Subgroups — C₁₃×#19864 #15706203

Order 3328.

578 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3360	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3357	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3341	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1723	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1691	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1683	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1676	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1675	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1646	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1638	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1634	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1632	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1581	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#556	C₂²	1	1	yes	characteristic
17	C₁₃×#555	C₂²	1	1	yes	characteristic
18	C₁₃×#555	C₂²	1	1	yes	characteristic
19	C₁₃×#554	C₂²	1	1	yes	characteristic
20	C₁₃×#500	C₂²	1	1	yes	characteristic
21	C₁₃×#500	C₂²	1	1	yes	characteristic
22	C₁₃×#498	C₂²	1	1	yes	characteristic
23	C₁₃×#494	C₂²	1	1	yes	characteristic
24	C₁₃×#488	—	2	1	no	—
25	C₁₃×#487	C₂²	1	1	yes	characteristic
26	C₁₃×#487	C₂²	1	1	yes	characteristic
27	C₁₃×#485	—	2	1	no	—
28	C₁₃×#485	—	2	1	no	—
29	C₁₃×#482	—	2	1	no	—
30	C₁₃×#482	—	2	1	no	—
31	C₁₃×#482	—	2	1	no	—
32	C₁₃×#480	—	2	1	no	—
33	C₁₃×#479	—	2	1	no	—
34	C₁₃×#477	C₂²	1	1	yes	characteristic
35	C₁₃×#477	C₂²	1	1	yes	characteristic
36	C₁₃×#476	C₂²	1	1	yes	characteristic
37	C₁₃×#476	C₂²	1	1	yes	characteristic
38	C₁₃×#476	C₂²	1	1	yes	characteristic
39	C₁₃×#476	C₂²	1	1	yes	characteristic
40	C₁₃×#474	C₂²	1	1	yes	characteristic
41	C₁₃×#468	—	2	1	no	—
42	C₁₃×#466	—	2	1	no	—
43	C₁₃×#465	—	2	1	no	—
44	C₁₃×#463	—	2	1	no	—
45	C₁₃×#461	C₂²	1	1	yes	characteristic
46	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×SD₁₆	—	2	1	no	—
48	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
49	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
50	C₁₃×#436	C₂²	1	1	yes	characteristic
51	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
53	C₁₃×#428	—	2	1	no	—
54	C₁₃×#427	—	2	1	no	—
55	C₁₃×#427	—	2	1	no	—
56	C₁₃×#335	C₂²	1	1	yes	characteristic
57	C₁₃×#335	C₂²	1	1	yes	characteristic
58	C₁₃×#333	C₂²	1	1	yes	characteristic
59	C₁₃×#333	C₂²	1	1	yes	characteristic
60	C₁₃×#333	C₂²	1	1	yes	characteristic
61	C₁₃×#332	C₂²	1	1	yes	characteristic
62	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₃×#322	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×Q₁₆	—	4	1	no	—
68	C₂×C₁₃×SD₁₆	—	2	1	no	—
69	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
70	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
71	C₂×C₁₃×M₁₆	—	2	1	no	—
72	C₂²×C₈×C₁₃	—	2	1	no	—
73	C₂²×C₈×C₁₃	—	2	1	no	—
74	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
75	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
76	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
77	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
78	C₁₃×#126	—	4	1	no	—
79	C₁₃×#125	—	2	1	no	—
80	C₁₃×#124	—	2	1	no	—
81	C₁₃×#124	—	4	1	no	—
82	C₁₃×#124	—	4	1	no	—
83	C₁₃×C₂²⋊Q₈	—	2	1	no	—
84	C₁₃×C₂²⋊Q₈	—	2	1	no	—
85	C₁₃×C₂²⋊Q₈	—	4	1	no	—
86	C₁₃×#121	—	2	1	no	—
87	C₁₃×#121	—	2	1	no	—
88	C₁₃×#121	—	2	1	no	—
