Subgroups — C₁₃×#19766 #15706105

Order 3328.

650 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3335	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3298	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3283	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1716	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1690	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1679	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1671	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1671	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1654	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1651	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1643	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1635	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1582	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1580	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#135	—	2	1	no	—
17	C₁₃×#554	C₂²	1	1	yes	characteristic
18	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#547	C₂²	1	1	yes	characteristic
20	C₁₃×#547	C₂²	1	1	yes	characteristic
21	C₁₃×#501	—	2	1	no	—
22	C₁₃×#498	C₂²	1	1	yes	characteristic
23	C₁₃×#498	C₂²	1	1	yes	characteristic
24	C₁₃×#498	C₂²	1	1	yes	characteristic
25	C₁₃×#494	C₂²	1	1	yes	characteristic
26	C₁₃×#487	C₂²	1	1	yes	characteristic
27	C₁₃×#487	C₂²	1	1	yes	characteristic
28	C₁₃×#483	—	2	1	no	—
29	C₁₃×#483	—	2	1	no	—
30	C₁₃×#481	—	2	1	no	—
31	C₁₃×#478	—	2	1	no	—
32	C₁₃×#476	—	2	1	no	—
33	C₁₃×#476	C₂²	1	1	yes	characteristic
34	C₁₃×#476	C₂²	1	1	yes	characteristic
35	C₁₃×#475	C₂²	1	1	yes	characteristic
36	C₁₃×#475	C₂²	1	1	yes	characteristic
37	C₁₃×#474	C₂²	1	1	yes	characteristic
38	C₁₃×#467	—	2	1	no	—
39	C₁₃×#465	—	2	1	no	—
40	C₁₃×#465	—	2	1	no	—
41	C₁₃×#461	C₂²	1	1	yes	characteristic
42	C₁₃×#461	C₂²	1	1	yes	characteristic
43	C₁₃×#461	C₂²	1	1	yes	characteristic
44	C₁₃×#452	—	2	1	no	—
45	C₁₃×#452	—	2	1	no	—
46	C₁₃×#448	—	2	1	no	—
47	C₁₃×#446	C₂²	1	1	yes	characteristic
48	C₁₃×#442	—	2	1	no	—
49	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
51	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#106	—	2	1	no	—
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×#332	C₂²	1	1	yes	characteristic
60	C₁₃×#332	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×#41	—	2	1	no	—
68	C₂×C₁₃×#41	—	2	1	no	—
69	C₂²×Q₈×C₁₃	—	2	1	no	—
70	C₁₃×#135	—	4	4	no	—
71	C₂×C₁₃×Q₁₆	—	2	1	no	—
72	C₂×C₁₃×Q₁₆	—	2	1	no	—
73	C₂×C₁₃×SD₁₆	—	2	1	no	—
74	C₂×C₁₃×SD₁₆	—	2	1	no	—
75	C₂×C₁₃×SD₁₆	—	2	1	no	—
76	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
77	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
78	C₂²×C₈×C₁₃	—	2	1	no	—
79	C₂²×C₈×C₁₃	—	2	1	no	—
80	C₂²×C₈×C₁₃	—	2	1	no	—
81	C₁₃×C₄⋊Q₈	—	2	1	no	—
82	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₃×#125	—	2	1	no	—
87	C₁₃×#123	—	4	1	no	—
88	C₁₃×#123	—	4	1	no	—
89	C₁₃×C₂²⋊Q₈	—	2	1	no	—
90	C₁₃×C₂²⋊Q₈	—	2	1	no	—
91	C₁₃×C₂²⋊Q₈	—	2	1	no	—
92	C₁₃×C₂²⋊Q₈	—	2	1	no	—
93	C₁₃×C₂²⋊Q₈	—	4	1	no	—
94	C₁₃×C₂²⋊Q₈	—	4	1	no	—
95	C₁₃×#121	—	2	1	no	—
96	C₁₃×#121	—	2	1	no	—
