Subgroups — C₁₃×#34977 #15721316

Order 3328.

2962 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2610	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2567	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2563	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2548	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2541	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2500	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2431	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2414	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2388	C₂	1	4	yes	maximal, complemented
12	C₄×C₁₃×#127	C₂	1	2	yes	maximal, complemented
13	C₄×C₁₃×#124	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₃×#121	C₂	1	4	yes	maximal, complemented
15	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×#41	C₂²	1	2	yes	—
18	C₁₃×#532	—	2	8	no	—
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#127	C₂²	1	2	yes	—
22	C₂×C₁₃×#124	C₂²	1	2	yes	—
23	C₂×C₁₃×#124	C₂²	1	2	yes	—
24	C₂×C₁₃×#121	C₂²	1	2	yes	—
25	C₂×C₁₃×#121	C₂²	1	4	yes	—
26	C₂×C₁₃×#121	C₂²	1	2	yes	—
27	C₄×C₁₃×#41	—	2	8	no	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
37	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#117	C₂²	1	2	yes	—
39	C₂×C₁₃×#117	C₂²	1	2	yes	—
40	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
41	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
42	C₁₃×#395	C₂²	1	4	yes	—
43	C₁₃×#394	C₂²	1	8	yes	—
44	C₁₃×#394	C₂²	1	4	yes	—
45	C₁₃×#393	C₂²	1	4	yes	—
46	C₁₃×#392	C₂²	1	4	yes	—
47	C₁₃×#392	C₂²	1	8	yes	—
48	C₁₃×#391	C₂²	1	2	yes	—
49	C₁₃×#390	C₂²	1	2	yes	—
50	C₁₃×#390	C₂²	1	2	yes	—
51	C₁₃×#390	C₂²	1	4	yes	—
52	C₁₃×#390	C₂²	1	2	yes	—
53	C₁₃×#390	C₂²	1	8	yes	—
54	C₁₃×#389	C₂²	1	4	yes	—
55	C₁₃×#388	C₂²	1	8	yes	—
56	C₁₃×#388	C₂²	1	8	yes	—
57	C₁₃×#386	C₂²	1	8	yes	—
58	C₁₃×#384	C₂²	1	2	yes	—
59	C₁₃×#382	C₂²	1	2	yes	—
60	C₁₃×#380	C₂²	1	4	yes	—
61	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
62	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
63	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
64	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
65	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
66	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
67	C₁₃×#376	C₂²	1	2	yes	—
68	C₄³×C₁₃	C₂²	1	2	yes	—
69	C₂×C₁₃×#41	—	2	4	no	—
70	C₂×C₁₃×#41	—	2	4	no	—
71	C₂×C₁₃×#41	—	2	4	no	—
72	C₂×C₁₃×#41	—	2	8	no	—
73	C₂×C₁₃×#41	—	4	8	no	—
74	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
76	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
77	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
78	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
79	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
80	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
82	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
85	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
86	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
87	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₁₃×C₄⋊Q₈	—	2	4	no	—
91	C₁₃×#127	—	2	8	no	—
92	C₁₃×#127	—	2	4	no	—
93	C₁₃×#124	—	2	8	no	—