89	C₁₃×#121	—	2	1	no	—
90	C₄×Q₈×C₁₃	—	2	1	no	—
91	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₄×D₄×C₁₃	—	2	1	no	—
93	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₁₃×#117	—	2	1	no	—
97	C₁₃×#117	—	2	1	no	—
98	C₁₃×#117	—	2	1	no	—
99	C₁₃×#117	—	2	1	no	—
100	C₁₃×#117	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₁₃×#107	—	2	1	no	—
103	C₁₃×#107	—	2	1	no	—
104	C₁₃×#107	—	2	1	no	—
105	C₁₃×#107	—	2	1	no	—
106	C₁₃×#107	—	2	1	no	—
107	C₁₃×#107	—	2	1	no	—
108	C₁₃×#107	—	2	1	no	—
109	C₁₃×#107	D₄	1	1	yes	characteristic
110	C₁₃×#106	—	2	1	no	—
111	C₁₃×#106	—	2	1	no	—
112	C₁₃×#106	—	2	1	no	—
113	C₁₃×#106	—	2	1	no	—
114	C₁₃×#106	—	2	1	no	—
115	C₁₃×#106	—	2	1	no	—
116	C₁₃×#106	D₄	1	1	yes	characteristic
117	C₁₃×C₄⋊C₈	—	2	1	no	—
118	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₁₃×#103	—	2	1	no	—
123	C₁₃×#103	—	2	1	no	—
124	C₁₃×#103	—	2	1	no	—
125	C₁₃×#103	—	2	1	no	—
126	C₁₃×#103	—	2	1	no	—
127	C₁₃×#103	—	4	1	no	—
128	C₁₃×#103	D₄	1	1	yes	characteristic
129	C₁₃×#102	—	2	1	no	—
130	C₁₃×#102	—	2	1	no	—
131	C₁₃×#102	—	2	1	no	—
132	C₁₃×#102	—	2	1	no	—
133	C₁₃×#102	—	2	1	no	—
134	C₁₃×#102	D₄	1	1	yes	characteristic
135	C₁₃×#102	D₄	1	1	yes	characteristic
136	C₁₃×#102	D₄	1	1	yes	characteristic
137	C₁₃×C₂²⋊C₈	—	2	1	no	—
138	C₁₃×C₂²⋊C₈	—	2	1	no	—
139	C₁₃×C₂²⋊C₈	—	2	1	no	—
140	C₄×C₈×C₁₃	—	2	1	no	—
141	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	#19864	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂×Q₈×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂×D₄×C₁₃	—	4	1	no	—
151	C₂×D₄×C₁₃	—	4	1	no	—
152	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	4	1	no	—
159	C₁₃×Q₁₆	—	8	2	no	—
160	C₁₃×SD₁₆	—	2	2	no	—
161	C₁₃×SD₁₆	—	4	2	no	—
162	C₁₃×D₈	—	4	1	no	—
163	C₁₃×M₁₆	—	4	2	no	—
164	C₂×C₈×C₁₃	—	2	1	no	—
165	C₂×C₈×C₁₃	—	2	1	no	—
166	C₂×C₈×C₁₃	—	2	1	no	—
167	C₂×C₈×C₁₃	—	2	1	no	—
168	C₂×C₈×C₁₃	—	2	1	no	—
169	C₂×C₈×C₁₃	—	4	2	no	—
170	C₂×C₈×C₁₃	—	4	2	no	—
171	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₁₃×C₄⋊C₄	—	4	1	no	—
185	C₁₃×C₄⋊C₄	—	4	1	no	—
186	C₁₃×C₄⋊C₄	—	4	1	no	—
187	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
188	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
189	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
190	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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	1	no	—
195	C₁₃×C₂²⋊C₄	—	4	1	no	—
196	C₁₃×C₂²⋊C₄	—	4	1	no	—
197	C₁₃×C₂²⋊C₄	—	4	1	no	—
198	C₁₃×C₂²⋊C₄	—	4	1	no	—
199	C₁₃×C₂²⋊C₄	—	4	1	no	—
200	C₁₃×C₂²⋊C₄	—	4	1	no	—
201	C₄²×C₁₃	—	2	1	no	—
202	C₄²×C₁₃	—	4	1	no	—
203	C₄²×C₁₃	—	4	1	no	—
204	C₄²×C₁₃	—	4	1	no	—
205	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
206	#3360	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#3357	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#3341	C₂×C₁₃	1	1	yes	characteristic
209	#3340	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#1723	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#1691	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#1683	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1676	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#1675	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1646	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1638	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1634	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1632	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1581	C₂×C₁₃	1	1	yes	characteristic, complemented
