Subgroups — C₁₃×#34629 #15720968

Order 3328.

1558 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2655	C₂	1	4	yes	maximal, complemented
2	C₁₃×#2652	C₂	1	4	yes	maximal
3	C₁₃×#2647	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2645	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2642	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2629	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2625	C₂	1	2	yes	maximal
8	C₁₃×#2621	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2402	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2401	C₂	1	4	yes	maximal
11	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal
14	C₁₃×#2295	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
20	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#401	C₂²	1	4	yes	—
24	C₁₃×#400	C₂²	1	4	yes	—
25	C₁₃×#400	C₂²	1	4	yes	—
26	C₁₃×#400	C₂²	1	4	yes	—
27	C₁₃×#400	C₂²	1	4	yes	—
28	C₁₃×#400	C₂²	1	4	yes	—
29	C₁₃×#400	C₂²	1	4	yes	—
30	C₁₃×#400	C₂²	1	4	yes	—
31	C₁₃×#398	C₂²	1	4	yes	—
32	C₁₃×#398	C₂²	1	4	yes	—
33	C₁₃×#398	C₂²	1	4	yes	—
34	C₁₃×#398	C₂²	1	4	yes	—
35	C₁₃×#397	C₂²	1	4	yes	—
36	C₁₃×#397	C₂²	1	4	yes	—
37	C₁₃×#397	C₂²	1	4	yes	—
38	C₁₃×#396	C₂²	1	4	yes	—
39	C₁₃×#391	C₂²	1	2	yes	—
40	C₁₃×#391	C₂²	1	2	yes	—
41	C₁₃×#391	C₂²	1	2	yes	—
42	C₁₃×#391	C₂²	1	2	yes	—
43	C₁₃×#389	C₂²	1	2	yes	—
44	C₁₃×#389	C₂²	1	2	yes	—
45	C₁₃×#389	C₂²	1	2	yes	—
46	C₁₃×#389	C₂²	1	2	yes	—
47	C₁₃×#389	C₂²	1	4	yes	—
48	C₁₃×#387	C₂²	1	4	yes	—
49	C₁₃×#387	C₂²	1	4	yes	—
50	C₁₃×#387	C₂²	1	4	yes	—
51	C₁₃×#387	C₂²	1	4	yes	—
52	C₁₃×#385	C₂²	1	4	yes	—
53	C₁₃×#384	C₂²	1	1	yes	characteristic
54	C₁₃×#382	C₂²	1	1	yes	characteristic
55	C₁₃×#380	C₂²	1	2	yes	—
56	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
57	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
58	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
59	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
60	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
61	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
62	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
63	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
64	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
65	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
66	C₁₃×#376	C₂²	1	1	yes	characteristic
67	C₁₃×#376	C₂²	1	1	yes	characteristic
68	C₁₃×#376	C₂²	1	4	yes	—
69	C₄³×C₁₃	C₂²	1	1	yes	characteristic
70	C₄³×C₁₃	C₂²	1	1	yes	characteristic
71	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
72	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×C₄⋊Q₈	—	2	4	no	—
76	C₁₃×#125	—	2	4	no	—
77	C₁₃×C₂²⋊Q₈	—	2	8	no	—
78	C₄×Q₈×C₁₃	—	2	8	no	—
79	C₁₃×#117	—	2	4	no	—
80	C₁₃×#117	—	2	4	no	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
99	C₂×C₄²×C₁₃	—	2	4	no	—
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
106	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
107	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
108	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
109	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
111	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₁₃×#95	C₂³	1	2	yes	—
115	C₁₃×#95	C₂³	1	2	yes	—
116	C₁₃×#95	C₂³	1	2	yes	—
117	C₁₃×#95	C₂³	1	2	yes	—
118	C₁₃×#95	C₂³	1	4	yes	—
119	C₁₃×#95	C₂³	1	4	yes	—
120	C₁₃×#95	C₂³	1	4	yes	—
121	C₁₃×#95	C₂³	1	4	yes	—
122	C₁₃×#95	C₂³	1	4	yes	—
123	C₁₃×#95	C₂³	1	4	yes	—
124	C₁₃×#95	C₂³	1	4	yes	—
125	C₁₃×#95	C₂³	1	4	yes	—
126	C₁₃×#95	C₂³	1	4	yes	—
127	C₁₃×#95	C₂³	1	4	yes	—
128	C₁₃×#95	C₂³	1	4	yes	—
129	C₁₃×#95	C₂³	1	4	yes	—
130	C₁₃×#95	C₂³	1	4	yes	—
131	C₁₃×#95	C₂³	1	4	yes	—
132	C₁₃×#95	C₂³	1	4	yes	—
133	#34629	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₂×Q₈×C₁₃	—	2	4	no	—
136	C₂×Q₈×C₁₃	—	2	4	no	—
137	C₂×Q₈×C₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₃	—	2	2	no	—
139	C₂²×C₄×C₁₃	—	2	2	no	—
140	C₂²×C₄×C₁₃	—	2	2	no	—
141	C₂²×C₄×C₁₃	—	2	2	no	—
142	C₂²×C₄×C₁₃	—	2	4	no	—
143	C₂²×C₄×C₁₃	—	4	2	no	—
144	C₂²×C₄×C₁₃	#41	1	4	yes	—
145	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
159	C₁₃×C₄⋊C₄	—	2	4	no	—