97	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₄×D₄×C₁₃	—	2	1	no	—
99	C₄×D₄×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₁₃×#107	—	2	1	no	—
107	C₁₃×#107	D₄	1	1	yes	characteristic
108	C₁₃×#106	—	2	1	no	—
109	C₁₃×#106	—	2	1	no	—
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	—	4	1	no	—
117	C₁₃×#106	D₄	1	1	yes	characteristic
118	C₁₃×C₄⋊C₈	—	2	1	no	—
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
128	C₁₃×#103	—	2	1	no	—
129	C₁₃×#103	—	2	1	no	—
130	C₁₃×#103	—	4	1	no	—
131	C₁₃×#103	D₄	1	1	yes	characteristic
132	C₁₃×#102	—	2	1	no	—
133	C₁₃×#102	—	2	1	no	—
134	C₁₃×#102	—	2	1	no	—
135	C₁₃×#102	D₄	1	1	yes	characteristic
136	C₁₃×#102	D₄	1	1	yes	characteristic
137	C₁₃×#102	D₄	1	1	yes	characteristic
138	C₁₃×C₂²⋊C₈	—	2	1	no	—
139	C₁₃×C₂²⋊C₈	—	2	1	no	—
140	C₁₃×C₂²⋊C₈	—	2	1	no	—
141	C₁₃×#97	—	2	1	no	—
142	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
145	#19766	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₁₃×#41	—	4	2	no	—
147	C₁₃×#41	—	4	2	no	—
148	C₁₃×#41	—	8	1	no	—
149	C₁₃×#41	—	8	1	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	2	1	no	—
152	C₂×Q₈×C₁₃	—	2	1	no	—
153	C₂×Q₈×C₁₃	—	2	1	no	—
154	C₂×Q₈×C₁₃	—	4	1	no	—
155	C₂×Q₈×C₁₃	—	4	2	no	—
156	C₂×Q₈×C₁₃	—	8	1	no	—
157	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂×D₄×C₁₃	—	4	1	no	—
159	C₂×D₄×C₁₃	—	4	1	no	—
160	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	4	1	no	—
167	C₂²×C₄×C₁₃	—	4	1	no	—
168	C₂²×C₄×C₁₃	—	4	1	no	—
169	C₂²×C₄×C₁₃	—	4	1	no	—
170	C₁₃×Q₁₆	—	4	2	no	—
171	C₁₃×Q₁₆	—	8	1	no	—
172	C₁₃×SD₁₆	—	4	1	no	—
173	C₁₃×SD₁₆	—	4	2	no	—
174	C₁₃×SD₁₆	—	4	2	no	—
175	C₁₃×SD₁₆	—	8	1	no	—
176	C₁₃×D₈	SD₁₆	1	4	yes	complemented
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	4	2	no	—
183	C₂×C₈×C₁₃	—	4	2	no	—
184	C₂×C₈×C₁₃	—	8	1	no	—
185	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	—	4	1	no	—
199	C₁₃×C₄⋊C₄	—	4	1	no	—
200	C₁₃×C₄⋊C₄	—	4	1	no	—
201	C₁₃×C₄⋊C₄	—	4	1	no	—
202	C₁₃×C₄⋊C₄	—	4	1	no	—
203	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
204	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
205	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
206	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
207	C₁₃×C₂²⋊C₄	—	2	1	no	—
208	C₁₃×C₂²⋊C₄	—	2	1	no	—
209	C₁₃×C₂²⋊C₄	—	2	1	no	—
210	C₁₃×C₂²⋊C₄	—	4	1	no	—
211	C₁₃×C₂²⋊C₄	—	4	1	no	—
212	C₁₃×C₂²⋊C₄	—	4	1	no	—
213	C₁₃×C₂²⋊C₄	—	4	1	no	—
214	C₄²×C₁₃	—	2	1	no	—
215	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
216	#3384	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#3335	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#3298	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#3283	C₂×C₁₃	1	1	yes	characteristic
220	#1716	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1690	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1679	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1671	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1671	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1654	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1651	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1643	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1635	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1582	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#1580	C₂×C₁₃	1	1	yes	characteristic, complemented