220	SD₁₆⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
221	C₂³×C₁₃	—	2	1	no	—
222	C₂³×C₁₃	—	2	1	no	—
223	C₂³×C₁₃	—	2	1	no	—
224	Q₈×C₁₃	—	2	1	no	—
225	Q₈×C₁₃	—	2	1	no	—
226	Q₈×C₁₃	—	4	1	no	—
227	Q₈×C₁₃	—	4	1	no	—
228	Q₈×C₁₃	—	8	1	no	—
229	Q₈×C₁₃	—	8	1	no	—
230	Q₈×C₁₃	—	8	1	no	—
231	D₄×C₁₃	—	2	1	no	—
232	D₄×C₁₃	—	2	1	no	—
233	D₄×C₁₃	—	2	1	no	—
234	D₄×C₁₃	—	2	1	no	—
235	D₄×C₁₃	—	2	1	no	—
236	D₄×C₁₃	—	2	1	no	—
237	D₄×C₁₃	—	16	1	no	—
238	D₄×C₁₃	—	16	1	no	—
239	C₂×C₄×C₁₃	—	2	1	no	—
240	C₂×C₄×C₁₃	—	2	1	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	1	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	4	1	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	16	1	no	—
255	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
258	C₈×C₁₃	—	2	1	no	—
259	C₈×C₁₃	—	2	1	no	—
260	C₈×C₁₃	—	2	1	no	—
261	C₈×C₁₃	—	4	1	no	—
262	C₈×C₁₃	—	4	1	no	—
263	C₈×C₁₃	—	4	1	no	—
264	C₈×C₁₃	—	4	1	no	—
265	C₈×C₁₃	—	4	1	no	—
266	C₈×C₁₃	#135	1	2	yes	—
267	#556	C₂²×C₁₃	1	1	yes	characteristic
268	#555	C₂²×C₁₃	1	1	yes	characteristic
269	#555	C₂²×C₁₃	1	1	yes	characteristic
270	#554	C₂²×C₁₃	1	1	yes	characteristic
271	#500	C₂²×C₁₃	1	1	yes	characteristic
272	#500	C₂²×C₁₃	1	1	yes	characteristic
273	#498	C₂²×C₁₃	1	1	yes	characteristic
274	#494	C₂²×C₁₃	1	1	yes	characteristic
275	#488	—	2	1	no	—
276	#487	C₂²×C₁₃	1	1	yes	characteristic
277	#487	C₂²×C₁₃	1	1	yes	characteristic
278	#485	—	2	1	no	—
279	#485	—	2	1	no	—
280	#482	—	2	1	no	—
281	#482	—	2	1	no	—
282	#482	—	2	1	no	—
283	#480	—	2	1	no	—
284	#479	—	2	1	no	—
285	#477	C₂²×C₁₃	1	1	yes	characteristic
286	#477	C₂²×C₁₃	1	1	yes	characteristic
287	#476	C₂²×C₁₃	1	1	yes	characteristic
288	#476	C₂²×C₁₃	1	1	yes	characteristic
289	#476	C₂²×C₁₃	1	1	yes	characteristic
290	#476	C₂²×C₁₃	1	1	yes	characteristic
291	#474	C₂²×C₁₃	1	1	yes	characteristic
292	#468	—	2	1	no	—
293	#466	—	2	1	no	—
294	#465	—	2	1	no	—
295	#463	—	2	1	no	—
296	#461	C₂²×C₁₃	1	1	yes	characteristic
297	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
298	C₄×SD₁₆	—	2	1	no	—
299	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
300	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
301	#436	C₂²×C₁₃	1	1	yes	characteristic
302	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
303	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
304	#428	—	2	1	no	—
305	#427	—	2	1	no	—
306	#427	—	2	1	no	—
307	#335	C₂²×C₁₃	1	1	yes	characteristic
308	#335	C₂²×C₁₃	1	1	yes	characteristic
309	#333	C₂²×C₁₃	1	1	yes	characteristic
310	#333	C₂²×C₁₃	1	1	yes	characteristic
311	#333	C₂²×C₁₃	1	1	yes	characteristic
312	#332	C₂²×C₁₃	1	1	yes	characteristic
313	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
314	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
315	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
316	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
317	#322	C₂²×C₁₃	1	1	yes	characteristic
318	C₂²×C₁₃	—	4	1	no	—
319	C₂²×C₁₃	—	4	1	no	—
320	C₂²×C₁₃	—	4	1	no	—
321	C₂²×C₁₃	—	4	1	no	—
322	C₂²×C₁₃	—	4	1	no	—
323	C₂²×C₁₃	—	4	1	no	—
324	C₂²×C₁₃	—	4	1	no	—
325	C₂²×C₁₃	—	4	1	no	—
326	C₂²×C₁₃	—	4	1	no	—
327	C₂²×C₁₃	D₄²	1	1	yes	characteristic
328	C₄×C₁₃	—	2	1	no	—
