Subgroups — C₁₃×#34593 #15720932

Order 3328.

2934 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2636	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2633	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2631	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2626	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2623	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2617	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2613	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2398	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2397	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2392	C₂	1	4	yes	maximal, complemented
13	C₄×C₁₃×#120	C₂	1	4	yes	maximal, complemented
14	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
17	C₁₃×#529	—	2	8	no	—
18	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
19	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₃×#123	C₂²	1	2	yes	—
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#120	C₂²	1	4	yes	—
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄×D₄×C₁₃	—	2	8	no	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
34	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
35	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
37	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
38	C₁₃×#400	C₂²	1	4	yes	complemented
39	C₁₃×#399	C₂²	1	4	yes	complemented
40	C₁₃×#399	C₂²	1	4	yes	complemented
41	C₁₃×#398	C₂²	1	4	yes	complemented
42	C₁₃×#397	C₂²	1	4	yes	complemented
43	C₁₃×#397	C₂²	1	4	yes	complemented
44	C₁₃×#396	C₂²	1	8	yes	complemented
45	C₁₃×#394	C₂²	1	4	yes	—
46	C₁₃×#394	C₂²	1	4	yes	—
47	C₁₃×#394	C₂²	1	8	yes	complemented
48	C₁₃×#393	C₂²	1	4	yes	complemented
49	C₁₃×#392	C₂²	1	4	yes	—
50	C₁₃×#392	C₂²	1	4	yes	—
51	C₁₃×#392	C₂²	1	4	yes	complemented
52	C₁₃×#386	C₂²	1	4	yes	—
53	C₁₃×#386	C₂²	1	8	yes	complemented
54	C₁₃×#385	C₂²	1	4	yes	—
55	C₁₃×#385	C₂²	1	8	yes	complemented
56	C₁₃×#383	C₂²	1	2	yes	complemented
57	C₁₃×#382	C₂²	1	2	yes	complemented
58	C₁₃×#381	C₂²	1	2	yes	—
59	C₁₃×#380	C₂²	1	2	yes	—
60	C₁₃×#379	C₂²	1	4	yes	—
61	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
62	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
63	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
64	C₁₃×#376	C₂²	1	2	yes	complemented
65	C₂⁵×C₁₃	C₂³	1	2	yes	—
66	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₁₃	—	2	8	no	—
68	C₂²×D₄×C₁₃	—	2	4	no	—
69	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
73	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	—	2	8	no	—
75	C₂³×C₄×C₁₃	—	4	8	no	—
76	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
77	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
78	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
81	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₁₃×#126	—	2	8	no	—
84	C₁₃×#125	—	2	4	no	—
85	C₁₃×#124	—	2	4	no	—
86	C₁₃×#123	—	2	8	no	—
87	C₁₃×C₂²⋊Q₈	—	2	4	no	—
88	C₁₃×#121	—	2	4	no	—
89	C₁₃×#120	—	2	16	no	—
90	C₄×Q₈×C₁₃	—	2	4	no	—
91	C₄×D₄×C₁₃	—	2	8	no	—
92	C₄×D₄×C₁₃	—	2	8	no	—
93	C₄×D₄×C₁₃	—	2	8	no	—
94	C₄×D₄×C₁₃	—	2	8	no	—
95	C₄×D₄×C₁₃	—	2	8	no	—
96	C₄×D₄×C₁₃	—	2	4	no	—
97	C₄×D₄×C₁₃	—	4	16	no	—
98	C₁₃×#117	—	2	8	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
111	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
113	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
116	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
117	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
