Subgroups — C₁₃×#24805 #15711144

Order 3328.

870 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#471	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3056	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3055	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2930	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#430	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2064	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2052	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2051	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1977	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1952	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1901	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1900	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1816	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
23	C₁₃×#525	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
26	C₁₃×#471	—	2	4	no	—
27	C₁₃×#470	—	2	1	no	—
28	C₁₃×#469	—	2	1	no	—
29	C₁₃×#468	—	2	1	no	—
30	C₁₃×#468	—	2	1	no	—
31	C₁₃×#468	—	2	1	no	—
32	C₁₃×#468	—	2	1	no	—
33	C₁₃×#468	—	2	1	no	—
34	C₁₃×#468	—	2	1	no	—
35	C₁₃×#467	—	2	1	no	—
36	C₁₃×#466	—	2	1	no	—
37	C₁₃×#465	—	2	1	no	—
38	C₁₃×#465	—	2	1	no	—
39	C₁₃×#436	—	2	1	no	—
40	C₁₃×#436	—	2	1	no	—
41	C₁₃×#435	—	2	1	no	—
42	C₁₃×#435	—	2	1	no	—
43	C₁₃×#430	—	2	4	no	—
44	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
48	C₁₃×#428	C₂²	1	1	yes	characteristic
49	C₁₃×#428	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
51	C₁₃×#424	C₂²	1	1	yes	characteristic
52	C₁₃×#419	C₂²	1	1	yes	characteristic
53	C₁₃×#418	C₂²	1	1	yes	characteristic
54	C₁₃×#417	C₂²	1	1	yes	characteristic
55	C₁₃×#417	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
62	C₁₃×#408	C₂²	1	1	yes	characteristic
63	C₁₃×#407	C₂²	1	1	yes	characteristic
64	C₁₃×#405	C₂²	1	1	yes	characteristic
65	C₁₃×#343	C₂²	1	1	yes	characteristic
66	C₁₃×#343	C₂²	1	1	yes	characteristic
67	C₁₃×#343	C₂²	1	1	yes	characteristic
68	C₁₃×#343	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₃	—	2	1	no	—
72	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×#137	—	2	2	no	—
75	C₁₃×#137	—	4	1	no	—
76	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
77	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
78	C₂×C₁₃×Q₁₆	—	2	1	no	—
79	C₂×C₁₃×SD₁₆	—	2	1	no	—
80	C₂×C₁₃×SD₁₆	—	2	1	no	—
81	C₂×C₁₃×SD₁₆	—	2	1	no	—
82	C₂×C₁₃×SD₁₆	—	2	1	no	—
83	C₂×C₁₃×SD₁₆	—	2	2	no	—
84	C₂×C₁₃×SD₁₆	—	2	2	no	—
85	C₂×C₁₃×D₈	—	2	1	no	—
86	C₁₃×#131	—	2	2	no	—
87	C₁₃×#131	—	2	2	no	—
88	C₂×C₁₃×M₁₆	—	2	1	no	—
89	C₂×C₁₃×M₁₆	—	2	1	no	—
90	C₂×C₁₃×M₁₆	—	2	2	no	—
91	C₂×C₁₃×M₁₆	—	2	1	no	—
92	C₂×C₁₃×M₁₆	—	2	2	no	—
93	C₂×C₁₃×M₁₆	—	2	2	no	—
94	C₂×C₁₃×M₁₆	—	2	2	no	—
