Subgroups — C₁₃×#34575 #15720914

Order 3328.

2794 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#525	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2663	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2661	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2659	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2656	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2639	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2617	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2395	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2388	C₂	1	4	yes	maximal, complemented
10	C₄×C₁₃×#121	C₂	1	4	yes	maximal, complemented
11	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	2	yes	—
13	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#525	—	2	16	no	—
15	C₂×C₁₃×#123	C₂²	1	4	yes	—
16	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×#121	C₂²	1	4	yes	—
19	C₂×C₁₃×#121	C₂²	1	2	yes	—
20	C₂×C₁₃×#121	C₂²	1	2	yes	—
21	C₂×C₁₃×#120	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
24	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
25	C₂×C₁₃×#117	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
28	C₁₃×#400	C₂²	1	4	yes	complemented
29	C₁₃×#399	C₂²	1	4	yes	complemented
30	C₁₃×#398	C₂²	1	4	yes	complemented
31	C₁₃×#397	C₂²	1	8	yes	—
32	C₁₃×#397	C₂²	1	4	yes	complemented
33	C₁₃×#395	C₂²	1	4	yes	complemented
34	C₁₃×#394	C₂²	1	8	yes	—
35	C₁₃×#394	C₂²	1	8	yes	—
36	C₁₃×#394	C₂²	1	4	yes	complemented
37	C₁₃×#393	C₂²	1	4	yes	complemented
38	C₁₃×#392	C₂²	1	8	yes	—
39	C₁₃×#392	C₂²	1	4	yes	complemented
40	C₁₃×#390	C₂²	1	4	yes	complemented
41	C₁₃×#389	C₂²	1	4	yes	complemented
42	C₁₃×#388	C₂²	1	8	yes	complemented
43	C₁₃×#386	C₂²	1	8	yes	—
44	C₁₃×#380	C₂²	1	4	yes	—
45	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
46	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
47	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
48	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
49	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
51	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₁₃×#41	—	2	8	no	—
53	C₂×C₁₃×#41	—	4	8	no	—
54	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
55	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
56	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
57	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
58	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
59	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃	—	4	4	no	—
61	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
62	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
66	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
69	C₁₃×#123	—	2	16	no	—
70	C₁₃×C₂²⋊Q₈	—	2	8	no	—
71	C₁₃×C₂²⋊Q₈	—	2	8	no	—
72	C₁₃×#121	—	2	8	no	—
73	C₁₃×#121	—	2	8	no	—
74	C₁₃×#121	—	2	16	no	—
75	C₁₃×#120	—	2	16	no	—
76	C₄×D₄×C₁₃	—	2	16	no	—
77	C₄×D₄×C₁₃	—	2	16	no	—
78	C₄×D₄×C₁₃	—	4	8	no	—
79	C₁₃×#117	—	2	8	no	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	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×C₂²⋊C₄	—	2	8	no	—
88	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
89	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
90	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
91	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
92	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
97	C₂×C₄²×C₁₃	—	4	4	no	—
98	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
99	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
100	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
101	C₁₃×#95	C₂³	1	4	yes	—
102	C₁₃×#95	C₂³	1	4	yes	—
103	C₁₃×#95	C₂³	1	8	yes	—
104	C₁₃×#95	C₂³	1	8	yes	—
105	C₁₃×#95	C₂³	1	8	yes	—
