	no	—
90	C₁₃×#121	—	2	1	no	—
91	C₁₃×#121	C₂×C₄	1	2	yes	complemented
92	C₁₃×#121	C₂³	1	1	yes	characteristic
93	C₁₃×#120	—	2	2	no	—
94	C₄×Q₈×C₁₃	—	2	1	no	—
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
97	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	complemented
98	C₄×D₄×C₁₃	—	2	8	no	—
99	C₄×D₄×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	—	2	2	no	—
101	C₄×D₄×C₁₃	—	2	2	no	—
102	C₄×D₄×C₁₃	—	2	1	no	—
103	C₄×D₄×C₁₃	—	2	2	no	—
104	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
105	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
106	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
107	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
108	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
109	C₄×D₄×C₁₃	D₄	1	2	yes	—
110	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
111	C₁₃×#117	—	2	1	no	—
112	C₁₃×#117	—	2	2	no	—
113	C₁₃×#117	—	2	1	no	—
114	C₁₃×#117	C₂×C₄	1	2	yes	complemented
115	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	complemented
119	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
120	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
122	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
123	C₂×C₄²×C₁₃	—	2	1	no	—
124	C₂×C₄²×C₁₃	—	2	1	no	—
125	C₂×C₄²×C₁₃	—	2	2	no	—
126	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
127	C₁₃×C₄⋊C₈	—	2	1	no	—
128	C₁₃×C₄⋊C₈	—	2	1	no	—
129	C₁₃×C₂²⋊C₈	—	2	2	no	—
130	C₁₃×C₂²⋊C₈	—	2	2	no	—
131	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
132	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
133	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
134	C₁₃×#97	—	2	1	no	—
135	C₄×C₈×C₁₃	—	2	1	no	—
136	C₁₃×#95	—	2	1	no	—
137	C₁₃×#95	—	2	2	no	—
138	C₁₃×#95	C₂³	1	1	yes	characteristic
139	C₁₃×#95	C₂³	1	2	yes	—
140	C₁₃×#95	C₂³	1	1	yes	characteristic
141	#17548	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
143	C₁₃×#41	—	4	4	no	—
144	C₁₃×#41	—	8	2	no	—
145	C₂×Q₈×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	—	2	2	no	—
147	C₂×Q₈×C₁₃	—	8	2	no	—
148	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
150	C₂×D₄×C₁₃	—	2	4	no	—
151	C₂×D₄×C₁₃	—	2	2	no	—
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	—	2	2	no	—
154	C₂×D₄×C₁₃	C₂²⋊C₄	1	2	yes	—
155	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
156	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
157	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	—	2	2	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	2	no	—
162	C₂²×C₄×C₁₃	—	2	8	no	—
163	C₂²×C₄×C₁₃	—	2	2	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	2	no	—
166	C₂²×C₄×C₁₃	—	8	2	no	—
167	C₂²×C₄×C₁₃	—	8	2	no	—
168	C₂²×C₄×C₁₃	—	8	2	no	—
169	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
170	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₁₃×M₁₆	—	8	2	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	2	no	—
181	C₂×C₈×C₁₃	—	8	2	no	—
182	C₁₃×C₄⋊C₄	—	2	4	no	—
183	C₁₃×C₄⋊C₄	—	2	2	no	—
184	C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₁₃×C₄⋊C₄	—	2	2	no	—
186	C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	2	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
197	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
198	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
199	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
200	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
201	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
202	C₁₃×C₂²⋊C₄	—	2	8	no	—
203	C₁₃×C₂²⋊C₄	—	2	2	no	—
204	C₁₃×C₂²⋊C₄	—	2	2	no	—
205	C₁₃×C₂²⋊C₄	—	2	2	no	—
206	C₁₃×C₂²⋊C₄	—	2	2	no	—
207	C₁₃×C₂²⋊C₄	—	2	1	no	—
208	C₁₃×C₂²⋊C₄	—	2	2	no	—
209	C₁₃×C₂²⋊C₄	—	2	1	no	—
210	C₁₃×C₂²⋊C₄	—	2	1	no	—
211	C₁₃×C₂²⋊C₄	—	2	2	no	—
212	C₁₃×C₂²⋊C₄	—	2	1	no	—
213	C₁₃×C₂²⋊C₄	—	2	1	no	—
214	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
215	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