95	C₂×C₁₃×M₁₆	—	4	1	no	—
96	C₂×C₁₃×M₁₆	—	4	1	no	—
97	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
98	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
99	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
100	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
101	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
106	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₁₃	—	2	1	no	—
108	C₂²×C₈×C₁₃	—	2	1	no	—
109	C₂²×C₈×C₁₃	—	2	1	no	—
110	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
112	C₁₃×#123	—	2	1	no	—
113	C₁₃×C₂²⋊Q₈	—	2	1	no	—
114	C₁₃×C₂²⋊Q₈	—	2	1	no	—
115	C₁₃×C₂²⋊Q₈	—	2	1	no	—
116	C₁₃×C₂²⋊Q₈	—	2	1	no	—
117	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
118	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
119	C₁₃×#121	—	2	1	no	—
120	C₁₃×#121	—	2	1	no	—
121	C₁₃×#121	—	2	1	no	—
122	C₁₃×#121	—	2	1	no	—
123	C₁₃×#121	D₄	1	1	yes	characteristic
124	C₁₃×#121	D₄	1	1	yes	characteristic
125	C₁₃×#120	—	2	1	no	—
126	C₄×D₄×C₁₃	—	2	1	no	—
127	C₄×D₄×C₁₃	—	2	1	no	—
128	C₁₃×#117	C₂³	1	1	yes	characteristic
129	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
132	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
133	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
134	C₁₃×#108	—	2	2	no	—
135	C₁₃×#108	—	2	2	no	—
136	C₁₃×#108	—	2	2	no	—
137	C₁₃×#108	D₄	1	4	yes	complemented
138	C₁₃×#107	—	2	1	no	—
139	C₁₃×#107	—	2	1	no	—
140	C₁₃×#107	—	2	1	no	—
141	C₁₃×#107	—	2	1	no	—
142	C₁₃×#106	—	2	1	no	—
143	C₁₃×#106	—	2	1	no	—
144	C₁₃×C₄⋊C₈	—	2	1	no	—
145	C₁₃×C₄⋊C₈	—	2	1	no	—
146	C₁₃×#103	—	2	1	no	—
147	C₁₃×#103	—	2	1	no	—
148	C₁₃×#103	—	2	1	no	—
149	C₁₃×#103	—	2	1	no	—
150	C₁₃×#103	—	2	1	no	—
151	C₁₃×#103	—	2	1	no	—
152	C₁₃×#102	—	2	1	no	—
153	C₁₃×#102	—	2	1	no	—
154	C₁₃×#102	—	2	1	no	—
155	C₁₃×#102	—	2	1	no	—
156	C₁₃×#102	—	2	1	no	—
157	C₁₃×#102	—	2	1	no	—
158	C₁₃×#101	—	2	2	no	—
159	C₁₃×#101	—	4	1	no	—
160	C₁₃×#100	—	2	2	no	—
161	C₁₃×#100	—	4	1	no	—
162	C₁₃×C₂²⋊C₈	—	2	1	no	—
163	C₁₃×C₂²⋊C₈	—	2	1	no	—
164	C₁₃×C₂²⋊C₈	—	2	1	no	—
165	C₁₃×C₂²⋊C₈	—	2	1	no	—
166	C₁₃×#97	—	2	1	no	—
167	C₄×C₈×C₁₃	—	2	1	no	—
168	#24805	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂⁴×C₁₃	—	2	1	no	—
170	C₂⁴×C₁₃	#41	1	1	yes	characteristic
171	C₁₃×#41	—	2	1	no	—
172	C₁₃×#41	—	2	1	no	—
173	C₁₃×#41	—	2	1	no	—
174	C₁₃×#41	—	2	1	no	—
175	C₂×Q₈×C₁₃	—	2	1	no	—
176	C₂×Q₈×C₁₃	—	2	1	no	—
177	C₂×Q₈×C₁₃	—	2	1	no	—
178	C₂×Q₈×C₁₃	—	2	1	no	—
179	C₂×Q₈×C₁₃	—	2	1	no	—
180	C₂×Q₈×C₁₃	—	2	1	no	—
181	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂×D₄×C₁₃	—	2	1	no	—
183	C₂×D₄×C₁₃	—	2	1	no	—
184	C₂×D₄×C₁₃	—	2	1	no	—
185	C₂×D₄×C₁₃	—	2	1	no	—
186	C₂×D₄×C₁₃	—	2	1	no	—
187	C₂×D₄×C₁₃	—	2	1	no	—
188	C₂×D₄×C₁₃	—	2	1	no	—
189	C₂×D₄×C₁₃	—	2	1	no	—