106	#34575	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₂⁴×C₁₃	—	2	4	no	—
108	C₂⁴×C₁₃	—	4	2	no	—
109	C₂⁴×C₁₃	—	4	1	no	—
110	C₂⁴×C₁₃	—	4	1	no	—
111	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
112	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
113	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
114	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
115	C₁₃×#41	—	4	32	no	—
116	C₂×Q₈×C₁₃	—	2	4	no	—
117	C₂×Q₈×C₁₃	—	4	4	no	—
118	C₂×D₄×C₁₃	—	2	8	no	—
119	C₂×D₄×C₁₃	—	2	8	no	—
120	C₂×D₄×C₁₃	—	2	8	no	—
121	C₂×D₄×C₁₃	—	2	16	no	—
122	C₂×D₄×C₁₃	—	2	4	no	—
123	C₂×D₄×C₁₃	—	2	8	no	—
124	C₂×D₄×C₁₃	—	4	4	no	—
125	C₂×D₄×C₁₃	—	4	4	no	—
126	C₂×D₄×C₁₃	—	4	4	no	—
127	C₂×D₄×C₁₃	—	4	4	no	—
128	C₂×D₄×C₁₃	—	4	4	no	—
129	C₂×D₄×C₁₃	—	4	8	no	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	2	8	no	—
132	C₂²×C₄×C₁₃	—	2	4	no	—
133	C₂²×C₄×C₁₃	—	2	8	no	—
134	C₂²×C₄×C₁₃	—	2	16	no	—
135	C₂²×C₄×C₁₃	—	4	16	no	—
136	C₂²×C₄×C₁₃	—	4	2	no	—
137	C₂²×C₄×C₁₃	—	4	2	no	—
138	C₂²×C₄×C₁₃	—	4	4	no	—
139	C₂²×C₄×C₁₃	—	4	2	no	—
140	C₂²×C₄×C₁₃	—	4	2	no	—
141	C₂²×C₄×C₁₃	—	4	2	no	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
146	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
147	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
155	C₁₃×C₄⋊C₄	—	2	4	no	—
156	C₁₃×C₄⋊C₄	—	2	4	no	—
157	C₁₃×C₄⋊C₄	—	2	8	no	—
158	C₁₃×C₄⋊C₄	—	2	8	no	—
159	C₁₃×C₄⋊C₄	—	2	8	no	—
160	C₁₃×C₄⋊C₄	—	4	4	no	—
161	C₁₃×C₄⋊C₄	—	4	4	no	—
162	C₁₃×C₂²⋊C₄	—	2	8	no	—
163	C₁₃×C₂²⋊C₄	—	2	8	no	—
164	C₁₃×C₂²⋊C₄	—	2	8	no	—
165	C₁₃×C₂²⋊C₄	—	2	8	no	—
166	C₁₃×C₂²⋊C₄	—	2	8	no	—
167	C₁₃×C₂²⋊C₄	—	2	16	no	—
168	C₁₃×C₂²⋊C₄	—	2	16	no	—
169	C₁₃×C₂²⋊C₄	—	4	8	no	—
170	C₁₃×C₂²⋊C₄	—	4	8	no	—
171	C₄²×C₁₃	—	2	8	no	—
172	C₄²×C₁₃	—	2	8	no	—
173	C₄²×C₁₃	—	4	4	no	—
174	C₂×#525	C₂×C₁₃	1	2	yes	complemented
175	#2663	C₂×C₁₃	1	4	yes	complemented
176	#2661	C₂×C₁₃	1	4	yes	complemented
177	#2659	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#2656	C₂×C₁₃	1	1	yes	characteristic, complemented
179	#2639	C₂×C₁₃	1	2	yes	complemented
180	#2617	C₂×C₁₃	1	4	yes	complemented
181	#2395	C₂×C₁₃	1	4	yes	complemented
182	#2388	C₂×C₁₃	1	4	yes	complemented
183	C₄×#121	C₂×C₁₃	1	4	yes	complemented
184	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂³×C₁₃	—	2	2	no	—
186	C₂³×C₁₃	—	2	1	no	—
187	C₂³×C₁₃	—	2	1	no	—
188	C₂³×C₁₃	—	2	8	no	—
189	C₂³×C₁₃	—	2	4	no	—
190	C₂³×C₁₃	—	2	4	no	—
191	C₂³×C₁₃	—	2	2	no	—
192	C₂³×C₁₃	—	2	2	no	—
193	C₂³×C₁₃	—	2	4	no	—
194	C₂³×C₁₃	—	2	8	no	—
195	C₂³×C₁₃	—	2	8	no	—
196	C₂³×C₁₃	—	2	4	no	—
197	C₂³×C₁₃	—	2	4	no	—
198	C₂³×C₁₃	—	4	4	no	—
199	C₂³×C₁₃	—	4	4	no	—
200	C₂³×C₁₃	—	4	8	no	—
201	C₂³×C₁₃	—	4	8	no	—
202	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
203	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
204	C₂³×C₁₃	C₂×#41	1	4	yes	—
205	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
206	Q₈×C₁₃	—	4	8	no	—
207	D₄×C₁₃	—	4	16	no	—
208	D₄×C₁₃	—	4	8	no	—
209	D₄×C₁₃	—	4	16	no	—
210	D₄×C₁₃	—	4	16	no	—
211	D₄×C₁₃	—	4	16	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	2	4	no	—
216	C₂×C₄×C₁₃	—	2	8	no	—
217	C₂×C₄×C₁₃	—	2	16	no	—
218	C₂×C₄×C₁₃	—	2	4	no	—
219	C₂×C₄×C₁₃	—	2	4	no	—
220	C₂×C₄×C₁₃	—	2	4	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	8	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	8	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	—	4	8	no	—
229	C₂×C₄×C₁₃	—	4	4	no	—
230	C₂×C₄×C₁₃	—	4	8	no	—
231	C₂×C₄×C₁₃	—	4	8	no	—
232	C₂×C₄×C₁₃	—	4	16	no	—
233	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
234	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
235	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
236	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