94	C₁₃×#124	—	2	8	no	—
95	C₁₃×#121	—	2	8	no	—
96	C₁₃×#121	—	2	8	no	—
97	C₁₃×#121	—	2	16	no	—
98	C₄×Q₈×C₁₃	—	2	4	no	—
99	C₄×Q₈×C₁₃	—	2	4	no	—
100	C₄×D₄×C₁₃	—	2	8	no	—
101	C₄×D₄×C₁₃	—	2	8	no	—
102	C₄×D₄×C₁₃	—	2	4	no	—
103	C₄×D₄×C₁₃	—	2	4	no	—
104	C₄×D₄×C₁₃	—	2	8	no	—
105	C₄×D₄×C₁₃	—	2	8	no	—
106	C₄×D₄×C₁₃	—	4	16	no	—
107	C₁₃×#117	—	2	4	no	—
108	C₁₃×#117	—	2	8	no	—
109	C₁₃×#117	—	2	8	no	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
118	C₂×C₁₃×C₄⋊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	4	yes	—
123	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
125	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
126	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
129	C₂×C₄²×C₁₃	—	2	8	no	—
130	C₂×C₄²×C₁₃	D₄	1	8	yes	complemented
131	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
132	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
134	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
135	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
136	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
137	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
138	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
142	C₁₃×#95	C₂³	1	4	yes	—
143	C₁₃×#95	C₂³	1	2	yes	—
144	C₁₃×#95	C₂³	1	2	yes	—
145	C₁₃×#95	C₂³	1	8	yes	—
146	C₁₃×#95	C₂³	1	8	yes	—
147	#34977	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
149	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
150	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
151	C₁₃×#41	—	2	32	no	—
152	C₁₃×#41	—	4	32	no	—
153	C₂×Q₈×C₁₃	—	2	2	no	—
154	C₂×Q₈×C₁₃	—	2	4	no	—
155	C₂×Q₈×C₁₃	—	2	2	no	—
156	C₂×Q₈×C₁₃	—	4	4	no	—
157	C₂×Q₈×C₁₃	#41	1	4	yes	complemented
158	C₂×D₄×C₁₃	—	2	4	no	—
159	C₂×D₄×C₁₃	—	2	4	no	—
160	C₂×D₄×C₁₃	—	2	8	no	—
161	C₂×D₄×C₁₃	—	2	16	no	—
162	C₂×D₄×C₁₃	—	2	2	no	—
163	C₂×D₄×C₁₃	—	2	4	no	—
164	C₂×D₄×C₁₃	—	2	4	no	—
165	C₂×D₄×C₁₃	—	2	4	no	—
166	C₂×D₄×C₁₃	—	2	4	no	—
167	C₂×D₄×C₁₃	—	2	2	no	—
168	C₂×D₄×C₁₃	—	2	16	no	—
169	C₂×D₄×C₁₃	—	2	8	no	—
170	C₂×D₄×C₁₃	—	2	4	no	—
171	C₂×D₄×C₁₃	—	2	4	no	—
172	C₂×D₄×C₁₃	—	4	8	no	—
173	C₂×D₄×C₁₃	—	4	4	no	—
174	C₂×D₄×C₁₃	—	4	8	no	—
175	C₂×D₄×C₁₃	#41	1	4	yes	complemented
176	C₂²×C₄×C₁₃	—	2	4	no	—
177	C₂²×C₄×C₁₃	—	2	4	no	—
178	C₂²×C₄×C₁₃	—	2	4	no	—
179	C₂²×C₄×C₁₃	—	2	4	no	—
180	C₂²×C₄×C₁₃	—	2	2	no	—
181	C₂²×C₄×C₁₃	—	2	2	no	—
182	C₂²×C₄×C₁₃	—	2	4	no	—
183	C₂²×C₄×C₁₃	—	2	4	no	—
184	C₂²×C₄×C₁₃	—	2	4	no	—
185	C₂²×C₄×C₁₃	—	2	8	no	—
186	C₂²×C₄×C₁₃	—	2	8	no	—
187	C₂²×C₄×C₁₃	—	2	8	no	—
188	C₂²×C₄×C₁₃	—	2	16	no	—
189	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
190	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
191	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
192	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
204	C₁₃×C₄⋊C₄	—	2	4	no	—
205	C₁₃×C₄⋊C₄	—	2	4	no	—
206	C₁₃×C₄⋊C₄	—	2	2	no	—
207	C₁₃×C₄⋊C₄	—	2	2	no	—
208	C₁₃×C₄⋊C₄	—	2	4	no	—
209	C₁₃×C₄⋊C₄	—	2	4	no	—
210	C₁₃×C₄⋊C₄	—	2	4	no	—
211	C₁₃×C₄⋊C₄	—	4	8	no	—
212	C₁₃×C₄⋊C₄	#41	1	8	yes	complemented
213	C₁₃×C₂²⋊C₄	—	2	4	no	—
214	C₁₃×C₂²⋊C₄	—	2	4	no	—
215	C₁₃×C₂²⋊C₄	—	2	4	no	—
216	C₁₃×C₂²⋊C₄	—	2	8	no	—
217	C₁₃×C₂²⋊C₄	—	2	8	no	—