190	C₂×D₄×C₁₃	—	2	1	no	—
191	C₂×D₄×C₁₃	—	4	1	no	—
192	C₂×D₄×C₁₃	—	4	1	no	—
193	C₂×D₄×C₁₃	—	8	2	no	—
194	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₃	—	2	1	no	—
196	C₂²×C₄×C₁₃	—	2	1	no	—
197	C₂²×C₄×C₁₃	—	2	1	no	—
198	C₂²×C₄×C₁₃	—	2	1	no	—
199	C₂²×C₄×C₁₃	—	2	1	no	—
200	C₂²×C₄×C₁₃	—	2	1	no	—
201	C₂²×C₄×C₁₃	—	2	1	no	—
202	C₂²×C₄×C₁₃	—	2	1	no	—
203	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
208	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
209	C₁₃×Q₁₆	—	4	2	no	—
210	C₁₃×SD₁₆	—	4	2	no	—
211	C₁₃×SD₁₆	—	4	2	no	—
212	C₁₃×SD₁₆	—	4	2	no	—
213	C₁₃×SD₁₆	—	4	2	no	—
214	C₁₃×D₈	—	4	2	no	—
215	C₁₃×M₁₆	—	2	1	no	—
216	C₁₃×M₁₆	—	2	1	no	—
217	C₁₃×M₁₆	—	2	2	no	—
218	C₁₃×M₁₆	—	2	2	no	—
219	C₁₃×M₁₆	—	2	2	no	—
220	C₁₃×M₁₆	—	2	2	no	—
221	C₁₃×M₁₆	—	2	1	no	—
222	C₁₃×M₁₆	—	2	1	no	—
223	C₁₃×M₁₆	—	2	1	no	—
224	C₁₃×M₁₆	—	2	1	no	—
225	C₁₃×M₁₆	—	2	1	no	—
226	C₁₃×M₁₆	—	2	1	no	—
227	C₁₃×M₁₆	—	2	1	no	—
228	C₁₃×M₁₆	—	2	1	no	—
229	C₁₃×M₁₆	—	4	2	no	—
230	C₁₃×M₁₆	—	4	2	no	—
231	C₁₃×M₁₆	—	4	2	no	—
232	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
233	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
234	C₂×C₈×C₁₃	—	2	1	no	—
235	C₂×C₈×C₁₃	—	2	1	no	—
236	C₂×C₈×C₁₃	—	2	1	no	—
237	C₂×C₈×C₁₃	—	2	1	no	—
238	C₂×C₈×C₁₃	—	2	1	no	—
239	C₂×C₈×C₁₃	—	2	1	no	—
240	C₂×C₈×C₁₃	—	2	1	no	—
241	C₂×C₈×C₁₃	—	2	1	no	—
242	C₂×C₈×C₁₃	—	4	2	no	—
243	C₂×C₈×C₁₃	—	4	2	no	—
244	C₂×C₈×C₁₃	—	4	2	no	—
245	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
248	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
249	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
250	C₂×C₈×C₁₃	#41	1	2	yes	—
251	C₁₃×C₄⋊C₄	—	2	1	no	—
252	C₁₃×C₄⋊C₄	—	2	1	no	—
253	C₁₃×C₄⋊C₄	—	2	1	no	—
254	C₁₃×C₄⋊C₄	—	2	1	no	—
255	C₁₃×C₄⋊C₄	—	2	1	no	—
256	C₁₃×C₄⋊C₄	—	2	1	no	—
257	C₁₃×C₄⋊C₄	—	4	1	no	—
258	C₁₃×C₄⋊C₄	—	4	1	no	—
259	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
260	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
261	C₁₃×C₂²⋊C₄	—	2	1	no	—
262	C₁₃×C₂²⋊C₄	—	2	1	no	—
263	C₁₃×C₂²⋊C₄	—	2	1	no	—
264	C₁₃×C₂²⋊C₄	—	2	1	no	—
265	C₁₃×C₂²⋊C₄	—	2	1	no	—
266	C₁₃×C₂²⋊C₄	—	4	1	no	—
267	C₁₃×C₂²⋊C₄	—	4	1	no	—
268	C₁₃×C₂²⋊C₄	—	4	1	no	—
269	C₁₃×C₂²⋊C₄	—	4	1	no	—
270	C₄²×C₁₃	—	2	1	no	—
271	C₂×#471	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#3056	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#3055	C₂×C₁₃	1	1	yes	characteristic
274	C₂×#468	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#2930	C₂×C₁₃	1	1	yes	characteristic, complemented
276	C₂×#430	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#2064	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#2063	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#2052	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#2051	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#1977	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#1952	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#1901	C₂×C₁₃	1	1	yes	characteristic, complemented