118	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
123	C₂×C₄²×C₁₃	D₄	1	8	yes	complemented
124	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
125	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
126	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
130	C₁₃×#95	C₂³	1	4	yes	—
131	C₁₃×#95	C₂³	1	8	yes	—
132	C₁₃×#95	C₂³	1	8	yes	—
133	C₁₃×#95	C₂³	1	4	yes	—
134	C₁₃×#95	C₂³	1	4	yes	—
135	C₁₃×#95	C₂³	1	4	yes	—
136	#34593	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂⁴×C₁₃	—	2	4	no	—
138	C₂⁴×C₁₃	—	2	4	no	—
139	C₂⁴×C₁₃	—	4	4	no	—
140	C₂⁴×C₁₃	—	4	4	no	—
141	C₂⁴×C₁₃	#41	1	8	yes	—
142	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
143	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
144	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
145	C₂×Q₈×C₁₃	—	2	2	no	—
146	C₂×Q₈×C₁₃	—	4	2	no	—
147	C₂×D₄×C₁₃	—	2	32	no	—
148	C₂×D₄×C₁₃	—	2	8	no	—
149	C₂×D₄×C₁₃	—	2	8	no	—
150	C₂×D₄×C₁₃	—	2	4	no	—
151	C₂×D₄×C₁₃	—	2	16	no	—
152	C₂×D₄×C₁₃	—	2	8	no	—
153	C₂×D₄×C₁₃	—	2	4	no	—
154	C₂×D₄×C₁₃	—	2	4	no	—
155	C₂×D₄×C₁₃	—	2	2	no	—
156	C₂×D₄×C₁₃	—	4	8	no	—
157	C₂×D₄×C₁₃	—	4	2	no	—
158	C₂×D₄×C₁₃	—	4	8	no	—
159	C₂²×C₄×C₁₃	—	2	4	no	—
160	C₂²×C₄×C₁₃	—	2	4	no	—
161	C₂²×C₄×C₁₃	—	2	4	no	—
162	C₂²×C₄×C₁₃	—	2	4	no	—
163	C₂²×C₄×C₁₃	—	2	8	no	—
164	C₂²×C₄×C₁₃	—	2	8	no	—
165	C₂²×C₄×C₁₃	—	2	8	no	—
166	C₂²×C₄×C₁₃	—	2	16	no	—
167	C₂²×C₄×C₁₃	—	4	8	no	—
168	C₂²×C₄×C₁₃	—	4	4	no	—
169	C₂²×C₄×C₁₃	—	4	2	no	—
170	C₂²×C₄×C₁₃	—	4	32	no	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
173	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
185	C₁₃×C₄⋊C₄	—	2	4	no	—
186	C₁₃×C₄⋊C₄	—	2	4	no	—
187	C₁₃×C₄⋊C₄	—	2	4	no	—
188	C₁₃×C₄⋊C₄	—	2	4	no	—
189	C₁₃×C₄⋊C₄	—	2	2	no	—
190	C₁₃×C₄⋊C₄	—	2	4	no	—
191	C₁₃×C₄⋊C₄	—	2	2	no	—
192	C₁₃×C₄⋊C₄	—	2	4	no	—
193	C₁₃×C₄⋊C₄	—	4	4	no	—
194	C₁₃×C₄⋊C₄	—	4	8	no	—
195	C₁₃×C₂²⋊C₄	—	2	4	no	—
196	C₁₃×C₂²⋊C₄	—	2	16	no	—
197	C₁₃×C₂²⋊C₄	—	2	8	no	—
198	C₁₃×C₂²⋊C₄	—	2	8	no	—
199	C₁₃×C₂²⋊C₄	—	2	8	no	—
200	C₁₃×C₂²⋊C₄	—	2	4	no	—
201	C₁₃×C₂²⋊C₄	—	2	4	no	—
202	C₁₃×C₂²⋊C₄	—	2	4	no	—
203	C₁₃×C₂²⋊C₄	—	2	4	no	—
204	C₁₃×C₂²⋊C₄	—	4	8	no	—
205	C₁₃×C₂²⋊C₄	—	4	8	no	—
206	C₁₃×C₂²⋊C₄	—	4	8	no	—
207	C₄²×C₁₃	—	2	4	no	—
208	C₄²×C₁₃	—	2	8	no	—
209	C₄²×C₁₃	C₂×D₄	1	4	yes	—
210	C₄²×C₁₃	C₂×D₄	1	4	yes	—
211	C₄²×C₁₃	C₂×D₄	1	4	yes	—
212	C₄²×C₁₃	C₂×D₄	1	4	yes	—
213	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
214	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#2636	C₂×C₁₃	1	4	yes	complemented
216	#2633	C₂×C₁₃	1	2	yes	complemented
217	#2631	C₂×C₁₃	1	2	yes	complemented
218	#2626	C₂×C₁₃	1	2	yes	complemented
219	#2623	C₂×C₁₃	1	2	yes	complemented
220	#2617	C₂×C₁₃	1	2	yes	complemented
221	#2613	C₂×C₁₃	1	2	yes	complemented
222	#2398	C₂×C₁₃	1	2	yes	complemented
223	#2397	C₂×C₁₃	1	2	yes	complemented
224	#2392	C₂×C₁₃	1	4	yes	complemented
225	C₄×#120	C₂×C₁₃	1	4	yes	complemented
226	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
227	C₂³×C₁₃	—	2	2	no	—
228	C₂³×C₁₃	—	2	2	no	—
229	C₂³×C₁₃	—	2	16	no	—
230	C₂³×C₁₃	—	2	4	no	—
231	C₂³×C₁₃	—	2	4	no	—
232	C₂³×C₁₃	—	2	8	no	—
233	C₂³×C₁₃	—	2	8	no	—
234	C₂³×C₁₃	—	2	2	no	—
235	C₂³×C₁₃	—	2	4	no	—
236	C₂³×C₁₃	—	2	4	no	—
237	C₂³×C₁₃	—	2	4	no	—
238	C₂³×C₁₃	—	4	16	no	—
239	C₂³×C₁₃	—	4	8	no	—
240	C₂³×C₁₃	—	4	8	no	—
241	C₂³×C₁₃	—	4	16	no	—
242	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
243	C₂³×C₁₃	C₂×#41	1	8	yes	—
244	C₂³×C₁₃	C₂×#41	1	4	yes	—
245	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