218	C₁₃×C₂²⋊C₄	—	2	8	no	—
219	C₁₃×C₂²⋊C₄	—	2	16	no	—
220	C₁₃×C₂²⋊C₄	—	2	16	no	—
221	C₁₃×C₂²⋊C₄	—	4	8	no	—
222	C₁₃×C₂²⋊C₄	—	4	8	no	—
223	C₄²×C₁₃	—	2	4	no	—
224	C₄²×C₁₃	—	2	4	no	—
225	C₄²×C₁₃	—	2	4	no	—
226	C₄²×C₁₃	—	2	8	no	—
227	C₄²×C₁₃	—	2	4	no	—
228	C₄²×C₁₃	—	2	4	no	—
229	C₄²×C₁₃	—	2	8	no	—
230	C₄²×C₁₃	C₂×D₄	1	4	yes	—
231	C₄²×C₁₃	C₂×D₄	1	4	yes	—
232	C₄²×C₁₃	C₂×D₄	1	4	yes	—
233	C₄²×C₁₃	C₂×D₄	1	4	yes	—
234	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
235	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#2610	C₂×C₁₃	1	4	yes	complemented
237	#2567	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#2563	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#2548	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#2541	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#2500	C₂×C₁₃	1	2	yes	complemented
242	#2431	C₂×C₁₃	1	2	yes	complemented
243	#2414	C₂×C₁₃	1	4	yes	complemented
244	#2388	C₂×C₁₃	1	4	yes	complemented
245	C₄×#127	C₂×C₁₃	1	2	yes	complemented
246	C₄×#124	C₂×C₁₃	1	2	yes	complemented
247	C₄×#121	C₂×C₁₃	1	4	yes	complemented
248	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
249	C₂³×C₁₃	—	2	2	no	—
250	C₂³×C₁₃	—	2	2	no	—
251	C₂³×C₁₃	—	2	1	no	—
252	C₂³×C₁₃	—	2	1	no	—
253	C₂³×C₁₃	—	2	2	no	—
254	C₂³×C₁₃	—	2	4	no	—
255	C₂³×C₁₃	—	2	4	no	—
256	C₂³×C₁₃	—	2	2	no	—
257	C₂³×C₁₃	—	2	4	no	—
258	C₂³×C₁₃	—	2	4	no	—
259	C₂³×C₁₃	—	2	8	no	—
260	C₂³×C₁₃	—	2	4	no	—
261	C₂³×C₁₃	—	2	8	no	—
262	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
263	C₂³×C₁₃	C₂×#41	1	4	yes	—
264	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
265	Q₈×C₁₃	—	2	8	no	—
266	Q₈×C₁₃	—	4	8	no	—
267	D₄×C₁₃	—	2	16	no	—
268	D₄×C₁₃	—	2	8	no	—
269	D₄×C₁₃	—	4	32	no	—
270	D₄×C₁₃	—	4	8	no	—
271	D₄×C₁₃	—	4	16	no	—
272	D₄×C₁₃	—	4	8	no	—
273	D₄×C₁₃	—	4	8	no	—
274	C₂×C₄×C₁₃	—	2	16	no	—
275	C₂×C₄×C₁₃	—	2	2	no	—
276	C₂×C₄×C₁₃	—	2	2	no	—
277	C₂×C₄×C₁₃	—	2	4	no	—
278	C₂×C₄×C₁₃	—	2	1	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	2	no	—
281	C₂×C₄×C₁₃	—	2	4	no	—
282	C₂×C₄×C₁₃	—	2	2	no	—
283	C₂×C₄×C₁₃	—	2	8	no	—
284	C₂×C₄×C₁₃	—	2	8	no	—
285	C₂×C₄×C₁₃	—	2	8	no	—
286	C₂×C₄×C₁₃	—	2	2	no	—
287	C₂×C₄×C₁₃	—	2	2	no	—
288	C₂×C₄×C₁₃	—	2	4	no	—
289	C₂×C₄×C₁₃	—	2	4	no	—
290	C₂×C₄×C₁₃	—	2	4	no	—
291	C₂×C₄×C₁₃	—	2	4	no	—
292	C₂×C₄×C₁₃	—	2	4	no	—
293	C₂×C₄×C₁₃	—	2	4	no	—
294	C₂×C₄×C₁₃	—	2	8	no	—
295	C₂×C₄×C₁₃	—	4	8	no	—
296	C₂×C₄×C₁₃	—	4	8	no	—
297	C₂×C₄×C₁₃	—	4	16	no	—
298	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
299	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
300	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
301	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
302	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
305	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
306	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
307	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
308	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
309	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
310	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
311	C₂²×#41	C₂²×C₁₃	1	2	yes	—