237	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
238	C₂²×#41	C₂²×C₁₃	1	2	yes	—
239	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
240	#525	—	2	16	no	—
241	C₂×#123	C₂²×C₁₃	1	4	yes	—
242	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
243	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
244	C₂×#121	C₂²×C₁₃	1	4	yes	—
245	C₂×#121	C₂²×C₁₃	1	2	yes	—
246	C₂×#121	C₂²×C₁₃	1	2	yes	—
247	C₂×#120	C₂²×C₁₃	1	4	yes	—
248	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
249	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
250	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
251	C₂×#117	C₂²×C₁₃	1	2	yes	—
252	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
253	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
254	#400	C₂²×C₁₃	1	4	yes	complemented
255	#399	C₂²×C₁₃	1	4	yes	complemented
256	#398	C₂²×C₁₃	1	4	yes	complemented
257	#397	C₂²×C₁₃	1	8	yes	—
258	#397	C₂²×C₁₃	1	4	yes	complemented
259	#395	C₂²×C₁₃	1	4	yes	complemented
260	#394	C₂²×C₁₃	1	8	yes	—
261	#394	C₂²×C₁₃	1	8	yes	—
262	#394	C₂²×C₁₃	1	4	yes	complemented
263	#393	C₂²×C₁₃	1	4	yes	complemented
264	#392	C₂²×C₁₃	1	8	yes	—
265	#392	C₂²×C₁₃	1	4	yes	complemented
266	#390	C₂²×C₁₃	1	4	yes	complemented
267	#389	C₂²×C₁₃	1	4	yes	complemented
268	#388	C₂²×C₁₃	1	8	yes	complemented
269	#386	C₂²×C₁₃	1	8	yes	—
270	#380	C₂²×C₁₃	1	4	yes	—
271	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
272	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
273	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
274	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
275	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
277	C₂²×C₁₃	—	2	2	no	—
278	C₂²×C₁₃	—	2	2	no	—
279	C₂²×C₁₃	—	2	4	no	—
280	C₂²×C₁₃	—	2	4	no	—
281	C₂²×C₁₃	—	2	4	no	—
282	C₂²×C₁₃	—	2	4	no	—
283	C₂²×C₁₃	—	2	4	no	—
284	C₂²×C₁₃	—	4	16	no	—
285	C₂²×C₁₃	—	4	4	no	—
286	C₂²×C₁₃	—	4	4	no	—
287	C₂²×C₁₃	—	4	4	no	—
288	C₂²×C₁₃	—	4	4	no	—
289	C₂²×C₁₃	—	4	4	no	—
290	C₂²×C₁₃	—	4	8	no	—
291	C₂²×C₁₃	—	4	8	no	—
292	C₂²×C₁₃	#532	1	4	yes	—
293	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
294	C₂²×C₁₃	C₂²×#41	1	2	yes	—
295	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
296	C₂²×C₁₃	#585	1	1	yes	characteristic
297	C₂²×C₁₃	#585	1	1	yes	characteristic
298	C₄×C₁₃	—	2	2	no	—
299	C₄×C₁₃	—	2	4	no	—
300	C₄×C₁₃	—	2	8	no	—
301	C₄×C₁₃	—	4	4	no	—
302	C₄×C₁₃	—	4	4	no	—
303	C₄×C₁₃	—	4	4	no	—
304	C₄×C₁₃	—	4	4	no	—
305	C₄×C₁₃	#534	1	4	yes	—
306	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
307	C₂×#41	—	2	8	no	—
308	C₂×#41	—	4	8	no	—
309	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
310	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
311	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
312	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
313	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
314	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
315	C₂³×C₄	—	4	4	no	—
316	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
317	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
318	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
319	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
321	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
323	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
324	#123	—	2	16	no	—
325	C₂²⋊Q₈	—	2	8	no	—
326	C₂²⋊Q₈	—	2	8	no	—
327	#121	—	2	8	no	—
328	#121	—	2	8	no	—
329	#121	—	2	16	no	—
330	#120	—	2	16	no	—
331	C₄×D₄	—	2	16	no	—
332	C₄×D₄	—	2	16	no	—
333	C₄×D₄	—	4	8	no	—
334	#117	—	2	8	no	—
335	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
336	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
337	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
