Subgroups — C₁₃×#19798 #15706137

Order 3328.

592 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3375	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3361	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#3299	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1720	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1704	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1678	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1677	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1672	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1640	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1633	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1632	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1627	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1582	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1579	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#559	C₂²	1	1	yes	characteristic
17	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#554	C₂²	1	1	yes	characteristic
19	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#498	—	2	1	no	—
21	C₁₃×#498	C₂²	1	1	yes	characteristic
22	C₁₃×#494	C₂²	1	1	yes	characteristic
23	C₁₃×#489	—	2	1	no	—
24	C₁₃×#488	—	2	1	no	—
25	C₁₃×#487	C₂²	1	1	yes	characteristic
26	C₁₃×#486	C₂²	1	1	yes	characteristic
27	C₁₃×#486	C₂²	1	1	yes	characteristic
28	C₁₃×#486	C₂²	1	1	yes	characteristic
29	C₁₃×#484	—	2	1	no	—
30	C₁₃×#478	—	2	1	no	—
31	C₁₃×#477	C₂²	1	1	yes	characteristic
32	C₁₃×#477	C₂²	1	1	yes	characteristic
33	C₁₃×#477	C₂²	1	1	yes	characteristic
34	C₁₃×#476	—	2	1	no	—
35	C₁₃×#476	C₂²	1	1	yes	characteristic
36	C₁₃×#475	—	2	1	no	—
37	C₁₃×#475	C₂²	1	1	yes	characteristic
38	C₁₃×#474	—	2	1	no	—
39	C₁₃×#467	—	2	1	no	—
40	C₁₃×#464	—	2	1	no	—
41	C₁₃×#463	—	2	1	no	—
42	C₁₃×#462	C₂²	1	1	yes	characteristic
43	C₁₃×#460	C₂²	1	1	yes	characteristic
44	C₁₃×#459	C₂²	1	1	yes	characteristic
45	C₁₃×#451	—	2	1	no	—
46	C₁₃×#446	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
49	C₁₃×#440	—	2	1	no	—
50	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×SD₁₆	—	2	1	no	—
52	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
53	C₄×C₁₃×D₈	—	2	1	no	—
54	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#103	—	2	1	no	—
56	C₁₃×#334	C₂²	1	1	yes	characteristic
57	C₁₃×#334	C₂²	1	1	yes	characteristic
58	C₁₃×#333	C₂²	1	1	yes	characteristic
59	C₁₃×#333	C₂²	1	1	yes	characteristic
60	C₁₃×#332	C₂²	1	1	yes	characteristic
61	C₁₃×#331	C₂²	1	1	yes	characteristic
62	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₃×#322	C₂²	1	1	yes	characteristic
67	C₂²×Q₈×C₁₃	—	2	1	no	—
68	C₂×C₁₃×Q₁₆	—	2	1	no	—
69	C₂×C₁₃×Q₁₆	—	4	1	no	—
70	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
71	C₂×C₁₃×SD₁₆	—	2	1	no	—
72	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
73	C₂×C₁₃×D₈	—	2	1	no	—
74	C₂²×C₈×C₁₃	—	2	1	no	—
75	C₁₃×C₄⋊Q₈	—	2	1	no	—
76	C₁₃×C₄⋊Q₈	—	2	1	no	—
77	C₁₃×C₄⋊Q₈	—	2	1	no	—
78	C₁₃×C₄⋊Q₈	—	4	1	no	—
79	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₃×#127	C₂³	1	1	yes	characteristic
83	C₁₃×#125	—	2	1	no	—
84	C₁₃×#124	—	2	1	no	—
85	C₁₃×#124	—	2	1	no	—
86	C₁₃×#123	—	4	1	no	—
87	C₁₃×C₂²⋊Q₈	—	2	1	no	—
88	C₁₃×C₂²⋊Q₈	—	2	1	no	—
89	C₁₃×C₂²⋊Q₈	—	4	1	no	—
90	C₁₃×C₂²⋊Q₈	—	4	1	no	—
91	C₄×Q₈×C₁₃	—	2	1	no	—
92	C₄×Q₈×C₁₃	—	2	1	no	—