284	#1900	C₂×C₁₃	1	1	yes	characteristic, complemented
285	#1816	C₂×C₁₃	1	1	yes	characteristic, complemented
286	C₂³×C₁₃	—	2	1	no	—
287	C₂³×C₁₃	—	2	1	no	—
288	C₂³×C₁₃	—	2	1	no	—
289	C₂³×C₁₃	—	4	1	no	—
290	C₂³×C₁₃	—	4	1	no	—
291	C₂³×C₁₃	—	4	1	no	—
292	C₂³×C₁₃	—	4	1	no	—
293	C₂³×C₁₃	—	4	1	no	—
294	C₂³×C₁₃	—	8	1	no	—
295	C₂³×C₁₃	—	8	1	no	—
296	C₂³×C₁₃	#121	1	1	yes	characteristic
297	C₂³×C₁₃	#121	1	1	yes	characteristic
298	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
299	Q₈×C₁₃	—	2	1	no	—
300	Q₈×C₁₃	—	2	1	no	—
301	Q₈×C₁₃	—	4	1	no	—
302	Q₈×C₁₃	—	4	1	no	—
303	Q₈×C₁₃	—	4	1	no	—
304	Q₈×C₁₃	—	4	1	no	—
305	D₄×C₁₃	—	2	1	no	—
306	D₄×C₁₃	—	2	1	no	—
307	D₄×C₁₃	—	4	1	no	—
308	D₄×C₁₃	—	4	1	no	—
309	D₄×C₁₃	—	4	1	no	—
310	D₄×C₁₃	—	4	1	no	—
311	D₄×C₁₃	—	4	1	no	—
312	D₄×C₁₃	—	4	1	no	—
313	D₄×C₁₃	—	8	1	no	—
314	D₄×C₁₃	—	8	1	no	—
315	D₄×C₁₃	—	8	2	no	—
316	D₄×C₁₃	—	8	2	no	—
317	C₂×C₄×C₁₃	—	2	1	no	—
318	C₂×C₄×C₁₃	—	2	1	no	—
319	C₂×C₄×C₁₃	—	2	1	no	—
320	C₂×C₄×C₁₃	—	2	1	no	—
321	C₂×C₄×C₁₃	—	2	1	no	—
322	C₂×C₄×C₁₃	—	2	1	no	—
323	C₂×C₄×C₁₃	—	2	1	no	—
324	C₂×C₄×C₁₃	—	2	1	no	—
325	C₂×C₄×C₁₃	—	2	1	no	—
326	C₂×C₄×C₁₃	—	2	1	no	—
327	C₂×C₄×C₁₃	—	2	1	no	—
328	C₂×C₄×C₁₃	—	2	1	no	—
329	C₂×C₄×C₁₃	—	2	1	no	—
330	C₂×C₄×C₁₃	—	4	1	no	—
331	C₂×C₄×C₁₃	—	4	1	no	—
332	C₂×C₄×C₁₃	—	4	1	no	—
333	C₂×C₄×C₁₃	—	4	1	no	—
334	C₂×C₄×C₁₃	—	4	1	no	—
335	C₂×C₄×C₁₃	—	4	1	no	—
336	C₂×C₄×C₁₃	—	4	1	no	—
337	C₂×C₄×C₁₃	—	8	1	no	—
338	C₂×C₄×C₁₃	—	8	1	no	—
339	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
340	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
341	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
345	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
346	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
347	C₈×C₁₃	—	2	1	no	—
348	C₈×C₁₃	—	2	1	no	—
349	C₈×C₁₃	—	2	2	no	—
350	C₈×C₁₃	—	2	2	no	—
351	C₈×C₁₃	—	4	1	no	—
352	C₈×C₁₃	—	4	1	no	—
353	C₈×C₁₃	—	4	1	no	—
354	C₈×C₁₃	—	4	1	no	—
355	C₈×C₁₃	#121	1	2	yes	—
356	C₈×C₁₃	#121	1	2	yes	—
357	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
358	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
359	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
360	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
361	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
362	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
363	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
364	#525	C₂²×C₁₃	1	1	yes	characteristic
365	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