246	Q₈×C₁₃	—	4	4	no	—
247	D₄×C₁₃	—	2	16	no	—
248	D₄×C₁₃	—	2	16	no	—
249	D₄×C₁₃	—	4	4	no	—
250	D₄×C₁₃	—	4	32	no	—
251	D₄×C₁₃	—	4	8	no	—
252	C₂×C₄×C₁₃	—	2	8	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	2	8	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	2	no	—
262	C₂×C₄×C₁₃	—	2	4	no	—
263	C₂×C₄×C₁₃	—	2	4	no	—
264	C₂×C₄×C₁₃	—	2	8	no	—
265	C₂×C₄×C₁₃	—	2	8	no	—
266	C₂×C₄×C₁₃	—	2	4	no	—
267	C₂×C₄×C₁₃	—	2	8	no	—
268	C₂×C₄×C₁₃	—	2	4	no	—
269	C₂×C₄×C₁₃	—	2	8	no	—
270	C₂×C₄×C₁₃	—	4	4	no	—
271	C₂×C₄×C₁₃	—	4	16	no	—
272	C₂×C₄×C₁₃	—	4	8	no	—
273	C₂×C₄×C₁₃	—	4	8	no	—
274	C₂×C₄×C₁₃	—	4	16	no	—
275	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
276	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
277	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
278	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
279	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
280	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
281	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
282	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
283	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
284	#529	—	2	8	no	—
285	C₂×#126	C₂²×C₁₃	1	2	yes	complemented
286	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
287	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
288	C₂×#123	C₂²×C₁₃	1	2	yes	—
289	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×#120	C₂²×C₁₃	1	4	yes	—
292	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
293	C₂×C₄×D₄	—	2	8	no	—
294	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
295	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
296	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
297	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
298	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
299	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
300	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
301	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
302	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
303	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
304	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
305	#400	C₂²×C₁₃	1	4	yes	complemented
306	#399	C₂²×C₁₃	1	4	yes	complemented
307	#399	C₂²×C₁₃	1	4	yes	complemented
308	#398	C₂²×C₁₃	1	4	yes	complemented
309	#397	C₂²×C₁₃	1	4	yes	complemented
310	#397	C₂²×C₁₃	1	4	yes	complemented
311	#396	C₂²×C₁₃	1	8	yes	complemented
312	#394	C₂²×C₁₃	1	4	yes	—
313	#394	C₂²×C₁₃	1	4	yes	—
314	#394	C₂²×C₁₃	1	8	yes	complemented
315	#393	C₂²×C₁₃	1	4	yes	complemented
316	#392	C₂²×C₁₃	1	4	yes	—
317	#392	C₂²×C₁₃	1	4	yes	—
318	#392	C₂²×C₁₃	1	4	yes	complemented
319	#386	C₂²×C₁₃	1	4	yes	—
320	#386	C₂²×C₁₃	1	8	yes	complemented
321	#385	C₂²×C₁₃	1	4	yes	—
322	#385	C₂²×C₁₃	1	8	yes	complemented
323	#383	C₂²×C₁₃	1	2	yes	complemented
324	#382	C₂²×C₁₃	1	2	yes	complemented
325	#381	C₂²×C₁₃	1	2	yes	—
326	#380	C₂²×C₁₃	1	2	yes	—
327	#379	C₂²×C₁₃	1	4	yes	—
328	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
329	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
330	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
331	#376	C₂²×C₁₃	1	2	yes	complemented
332	C₂²×C₁₃	—	2	2	no	—
333	C₂²×C₁₃	—	2	2	no	—
334	C₂²×C₁₃	—	2	8	no	—
335	C₂²×C₁₃	—	2	8	no	—
336	C₂²×C₁₃	—	2	16	no	—
337	C₂²×C₁₃	—	4	32	no	—
338	C₂²×C₁₃	—	4	4	no	—
339	C₂²×C₁₃	—	4	4	no	—
340	C₂²×C₁₃	—	4	8	no	—
341	C₂²×C₁₃	—	4	2	no	—
342	C₂²×C₁₃	—	4	2	no	—
343	C₂²×C₁₃	—	4	2	no	—