93	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₁₃	—	2	1	no	—
97	C₄×D₄×C₁₃	—	2	1	no	—
98	C₄×D₄×C₁₃	—	2	1	no	—
99	C₄×D₄×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
106	C₁₃×#106	—	2	1	no	—
107	C₁₃×#106	—	2	1	no	—
108	C₁₃×#106	—	2	1	no	—
109	C₁₃×#106	—	2	1	no	—
110	C₁₃×#106	D₄	1	1	yes	characteristic
111	C₁₃×C₄⋊C₈	—	2	1	no	—
112	C₁₃×C₄⋊C₈	—	2	1	no	—
113	C₁₃×C₄⋊C₈	—	2	1	no	—
114	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₃×#103	—	2	1	no	—
119	C₁₃×#103	—	2	1	no	—
120	C₁₃×#103	—	2	1	no	—
121	C₁₃×#103	—	2	1	no	—
122	C₁₃×#103	—	2	1	no	—
123	C₁₃×#103	—	2	1	no	—
124	C₁₃×#103	—	2	1	no	—
125	C₁₃×#103	D₄	1	1	yes	characteristic
126	C₁₃×#103	D₄	1	1	yes	characteristic
127	C₁₃×#103	D₄	1	1	yes	characteristic
128	C₁₃×#102	—	2	1	no	—
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	—	2	1	no	—
135	C₁₃×#102	—	4	1	no	—
136	C₁₃×#102	D₄	1	1	yes	characteristic
137	C₁₃×C₂²⋊C₈	—	2	1	no	—
138	C₁₃×#97	—	2	1	no	—
139	C₄×C₈×C₁₃	—	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	#19798	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	—	4	1	no	—
149	C₂×Q₈×C₁₃	—	4	1	no	—
150	C₂×Q₈×C₁₃	—	4	2	no	—
151	C₂×Q₈×C₁₃	—	8	1	no	—
152	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	4	1	no	—
161	C₂²×C₄×C₁₃	—	4	1	no	—
162	C₂²×C₄×C₁₃	—	4	1	no	—
163	C₁₃×Q₁₆	—	2	2	no	—
164	C₁₃×Q₁₆	—	8	1	no	—
165	C₁₃×Q₁₆	—	8	2	no	—
166	C₁₃×SD₁₆	—	2	2	no	—
167	C₁₃×SD₁₆	—	4	2	no	—
168	C₁₃×D₈	—	4	2	no	—
169	C₂×C₈×C₁₃	—	2	1	no	—
170	C₂×C₈×C₁₃	—	2	1	no	—
171	C₂×C₈×C₁₃	—	2	1	no	—
172	C₂×C₈×C₁₃	—	2	1	no	—
173	C₂×C₈×C₁₃	—	2	1	no	—
174	C₂×C₈×C₁₃	—	8	1	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	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	—	2	1	no	—
185	C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	4	1	no	—
189	C₁₃×C₄⋊C₄	—	4	1	no	—
190	C₁₃×C₄⋊C₄	—	4	1	no	—
191	C₁₃×C₄⋊C₄	—	4	1	no	—
192	C₁₃×C₄⋊C₄	—	4	1	no	—
193	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
194	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
195	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
196	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
197	C₁₃×C₂²⋊C₄	—	2	1	no	—
198	C₁₃×C₂²⋊C₄	—	4	1	no	—
199	C₁₃×C₂²⋊C₄	—	4	1	no	—
200	C₁₃×C₂²⋊C₄	—	4	1	no	—
201	C₁₃×C₂²⋊C₄	—	4	1	no	—
202	C₁₃×C₂²⋊C₄	—	4	1	no	—
203	C₄²×C₁₃	—	2	1	no	—
204	C₄²×C₁₃	—	2	1	no	—
205	C₄²×C₁₃	—	2	1	no	—
206	C₄²×C₁₃	—	4	1	no	—
207	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
208	Q₈×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#3375	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#3361	C₂×C₁₃	1	1	yes	characteristic
211	#3299	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#1720	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1704	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#1678	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1677	C₂×C₁₃	1	1	yes	characteristic
216	#1672	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1640	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1633	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1632	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1627	C₂×C₁₃	1	1	yes	characteristic
221	#1582	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1579	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₂³×C₁₃	—	2	1	no	—