366	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
367	#471	—	2	4	no	—
368	#470	—	2	1	no	—
369	#469	—	2	1	no	—
370	#468	—	2	1	no	—
371	#468	—	2	1	no	—
372	#468	—	2	1	no	—
373	#468	—	2	1	no	—
374	#468	—	2	1	no	—
375	#468	—	2	1	no	—
376	#467	—	2	1	no	—
377	#466	—	2	1	no	—
378	#465	—	2	1	no	—
379	#465	—	2	1	no	—
380	#436	—	2	1	no	—
381	#436	—	2	1	no	—
382	#435	—	2	1	no	—
383	#435	—	2	1	no	—
384	#430	—	2	4	no	—
385	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
386	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
388	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
389	#428	C₂²×C₁₃	1	1	yes	characteristic
390	#428	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
392	#424	C₂²×C₁₃	1	1	yes	characteristic
393	#419	C₂²×C₁₃	1	1	yes	characteristic
394	#418	C₂²×C₁₃	1	1	yes	characteristic
395	#417	C₂²×C₁₃	1	1	yes	characteristic
396	#417	C₂²×C₁₃	1	1	yes	characteristic
397	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
399	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
402	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
403	#408	C₂²×C₁₃	1	1	yes	characteristic
404	#407	C₂²×C₁₃	1	1	yes	characteristic
405	#405	C₂²×C₁₃	1	1	yes	characteristic
406	#343	C₂²×C₁₃	1	1	yes	characteristic
407	#343	C₂²×C₁₃	1	1	yes	characteristic
408	#343	C₂²×C₁₃	1	1	yes	characteristic
409	#343	C₂²×C₁₃	1	1	yes	characteristic
410	C₂²×C₁₃	—	2	1	no	—
411	C₂²×C₁₃	—	2	1	no	—
412	C₂²×C₁₃	—	2	1	no	—
413	C₂²×C₁₃	—	2	1	no	—
414	C₂²×C₁₃	—	2	1	no	—
415	C₂²×C₁₃	—	2	1	no	—
416	C₂²×C₁₃	—	2	1	no	—
417	C₂²×C₁₃	—	2	1	no	—
418	C₂²×C₁₃	—	4	1	no	—
419	C₂²×C₁₃	—	4	1	no	—
420	C₂²×C₁₃	—	4	1	no	—
421	C₂²×C₁₃	—	8	1	no	—
422	C₂²×C₁₃	—	8	1	no	—
423	C₂²×C₁₃	—	8	1	no	—
424	C₂²×C₁₃	—	8	1	no	—
425	C₂²×C₁₃	—	8	1	no	—
426	C₂²×C₁₃	—	16	1	no	—
427	C₂²×C₁₃	—	16	1	no	—
428	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
429	C₂²×C₁₃	#548	1	1	yes	characteristic
430	C₂²×C₁₃	#553	1	1	yes	characteristic
431	C₄×C₁₃	—	2	1	no	—
432	C₄×C₁₃	—	2	1	no	—
433	C₄×C₁₃	—	4	1	no	—
434	C₄×C₁₃	—	4	1	no	—
435	C₄×C₁₃	—	4	1	no	—
436	C₄×C₁₃	—	8	1	no	—
437	C₄×C₁₃	—	8	1	no	—
438	C₄×C₁₃	—	8	1	no	—
439	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
440	C₄×C₁₃	#537	1	1	yes	characteristic
441	C₄×C₁₃	D₄²	1	1	yes	characteristic
442	C₄×C₁₃	#547	1	1	yes	characteristic
443	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
444	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
445	C₂²×D₄	—	2	1	no	—
446	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
447	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
448	#137	—	2	2	no	—
449	#137	—	4	1	no	—
450	AGL(1,ℤ/8)	—	2	2	no	—
451	AGL(1,ℤ/8)	—	4	1	no	—
452	C₂×Q₁₆	—	2	1	no	—
453	C₂×SD₁₆	—	2	1	no	—
454	C₂×SD₁₆	—	2	1	no	—
