Subgroups — C₁₃×#24804 #15711143

Order 3328.

858 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#473	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3056	C₂	1	2	yes	maximal
3	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2929	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2064	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2052	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1979	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1952	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1901	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1816	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#137	C₂²	1	2	yes	—
13	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
16	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#525	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₁₃×#473	—	2	4	no	—
20	C₁₃×#470	—	2	2	no	—
21	C₁₃×#468	—	2	2	no	—
22	C₁₃×#467	—	2	1	no	—
23	C₁₃×#467	—	2	1	no	—
24	C₁₃×#467	—	2	1	no	—
25	C₁₃×#467	—	2	1	no	—
26	C₁₃×#467	—	2	2	no	—
27	C₁₃×#465	—	2	2	no	—
28	C₁₃×#435	—	2	1	no	—
29	C₁₃×#435	—	2	1	no	—
30	C₈×D₄×C₁₃	—	2	1	no	—
31	C₈×D₄×C₁₃	—	2	1	no	—
32	C₂×C₁₃×#108	—	2	4	no	—
33	C₂×C₁₃×#108	C₂²	1	2	yes	—
34	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
36	C₁₃×#428	C₂²	1	2	yes	—
37	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
38	C₁₃×#424	C₂²	1	1	yes	characteristic
39	C₁₃×#419	C₂²	1	2	yes	—
40	C₁₃×#417	C₂²	1	2	yes	—
41	C₂×C₁₃×#103	C₂²	1	2	yes	—
42	C₂×C₁₃×#101	C₂²	1	2	yes	—
43	C₂×C₁₃×#101	C₂²	1	2	yes	—
44	C₁₃×#408	C₂²	1	1	yes	characteristic
45	C₁₃×#407	C₂²	1	1	yes	characteristic
46	C₁₃×#405	C₂²	1	1	yes	characteristic
47	C₁₃×#343	C₂²	1	2	yes	—
48	C₁₃×#343	C₂²	1	2	yes	—
49	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
50	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₁₃×#137	—	2	4	no	—
53	C₁₃×#137	—	4	2	no	—
54	C₂×C₁₃×Q₁₆	—	2	2	no	—
55	C₂×C₁₃×Q₁₆	—	2	1	no	—
56	C₂×C₁₃×Q₁₆	—	2	1	no	—
57	C₂×C₁₃×Q₁₆	—	2	2	no	—
58	C₂×C₁₃×Q₁₆	—	2	2	no	—
59	C₂×C₁₃×SD₁₆	—	2	2	no	—
60	C₁₃×#131	—	2	2	no	—
61	C₁₃×#131	—	2	2	no	—
62	C₂×C₁₃×M₁₆	—	2	2	no	—
63	C₂×C₁₃×M₁₆	—	2	1	no	—
64	C₂×C₁₃×M₁₆	—	2	4	no	—
65	C₂×C₁₃×M₁₆	—	4	2	no	—
66	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
69	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
70	C₂²×C₈×C₁₃	—	2	2	no	—
71	C₂²×C₈×C₁₃	—	2	2	no	—
72	C₂²×C₈×C₁₃	—	2	2	no	—
73	C₂²×C₈×C₁₃	—	2	1	no	—
74	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
76	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
78	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×#123	—	2	1	no	—
81	C₁₃×C₂²⋊Q₈	—	2	2	no	—
82	C₁₃×C₂²⋊Q₈	—	2	2	no	—
83	C₁₃×C₂²⋊Q₈	—	2	2	no	—
84	C₁₃×C₂²⋊Q₈	—	2	2	no	—
85	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
86	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
87	C₁₃×#121	D₄	1	1	yes	characteristic
88	C₁₃×#121	D₄	1	1	yes	characteristic
89	C₁₃×#120	—	2	1	no	—
90	C₄×D₄×C₁₃	—	2	1	no	—
91	C₄×D₄×C₁₃	—	2	1	no	—
92	C₁₃×#117	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
96	C₁₃×#108	—	2	4	no	—
97	C₁₃×#108	—	2	2	no	—
98	C₁₃×#108	D₄	1	4	yes	complemented
99	C₁₃×#107	—	2	1	no	—