224	C₂³×C₁₃	—	4	1	no	—
225	Q₈×C₁₃	—	2	1	no	—
226	Q₈×C₁₃	—	2	1	no	—
227	Q₈×C₁₃	—	2	1	no	—
228	Q₈×C₁₃	—	2	1	no	—
229	Q₈×C₁₃	—	2	1	no	—
230	Q₈×C₁₃	—	4	1	no	—
231	Q₈×C₁₃	—	4	1	no	—
232	Q₈×C₁₃	—	8	2	no	—
233	Q₈×C₁₃	—	8	1	no	—
234	Q₈×C₁₃	—	8	1	no	—
235	Q₈×C₁₃	—	16	1	no	—
236	Q₈×C₁₃	#135	1	2	yes	—
237	D₄×C₁₃	—	2	1	no	—
238	D₄×C₁₃	—	4	1	no	—
239	D₄×C₁₃	—	4	1	no	—
240	D₄×C₁₃	—	4	1	no	—
241	D₄×C₁₃	—	4	1	no	—
242	D₄×C₁₃	—	8	1	no	—
243	D₄×C₁₃	#137	1	2	yes	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	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	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	8	2	no	—
257	C₂×C₄×C₁₃	—	16	1	no	—
258	C₂×C₄×C₁₃	—	16	1	no	—
259	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
262	C₈×C₁₃	—	2	1	no	—
263	C₈×C₁₃	—	2	1	no	—
264	C₈×C₁₃	—	2	1	no	—
265	C₈×C₁₃	—	2	1	no	—
266	C₈×C₁₃	—	4	1	no	—
267	C₈×C₁₃	—	4	1	no	—
268	C₈×C₁₃	—	4	1	no	—
269	C₈×C₁₃	—	4	1	no	—
270	C₈×C₁₃	—	4	1	no	—
271	#559	C₂²×C₁₃	1	1	yes	characteristic
272	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
273	#554	C₂²×C₁₃	1	1	yes	characteristic
274	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
275	#498	—	2	1	no	—
276	#498	C₂²×C₁₃	1	1	yes	characteristic
277	#494	C₂²×C₁₃	1	1	yes	characteristic
278	#489	—	2	1	no	—
279	#488	—	2	1	no	—
280	#487	C₂²×C₁₃	1	1	yes	characteristic
281	#486	C₂²×C₁₃	1	1	yes	characteristic
282	#486	C₂²×C₁₃	1	1	yes	characteristic
283	#486	C₂²×C₁₃	1	1	yes	characteristic
284	#484	—	2	1	no	—
285	#478	—	2	1	no	—
286	#477	C₂²×C₁₃	1	1	yes	characteristic
287	#477	C₂²×C₁₃	1	1	yes	characteristic
288	#477	C₂²×C₁₃	1	1	yes	characteristic
289	#476	—	2	1	no	—
290	#476	C₂²×C₁₃	1	1	yes	characteristic
291	#475	—	2	1	no	—
292	#475	C₂²×C₁₃	1	1	yes	characteristic
293	#474	—	2	1	no	—
294	#467	—	2	1	no	—
295	#464	—	2	1	no	—
296	#463	—	2	1	no	—
297	#462	C₂²×C₁₃	1	1	yes	characteristic
298	#460	C₂²×C₁₃	1	1	yes	characteristic
299	#459	C₂²×C₁₃	1	1	yes	characteristic
300	#451	—	2	1	no	—
301	#446	C₂²×C₁₃	1	1	yes	characteristic
302	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
303	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
304	#440	—	2	1	no	—
305	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
306	C₄×SD₁₆	—	2	1	no	—
307	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
308	C₄×D₈	—	2	1	no	—
309	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×#103	—	2	1	no	—
311	#334	C₂²×C₁₃	1	1	yes	characteristic
312	#334	C₂²×C₁₃	1	1	yes	characteristic
313	#333	C₂²×C₁₃	1	1	yes	characteristic
314	#333	C₂²×C₁₃	1	1	yes	characteristic
315	#332	C₂²×C₁₃	1	1	yes	characteristic
316	#331	C₂²×C₁₃	1	1	yes	characteristic
317	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
318	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
319	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
320	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
321	#322	C₂²×C₁₃	1	1	yes	characteristic
322	C₂²×C₁₃	—	2	2	no	—
323	C₂²×C₁₃	—	4	1	no	—
324	C₂²×C₁₃	—	4	1	no	—
325	C₂²×C₁₃	—	8	1	no	—
326	C₂²×C₁₃	—	8	1	no	—
327	C₂²×C₁₃	—	8	1	no	—
328	C₂²×C₁₃	D₄²	1	1	yes	characteristic
329	C₄×C₁₃	—	2	2	no	—
330	C₄×C₁₃	—	2	1	no	—
331	C₄×C₁₃	—	4	1	no	—
332	C₄×C₁₃	—	4	1	no	—
333	C₄×C₁₃	—	4	1	no	—
334	C₄×C₁₃	—	4	1	no	—
335	C₄×C₁₃	—	4	1	no	—
336	C₄×C₁₃	—	4	1	no	—
337	C₄×C₁₃	—	8	1	no	—