160	C₁₃×C₄⋊C₄	—	2	4	no	—
161	C₁₃×C₄⋊C₄	—	2	4	no	—
162	C₁₃×C₄⋊C₄	—	2	8	no	—
163	C₁₃×C₄⋊C₄	—	2	4	no	—
164	C₁₃×C₄⋊C₄	—	2	8	no	—
165	C₁₃×C₄⋊C₄	—	2	8	no	—
166	C₁₃×C₄⋊C₄	—	2	4	no	—
167	C₁₃×C₄⋊C₄	—	2	8	no	—
168	C₁₃×C₄⋊C₄	—	4	4	no	—
169	C₁₃×C₄⋊C₄	—	4	4	no	—
170	C₁₃×C₄⋊C₄	—	4	4	no	—
171	C₁₃×C₄⋊C₄	—	4	4	no	—
172	C₁₃×C₄⋊C₄	—	4	4	no	—
173	C₁₃×C₂²⋊C₄	—	2	4	no	—
174	C₁₃×C₂²⋊C₄	—	2	8	no	—
175	C₁₃×C₂²⋊C₄	—	2	4	no	—
176	C₁₃×C₂²⋊C₄	—	4	4	no	—
177	C₄²×C₁₃	—	2	2	no	—
178	C₄²×C₁₃	—	2	2	no	—
179	C₄²×C₁₃	—	2	2	no	—
180	C₄²×C₁₃	—	2	2	no	—
181	C₄²×C₁₃	—	2	2	no	—
182	C₄²×C₁₃	—	2	2	no	—
183	C₄²×C₁₃	—	2	8	no	—
184	C₄²×C₁₃	—	2	4	no	—
185	C₄²×C₁₃	—	2	8	no	—
186	C₄²×C₁₃	—	2	4	no	—
187	C₄²×C₁₃	—	4	2	no	—
188	C₄²×C₁₃	—	4	2	no	—
189	C₄²×C₁₃	#41	1	4	yes	—
190	C₄²×C₁₃	#41	1	4	yes	—
191	#2655	C₂×C₁₃	1	4	yes	complemented
192	#2652	C₂×C₁₃	1	4	yes	—
193	#2647	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#2645	C₂×C₁₃	1	2	yes	complemented
195	#2642	C₂×C₁₃	1	1	yes	characteristic, complemented
196	#2629	C₂×C₁₃	1	1	yes	characteristic
197	#2625	C₂×C₁₃	1	2	yes	—
198	#2621	C₂×C₁₃	1	1	yes	characteristic
199	#2402	C₂×C₁₃	1	4	yes	complemented
200	#2401	C₂×C₁₃	1	4	yes	—
201	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
202	C₄×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
203	C₄×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	—
204	#2295	C₂×C₁₃	1	2	yes	complemented
205	C₄×#117	C₂×C₁₃	1	1	yes	characteristic
206	C₂³×C₁₃	—	2	1	no	—
207	C₂³×C₁₃	—	2	1	no	—
208	C₂³×C₁₃	—	2	2	no	—
209	C₂³×C₁₃	—	2	2	no	—
210	C₂³×C₁₃	C₂×#41	1	2	yes	—
211	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
212	Q₈×C₁₃	—	4	8	no	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	2	1	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	8	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	4	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	2	4	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	4	no	—
234	C₂×C₄×C₁₃	—	2	4	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	2	4	no	—
242	C₂×C₄×C₁₃	—	2	4	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	4	4	no	—
245	C₂×C₄×C₁₃	—	4	4	no	—
246	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
247	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
248	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
249	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
250	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
251	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
252	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
253	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
254	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
255	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
257	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
258	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
259	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
260	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
261	#401	C₂²×C₁₃	1	4	yes	—
262	#400	C₂²×C₁₃	1	4	yes	—
263	#400	C₂²×C₁₃	1	4	yes	—
264	#400	C₂²×C₁₃	1	4	yes	—
265	#400	C₂²×C₁₃	1	4	yes	—
266	#400	C₂²×C₁₃	1	4	yes	—
267	#400	C₂²×C₁₃	1	4	yes	—
268	#400	C₂²×C₁₃	1	4	yes	—
269	#398	C₂²×C₁₃	1	4	yes	—
270	#398	C₂²×C₁₃	1	4	yes	—
271	#398	C₂²×C₁₃	1	4	yes	—
272	#398	C₂²×C₁₃	1	4	yes	—
273	#397	C₂²×C₁₃	1	4	yes	—
274	#397	C₂²×C₁₃	1	4	yes	—
275	#397	C₂²×C₁₃	1	4	yes	—
276	#396	C₂²×C₁₃	1	4	yes	—
277	#391	C₂²×C₁₃	1	2	yes	—
278	#391	C₂²×C₁₃	1	2	yes	—
279	#391	C₂²×C₁₃	1	2	yes	—
280	#391	C₂²×C₁₃	1	2	yes	—
281	#389	C₂²×C₁₃	1	2	yes	—
282	#389	C₂²×C₁₃	1	4	yes	—
283	#389	C₂²×C₁₃	1	2	yes	—
284	#389	C₂²×C₁₃	1	2	yes	—
285	#389	C₂²×C₁₃	1	2	yes	—
286	#387	C₂²×C₁₃	1	4	yes	—
287	#387	C₂²×C₁₃	1	4	yes	—
288	#387	C₂²×C₁₃	1	4	yes	—
289	#387	C₂²×C₁₃	1	4	yes	—
290	#385	C₂²×C₁₃	1	4	yes	—
291	#384	C₂²×C₁₃	1	1	yes	characteristic
292	#382	C₂²×C₁₃	1	1	yes	characteristic
293	#380	C₂²×C₁₃	1	2	yes	—
294	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
295	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
296	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