100	C₁₃×#107	—	2	1	no	—
101	C₁₃×#107	—	2	2	no	—
102	C₁₃×#106	—	2	2	no	—
103	C₁₃×C₄⋊C₈	—	2	1	no	—
104	C₁₃×C₄⋊C₈	—	2	1	no	—
105	C₁₃×#103	—	2	2	no	—
106	C₁₃×#103	—	2	2	no	—
107	C₁₃×#103	—	2	2	no	—
108	C₁₃×#103	—	2	2	no	—
109	C₁₃×#103	—	2	2	no	—
110	C₁₃×#102	—	2	2	no	—
111	C₁₃×#101	—	2	4	no	—
112	C₁₃×#101	—	4	2	no	—
113	C₁₃×C₂²⋊C₈	—	2	1	no	—
114	C₁₃×C₂²⋊C₈	—	2	1	no	—
115	C₁₃×C₂²⋊C₈	—	2	1	no	—
116	C₁₃×C₂²⋊C₈	—	2	1	no	—
117	C₁₃×#97	—	2	1	no	—
118	C₄×C₈×C₁₃	—	2	1	no	—
119	#24804	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂⁴×C₁₃	#41	1	1	yes	characteristic
121	C₁₃×#41	—	2	1	no	—
122	C₁₃×#41	—	2	1	no	—
123	C₁₃×#41	—	2	1	no	—
124	C₁₃×#41	—	2	1	no	—
125	C₂×Q₈×C₁₃	—	2	2	no	—
126	C₂×Q₈×C₁₃	—	2	2	no	—
127	C₂×Q₈×C₁₃	—	2	2	no	—
128	C₂×Q₈×C₁₃	—	2	2	no	—
129	C₂×Q₈×C₁₃	—	2	2	no	—
130	C₂×Q₈×C₁₃	—	2	2	no	—
131	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂×D₄×C₁₃	—	2	1	no	—
133	C₂×D₄×C₁₃	—	2	1	no	—
134	C₂×D₄×C₁₃	—	2	1	no	—
135	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	2	no	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₁₃×Q₁₆	—	4	4	no	—
150	C₁₃×Q₁₆	—	4	2	no	—
151	C₁₃×Q₁₆	—	4	2	no	—
152	C₁₃×SD₁₆	—	4	4	no	—
153	C₁₃×M₁₆	—	2	2	no	—
154	C₁₃×M₁₆	—	2	1	no	—
155	C₁₃×M₁₆	—	2	2	no	—
156	C₁₃×M₁₆	—	2	1	no	—
157	C₁₃×M₁₆	—	2	1	no	—
158	C₁₃×M₁₆	—	2	2	no	—
159	C₁₃×M₁₆	—	2	1	no	—
160	C₁₃×M₁₆	—	4	4	no	—
161	C₁₃×M₁₆	—	4	2	no	—
162	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
163	C₂×C₈×C₁₃	—	2	2	no	—
164	C₂×C₈×C₁₃	—	2	1	no	—
165	C₂×C₈×C₁₃	—	2	1	no	—
166	C₂×C₈×C₁₃	—	2	2	no	—
167	C₂×C₈×C₁₃	—	2	2	no	—
168	C₂×C₈×C₁₃	—	2	2	no	—
169	C₂×C₈×C₁₃	—	2	2	no	—
170	C₂×C₈×C₁₃	—	2	1	no	—
171	C₂×C₈×C₁₃	—	2	1	no	—
172	C₂×C₈×C₁₃	—	2	2	no	—
173	C₂×C₈×C₁₃	—	4	4	no	—
174	C₂×C₈×C₁₃	—	4	2	no	—
175	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
180	C₂×C₈×C₁₃	#41	1	2	yes	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	2	2	no	—
184	C₁₃×C₄⋊C₄	—	2	2	no	—
185	C₁₃×C₄⋊C₄	—	4	2	no	—
186	C₁₃×C₄⋊C₄	—	4	2	no	—
187	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
188	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
189	C₁₃×C₂²⋊C₄	—	2	1	no	—
190	C₁₃×C₂²⋊C₄	—	2	1	no	—
191	C₁₃×C₂²⋊C₄	—	2	1	no	—
192	C₁₃×C₂²⋊C₄	—	2	1	no	—
193	C₁₃×C₂²⋊C₄	—	2	1	no	—
194	C₁₃×C₂²⋊C₄	—	4	2	no	—
195	C₁₃×C₂²⋊C₄	—	4	2	no	—
196	C₄²×C₁₃	—	2	1	no	—
197	C₂×#473	C₂×C₁₃	1	1	yes	characteristic, complemented
198	#3056	C₂×C₁₃	1	2	yes	—
199	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#2929	C₂×C₁₃	1	1	yes	characteristic
201	C₂²×#108	C₂×C₁₃	1	1	yes	characteristic, complemented
202	#2064	C₂×C₁₃	1	2	yes	complemented
203	#2052	C₂×C₁₃	1	2	yes	complemented
204	#1979	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#1952	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#1901	C₂×C₁₃	1	2	yes	complemented
207	#1816	C₂×C₁₃	1	1	yes	characteristic, complemented
208	C₂³×C₁₃	—	2	1	no	—
209	C₂³×C₁₃	—	2	1	no	—
210	C₂³×C₁₃	—	2	2	no	—
211	C₂³×C₁₃	—	2	1	no	—
212	C₂³×C₁₃	—	4	1	no	—
213	C₂³×C₁₃	#121	1	1	yes	characteristic
214	C₂³×C₁₃	#121	1	1	yes	characteristic
215	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
216	Q₈×C₁₃	—	2	1	no	—
217	Q₈×C₁₃	—	2	1	no	—
218	Q₈×C₁₃	—	4	2	no	—