216	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
217	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
218	C₄²×C₁₃	—	2	4	no	—
219	C₄²×C₁₃	—	2	2	no	—
220	C₄²×C₁₃	—	2	2	no	—
221	C₄²×C₁₃	—	2	1	no	—
222	C₄²×C₁₃	—	8	1	no	—
223	C₄²×C₁₃	—	8	2	no	—
224	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
225	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
226	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
228	#3520	C₂×C₁₃	1	1	yes	characteristic
229	#2974	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#2275	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#1509	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#1508	C₂×C₁₃	1	2	yes	complemented
233	#1506	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#1504	C₂×C₁₃	1	2	yes	complemented
235	#1503	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#1501	C₂×C₁₃	1	2	yes	complemented
237	#1500	C₂×C₁₃	1	1	yes	characteristic, complemented
238	C₂×#328	C₂×C₁₃	1	2	yes	complemented
239	C₂³×C₁₃	—	2	2	no	—
240	C₂³×C₁₃	—	2	2	no	—
241	C₂³×C₁₃	—	2	4	no	—
242	C₂³×C₁₃	—	2	1	no	—
243	C₂³×C₁₃	—	4	2	no	—
244	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
245	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
246	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
247	Q₈×C₁₃	—	4	1	no	—
248	Q₈×C₁₃	—	4	2	no	—
249	Q₈×C₁₃	—	4	2	no	—
250	Q₈×C₁₃	—	8	2	no	—
251	D₄×C₁₃	—	2	4	no	—
252	D₄×C₁₃	—	2	2	no	—
253	D₄×C₁₃	—	4	1	no	—
254	D₄×C₁₃	—	4	1	no	—
255	D₄×C₁₃	—	4	1	no	—
256	D₄×C₁₃	—	4	4	no	—
257	D₄×C₁₃	—	8	2	no	—
258	D₄×C₁₃	#104	1	4	yes	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	2	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	2	no	—
264	C₂×C₄×C₁₃	—	2	4	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	2	1	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	4	2	no	—
271	C₂×C₄×C₁₃	—	4	2	no	—
272	C₂×C₄×C₁₃	—	4	2	no	—
273	C₂×C₄×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	4	2	no	—
275	C₂×C₄×C₁₃	—	4	2	no	—
276	C₂×C₄×C₁₃	—	4	1	no	—
277	C₂×C₄×C₁₃	—	4	2	no	—
278	C₂×C₄×C₁₃	—	4	1	no	—
279	C₂×C₄×C₁₃	—	4	2	no	—
280	C₂×C₄×C₁₃	—	4	1	no	—
281	C₂×C₄×C₁₃	—	4	1	no	—
282	C₂×C₄×C₁₃	—	4	4	no	—
283	C₂×C₄×C₁₃	—	4	2	no	—
284	C₂×C₄×C₁₃	—	8	2	no	—
285	C₂×C₄×C₁₃	—	8	2	no	—
286	C₂×C₄×C₁₃	—	8	8	no	—
287	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
288	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
289	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
290	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
291	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
292	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
293	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
294	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
295	C₈×C₁₃	—	4	1	no	—
296	C₈×C₁₃	—	4	2	no	—
297	C₈×C₁₃	—	4	1	no	—
298	#556	C₄×C₁₃	1	1	yes	characteristic, complemented
299	#554	—	2	1	no	—
300	#552	C₄×C₁₃	1	2	yes	complemented
301	#551	—	2	2	no	—
302	D₄×Q₈	C₄×C₁₃	1	1	yes	characteristic, complemented
303	#548	C₄×C₁₃	1	2	yes	complemented
304	#547	C₄×C₁₃	1	1	yes	characteristic, complemented
305	#547	C₄×C₁₃	1	1	yes	characteristic, complemented
306	#546	—	2	1	no	—
307	#542	—	2	1	no	—
308	#539	—	2	2	no	—
309	#533	C₂²×C₁₃	1	1	yes	characteristic
310	#529	C₂²×C₁₃	1	1	yes	characteristic
311	#525	C₂²×C₁₃	1	2	yes	—
312	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
313	#520	—	2	1	no	—
314	C₂×C₄×D₄	—	2	1	no	—
315	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
316	#436	—	2	1	no	—
317	#435	—	2	2	no	—
318	C₈×D₄	—	2	1	no	—
319	#432	C₂²×C₁₃	1	1	yes	characteristic
320	#431	C₂²×C₁₃	1	1	yes	characteristic
321	#407	C₂²×C₁₃	1	2	yes	—
322	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
323	C₄×C₄⋊C₄	—	2	1	no	—
324	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
325	C₄×C₂²⋊C₄	—	2	2	no	—
326	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