455	C₂×SD₁₆	—	2	1	no	—
456	C₂×SD₁₆	—	2	1	no	—
457	C₂×SD₁₆	—	2	2	no	—
458	C₂×SD₁₆	—	2	2	no	—
459	C₂×D₈	—	2	1	no	—
460	#131	—	2	2	no	—
461	#131	—	2	2	no	—
462	C₂×M₁₆	—	2	1	no	—
463	C₂×M₁₆	—	2	1	no	—
464	C₂×M₁₆	—	2	2	no	—
465	C₂×M₁₆	—	2	1	no	—
466	C₂×M₁₆	—	2	2	no	—
467	C₂×M₁₆	—	2	2	no	—
468	C₂×M₁₆	—	2	2	no	—
469	C₂×M₁₆	—	4	1	no	—
470	C₂×M₁₆	—	4	1	no	—
471	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
472	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
473	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
474	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
475	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
476	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
477	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
478	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
479	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
480	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
481	C₂²×C₈	—	2	1	no	—
482	C₂²×C₈	—	2	1	no	—
483	C₂²×C₈	—	2	1	no	—
484	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
485	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
486	#123	—	2	1	no	—
487	C₂²⋊Q₈	—	2	1	no	—
488	C₂²⋊Q₈	—	2	1	no	—
489	C₂²⋊Q₈	—	2	1	no	—
490	C₂²⋊Q₈	—	2	1	no	—
491	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
492	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
493	#121	—	2	1	no	—
494	#121	—	2	1	no	—
495	#121	—	2	1	no	—
496	#121	—	2	1	no	—
497	#121	D₄×C₁₃	1	1	yes	characteristic
498	#121	D₄×C₁₃	1	1	yes	characteristic
499	#120	—	2	1	no	—
500	C₄×D₄	—	2	1	no	—
501	C₄×D₄	—	2	1	no	—
502	#117	C₂³×C₁₃	1	1	yes	characteristic
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	#108	—	2	2	no	—
509	#108	—	2	2	no	—
510	#108	—	2	2	no	—
511	#108	D₄×C₁₃	1	4	yes	complemented
512	#107	—	2	1	no	—
513	#107	—	2	1	no	—
514	#107	—	2	1	no	—
515	#107	—	2	1	no	—
516	#106	—	2	1	no	—
517	#106	—	2	1	no	—
518	C₄⋊C₈	—	2	1	no	—
519	C₄⋊C₈	—	2	1	no	—
520	#103	—	2	1	no	—
521	#103	—	2	1	no	—
522	#103	—	2	1	no	—
523	#103	—	2	1	no	—
524	#103	—	2	1	no	—
525	#103	—	2	1	no	—
526	#102	—	2	1	no	—
527	#102	—	2	1	no	—
528	#102	—	2	1	no	—
529	#102	—	2	1	no	—
530	#102	—	2	1	no	—
531	#102	—	2	1	no	—
532	#101	—	2	2	no	—
533	#101	—	4	1	no	—
534	#100	—	2	2	no	—
535	#100	—	4	1	no	—
536	C₂²⋊C₈	—	2	1	no	—
537	C₂²⋊C₈	—	2	1	no	—
538	C₂²⋊C₈	—	2	1	no	—
539	C₂²⋊C₈	—	2	1	no	—
540	#97	—	2	1	no	—
541	C₄×C₈	—	2	1	no	—
542	C₂×C₁₃	—	2	1	no	—
543	C₂×C₁₃	—	2	1	no	—
544	C₂×C₁₃	—	4	1	no	—
545	C₂×C₁₃	—	4	1	no	—
546	C₂×C₁₃	—	8	1	no	—
547	C₂×C₁₃	—	16	1	no	—
548	C₂×C₁₃	#2416	1	1	yes	characteristic
549	C₂×C₁₃	#3068	1	1	yes	characteristic
550	C₂×C₁₃	#3069	1	1	yes	characteristic
551	C₂⁴	—	2	1	no	—
552	C₂⁴	C₁₃×#41	1	1	yes	characteristic
553	#41	—	2	1	no	—