231	C₂³×C₁₃	—	2	1	no	—
232	C₂³×C₁₃	—	2	1	no	—
233	C₂³×C₁₃	—	2	1	no	—
234	Q₈×C₁₃	—	2	1	no	—
235	Q₈×C₁₃	—	2	1	no	—
236	Q₈×C₁₃	—	4	1	no	—
237	Q₈×C₁₃	—	4	1	no	—
238	Q₈×C₁₃	—	4	1	no	—
239	Q₈×C₁₃	—	4	1	no	—
240	Q₈×C₁₃	—	4	1	no	—
241	Q₈×C₁₃	—	4	1	no	—
242	Q₈×C₁₃	—	8	1	no	—
243	Q₈×C₁₃	—	8	2	no	—
244	D₄×C₁₃	—	2	1	no	—
245	D₄×C₁₃	—	2	1	no	—
246	D₄×C₁₃	—	2	1	no	—
247	D₄×C₁₃	—	2	1	no	—
248	D₄×C₁₃	—	8	2	no	—
249	D₄×C₁₃	—	8	2	no	—
250	D₄×C₁₃	C₂×SD₁₆	1	2	yes	—
251	D₄×C₁₃	C₂×SD₁₆	1	2	yes	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	—	8	2	no	—
268	C₂×C₄×C₁₃	—	8	2	no	—
269	C₂×C₄×C₁₃	—	8	2	no	—
270	C₂×C₄×C₁₃	—	16	1	no	—
271	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
274	C₈×C₁₃	—	2	1	no	—
275	C₈×C₁₃	—	2	1	no	—
276	C₈×C₁₃	—	2	1	no	—
277	C₈×C₁₃	—	4	1	no	—
278	C₈×C₁₃	—	4	1	no	—
279	C₈×C₁₃	—	4	1	no	—
280	C₈×C₁₃	—	4	1	no	—
281	C₈×C₁₃	—	4	1	no	—
282	C₈×C₁₃	C₂×SD₁₆	1	2	yes	—
283	C₂×#135	—	2	1	no	—
284	#554	C₂²×C₁₃	1	1	yes	characteristic
285	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
286	#547	C₂²×C₁₃	1	1	yes	characteristic
287	#547	C₂²×C₁₃	1	1	yes	characteristic
288	#501	—	2	1	no	—
289	#498	C₂²×C₁₃	1	1	yes	characteristic
290	#498	C₂²×C₁₃	1	1	yes	characteristic
291	#498	C₂²×C₁₃	1	1	yes	characteristic
292	#494	C₂²×C₁₃	1	1	yes	characteristic
293	#487	C₂²×C₁₃	1	1	yes	characteristic
294	#487	C₂²×C₁₃	1	1	yes	characteristic
295	#483	—	2	1	no	—
296	#483	—	2	1	no	—
297	#481	—	2	1	no	—
298	#478	—	2	1	no	—
299	#476	—	2	1	no	—
300	#476	C₂²×C₁₃	1	1	yes	characteristic
301	#476	C₂²×C₁₃	1	1	yes	characteristic
302	#475	C₂²×C₁₃	1	1	yes	characteristic
303	#475	C₂²×C₁₃	1	1	yes	characteristic
304	#474	C₂²×C₁₃	1	1	yes	characteristic
305	#467	—	2	1	no	—
306	#465	—	2	1	no	—
307	#465	—	2	1	no	—
308	#461	C₂²×C₁₃	1	1	yes	characteristic
309	#461	C₂²×C₁₃	1	1	yes	characteristic
310	#461	C₂²×C₁₃	1	1	yes	characteristic
311	#452	—	2	1	no	—
312	#452	—	2	1	no	—
313	#448	—	2	1	no	—
314	#446	C₂²×C₁₃	1	1	yes	characteristic
315	#442	—	2	1	no	—
316	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
317	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
318	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
319	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
320	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#106	—	2	1	no	—
322	C₂×#103	—	2	1	no	—
323	#334	C₂²×C₁₃	1	1	yes	characteristic
324	#334	C₂²×C₁₃	1	1	yes	characteristic
325	#333	C₂²×C₁₃	1	1	yes	characteristic
326	#332	C₂²×C₁₃	1	1	yes	characteristic
327	#332	C₂²×C₁₃	1	1	yes	characteristic
328	#332	C₂²×C₁₃	1	1	yes	characteristic
329	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
330	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
331	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
332	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
333	#322	C₂²×C₁₃	1	1	yes	characteristic