327	#376	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×#95	C₂²×C₁₃	1	2	yes	—
329	#328	C₂²×C₁₃	1	1	yes	characteristic
330	#328	C₂²×C₁₃	1	2	yes	—
331	#328	C₂²×C₁₃	1	2	yes	—
332	#328	C₂²×C₁₃	1	2	yes	—
333	#328	C₂²×C₁₃	1	1	yes	characteristic
334	#328	C₂²×C₁₃	1	2	yes	—
335	#328	C₂²×C₁₃	1	2	yes	—
336	#327	C₂²×C₁₃	1	1	yes	characteristic
337	#327	C₂²×C₁₃	1	1	yes	characteristic
338	#327	C₂²×C₁₃	1	2	yes	—
339	C₂²×C₁₃	—	2	1	no	—
340	C₂²×C₁₃	—	2	2	no	—
341	C₂²×C₁₃	—	2	2	no	—
342	C₂²×C₁₃	—	2	1	no	—
343	C₂²×C₁₃	—	2	2	no	—
344	C₂²×C₁₃	—	2	2	no	—
345	C₂²×C₁₃	—	2	2	no	—
346	C₂²×C₁₃	—	4	4	no	—
347	C₂²×C₁₃	—	4	4	no	—
348	C₂²×C₁₃	—	4	1	no	—
349	C₂²×C₁₃	—	4	1	no	—
350	C₂²×C₁₃	—	4	1	no	—
351	C₂²×C₁₃	C₂×#104	1	4	yes	—
352	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
353	C₂²×C₁₃	#577	1	1	yes	characteristic
354	C₂²×C₁₃	#578	1	1	yes	characteristic
355	C₄×C₁₃	—	2	1	no	—
356	C₄×C₁₃	—	2	1	no	—
357	C₄×C₁₃	—	2	2	no	—
358	C₄×C₁₃	—	2	2	no	—
359	C₄×C₁₃	—	2	1	no	—
360	C₄×C₁₃	—	2	1	no	—
361	C₄×C₁₃	—	2	1	no	—
362	C₄×C₁₃	—	4	2	no	—
363	C₄×C₁₃	—	4	4	no	—
364	C₄×C₁₃	—	4	2	no	—
365	C₄×C₁₃	—	4	2	no	—
366	C₄×C₁₃	—	4	1	no	—
367	C₄×C₁₃	—	4	1	no	—
368	C₄×C₁₃	—	4	1	no	—
369	C₄×C₁₃	—	4	2	no	—
370	C₄×C₁₃	C₂×#104	1	2	yes	—
371	C₂×#41	—	2	1	no	—
372	C₂×#41	C₂×C₄×C₁₃	1	2	yes	complemented
373	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	complemented
374	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
375	C₂³×C₄	—	2	2	no	—
376	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
377	C₂×M₁₆	—	2	2	no	—
378	C₂²×C₈	—	2	2	no	—
379	C₄⋊Q₈	—	2	1	no	—
380	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
381	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
382	#126	—	2	2	no	—
383	#126	—	2	2	no	—
384	#126	—	2	1	no	—
385	#125	—	2	2	no	—
386	#125	—	2	1	no	—
387	#125	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
388	#124	—	2	1	no	—
389	#124	—	2	2	no	—
390	#124	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
391	#123	—	2	2	no	—
392	#123	—	2	2	no	—
393	#123	—	2	1	no	—
394	#123	—	2	2	no	—
395	#123	—	2	2	no	—
396	C₂²⋊Q₈	—	2	2	no	—
397	C₂²⋊Q₈	—	2	2	no	—
398	C₂²⋊Q₈	—	2	1	no	—
399	C₂²⋊Q₈	—	2	2	no	—
400	C₂²⋊Q₈	—	2	1	no	—
401	C₂²⋊Q₈	—	2	2	no	—
402	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	complemented
403	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	complemented
404	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	complemented
405	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
406	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
407	#121	—	2	2	no	—
408	#121	—	2	1	no	—
409	#121	C₂×C₄×C₁₃	1	2	yes	complemented
410	#121	C₂³×C₁₃	1	1	yes	characteristic
411	#120	—	2	2	no	—
412	C₄×Q₈	—	2	1	no	—
413	C₄×Q₈	—	2	1	no	—
414	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
415	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	complemented
416	C₄×D₄	—	2	8	no	—
417	C₄×D₄	—	2	1	no	—
418	C₄×D₄	—	2	2	no	—
419	C₄×D₄	—	2	2	no	—
420	C₄×D₄	—	2	1	no	—
421	C₄×D₄	—	2	2	no	—
422	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
423	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
424	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
425	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
426	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
427	C₄×D₄	D₄×C₁₃	1	2	yes	—
428	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
429	#117	—	2	1	no	—
430	#117	—	2	2	no	—
431	#117	—	2	1	no	—
432	#117	C₂×C₄×C₁₃	1	2	yes	complemented
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	—	2	2	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	complemented
437	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
438	C₂×C₂²⋊C₄	—	2	2	no	—
439	C₂×C₂²⋊C₄	—	2	2	no	—
440	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
441	C₂×C₄²	—	2	1	no	—
442	C₂×C₄²	—	2	1	no	—
443	C₂×C₄²	—	2	2	no	—
444	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