219	Q₈×C₁₃	—	4	2	no	—
220	Q₈×C₁₃	—	4	2	no	—
221	Q₈×C₁₃	—	4	2	no	—
222	D₄×C₁₃	—	2	1	no	—
223	D₄×C₁₃	—	2	1	no	—
224	D₄×C₁₃	—	4	2	no	—
225	D₄×C₁₃	—	4	1	no	—
226	D₄×C₁₃	—	4	1	no	—
227	D₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	2	1	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	2	1	no	—
239	C₂×C₄×C₁₃	—	2	1	no	—
240	C₂×C₄×C₁₃	—	2	1	no	—
241	C₂×C₄×C₁₃	—	4	1	no	—
242	C₂×C₄×C₁₃	—	4	1	no	—
243	C₂×C₄×C₁₃	—	4	2	no	—
244	C₂×C₄×C₁₃	—	4	2	no	—
245	C₂×C₄×C₁₃	—	4	2	no	—
246	C₂×C₄×C₁₃	—	4	2	no	—
247	C₂×C₄×C₁₃	—	8	2	no	—
248	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
249	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
255	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
256	C₈×C₁₃	—	2	1	no	—
257	C₈×C₁₃	—	2	1	no	—
258	C₈×C₁₃	—	2	4	no	—
259	C₈×C₁₃	—	4	1	no	—
260	C₈×C₁₃	—	4	1	no	—
261	C₈×C₁₃	—	4	2	no	—
262	C₈×C₁₃	#121	1	2	yes	—
263	C₈×C₁₃	#121	1	2	yes	—
264	C₂×#137	C₂²×C₁₃	1	2	yes	—
265	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
267	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
268	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
269	#525	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
271	#473	—	2	4	no	—
272	#470	—	2	2	no	—
273	#468	—	2	2	no	—
274	#467	—	2	1	no	—
275	#467	—	2	1	no	—
276	#467	—	2	1	no	—
277	#467	—	2	1	no	—
278	#467	—	2	2	no	—
279	#465	—	2	2	no	—
280	#435	—	2	1	no	—
281	#435	—	2	1	no	—
282	C₈×D₄	—	2	1	no	—
283	C₈×D₄	—	2	1	no	—
284	C₂×#108	—	2	4	no	—
285	C₂×#108	C₂²×C₁₃	1	2	yes	—
286	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
288	#428	C₂²×C₁₃	1	2	yes	—
289	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
290	#424	C₂²×C₁₃	1	1	yes	characteristic
291	#419	C₂²×C₁₃	1	2	yes	—
292	#417	C₂²×C₁₃	1	2	yes	—
293	C₂×#103	C₂²×C₁₃	1	2	yes	—
294	C₂×#101	C₂²×C₁₃	1	2	yes	—
295	C₂×#101	C₂²×C₁₃	1	2	yes	—
296	#408	C₂²×C₁₃	1	1	yes	characteristic
297	#407	C₂²×C₁₃	1	1	yes	characteristic
298	#405	C₂²×C₁₃	1	1	yes	characteristic
299	#343	C₂²×C₁₃	1	2	yes	—
300	#343	C₂²×C₁₃	1	2	yes	—
301	C₂²×C₁₃	—	2	1	no	—
302	C₂²×C₁₃	—	2	1	no	—
303	C₂²×C₁₃	—	2	1	no	—
304	C₂²×C₁₃	—	2	1	no	—
305	C₂²×C₁₃	—	2	1	no	—
306	C₂²×C₁₃	—	2	1	no	—
307	C₂²×C₁₃	—	2	1	no	—
308	C₂²×C₁₃	—	4	2	no	—
309	C₂²×C₁₃	—	4	2	no	—
310	C₂²×C₁₃	—	4	1	no	—
311	C₂²×C₁₃	—	4	1	no	—
312	C₂²×C₁₃	—	4	1	no	—
313	C₂²×C₁₃	#473	1	2	yes	complemented
314	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
315	C₂²×C₁₃	#548	1	1	yes	characteristic
316	C₂²×C₁₃	#553	1	1	yes	characteristic
317	C₄×C₁₃	—	2	1	no	—
318	C₄×C₁₃	—	2	1	no	—
319	C₄×C₁₃	—	4	1	no	—
320	C₄×C₁₃	—	4	1	no	—
321	C₄×C₁₃	—	4	1	no	—
322	C₄×C₁₃	—	8	2	no	—
323	C₄×C₁₃	—	8	2	no	—
324	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
325	C₄×C₁₃	#537	1	1	yes	characteristic
326	C₄×C₁₃	D₄²	1	1	yes	characteristic
327	C₄×C₁₃	#547	1	1	yes	characteristic
328	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
329	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
330	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
331	#137	—	2	4	no	—
332	#137	—	4	2	no	—
333	C₂×Q₁₆	—	2	2	no	—
334	C₂×Q₁₆	—	2	1	no	—
335	C₂×Q₁₆	—	2	1	no	—
336	C₂×Q₁₆	—	2	2	no	—
337	C₂×Q₁₆	—	2	2	no	—