329	C₄×C₁₃	—	4	1	no	—
330	C₄×C₁₃	—	4	1	no	—
331	C₄×C₁₃	—	4	1	no	—
332	C₄×C₁₃	—	4	1	no	—
333	C₄×C₁₃	—	4	1	no	—
334	C₄×C₁₃	—	8	1	no	—
335	C₄×C₁₃	—	8	1	no	—
336	C₄×C₁₃	—	8	1	no	—
337	C₄×C₁₃	—	8	1	no	—
338	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
339	C₄×C₁₃	#575	1	1	yes	characteristic
340	C₄×C₁₃	#578	1	1	yes	characteristic
341	C₄×C₁₃	#578	1	1	yes	characteristic
342	C₂×Q₁₆	—	4	1	no	—
343	C₂×SD₁₆	—	2	1	no	—
344	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
345	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
346	C₂×M₁₆	—	2	1	no	—
347	C₂²×C₈	—	2	1	no	—
348	C₂²×C₈	—	2	1	no	—
349	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
350	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
351	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
352	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
353	#126	—	4	1	no	—
354	#125	—	2	1	no	—
355	#124	—	2	1	no	—
356	#124	—	4	1	no	—
357	#124	—	4	1	no	—
358	C₂²⋊Q₈	—	2	1	no	—
359	C₂²⋊Q₈	—	2	1	no	—
360	C₂²⋊Q₈	—	4	1	no	—
361	#121	—	2	1	no	—
362	#121	—	2	1	no	—
363	#121	—	2	1	no	—
364	#121	—	2	1	no	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
369	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
370	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
371	#117	—	2	1	no	—
372	#117	—	2	1	no	—
373	#117	—	2	1	no	—
374	#117	—	2	1	no	—
375	#117	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	#107	—	2	1	no	—
378	#107	—	2	1	no	—
379	#107	—	2	1	no	—
380	#107	—	2	1	no	—
381	#107	—	2	1	no	—
382	#107	—	2	1	no	—
383	#107	—	2	1	no	—
384	#107	D₄×C₁₃	1	1	yes	characteristic
385	#106	—	2	1	no	—
386	#106	—	2	1	no	—
387	#106	—	2	1	no	—
388	#106	—	2	1	no	—
389	#106	—	2	1	no	—
390	#106	—	2	1	no	—
391	#106	D₄×C₁₃	1	1	yes	characteristic
392	C₄⋊C₈	—	2	1	no	—
393	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
394	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
395	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
396	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
397	#103	—	2	1	no	—
398	#103	—	2	1	no	—
399	#103	—	2	1	no	—
400	#103	—	2	1	no	—
401	#103	—	2	1	no	—
402	#103	—	4	1	no	—
403	#103	D₄×C₁₃	1	1	yes	characteristic
404	#102	—	2	1	no	—
405	#102	—	2	1	no	—
406	#102	—	2	1	no	—
407	#102	—	2	1	no	—
408	#102	—	2	1	no	—
409	#102	D₄×C₁₃	1	1	yes	characteristic
410	#102	D₄×C₁₃	1	1	yes	characteristic
411	#102	D₄×C₁₃	1	1	yes	characteristic
412	C₂²⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	—	2	1	no	—
414	C₂²⋊C₈	—	2	1	no	—
415	C₄×C₈	—	2	1	no	—
416	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
417	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
418	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
419	C₂×C₁₃	—	8	1	no	—
420	C₂×C₁₃	—	8	1	no	—
421	C₂×C₁₃	—	8	1	no	—
422	C₂×C₁₃	#3269	1	1	yes	characteristic
423	C₂×C₁₃	#3283	1	1	yes	characteristic
424	C₂×C₁₃	#3288	1	1	yes	characteristic
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
430	C₂×D₄	—	4	1	no	—
431	C₂×D₄	—	4	1	no	—
432	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
433	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	4	1	no	—
439	Q₁₆	—	8	2	no	—
440	SD₁₆	—	2	2	no	—
441	SD₁₆	—	4	2	no	—
442	D₈	—	4	1	no	—
443	M₁₆	—	4	2	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	4	2	no	—
450	C₂×C₈	—	4	2	no	—
451	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