445	C₄⋊C₈	—	2	1	no	—
446	C₄⋊C₈	—	2	1	no	—
447	C₂²⋊C₈	—	2	2	no	—
448	C₂²⋊C₈	—	2	2	no	—
449	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
450	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
451	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
452	#97	—	2	1	no	—
453	C₄×C₈	—	2	1	no	—
454	#95	—	2	2	no	—
455	#95	—	2	1	no	—
456	#95	C₂³×C₁₃	1	1	yes	characteristic
457	#95	C₂³×C₁₃	1	2	yes	—
458	#95	C₂³×C₁₃	1	1	yes	characteristic
459	C₂×C₁₃	—	2	1	no	—
460	C₂×C₁₃	—	2	1	no	—
461	C₂×C₁₃	—	2	4	no	—
462	C₂×C₁₃	—	4	2	no	—
463	C₂×C₁₃	—	8	1	no	—
464	C₂×C₁₃	#2883	1	1	yes	characteristic
465	C₂×C₁₃	#2898	1	1	yes	characteristic
466	C₂×C₁₃	C₂²×#104	1	1	yes	characteristic
467	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
468	#41	—	4	4	no	—
469	#41	—	8	2	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	2	no	—
472	C₂×Q₈	—	8	2	no	—
473	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
474	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
475	C₂×D₄	—	2	4	no	—
476	C₂×D₄	—	2	2	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	2	no	—
479	C₂×D₄	C₁₃×C₂²⋊C₄	1	2	yes	—
480	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
481	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
482	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	8	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	8	2	no	—
492	C₂²×C₄	—	8	2	no	—
493	C₂²×C₄	—	8	2	no	—
494	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
495	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
496	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
497	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
499	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
500	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
501	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
502	M₁₆	—	8	2	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	8	2	no	—
507	C₄⋊C₄	—	2	4	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
522	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
523	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
526	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
527	C₂²⋊C₄	—	2	8	no	—
528	C₂²⋊C₄	—	2	2	no	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	2	1	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	2	1	no	—
535	C₂²⋊C₄	—	2	1	no	—
536	C₂²⋊C₄	—	2	2	no	—
537	C₂²⋊C₄	—	2	1	no	—
538	C₂²⋊C₄	—	2	1	no	—
539	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
540	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
541	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
542	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
543	C₄²	—	2	4	no	—
544	C₄²	—	2	2	no	—
545	C₄²	—	2	2	no	—
546	C₄²	—	2	1	no	—
547	C₄²	—	8	1	no	—
548	C₄²	—	8	2	no	—
549	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
550	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
551	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
552	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
553	C₁₃	#17548	1	1	yes	characteristic, direct product factor, Sylow
554	C₂³	—	2	4	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	2	2	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	4	2	no	—
559	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
560	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
561	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
562	Q₈	—	4	1	no	—
563	Q₈	—	4	2	no	—
564	Q₈	—	4	2	no	—
565	Q₈	—	8	2	no	—
566	D₄	—	2	4	no	—
567	D₄	—	2	2	no	—
568	D₄	—	4	1	no	—
569	D₄	—	4	4	no	—
570	D₄	—	4	1	no	—
571	D₄	—	4	1	no	—
572	D₄	—	8	2	no	—
573	D₄	C₁₃×#104	1	4	yes	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	4	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	8	2	no	—
600	C₂×C₄	—	8	2	no	—
601	C₂×C₄	—	8	8	no	—
602	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