554	#41	—	2	1	no	—
555	#41	—	2	1	no	—
556	#41	—	2	1	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	4	1	no	—
574	C₂×D₄	—	4	1	no	—
575	C₂×D₄	—	8	2	no	—
576	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
586	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
587	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
588	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
589	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
591	Q₁₆	—	4	2	no	—
592	SD₁₆	—	4	2	no	—
593	SD₁₆	—	4	2	no	—
594	SD₁₆	—	4	2	no	—
595	SD₁₆	—	4	2	no	—
596	D₈	—	4	2	no	—
597	M₁₆	—	2	1	no	—
598	M₁₆	—	2	1	no	—
599	M₁₆	—	2	2	no	—
600	M₁₆	—	2	2	no	—
601	M₁₆	—	2	2	no	—
602	M₁₆	—	2	2	no	—
603	M₁₆	—	2	1	no	—
604	M₁₆	—	2	1	no	—
605	M₁₆	—	2	1	no	—
606	M₁₆	—	2	1	no	—
607	M₁₆	—	2	1	no	—
608	M₁₆	—	2	1	no	—
609	M₁₆	—	2	1	no	—
610	M₁₆	—	2	1	no	—
611	M₁₆	—	4	2	no	—
612	M₁₆	—	4	2	no	—
613	M₁₆	—	4	2	no	—
614	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
615	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	4	2	no	—
625	C₂×C₈	—	4	2	no	—
626	C₂×C₈	—	4	2	no	—
627	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
628	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
629	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
630	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
631	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
632	C₂×C₈	C₁₃×#41	1	2	yes	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	4	1	no	—
640	C₄⋊C₄	—	4	1	no	—
641	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
642	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
643	C₂²⋊C₄	—	2	1	no	—
644	C₂²⋊C₄	—	2	1	no	—
645	C₂²⋊C₄	—	2	1	no	—
646	C₂²⋊C₄	—	2	1	no	—
647	C₂²⋊C₄	—	2	1	no	—
648	C₂²⋊C₄	—	4	1	no	—
649	C₂²⋊C₄	—	4	1	no	—
650	C₂²⋊C₄	—	4	1	no	—
651	C₂²⋊C₄	—	4	1	no	—
652	C₄²	—	2	1	no	—
653	C₁₃	#24805	1	1	yes	characteristic, direct product factor, Sylow
654	C₂³	—	2	1	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	4	1	no	—
662	C₂³	—	8	1	no	—
663	C₂³	—	8	1	no	—
664	C₂³	C₁₃×#121	1	1	yes	characteristic
665	C₂³	C₁₃×#121	1	1	yes	characteristic
666	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
667	Q₈	—	2	1	no	—
668	Q₈	—	2	1	no	—
669	Q₈	—	4	1	no	—
670	Q₈	—	4	1	no	—
671	Q₈	—	4	1	no	—
672	Q₈	—	4	1	no	—
673	D₄	—	2	1	no	—
674	D₄	—	2	1	no	—
675	D₄	—	4	1	no	—
676	D₄	—	4	1	no	—
677	D₄	—	4	1	no	—
678	D₄	—	4	1	no	—
679	D₄	—	4	1	no	—
680	D₄	—	4	1	no	—
681	D₄	—	8	1	no	—
682	D₄	—	8	1	no	—
683	D₄	—	8	2	no	—
684	D₄	—	8	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	8	1	no	—
706	C₂×C₄	—	8	1	no	—
707	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
708	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
710	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