338	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
339	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
340	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
341	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
342	C₂×C₂²⋊C₄	—	2	8	no	—
343	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
352	C₂×C₄²	—	4	4	no	—
353	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
354	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
355	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
356	#95	C₂³×C₁₃	1	4	yes	—
357	#95	C₂³×C₁₃	1	4	yes	—
358	#95	C₂³×C₁₃	1	8	yes	—
359	#95	C₂³×C₁₃	1	8	yes	—
360	#95	C₂³×C₁₃	1	8	yes	—
361	C₂×C₁₃	—	2	4	no	—
362	C₂×C₁₃	—	4	4	no	—
363	C₂×C₁₃	—	8	4	no	—
364	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
365	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
366	C₂×C₁₃	#3449	1	1	yes	characteristic
367	C₂×C₁₃	#3459	1	2	yes	—
368	C₂×C₁₃	#3460	1	2	yes	—
369	C₂⁴	—	2	4	no	—
370	C₂⁴	—	4	2	no	—
371	C₂⁴	—	4	1	no	—
372	C₂⁴	—	4	1	no	—
373	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
374	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
375	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
376	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
377	#41	—	4	32	no	—
378	C₂×Q₈	—	2	4	no	—
379	C₂×Q₈	—	4	4	no	—
380	C₂×D₄	—	2	8	no	—
381	C₂×D₄	—	2	8	no	—
382	C₂×D₄	—	2	8	no	—
383	C₂×D₄	—	2	16	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	8	no	—
386	C₂×D₄	—	4	4	no	—
387	C₂×D₄	—	4	4	no	—
388	C₂×D₄	—	4	8	no	—
389	C₂×D₄	—	4	4	no	—
390	C₂×D₄	—	4	4	no	—
391	C₂×D₄	—	4	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	8	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	8	no	—
396	C₂²×C₄	—	2	16	no	—
397	C₂²×C₄	—	4	16	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	—	4	4	no	—
401	C₂²×C₄	—	4	2	no	—
402	C₂²×C₄	—	4	2	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
405	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
406	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
407	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
408	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
409	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
410	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
411	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
412	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
413	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
414	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
415	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
416	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	8	no	—
420	C₄⋊C₄	—	2	8	no	—
421	C₄⋊C₄	—	2	8	no	—
422	C₄⋊C₄	—	4	4	no	—
423	C₄⋊C₄	—	4	4	no	—
424	C₂²⋊C₄	—	2	8	no	—
425	C₂²⋊C₄	—	2	8	no	—
426	C₂²⋊C₄	—	2	8	no	—
427	C₂²⋊C₄	—	2	8	no	—
428	C₂²⋊C₄	—	2	8	no	—
429	C₂²⋊C₄	—	2	16	no	—
430	C₂²⋊C₄	—	2	16	no	—
431	C₂²⋊C₄	—	4	8	no	—
432	C₂²⋊C₄	—	4	8	no	—
433	C₄²	—	2	8	no	—
434	C₄²	—	2	8	no	—
435	C₄²	—	4	4	no	—
436	C₁₃	#34575	1	1	yes	characteristic, direct product factor, Sylow
437	C₂³	—	2	2	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	2	8	no	—
441	C₂³	—	2	4	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	4	no	—
446	C₂³	—	2	8	no	—
447	C₂³	—	2	8	no	—
448	C₂³	—	2	4	no	—
449	C₂³	—	2	4	no	—
450	C₂³	—	4	4	no	—
451	C₂³	—	4	4	no	—
452	C₂³	—	4	8	no	—
453	C₂³	—	4	8	no	—
454	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
455	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
456	C₂³	C₂×C₁₃×#41	1	4	yes	—
457	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
458	Q₈	—	4	8	no	—
459	D₄	—	4	16	no	—
460	D₄	—	4	8	no	—
461	D₄	—	4	16	no	—
462	D₄	—	4	16	no	—
463	D₄	—	4	16	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	8	no	—