603	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
604	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
605	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
606	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
607	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
608	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
609	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
610	C₈	—	4	1	no	—
611	C₈	—	4	2	no	—
612	C₈	—	4	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	4	4	no	—
621	C₂²	—	4	4	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	1	no	—
625	C₂²	C₂×C₁₃×#104	1	4	yes	—
626	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
627	C₂²	C₁₃×#577	1	1	yes	characteristic
628	C₂²	C₁₃×#578	1	1	yes	characteristic
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	4	2	no	—
637	C₄	—	4	4	no	—
638	C₄	—	4	2	no	—
639	C₄	—	4	2	no	—
640	C₄	—	4	1	no	—
641	C₄	—	4	1	no	—
642	C₄	—	4	1	no	—
643	C₄	—	4	2	no	—
644	C₄	C₂×C₁₃×#104	1	2	yes	—
645	C₂	—	2	1	no	—
646	C₂	—	2	1	no	—
647	C₂	—	2	4	no	—
648	C₂	—	4	2	no	—
649	C₂	—	8	1	no	—
650	C₂	C₁₃×#2883	1	1	yes	characteristic
651	C₂	C₁₃×#2898	1	1	yes	characteristic
652	C₂	C₂²×C₁₃×#104	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3520	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2974	C₂	semidirect
3. C₁₃×#2275	C₂	semidirect
4. C₁₃×#1509	C₂	semidirect
5. C₁₃×#1508	C₂	semidirect
6. C₁₃×#1506	C₂	semidirect
7. C₁₃×#1504	C₂	semidirect
8. C₁₃×#1503	C₂	semidirect
9. C₁₃×#1501	C₂	semidirect
10. C₁₃×#1500	C₂	semidirect
11. C₂×C₁₃×#328	C₂	semidirect
12. C₁₃×#556	C₄	semidirect
14. C₁₃×#552	C₄	semidirect
16. D₄×Q₈×C₁₃	C₄	semidirect
17. C₁₃×#548	C₄	semidirect
18. C₁₃×#547	C₄	semidirect
19. C₁₃×#547	C₄	semidirect
54. C₂×C₁₃×#41	C₂×C₄	semidirect
55. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
62. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
63. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
69. C₁₃×#125	C₂×C₄	semidirect
72. C₁₃×#124	C₂×C₄	semidirect
84. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
85. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
86. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
91. C₁₃×#121	C₂×C₄	semidirect
96. C₄×Q₈×C₁₃	C₂×C₄	semidirect
97. C₄×Q₈×C₁₃	C₂×C₄	semidirect
107. C₄×D₄×C₁₃	C₂×C₄	semidirect
114. C₁₃×#117	C₂×C₄	semidirect
118. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
141. #17548	C₁₃	direct (N × H)
229. #2974	C₂×C₁₃	semidirect
230. #2275	C₂×C₁₃	semidirect
231. #1509	C₂×C₁₃	semidirect
232. #1508	C₂×C₁₃	semidirect
233. #1506	C₂×C₁₃	semidirect
234. #1504	C₂×C₁₃	semidirect
235. #1503	C₂×C₁₃	semidirect
236. #1501	C₂×C₁₃	semidirect
237. #1500	C₂×C₁₃	semidirect
238. C₂×#328	C₂×C₁₃	semidirect
298. #556	C₄×C₁₃	semidirect
300. #552	C₄×C₁₃	semidirect
302. D₄×Q₈	C₄×C₁₃	semidirect
303. #548	C₄×C₁₃	semidirect
304. #547	C₄×C₁₃	semidirect
305. #547	C₄×C₁₃	semidirect
372. C₂×#41	C₂×C₄×C₁₃	semidirect
373. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
380. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
381. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
387. #125	C₂×C₄×C₁₃	semidirect
390. #124	C₂×C₄×C₁₃	semidirect
402. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
403. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
404. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
409. #121	C₂×C₄×C₁₃	semidirect
414. C₄×Q₈	C₂×C₄×C₁₃	semidirect
415. C₄×Q₈	C₂×C₄×C₁₃	semidirect
425. C₄×D₄	C₂×C₄×C₁₃	semidirect
432. #117	C₂×C₄×C₁₃	semidirect
436. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
553. C₁₃	#17548	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×#3520	2
C₁₃×#2974	2
C₁₃×#2275	2
C₁₃×#1509	2
C₁₃×#1508	2
C₁₃×#1506	2
C₁₃×#1504	2
C₁₃×#1503	2
C₁₃×#1501	2
C₁₃×#1500	2
C₂×C₁₃×#328	2
#17548	13

Subgroups — C13×#17548 #15703887

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17548 #15703887