452	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
453	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
454	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	4	1	no	—
465	C₄⋊C₄	—	4	1	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
468	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
469	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
470	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₂²⋊C₄	—	4	1	no	—
476	C₂²⋊C₄	—	4	1	no	—
477	C₂²⋊C₄	—	4	1	no	—
478	C₂²⋊C₄	—	4	1	no	—
479	C₂²⋊C₄	—	4	1	no	—
480	C₂²⋊C₄	—	4	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	4	1	no	—
483	C₄²	—	4	1	no	—
484	C₄²	—	4	1	no	—
485	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
486	C₁₃	#19864	1	1	yes	characteristic, direct product factor, Sylow
487	C₂³	—	2	1	no	—
488	C₂³	—	2	1	no	—
489	C₂³	—	2	1	no	—
490	Q₈	—	2	1	no	—
491	Q₈	—	2	1	no	—
492	Q₈	—	4	1	no	—
493	Q₈	—	4	1	no	—
494	Q₈	—	8	1	no	—
495	Q₈	—	8	1	no	—
496	Q₈	—	8	1	no	—
497	D₄	—	2	1	no	—
498	D₄	—	2	1	no	—
499	D₄	—	2	1	no	—
500	D₄	—	2	1	no	—
501	D₄	—	2	1	no	—
502	D₄	—	2	1	no	—
503	D₄	—	16	1	no	—
504	D₄	—	16	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	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	16	1	no	—
521	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
522	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
523	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	4	1	no	—
532	C₈	C₁₃×#135	1	2	yes	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	D₄²×C₁₃	1	1	yes	characteristic
543	C₄	—	2	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	8	1	no	—
550	C₄	—	8	1	no	—
551	C₄	—	8	1	no	—
552	C₄	—	8	1	no	—
553	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
554	C₄	C₁₃×#575	1	1	yes	characteristic
555	C₄	C₁₃×#578	1	1	yes	characteristic
556	C₄	C₁₃×#578	1	1	yes	characteristic
557	C₂	—	8	1	no	—
558	C₂	—	8	1	no	—
559	C₂	—	8	1	no	—
560	C₂	C₁₃×#3269	1	1	yes	characteristic
561	C₂	C₁₃×#3283	1	1	yes	characteristic
562	C₂	C₁₃×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3341	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3360	C₂	semidirect
2. C₁₃×#3357	C₂	semidirect
4. C₁₃×#3340	C₂	semidirect
5. C₁₃×#1723	C₂	semidirect
6. C₁₃×#1691	C₂	semidirect
7. C₁₃×#1683	C₂	semidirect
8. C₁₃×#1676	C₂	semidirect
9. C₁₃×#1675	C₂	semidirect
10. C₁₃×#1646	C₂	semidirect
11. C₁₃×#1638	C₂	semidirect
12. C₁₃×#1634	C₂	semidirect
13. C₁₃×#1632	C₂	semidirect
14. C₁₃×#1581	C₂	semidirect
15. C₁₃×SD₁₆⋊C₈	C₂	semidirect
144. #19864	C₁₃	direct (N × H)
206. #3360	C₂×C₁₃	semidirect
207. #3357	C₂×C₁₃	semidirect
209. #3340	C₂×C₁₃	semidirect
210. #1723	C₂×C₁₃	semidirect
211. #1691	C₂×C₁₃	semidirect
212. #1683	C₂×C₁₃	semidirect
213. #1676	C₂×C₁₃	semidirect
214. #1675	C₂×C₁₃	semidirect
215. #1646	C₂×C₁₃	semidirect
216. #1638	C₂×C₁₃	semidirect
217. #1634	C₂×C₁₃	semidirect
218. #1632	C₂×C₁₃	semidirect
219. #1581	C₂×C₁₃	semidirect
220. SD₁₆⋊C₈	C₂×C₁₃	semidirect
486. C₁₃	#19864	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3360	2
C₁₃×#3357	2
C₁₃×#3341	2
C₁₃×#3340	2
C₁₃×#1723	2
C₁₃×#1691	2
C₁₃×#1683	2
C₁₃×#1676	2
C₁₃×#1675	2
C₁₃×#1646	2
C₁₃×#1638	2
C₁₃×#1634	2
C₁₃×#1632	2
C₁₃×#1581	2
C₁₃×SD₁₆⋊C₈	2
#19864	13

Subgroups — C13×#19864 #15706203

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19864 #15706203