469	C₂×C₄	—	2	16	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	8	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	8	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	4	8	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	—	4	8	no	—
483	C₂×C₄	—	4	8	no	—
484	C₂×C₄	—	4	16	no	—
485	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
486	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
487	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
488	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
489	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	4	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	2	4	no	—
495	C₂²	—	2	4	no	—
496	C₂²	—	2	4	no	—
497	C₂²	—	4	16	no	—
498	C₂²	—	4	4	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	4	8	no	—
504	C₂²	—	4	8	no	—
505	C₂²	C₁₃×#532	1	4	yes	—
506	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
507	C₂²	C₂²×C₁₃×#41	1	2	yes	—
508	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
509	C₂²	C₁₃×#585	1	1	yes	characteristic
510	C₂²	C₁₃×#585	1	1	yes	characteristic
511	C₄	—	2	2	no	—
512	C₄	—	2	4	no	—
513	C₄	—	2	8	no	—
514	C₄	—	4	4	no	—
515	C₄	—	4	4	no	—
516	C₄	—	4	4	no	—
517	C₄	—	4	4	no	—
518	C₄	C₁₃×#534	1	4	yes	—
519	C₂	—	2	4	no	—
520	C₂	—	4	4	no	—
521	C₂	—	8	4	no	—
522	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
523	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
524	C₂	C₁₃×#3449	1	1	yes	characteristic
525	C₂	C₁₃×#3459	1	2	yes	—
526	C₂	C₁₃×#3460	1	2	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×#525	C₂	semidirect
2. C₁₃×#2663	C₂	semidirect
3. C₁₃×#2661	C₂	semidirect
4. C₁₃×#2659	C₂	semidirect
5. C₁₃×#2656	C₂	semidirect
6. C₁₃×#2639	C₂	semidirect
7. C₁₃×#2617	C₂	semidirect
8. C₁₃×#2395	C₂	semidirect
9. C₁₃×#2388	C₂	semidirect
10. C₄×C₁₃×#121	C₂	semidirect
11. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
24. C₂×C₄×D₄×C₁₃	C₂²	semidirect
28. C₁₃×#400	C₂²	semidirect
29. C₁₃×#399	C₂²	semidirect
30. C₁₃×#398	C₂²	semidirect
32. C₁₃×#397	C₂²	semidirect
33. C₁₃×#395	C₂²	semidirect
36. C₁₃×#394	C₂²	semidirect
37. C₁₃×#393	C₂²	semidirect
39. C₁₃×#392	C₂²	semidirect
40. C₁₃×#390	C₂²	semidirect
41. C₁₃×#389	C₂²	semidirect
42. C₁₃×#388	C₂²	semidirect
45. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
48. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
61. C₂³×C₄×C₁₃	D₄	semidirect
106. #34575	C₁₃	direct (N × H)
146. C₂²×C₄×C₁₃	#41	semidirect
174. C₂×#525	C₂×C₁₃	semidirect
175. #2663	C₂×C₁₃	semidirect
176. #2661	C₂×C₁₃	semidirect
177. #2659	C₂×C₁₃	semidirect
178. #2656	C₂×C₁₃	semidirect
179. #2639	C₂×C₁₃	semidirect
180. #2617	C₂×C₁₃	semidirect
181. #2395	C₂×C₁₃	semidirect
182. #2388	C₂×C₁₃	semidirect
183. C₄×#121	C₂×C₁₃	semidirect
184. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
250. C₂×C₄×D₄	C₂²×C₁₃	semidirect
254. #400	C₂²×C₁₃	semidirect
255. #399	C₂²×C₁₃	semidirect
256. #398	C₂²×C₁₃	semidirect
258. #397	C₂²×C₁₃	semidirect
259. #395	C₂²×C₁₃	semidirect
262. #394	C₂²×C₁₃	semidirect
263. #393	C₂²×C₁₃	semidirect
265. #392	C₂²×C₁₃	semidirect
266. #390	C₂²×C₁₃	semidirect
267. #389	C₂²×C₁₃	semidirect
268. #388	C₂²×C₁₃	semidirect
271. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
274. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
316. C₂³×C₄	D₄×C₁₃	semidirect
408. C₂²×C₄	C₁₃×#41	semidirect
436. C₁₃	#34575	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×#525	2
C₁₃×#2663	2
C₁₃×#2661	2
C₁₃×#2659	2
C₁₃×#2656	2
C₁₃×#2639	2
C₁₃×#2617	2
C₁₃×#2395	2
C₁₃×#2388	2
C₄×C₁₃×#121	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#34575	13

Subgroups — C13×#34575 #15720914

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34575 #15720914