344	C₂²×C₁₃	—	4	8	no	—
345	C₂²×C₁₃	#525	1	4	yes	—
346	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
347	C₂²×C₁₃	C₂²×#41	1	2	yes	—
348	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
349	C₂²×C₁₃	#585	1	2	yes	—
350	C₄×C₁₃	—	2	2	no	—
351	C₄×C₁₃	—	2	2	no	—
352	C₄×C₁₃	—	2	2	no	—
353	C₄×C₁₃	—	2	2	no	—
354	C₄×C₁₃	—	2	2	no	—
355	C₄×C₁₃	—	4	2	no	—
356	C₄×C₁₃	—	4	2	no	—
357	C₄×C₁₃	—	4	4	no	—
358	C₄×C₁₃	—	4	2	no	—
359	C₄×C₁₃	—	4	8	no	—
360	C₄×C₁₃	#535	1	4	yes	—
361	C₂⁵	C₂³×C₁₃	1	2	yes	—
362	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
363	C₂²×D₄	—	2	8	no	—
364	C₂²×D₄	—	2	4	no	—
365	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
366	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
367	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
368	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
369	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
370	C₂³×C₄	—	2	8	no	—
371	C₂³×C₄	—	4	8	no	—
372	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
373	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
374	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
375	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
376	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
377	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
378	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
379	#126	—	2	8	no	—
380	#125	—	2	4	no	—
381	#124	—	2	4	no	—
382	#123	—	2	8	no	—
383	C₂²⋊Q₈	—	2	4	no	—
384	#121	—	2	4	no	—
385	#120	—	2	16	no	—
386	C₄×Q₈	—	2	4	no	—
387	C₄×D₄	—	2	8	no	—
388	C₄×D₄	—	2	8	no	—
389	C₄×D₄	—	2	8	no	—
390	C₄×D₄	—	2	8	no	—
391	C₄×D₄	—	2	8	no	—
392	C₄×D₄	—	2	4	no	—
393	C₄×D₄	—	4	16	no	—
394	#117	—	2	8	no	—
395	C₂×C₄⋊C₄	—	2	4	no	—
396	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
397	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
398	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
404	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
405	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
406	C₂×C₂²⋊C₄	—	2	8	no	—
407	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
419	C₂×C₄²	D₄×C₁₃	1	8	yes	complemented
420	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
421	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
422	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
425	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
426	#95	C₂³×C₁₃	1	4	yes	—
427	#95	C₂³×C₁₃	1	4	yes	—
428	#95	C₂³×C₁₃	1	4	yes	—
429	#95	C₂³×C₁₃	1	8	yes	—
430	#95	C₂³×C₁₃	1	8	yes	—
431	#95	C₂³×C₁₃	1	4	yes	—
432	C₂×C₁₃	—	2	4	no	—
433	C₂×C₁₃	—	4	8	no	—
434	C₂×C₁₃	—	8	2	no	—
435	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
436	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
437	C₂×C₁₃	#3449	1	1	yes	characteristic
438	C₂×C₁₃	#3459	1	4	yes	—
439	C₂⁴	—	2	4	no	—
440	C₂⁴	—	2	4	no	—
441	C₂⁴	—	4	4	no	—
442	C₂⁴	—	4	4	no	—
443	C₂⁴	C₁₃×#41	1	8	yes	—
444	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
445	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
446	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
447	C₂×Q₈	—	2	2	no	—
448	C₂×Q₈	—	4	2	no	—
449	C₂×D₄	—	2	32	no	—
450	C₂×D₄	—	2	8	no	—
451	C₂×D₄	—	2	8	no	—
452	C₂×D₄	—	2	4	no	—
453	C₂×D₄	—	2	16	no	—
454	C₂×D₄	—	2	8	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	4	8	no	—
459	C₂×D₄	—	4	2	no	—
460	C₂×D₄	—	4	8	no	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	8	no	—
466	C₂²×C₄	—	2	8	no	—
467	C₂²×C₄	—	2	8	no	—