312	#532	—	2	8	no	—
313	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
314	C₂×#127	C₂²×C₁₃	1	2	yes	—
315	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×#124	C₂²×C₁₃	1	2	yes	—
317	C₂×#124	C₂²×C₁₃	1	2	yes	—
318	C₂×#121	C₂²×C₁₃	1	2	yes	—
319	C₂×#121	C₂²×C₁₃	1	4	yes	—
320	C₂×#121	C₂²×C₁₃	1	2	yes	—
321	C₄×#41	—	2	8	no	—
322	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
326	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
328	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
329	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
330	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
331	C₂×#117	C₂²×C₁₃	1	2	yes	—
332	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
333	C₂×#117	C₂²×C₁₃	1	2	yes	—
334	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
335	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
336	#395	C₂²×C₁₃	1	4	yes	—
337	#394	C₂²×C₁₃	1	4	yes	—
338	#394	C₂²×C₁₃	1	8	yes	—
339	#393	C₂²×C₁₃	1	4	yes	—
340	#392	C₂²×C₁₃	1	4	yes	—
341	#392	C₂²×C₁₃	1	8	yes	—
342	#391	C₂²×C₁₃	1	2	yes	—
343	#390	C₂²×C₁₃	1	2	yes	—
344	#390	C₂²×C₁₃	1	8	yes	—
345	#390	C₂²×C₁₃	1	2	yes	—
346	#390	C₂²×C₁₃	1	4	yes	—
347	#390	C₂²×C₁₃	1	2	yes	—
348	#389	C₂²×C₁₃	1	4	yes	—
349	#388	C₂²×C₁₃	1	8	yes	—
350	#388	C₂²×C₁₃	1	8	yes	—
351	#386	C₂²×C₁₃	1	8	yes	—
352	#384	C₂²×C₁₃	1	2	yes	—
353	#382	C₂²×C₁₃	1	2	yes	—
354	#380	C₂²×C₁₃	1	4	yes	—
355	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
356	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
357	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
358	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
359	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
360	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
361	#376	C₂²×C₁₃	1	2	yes	—
362	C₄³	C₂²×C₁₃	1	2	yes	—
363	C₂²×C₁₃	—	2	2	no	—
364	C₂²×C₁₃	—	2	4	no	—
365	C₂²×C₁₃	—	2	2	no	—
366	C₂²×C₁₃	—	2	2	no	—
367	C₂²×C₁₃	—	2	8	no	—
368	C₂²×C₁₃	—	4	2	no	—
369	C₂²×C₁₃	—	4	2	no	—
370	C₂²×C₁₃	—	4	2	no	—
371	C₂²×C₁₃	—	4	2	no	—
372	C₂²×C₁₃	—	4	4	no	—
373	C₂²×C₁₃	—	4	4	no	—
374	C₂²×C₁₃	—	4	4	no	—
375	C₂²×C₁₃	—	4	4	no	—
376	C₂²×C₁₃	—	4	8	no	—
377	C₂²×C₁₃	—	4	8	no	—
378	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
379	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
380	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
381	C₂²×C₁₃	C₂²×#41	1	2	yes	—
382	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
383	C₄×C₁₃	—	2	2	no	—
384	C₄×C₁₃	—	2	4	no	—
385	C₄×C₁₃	—	2	2	no	—
386	C₄×C₁₃	—	2	2	no	—
387	C₄×C₁₃	—	2	8	no	—
388	C₄×C₁₃	—	4	2	no	—
389	C₄×C₁₃	—	4	2	no	—
390	C₄×C₁₃	—	4	4	no	—
391	C₄×C₁₃	—	4	4	no	—
392	C₄×C₁₃	#525	1	4	yes	—
393	C₄×C₁₃	#532	1	4	yes	—
394	C₄×C₁₃	#535	1	4	yes	—
395	C₂×#41	—	2	4	no	—
396	C₂×#41	—	2	4	no	—
397	C₂×#41	—	2	4	no	—
398	C₂×#41	—	2	8	no	—
399	C₂×#41	—	4	8	no	—
400	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
401	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
402	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
403	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
404	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