338	C₄×C₁₃	—	8	1	no	—
339	C₄×C₁₃	—	8	1	no	—
340	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
341	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
342	C₄×C₁₃	#577	1	1	yes	characteristic
343	C₄×C₁₃	#578	1	1	yes	characteristic
344	C₂²×Q₈	—	2	1	no	—
345	C₂×Q₁₆	—	2	1	no	—
346	C₂×Q₁₆	—	4	1	no	—
347	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
348	C₂×SD₁₆	—	2	1	no	—
349	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
350	C₂×D₈	—	2	1	no	—
351	C₂²×C₈	—	2	1	no	—
352	C₄⋊Q₈	—	2	1	no	—
353	C₄⋊Q₈	—	2	1	no	—
354	C₄⋊Q₈	—	2	1	no	—
355	C₄⋊Q₈	—	4	1	no	—
356	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
357	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
358	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
359	#127	C₂³×C₁₃	1	1	yes	characteristic
360	#125	—	2	1	no	—
361	#124	—	2	1	no	—
362	#124	—	2	1	no	—
363	#123	—	4	1	no	—
364	C₂²⋊Q₈	—	2	1	no	—
365	C₂²⋊Q₈	—	2	1	no	—
366	C₂²⋊Q₈	—	4	1	no	—
367	C₂²⋊Q₈	—	4	1	no	—
368	C₄×Q₈	—	2	1	no	—
369	C₄×Q₈	—	2	1	no	—
370	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
371	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
372	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	—	2	1	no	—
375	C₄×D₄	—	2	1	no	—
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
378	C₂×C₄⋊C₄	—	2	1	no	—
379	#107	—	2	1	no	—
380	#107	—	2	1	no	—
381	#107	—	2	1	no	—
382	#107	D₄×C₁₃	1	1	yes	characteristic
383	#106	—	2	1	no	—
384	#106	—	2	1	no	—
385	#106	—	2	1	no	—
386	#106	—	2	1	no	—
387	#106	D₄×C₁₃	1	1	yes	characteristic
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	—	2	1	no	—
390	C₄⋊C₈	—	2	1	no	—
391	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
392	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
393	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
394	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
395	#103	—	2	1	no	—
396	#103	—	2	1	no	—
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	D₄×C₁₃	1	1	yes	characteristic
403	#103	D₄×C₁₃	1	1	yes	characteristic
404	#103	D₄×C₁₃	1	1	yes	characteristic
405	#102	—	2	1	no	—
406	#102	—	2	1	no	—
407	#102	—	2	1	no	—
408	#102	—	2	1	no	—
409	#102	—	2	1	no	—
410	#102	—	2	1	no	—
411	#102	—	2	1	no	—
412	#102	—	4	1	no	—
413	#102	D₄×C₁₃	1	1	yes	characteristic
414	C₂²⋊C₈	—	2	1	no	—
415	#97	—	2	1	no	—
416	C₄×C₈	—	2	1	no	—
417	C₄×C₈	—	2	1	no	—
418	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
419	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
420	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
421	C₂×C₁₃	—	4	2	no	—
422	C₂×C₁₃	—	16	1	no	—
423	C₂×C₁₃	#3270	1	1	yes	characteristic
424	C₂×C₁₃	#3282	1	1	yes	characteristic
425	C₂×C₁₃	#3288	1	1	yes	characteristic
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	4	1	no	—
430	C₂×Q₈	—	4	1	no	—
431	C₂×Q₈	—	4	2	no	—
432	C₂×Q₈	—	8	1	no	—
433	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
435	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	4	1	no	—
442	C₂²×C₄	—	4	1	no	—
443	C₂²×C₄	—	4	1	no	—
444	Q₁₆	—	2	2	no	—
445	Q₁₆	—	8	1	no	—
446	Q₁₆	—	8	2	no	—
447	SD₁₆	—	2	2	no	—
448	SD₁₆	—	4	2	no	—
449	D₈	—	4	2	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	8	1	no	—
456	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
457	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