297	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
298	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
299	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
300	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
301	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
302	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
303	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
304	#376	C₂²×C₁₃	1	1	yes	characteristic
305	#376	C₂²×C₁₃	1	1	yes	characteristic
306	#376	C₂²×C₁₃	1	4	yes	—
307	C₄³	C₂²×C₁₃	1	1	yes	characteristic
308	C₄³	C₂²×C₁₃	1	1	yes	characteristic
309	C₂²×C₁₃	—	2	2	no	—
310	C₂²×C₁₃	—	2	4	no	—
311	C₂²×C₁₃	—	4	1	no	—
312	C₂²×C₁₃	—	4	1	no	—
313	C₂²×C₁₃	—	4	2	no	—
314	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
315	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
316	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
317	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
318	C₂²×C₁₃	#585	1	2	yes	—
319	C₄×C₁₃	—	2	2	no	—
320	C₄×C₁₃	—	2	2	no	—
321	C₄×C₁₃	—	2	4	no	—
322	C₄×C₁₃	—	4	4	no	—
323	C₄×C₁₃	—	4	1	no	—
324	C₄×C₁₃	—	4	4	no	—
325	C₄×C₁₃	—	4	1	no	—
326	C₄×C₁₃	—	4	2	no	—
327	C₄×C₁₃	—	4	4	no	—
328	C₄×C₁₃	—	4	2	no	—
329	C₄×C₁₃	—	4	2	no	—
330	C₄×C₁₃	—	4	4	no	—
331	C₄×C₁₃	#529	1	4	yes	—
332	C₄×C₁₃	#541	1	4	yes	—
333	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
334	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
335	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
336	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
337	C₄⋊Q₈	—	2	4	no	—
338	#125	—	2	4	no	—
339	C₂²⋊Q₈	—	2	8	no	—
340	C₄×Q₈	—	2	8	no	—
341	#117	—	2	4	no	—
342	#117	—	2	4	no	—
343	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
344	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
346	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
347	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
348	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
349	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
350	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
351	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
352	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
353	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
354	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
355	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
356	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
360	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
361	C₂×C₄²	—	2	4	no	—
362	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
363	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
364	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
366	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
367	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
368	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
369	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
370	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
371	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
372	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
373	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
374	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
376	#95	C₂³×C₁₃	1	2	yes	—
377	#95	C₂³×C₁₃	1	2	yes	—
378	#95	C₂³×C₁₃	1	2	yes	—
379	#95	C₂³×C₁₃	1	2	yes	—
380	#95	C₂³×C₁₃	1	4	yes	—
381	#95	C₂³×C₁₃	1	4	yes	—
382	#95	C₂³×C₁₃	1	4	yes	—
383	#95	C₂³×C₁₃	1	4	yes	—
384	#95	C₂³×C₁₃	1	4	yes	—
385	#95	C₂³×C₁₃	1	4	yes	—
386	#95	C₂³×C₁₃	1	4	yes	—
387	#95	C₂³×C₁₃	1	4	yes	—
388	#95	C₂³×C₁₃	1	4	yes	—
389	#95	C₂³×C₁₃	1	4	yes	—
390	#95	C₂³×C₁₃	1	4	yes	—
391	#95	C₂³×C₁₃	1	4	yes	—
392	#95	C₂³×C₁₃	1	4	yes	—
393	#95	C₂³×C₁₃	1	4	yes	—
394	#95	C₂³×C₁₃	1	4	yes	—
395	C₂×C₁₃	—	4	2	no	—
396	C₂×C₁₃	C₂×#529	1	1	yes	characteristic
397	C₂×C₁₃	C₂×#541	1	1	yes	characteristic
398	C₂×C₁₃	#3455	1	1	yes	characteristic
399	C₂×C₁₃	#3461	1	2	yes	—
400	C₂×C₁₃	#3461	1	2	yes	—
401	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
402	C₂×Q₈	—	2	4	no	—
403	C₂×Q₈	—	2	4	no	—