405	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
406	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
407	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
408	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
409	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
410	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
411	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
412	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
413	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
414	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
415	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
416	C₄⋊Q₈	—	2	4	no	—
417	#127	—	2	8	no	—
418	#127	—	2	4	no	—
419	#124	—	2	8	no	—
420	#124	—	2	8	no	—
421	#121	—	2	8	no	—
422	#121	—	2	8	no	—
423	#121	—	2	16	no	—
424	C₄×Q₈	—	2	4	no	—
425	C₄×Q₈	—	2	4	no	—
426	C₄×D₄	—	2	8	no	—
427	C₄×D₄	—	2	8	no	—
428	C₄×D₄	—	2	4	no	—
429	C₄×D₄	—	2	4	no	—
430	C₄×D₄	—	2	8	no	—
431	C₄×D₄	—	2	8	no	—
432	C₄×D₄	—	4	16	no	—
433	#117	—	2	4	no	—
434	#117	—	2	8	no	—
435	#117	—	2	8	no	—
436	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
440	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
441	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
442	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
444	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
455	C₂×C₄²	—	2	8	no	—
456	C₂×C₄²	D₄×C₁₃	1	8	yes	complemented
457	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
458	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
459	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
460	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
461	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
462	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
463	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
464	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
465	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
466	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
467	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
468	#95	C₂³×C₁₃	1	4	yes	—
469	#95	C₂³×C₁₃	1	2	yes	—
470	#95	C₂³×C₁₃	1	2	yes	—
471	#95	C₂³×C₁₃	1	8	yes	—
472	#95	C₂³×C₁₃	1	8	yes	—
473	C₂×C₁₃	—	4	2	no	—
474	C₂×C₁₃	—	4	4	no	—
475	C₂×C₁₃	—	8	4	no	—
476	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
477	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
478	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
479	C₂×C₁₃	#3481	1	2	yes	—
480	C₂×C₁₃	#3483	1	2	yes	—
481	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
482	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
483	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
484	#41	—	2	32	no	—
485	#41	—	4	32	no	—
486	C₂×Q₈	—	2	2	no	—
487	C₂×Q₈	—	2	4	no	—
488	C₂×Q₈	—	2	2	no	—
489	C₂×Q₈	—	4	4	no	—
490	C₂×Q₈	C₁₃×#41	1	4	yes	complemented
491	C₂×D₄	—	2	4	no	—
492	C₂×D₄	—	2	4	no	—
493	C₂×D₄	—	2	8	no	—
494	C₂×D₄	—	2	16	no	—
495	C₂×D₄	—	2	2	no	—
496	C₂×D₄	—	2	4	no	—
497	C₂×D₄	—	2	4	no	—
498	C₂×D₄	—	2	4	no	—
499	C₂×D₄	—	2	4	no	—
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	—	2	16	no	—