458	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
459	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	4	1	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₄⋊C₄	—	4	1	no	—
474	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
475	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	4	1	no	—
480	C₂²⋊C₄	—	4	1	no	—
481	C₂²⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	4	1	no	—
483	C₂²⋊C₄	—	4	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	4	1	no	—
488	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
489	C₁₃	#19798	1	1	yes	characteristic, direct product factor, Sylow
490	C₂³	—	2	1	no	—
491	C₂³	—	4	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	2	1	no	—
494	Q₈	—	2	1	no	—
495	Q₈	—	2	1	no	—
496	Q₈	—	2	1	no	—
497	Q₈	—	4	1	no	—
498	Q₈	—	4	1	no	—
499	Q₈	—	8	2	no	—
500	Q₈	—	8	1	no	—
501	Q₈	—	8	1	no	—
502	Q₈	—	16	1	no	—
503	Q₈	C₁₃×#135	1	2	yes	—
504	D₄	—	2	1	no	—
505	D₄	—	4	1	no	—
506	D₄	—	4	1	no	—
507	D₄	—	4	1	no	—
508	D₄	—	4	1	no	—
509	D₄	—	8	1	no	—
510	D₄	C₁₃×#137	1	2	yes	—
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	—	2	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	8	2	no	—
524	C₂×C₄	—	16	1	no	—
525	C₂×C₄	—	16	1	no	—
526	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
528	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
529	C₈	—	2	1	no	—
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	4	1	no	—
534	C₈	—	4	1	no	—
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	1	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	8	1	no	—
542	C₂²	—	8	1	no	—
543	C₂²	—	8	1	no	—
544	C₂²	D₄²×C₁₃	1	1	yes	characteristic
545	C₄	—	2	2	no	—
546	C₄	—	2	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	8	1	no	—
554	C₄	—	8	1	no	—
555	C₄	—	8	1	no	—
556	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
557	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
558	C₄	C₁₃×#577	1	1	yes	characteristic
559	C₄	C₁₃×#578	1	1	yes	characteristic
560	C₂	—	4	2	no	—
561	C₂	—	16	1	no	—
562	C₂	C₁₃×#3270	1	1	yes	characteristic
563	C₂	C₁₃×#3282	1	1	yes	characteristic
564	C₂	C₁₃×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#459	C₂²
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. Q₈×C₁₃×SD₁₆	C₂	semidirect
2. C₁₃×#3375	C₂	semidirect
4. C₁₃×#3299	C₂	semidirect
5. C₁₃×#1720	C₂	semidirect
6. C₁₃×#1704	C₂	semidirect
7. C₁₃×#1678	C₂	semidirect
9. C₁₃×#1672	C₂	semidirect
10. C₁₃×#1640	C₂	semidirect
11. C₁₃×#1633	C₂	semidirect
12. C₁₃×#1632	C₂	semidirect
14. C₁₃×#1582	C₂	semidirect
15. C₁₃×#1579	C₂	semidirect
144. #19798	C₁₃	direct (N × H)
208. Q₈×SD₁₆	C₂×C₁₃	semidirect
209. #3375	C₂×C₁₃	semidirect
211. #3299	C₂×C₁₃	semidirect
212. #1720	C₂×C₁₃	semidirect
213. #1704	C₂×C₁₃	semidirect
214. #1678	C₂×C₁₃	semidirect
216. #1672	C₂×C₁₃	semidirect
217. #1640	C₂×C₁₃	semidirect
218. #1633	C₂×C₁₃	semidirect
219. #1632	C₂×C₁₃	semidirect
221. #1582	C₂×C₁₃	semidirect
222. #1579	C₂×C₁₃	semidirect
489. C₁₃	#19798	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈×C₁₃×SD₁₆	2
C₁₃×#3375	2
C₁₃×#3361	2
C₁₃×#3299	2
C₁₃×#1720	2
C₁₃×#1704	2
C₁₃×#1678	2
C₁₃×#1677	2
C₁₃×#1672	2
C₁₃×#1640	2
C₁₃×#1633	2
C₁₃×#1632	2
C₁₃×#1627	2
C₁₃×#1582	2
C₁₃×#1579	2
#19798	13

Subgroups — C13×#19798 #15706137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19798 #15706137