711	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
712	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
713	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
714	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
715	C₈	—	2	1	no	—
716	C₈	—	2	1	no	—
717	C₈	—	2	2	no	—
718	C₈	—	2	2	no	—
719	C₈	—	4	1	no	—
720	C₈	—	4	1	no	—
721	C₈	—	4	1	no	—
722	C₈	—	4	1	no	—
723	C₈	C₁₃×#121	1	2	yes	—
724	C₈	C₁₃×#121	1	2	yes	—
725	C₂²	—	2	1	no	—
726	C₂²	—	2	1	no	—
727	C₂²	—	2	1	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	8	1	no	—
737	C₂²	—	8	1	no	—
738	C₂²	—	8	1	no	—
739	C₂²	—	8	1	no	—
740	C₂²	—	8	1	no	—
741	C₂²	—	16	1	no	—
742	C₂²	—	16	1	no	—
743	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
744	C₂²	C₁₃×#548	1	1	yes	characteristic
745	C₂²	C₁₃×#553	1	1	yes	characteristic
746	C₄	—	2	1	no	—
747	C₄	—	2	1	no	—
748	C₄	—	4	1	no	—
749	C₄	—	4	1	no	—
750	C₄	—	4	1	no	—
751	C₄	—	8	1	no	—
752	C₄	—	8	1	no	—
753	C₄	—	8	1	no	—
754	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
755	C₄	C₁₃×#537	1	1	yes	characteristic
756	C₄	D₄²×C₁₃	1	1	yes	characteristic
757	C₄	C₁₃×#547	1	1	yes	characteristic
758	C₂	—	2	1	no	—
759	C₂	—	2	1	no	—
760	C₂	—	4	1	no	—
761	C₂	—	4	1	no	—
762	C₂	—	8	1	no	—
763	C₂	—	16	1	no	—
764	C₂	C₁₃×#2416	1	1	yes	characteristic
765	C₂	C₁₃×#3068	1	1	yes	characteristic
766	C₂	C₁₃×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3055	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#471	C₂	semidirect
2. C₁₃×#3056	C₂	semidirect
4. C₂×C₁₃×#468	C₂	semidirect
5. C₁₃×#2930	C₂	semidirect
6. C₂×C₁₃×#430	C₂	semidirect
7. C₁₃×#2064	C₂	semidirect
8. C₁₃×#2063	C₂	semidirect
9. C₁₃×#2052	C₂	semidirect
10. C₁₃×#2051	C₂	semidirect
11. C₁₃×#1977	C₂	semidirect
12. C₁₃×#1952	C₂	semidirect
13. C₁₃×#1901	C₂	semidirect
14. C₁₃×#1900	C₂	semidirect
15. C₁₃×#1816	C₂	semidirect
137. C₁₃×#108	D₄	semidirect
168. #24805	C₁₃	direct (N × H)
271. C₂×#471	C₂×C₁₃	semidirect
272. #3056	C₂×C₁₃	semidirect
274. C₂×#468	C₂×C₁₃	semidirect
275. #2930	C₂×C₁₃	semidirect
276. C₂×#430	C₂×C₁₃	semidirect
277. #2064	C₂×C₁₃	semidirect
278. #2063	C₂×C₁₃	semidirect
279. #2052	C₂×C₁₃	semidirect
280. #2051	C₂×C₁₃	semidirect
281. #1977	C₂×C₁₃	semidirect
282. #1952	C₂×C₁₃	semidirect
283. #1901	C₂×C₁₃	semidirect
284. #1900	C₂×C₁₃	semidirect
285. #1816	C₂×C₁₃	semidirect
511. #108	D₄×C₁₃	semidirect
653. C₁₃	#24805	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×#471	2
C₁₃×#3056	2
C₁₃×#3055	2
C₂×C₁₃×#468	2
C₁₃×#2930	2
C₂×C₁₃×#430	2
C₁₃×#2064	2
C₁₃×#2063	2
C₁₃×#2052	2
C₁₃×#2051	2
C₁₃×#1977	2
C₁₃×#1952	2
C₁₃×#1901	2
C₁₃×#1900	2
C₁₃×#1816	2
#24805	13

Subgroups — C13×#24805 #15711144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24805 #15711144