502	C₂×D₄	—	2	8	no	—
503	C₂×D₄	—	2	4	no	—
504	C₂×D₄	—	2	4	no	—
505	C₂×D₄	—	4	8	no	—
506	C₂×D₄	—	4	4	no	—
507	C₂×D₄	—	4	8	no	—
508	C₂×D₄	C₁₃×#41	1	4	yes	complemented
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	2	4	no	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	2	4	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	2	4	no	—
518	C₂²×C₄	—	2	8	no	—
519	C₂²×C₄	—	2	8	no	—
520	C₂²×C₄	—	2	8	no	—
521	C₂²×C₄	—	2	16	no	—
522	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
523	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
524	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
525	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
526	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
528	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
530	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
531	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
532	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
533	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
534	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
535	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
536	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
537	C₄⋊C₄	—	2	4	no	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	4	no	—
542	C₄⋊C₄	—	2	4	no	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	—	4	8	no	—
545	C₄⋊C₄	C₁₃×#41	1	8	yes	complemented
546	C₂²⋊C₄	—	2	4	no	—
547	C₂²⋊C₄	—	2	4	no	—
548	C₂²⋊C₄	—	2	4	no	—
549	C₂²⋊C₄	—	2	8	no	—
550	C₂²⋊C₄	—	2	8	no	—
551	C₂²⋊C₄	—	2	8	no	—
552	C₂²⋊C₄	—	2	16	no	—
553	C₂²⋊C₄	—	2	16	no	—
554	C₂²⋊C₄	—	4	8	no	—
555	C₂²⋊C₄	—	4	8	no	—
556	C₄²	—	2	4	no	—
557	C₄²	—	2	4	no	—
558	C₄²	—	2	4	no	—
559	C₄²	—	2	8	no	—
560	C₄²	—	2	4	no	—
561	C₄²	—	2	4	no	—
562	C₄²	—	2	8	no	—
563	C₄²	C₂×D₄×C₁₃	1	4	yes	—
564	C₄²	C₂×D₄×C₁₃	1	4	yes	—
565	C₄²	C₂×D₄×C₁₃	1	4	yes	—
566	C₄²	C₂×D₄×C₁₃	1	4	yes	—
567	C₁₃	#34977	1	1	yes	characteristic, direct product factor, Sylow
568	C₂³	—	2	2	no	—
569	C₂³	—	2	2	no	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	2	4	no	—
574	C₂³	—	2	4	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	4	no	—
577	C₂³	—	2	4	no	—
578	C₂³	—	2	8	no	—
579	C₂³	—	2	4	no	—
580	C₂³	—	2	8	no	—
581	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
582	C₂³	C₂×C₁₃×#41	1	4	yes	—
583	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
584	Q₈	—	2	8	no	—
585	Q₈	—	4	8	no	—
586	D₄	—	2	16	no	—
587	D₄	—	2	8	no	—
588	D₄	—	4	32	no	—
589	D₄	—	4	8	no	—
590	D₄	—	4	16	no	—
591	D₄	—	4	8	no	—
592	D₄	—	4	8	no	—
593	C₂×C₄	—	2	16	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	4	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	8	no	—
603	C₂×C₄	—	2	8	no	—
604	C₂×C₄	—	2	8	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	8	no	—
614	C₂×C₄	—	4	8	no	—
615	C₂×C₄	—	4	8	no	—
616	C₂×C₄	—	4	16	no	—
617	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
618	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
619	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
620	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