468	C₂²×C₄	—	2	16	no	—
469	C₂²×C₄	—	4	8	no	—
470	C₂²×C₄	—	4	4	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	4	32	no	—
473	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
474	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
475	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
476	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
477	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
478	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
479	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
480	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
481	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
482	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
483	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
484	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
485	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
486	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
487	C₄⋊C₄	—	2	4	no	—
488	C₄⋊C₄	—	2	4	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	4	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	4	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	4	8	no	—
496	C₄⋊C₄	—	4	4	no	—
497	C₂²⋊C₄	—	2	4	no	—
498	C₂²⋊C₄	—	2	16	no	—
499	C₂²⋊C₄	—	2	8	no	—
500	C₂²⋊C₄	—	2	8	no	—
501	C₂²⋊C₄	—	2	8	no	—
502	C₂²⋊C₄	—	2	4	no	—
503	C₂²⋊C₄	—	2	4	no	—
504	C₂²⋊C₄	—	2	4	no	—
505	C₂²⋊C₄	—	2	4	no	—
506	C₂²⋊C₄	—	4	8	no	—
507	C₂²⋊C₄	—	4	8	no	—
508	C₂²⋊C₄	—	4	8	no	—
509	C₄²	—	2	4	no	—
510	C₄²	—	2	8	no	—
511	C₄²	C₂×D₄×C₁₃	1	4	yes	—
512	C₄²	C₂×D₄×C₁₃	1	4	yes	—
513	C₄²	C₂×D₄×C₁₃	1	4	yes	—
514	C₄²	C₂×D₄×C₁₃	1	4	yes	—
515	C₁₃	#34593	1	1	yes	characteristic, direct product factor, Sylow
516	C₂³	—	2	2	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	16	no	—
519	C₂³	—	2	4	no	—
520	C₂³	—	2	4	no	—
521	C₂³	—	2	8	no	—
522	C₂³	—	2	8	no	—
523	C₂³	—	2	2	no	—
524	C₂³	—	2	4	no	—
525	C₂³	—	2	4	no	—
526	C₂³	—	2	4	no	—
527	C₂³	—	4	16	no	—
528	C₂³	—	4	8	no	—
529	C₂³	—	4	8	no	—
530	C₂³	—	4	16	no	—
531	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
532	C₂³	C₂×C₁₃×#41	1	8	yes	—
533	C₂³	C₂×C₁₃×#41	1	4	yes	—
534	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
535	Q₈	—	4	4	no	—
536	D₄	—	2	16	no	—
537	D₄	—	2	16	no	—
538	D₄	—	4	4	no	—
539	D₄	—	4	32	no	—
540	D₄	—	4	8	no	—
541	C₂×C₄	—	2	8	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	8	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	8	no	—
554	C₂×C₄	—	2	8	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	8	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	8	no	—
559	C₂×C₄	—	4	4	no	—
560	C₂×C₄	—	4	16	no	—
561	C₂×C₄	—	4	8	no	—
562	C₂×C₄	—	4	16	no	—
563	C₂×C₄	—	4	8	no	—
564	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
565	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
566	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
567	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
568	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
569	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
570	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	8	no	—
574	C₂²	—	2	8	no	—
575	C₂²	—	2	16	no	—
576	C₂²	—	4	32	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	4	4	no	—
579	C₂²	—	4	8	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	8	no	—
584	C₂²	C₁₃×#525	1	4	yes	—
585	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
586	C₂²	C₂²×C₁₃×#41	1	2	yes	—
587	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