338	C₂×SD₁₆	—	2	2	no	—
339	#131	—	2	2	no	—
340	#131	—	2	2	no	—
341	C₂×M₁₆	—	2	2	no	—
342	C₂×M₁₆	—	2	1	no	—
343	C₂×M₁₆	—	2	4	no	—
344	C₂×M₁₆	—	4	2	no	—
345	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
346	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
347	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
348	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
349	C₂²×C₈	—	2	2	no	—
350	C₂²×C₈	—	2	2	no	—
351	C₂²×C₈	—	2	2	no	—
352	C₂²×C₈	—	2	1	no	—
353	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
354	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
355	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
356	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
357	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
358	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
359	#123	—	2	1	no	—
360	C₂²⋊Q₈	—	2	2	no	—
361	C₂²⋊Q₈	—	2	2	no	—
362	C₂²⋊Q₈	—	2	2	no	—
363	C₂²⋊Q₈	—	2	2	no	—
364	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
365	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
366	#121	D₄×C₁₃	1	1	yes	characteristic
367	#121	D₄×C₁₃	1	1	yes	characteristic
368	#120	—	2	1	no	—
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	—	2	1	no	—
371	#117	C₂³×C₁₃	1	1	yes	characteristic
372	C₂×C₄⋊C₄	—	2	2	no	—
373	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
374	C₂×C₂²⋊C₄	—	2	2	no	—
375	#108	—	2	4	no	—
376	#108	—	2	2	no	—
377	#108	D₄×C₁₃	1	4	yes	complemented
378	#107	—	2	1	no	—
379	#107	—	2	1	no	—
380	#107	—	2	2	no	—
381	#106	—	2	2	no	—
382	C₄⋊C₈	—	2	1	no	—
383	C₄⋊C₈	—	2	1	no	—
384	#103	—	2	2	no	—
385	#103	—	2	2	no	—
386	#103	—	2	2	no	—
387	#103	—	2	2	no	—
388	#103	—	2	2	no	—
389	#102	—	2	2	no	—
390	#101	—	2	4	no	—
391	#101	—	4	2	no	—
392	C₂²⋊C₈	—	2	1	no	—
393	C₂²⋊C₈	—	2	1	no	—
394	C₂²⋊C₈	—	2	1	no	—
395	C₂²⋊C₈	—	2	1	no	—
396	#97	—	2	1	no	—
397	C₄×C₈	—	2	1	no	—
398	C₂×C₁₃	—	2	1	no	—
399	C₂×C₁₃	—	2	1	no	—
400	C₂×C₁₃	—	2	2	no	—
401	C₂×C₁₃	—	4	1	no	—
402	C₂×C₁₃	—	8	1	no	—
403	C₂×C₁₃	#2416	1	1	yes	characteristic
404	C₂×C₁₃	C₂×#473	1	1	yes	characteristic
405	C₂×C₁₃	#3067	1	1	yes	characteristic
406	C₂⁴	C₁₃×#41	1	1	yes	characteristic
407	#41	—	2	1	no	—
408	#41	—	2	1	no	—
409	#41	—	2	1	no	—
410	#41	—	2	1	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
433	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
434	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
435	Q₁₆	—	4	4	no	—
436	Q₁₆	—	4	2	no	—
437	Q₁₆	—	4	2	no	—
438	SD₁₆	—	4	4	no	—
439	M₁₆	—	2	2	no	—
440	M₁₆	—	2	1	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	—	2	1	no	—
443	M₁₆	—	2	1	no	—
444	M₁₆	—	2	2	no	—
445	M₁₆	—	2	1	no	—
446	M₁₆	—	4	4	no	—
447	M₁₆	—	4	2	no	—
448	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	—	4	4	no	—
460	C₂×C₈	—	4	2	no	—
461	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
462	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
463	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
464	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
465	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
466	C₂×C₈	C₁₃×#41	1	2	yes	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	4	2	no	—