404	C₂×Q₈	—	2	4	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	C₁₃×#41	1	4	yes	—
412	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
413	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
414	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
416	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
417	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
418	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
419	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
420	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
421	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
422	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
423	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
424	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
425	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	8	no	—
430	C₄⋊C₄	—	2	4	no	—
431	C₄⋊C₄	—	2	8	no	—
432	C₄⋊C₄	—	2	8	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	8	no	—
435	C₄⋊C₄	—	4	4	no	—
436	C₄⋊C₄	—	4	4	no	—
437	C₄⋊C₄	—	4	4	no	—
438	C₄⋊C₄	—	4	4	no	—
439	C₄⋊C₄	—	4	4	no	—
440	C₂²⋊C₄	—	2	4	no	—
441	C₂²⋊C₄	—	2	8	no	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	—	4	4	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	8	no	—
451	C₄²	—	2	4	no	—
452	C₄²	—	2	4	no	—
453	C₄²	—	2	8	no	—
454	C₄²	—	4	2	no	—
455	C₄²	—	4	2	no	—
456	C₄²	C₁₃×#41	1	4	yes	—
457	C₄²	C₁₃×#41	1	4	yes	—
458	C₁₃	#34629	1	1	yes	characteristic, direct product factor, Sylow
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	C₂×C₁₃×#41	1	2	yes	—
464	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
465	Q₈	—	4	8	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	8	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	4	4	no	—
498	C₂×C₄	—	4	4	no	—
499	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
500	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
501	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
502	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
503	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
504	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
505	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
506	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	4	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
513	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
514	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
515	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
516	C₂²	C₁₃×#585	1	2	yes	—
517	C₄	—	2	2	no	—
518	C₄	—	2	2	no	—
519	C₄	—	2	4	no	—
520	C₄	—	4	4	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	4	no	—
523	C₄	—	4	1	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	4	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	4	no	—
529	C₄	C₁₃×#529	1	4	yes	—
530	C₄	C₁₃×#541	1	4	yes	—
531	C₂	—	4	2	no	—
532	C₂	C₂×C₁₃×#529	1	1	yes	characteristic
533	C₂	C₂×C₁₃×#541	1	1	yes	characteristic
534	C₂	C₁₃×#3455	1	1	yes	characteristic
535	C₂	C₁₃×#3461	1	2	yes	—
536	C₂	C₁₃×#3461	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂⁴×C₁₃	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2655	C₂	semidirect
3. C₁₃×#2647	C₂	semidirect
4. C₁₃×#2645	C₂	semidirect
5. C₁₃×#2642	C₂	semidirect
9. C₁₃×#2402	C₂	semidirect
11. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
12. C₄×C₁₃×#125	C₂	semidirect
14. C₁₃×#2295	C₂	semidirect
133. #34629	C₁₃	direct (N × H)
191. #2655	C₂×C₁₃	semidirect
193. #2647	C₂×C₁₃	semidirect
194. #2645	C₂×C₁₃	semidirect
195. #2642	C₂×C₁₃	semidirect
199. #2402	C₂×C₁₃	semidirect
201. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
202. C₄×#125	C₂×C₁₃	semidirect
204. #2295	C₂×C₁₃	semidirect
458. C₁₃	#34629	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×#2655	2
C₁₃×#2652	2
C₁₃×#2647	2
C₁₃×#2645	2
C₁₃×#2642	2
C₁₃×#2629	2
C₁₃×#2625	2
C₁₃×#2621	2
C₁₃×#2402	2
C₁₃×#2401	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×#125	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2295	2
C₄×C₁₃×#117	2
#34629	13

Subgroups — C13×#34629 #15720968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34629 #15720968