621	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
622	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
623	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
624	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
625	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
626	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
627	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
628	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	4	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	8	no	—
634	C₂²	—	4	2	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	4	2	no	—
637	C₂²	—	4	2	no	—
638	C₂²	—	4	4	no	—
639	C₂²	—	4	4	no	—
640	C₂²	—	4	4	no	—
641	C₂²	—	4	4	no	—
642	C₂²	—	4	8	no	—
643	C₂²	—	4	8	no	—
644	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
645	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
646	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
647	C₂²	C₂²×C₁₃×#41	1	2	yes	—
648	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
649	C₄	—	2	2	no	—
650	C₄	—	2	4	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	8	no	—
654	C₄	—	4	2	no	—
655	C₄	—	4	2	no	—
656	C₄	—	4	4	no	—
657	C₄	—	4	4	no	—
658	C₄	C₁₃×#525	1	4	yes	—
659	C₄	C₁₃×#532	1	4	yes	—
660	C₄	C₁₃×#535	1	4	yes	—
661	C₂	—	4	2	no	—
662	C₂	—	4	4	no	—
663	C₂	—	8	4	no	—
664	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
665	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
666	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
667	C₂	C₁₃×#3481	1	2	yes	—
668	C₂	C₁₃×#3483	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×#532	C₂	semidirect
2. C₂×C₄×C₁₃×#41	C₂	semidirect
3. C₁₃×#2610	C₂	semidirect
4. C₁₃×#2567	C₂	semidirect
5. C₁₃×#2563	C₂	semidirect
6. C₁₃×#2548	C₂	semidirect
7. C₁₃×#2541	C₂	semidirect
8. C₁₃×#2500	C₂	semidirect
9. C₁₃×#2431	C₂	semidirect
10. C₁₃×#2414	C₂	semidirect
11. C₁₃×#2388	C₂	semidirect
12. C₄×C₁₃×#127	C₂	semidirect
13. C₄×C₁₃×#124	C₂	semidirect
14. C₄×C₁₃×#121	C₂	semidirect
15. C₄×C₁₃×#117	C₂	semidirect
130. C₂×C₄²×C₁₃	D₄	semidirect
147. #34977	C₁₃	direct (N × H)
157. C₂×Q₈×C₁₃	#41	semidirect
175. C₂×D₄×C₁₃	#41	semidirect
212. C₁₃×C₄⋊C₄	#41	semidirect
234. C₂×#532	C₂×C₁₃	semidirect
235. C₂×C₄×#41	C₂×C₁₃	semidirect
236. #2610	C₂×C₁₃	semidirect
237. #2567	C₂×C₁₃	semidirect
238. #2563	C₂×C₁₃	semidirect
239. #2548	C₂×C₁₃	semidirect
240. #2541	C₂×C₁₃	semidirect
241. #2500	C₂×C₁₃	semidirect
242. #2431	C₂×C₁₃	semidirect
243. #2414	C₂×C₁₃	semidirect
244. #2388	C₂×C₁₃	semidirect
245. C₄×#127	C₂×C₁₃	semidirect
246. C₄×#124	C₂×C₁₃	semidirect
247. C₄×#121	C₂×C₁₃	semidirect
248. C₄×#117	C₂×C₁₃	semidirect
456. C₂×C₄²	D₄×C₁₃	semidirect
490. C₂×Q₈	C₁₃×#41	semidirect
508. C₂×D₄	C₁₃×#41	semidirect
545. C₄⋊C₄	C₁₃×#41	semidirect
567. C₁₃	#34977	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×#532	2
C₂×C₄×C₁₃×#41	2
C₁₃×#2610	2
C₁₃×#2567	2
C₁₃×#2563	2
C₁₃×#2548	2
C₁₃×#2541	2
C₁₃×#2500	2
C₁₃×#2431	2
C₁₃×#2414	2
C₁₃×#2388	2
C₄×C₁₃×#127	2
C₄×C₁₃×#124	2
C₄×C₁₃×#121	2
C₄×C₁₃×#117	2
#34977	13

Subgroups — C13×#34977 #15721316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34977 #15721316