588	C₂²	C₁₃×#585	1	2	yes	—
589	C₄	—	2	2	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	4	2	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	4	no	—
597	C₄	—	4	2	no	—
598	C₄	—	4	8	no	—
599	C₄	C₁₃×#535	1	4	yes	—
600	C₂	—	2	4	no	—
601	C₂	—	4	8	no	—
602	C₂	—	8	2	no	—
603	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
604	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
605	C₂	C₁₃×#3449	1	1	yes	characteristic
606	C₂	C₁₃×#3459	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
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. C₂×C₁₃×#529	C₂	semidirect
2. C₂²×C₄×D₄×C₁₃	C₂	semidirect
3. C₁₃×#2636	C₂	semidirect
4. C₁₃×#2633	C₂	semidirect
5. C₁₃×#2631	C₂	semidirect
6. C₁₃×#2626	C₂	semidirect
7. C₁₃×#2623	C₂	semidirect
8. C₁₃×#2617	C₂	semidirect
9. C₁₃×#2613	C₂	semidirect
10. C₁₃×#2398	C₂	semidirect
11. C₁₃×#2397	C₂	semidirect
12. C₁₃×#2392	C₂	semidirect
13. C₄×C₁₃×#120	C₂	semidirect
14. C₁₃×#2283	C₂	semidirect
18. C₂×C₁₃×#126	C₂²	semidirect
19. C₂×C₁₃×#125	C₂²	semidirect
20. C₂×C₁₃×#124	C₂²	semidirect
25. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
32. C₂×C₄×D₄×C₁₃	C₂²	semidirect
33. C₂×C₄×D₄×C₁₃	C₂²	semidirect
34. C₂×C₁₃×#117	C₂²	semidirect
38. C₁₃×#400	C₂²	semidirect
39. C₁₃×#399	C₂²	semidirect
40. C₁₃×#399	C₂²	semidirect
41. C₁₃×#398	C₂²	semidirect
42. C₁₃×#397	C₂²	semidirect
43. C₁₃×#397	C₂²	semidirect
44. C₁₃×#396	C₂²	semidirect
47. C₁₃×#394	C₂²	semidirect
48. C₁₃×#393	C₂²	semidirect
51. C₁₃×#392	C₂²	semidirect
53. C₁₃×#386	C₂²	semidirect
55. C₁₃×#385	C₂²	semidirect
56. C₁₃×#383	C₂²	semidirect
57. C₁₃×#382	C₂²	semidirect
61. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
63. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
64. C₁₃×#376	C₂²	semidirect
123. C₂×C₄²×C₁₃	D₄	semidirect
136. #34593	C₁₃	direct (N × H)
213. C₂×#529	C₂×C₁₃	semidirect
214. C₂²×C₄×D₄	C₂×C₁₃	semidirect
215. #2636	C₂×C₁₃	semidirect
216. #2633	C₂×C₁₃	semidirect
217. #2631	C₂×C₁₃	semidirect
218. #2626	C₂×C₁₃	semidirect
219. #2623	C₂×C₁₃	semidirect
220. #2617	C₂×C₁₃	semidirect
221. #2613	C₂×C₁₃	semidirect
222. #2398	C₂×C₁₃	semidirect
223. #2397	C₂×C₁₃	semidirect
224. #2392	C₂×C₁₃	semidirect
225. C₄×#120	C₂×C₁₃	semidirect
226. #2283	C₂×C₁₃	semidirect
285. C₂×#126	C₂²×C₁₃	semidirect
286. C₂×#125	C₂²×C₁₃	semidirect
287. C₂×#124	C₂²×C₁₃	semidirect
292. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
299. C₂×C₄×D₄	C₂²×C₁₃	semidirect
300. C₂×C₄×D₄	C₂²×C₁₃	semidirect
301. C₂×#117	C₂²×C₁₃	semidirect
305. #400	C₂²×C₁₃	semidirect
306. #399	C₂²×C₁₃	semidirect
307. #399	C₂²×C₁₃	semidirect
308. #398	C₂²×C₁₃	semidirect
309. #397	C₂²×C₁₃	semidirect
310. #397	C₂²×C₁₃	semidirect
311. #396	C₂²×C₁₃	semidirect
314. #394	C₂²×C₁₃	semidirect
315. #393	C₂²×C₁₃	semidirect
318. #392	C₂²×C₁₃	semidirect
320. #386	C₂²×C₁₃	semidirect
322. #385	C₂²×C₁₃	semidirect
323. #383	C₂²×C₁₃	semidirect
324. #382	C₂²×C₁₃	semidirect
328. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
330. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
331. #376	C₂²×C₁₃	semidirect
419. C₂×C₄²	D₄×C₁₃	semidirect
515. C₁₃	#34593	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#529	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2636	2
C₁₃×#2633	2
C₁₃×#2631	2
C₁₃×#2626	2
C₁₃×#2623	2
C₁₃×#2617	2
C₁₃×#2613	2
C₁₃×#2398	2
C₁₃×#2397	2
C₁₃×#2392	2
C₄×C₁₃×#120	2
C₁₃×#2283	2
#34593	13

Subgroups — C13×#34593 #15720932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34593 #15720932