472	C₄⋊C₄	—	4	2	no	—
473	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
474	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	—	4	2	no	—
481	C₂²⋊C₄	—	4	2	no	—
482	C₄²	—	2	1	no	—
483	C₁₃	#24804	1	1	yes	characteristic, direct product factor, Sylow
484	C₂³	—	2	2	no	—
485	C₂³	—	2	1	no	—
486	C₂³	—	2	1	no	—
487	C₂³	—	2	1	no	—
488	C₂³	—	4	1	no	—
489	C₂³	C₁₃×#121	1	1	yes	characteristic
490	C₂³	C₁₃×#121	1	1	yes	characteristic
491	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
492	Q₈	—	2	1	no	—
493	Q₈	—	2	1	no	—
494	Q₈	—	4	2	no	—
495	Q₈	—	4	2	no	—
496	Q₈	—	4	2	no	—
497	Q₈	—	4	2	no	—
498	D₄	—	2	1	no	—
499	D₄	—	2	1	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	2	no	—
502	D₄	—	4	1	no	—
503	D₄	—	4	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	8	2	no	—
524	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
525	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
526	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
529	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
530	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
531	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
532	C₈	—	2	1	no	—
533	C₈	—	2	1	no	—
534	C₈	—	2	4	no	—
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	2	no	—
538	C₈	C₁₃×#121	1	2	yes	—
539	C₈	C₁₃×#121	1	2	yes	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	C₁₃×#473	1	2	yes	complemented
553	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
554	C₂²	C₁₃×#548	1	1	yes	characteristic
555	C₂²	C₁₃×#553	1	1	yes	characteristic
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	8	2	no	—
562	C₄	—	8	2	no	—
563	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
564	C₄	C₁₃×#537	1	1	yes	characteristic
565	C₄	D₄²×C₁₃	1	1	yes	characteristic
566	C₄	C₁₃×#547	1	1	yes	characteristic
567	C₂	—	2	2	no	—
568	C₂	—	2	1	no	—
569	C₂	—	2	1	no	—
570	C₂	—	4	1	no	—
571	C₂	—	8	1	no	—
572	C₂	C₁₃×#2416	1	1	yes	characteristic
573	C₂	C₂×C₁₃×#473	1	1	yes	characteristic
574	C₂	C₁₃×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#525	C₂²
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×#473	C₂	semidirect
3. C₂×C₁₃×#467	C₂	semidirect
5. C₂²×C₁₃×#108	C₂	semidirect
6. C₁₃×#2064	C₂	semidirect
7. C₁₃×#2052	C₂	semidirect
8. C₁₃×#1979	C₂	semidirect
9. C₁₃×#1952	C₂	semidirect
10. C₁₃×#1901	C₂	semidirect
11. C₁₃×#1816	C₂	semidirect
98. C₁₃×#108	D₄	semidirect
119. #24804	C₁₃	direct (N × H)
197. C₂×#473	C₂×C₁₃	semidirect
199. C₂×#467	C₂×C₁₃	semidirect
201. C₂²×#108	C₂×C₁₃	semidirect
202. #2064	C₂×C₁₃	semidirect
203. #2052	C₂×C₁₃	semidirect
204. #1979	C₂×C₁₃	semidirect
205. #1952	C₂×C₁₃	semidirect
206. #1901	C₂×C₁₃	semidirect
207. #1816	C₂×C₁₃	semidirect
313. C₂²×C₁₃	#473	semidirect
377. #108	D₄×C₁₃	semidirect
483. C₁₃	#24804	direct (N × H)
552. C₂²	C₁₃×#473	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#473	2
C₁₃×#3056	2
C₂×C₁₃×#467	2
C₁₃×#2929	2
C₂²×C₁₃×#108	2
C₁₃×#2064	2
C₁₃×#2052	2
C₁₃×#1979	2
C₁₃×#1952	2
C₁₃×#1901	2
C₁₃×#1816	2
#24804	13

Subgroups — C13×#24804 #15711143

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24804 #15711143