334	C₂²×C₁₃	—	2	2	no	—
335	C₂²×C₁₃	—	2	2	no	—
336	C₂²×C₁₃	—	4	1	no	—
337	C₂²×C₁₃	—	4	1	no	—
338	C₂²×C₁₃	—	4	1	no	—
339	C₂²×C₁₃	—	4	1	no	—
340	C₂²×C₁₃	—	4	1	no	—
341	C₂²×C₁₃	—	4	1	no	—
342	C₂²×C₁₃	—	4	1	no	—
343	C₂²×C₁₃	D₄²	1	1	yes	characteristic
344	C₄×C₁₃	—	2	1	no	—
345	C₄×C₁₃	—	4	1	no	—
346	C₄×C₁₃	—	4	1	no	—
347	C₄×C₁₃	—	4	1	no	—
348	C₄×C₁₃	—	4	1	no	—
349	C₄×C₁₃	—	4	1	no	—
350	C₄×C₁₃	—	8	1	no	—
351	C₄×C₁₃	—	8	1	no	—
352	C₄×C₁₃	—	8	1	no	—
353	C₄×C₁₃	—	8	1	no	—
354	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
355	C₄×C₁₃	#575	1	1	yes	characteristic
356	C₄×C₁₃	#577	1	1	yes	characteristic
357	C₄×C₁₃	#577	1	1	yes	characteristic
358	C₂×#41	—	2	1	no	—
359	C₂×#41	—	2	1	no	—
360	C₂²×Q₈	—	2	1	no	—
361	#135	—	4	4	no	—
362	C₂×Q₁₆	—	2	1	no	—
363	C₂×Q₁₆	—	2	1	no	—
364	C₂×SD₁₆	—	2	1	no	—
365	C₂×SD₁₆	—	2	1	no	—
366	C₂×SD₁₆	—	2	1	no	—
367	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
368	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
369	C₂²×C₈	—	2	1	no	—
370	C₂²×C₈	—	2	1	no	—
371	C₂²×C₈	—	2	1	no	—
372	C₄⋊Q₈	—	2	1	no	—
373	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
374	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
375	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
376	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
377	#125	—	2	1	no	—
378	#123	—	4	1	no	—
379	#123	—	4	1	no	—
380	C₂²⋊Q₈	—	2	1	no	—
381	C₂²⋊Q₈	—	2	1	no	—
382	C₂²⋊Q₈	—	2	1	no	—
383	C₂²⋊Q₈	—	2	1	no	—
384	C₂²⋊Q₈	—	4	1	no	—
385	C₂²⋊Q₈	—	4	1	no	—
386	#121	—	2	1	no	—
387	#121	—	2	1	no	—
388	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
392	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
393	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	#107	—	2	1	no	—
398	#107	D₄×C₁₃	1	1	yes	characteristic
399	#106	—	2	1	no	—
400	#106	—	2	1	no	—
401	#106	—	2	1	no	—
402	#106	—	2	1	no	—
403	#106	—	2	1	no	—
404	#106	—	2	1	no	—
405	#106	—	2	1	no	—
406	#106	—	2	1	no	—
407	#106	—	4	1	no	—
408	#106	D₄×C₁₃	1	1	yes	characteristic
409	C₄⋊C₈	—	2	1	no	—
410	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
411	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
412	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
413	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
414	#103	—	2	1	no	—
415	#103	—	2	1	no	—
416	#103	—	2	1	no	—
417	#103	—	2	1	no	—
418	#103	—	2	1	no	—
419	#103	—	2	1	no	—
420	#103	—	2	1	no	—
421	#103	—	4	1	no	—
422	#103	D₄×C₁₃	1	1	yes	characteristic
423	#102	—	2	1	no	—
424	#102	—	2	1	no	—
425	#102	—	2	1	no	—
426	#102	D₄×C₁₃	1	1	yes	characteristic
427	#102	D₄×C₁₃	1	1	yes	characteristic
428	#102	D₄×C₁₃	1	1	yes	characteristic
429	C₂²⋊C₈	—	2	1	no	—
430	C₂²⋊C₈	—	2	1	no	—
431	C₂²⋊C₈	—	2	1	no	—
432	#97	—	2	1	no	—
433	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
434	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
435	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
436	C₂×C₁₃	—	4	2	no	—
437	C₂×C₁₃	—	4	2	no	—
438	C₂×C₁₃	—	8	1	no	—
439	C₂×C₁₃	#3267	1	1	yes	characteristic
440	C₂×C₁₃	D₄×SD₁₆	1	1	yes	characteristic
441	C₂×C₁₃	#3289	1	1	yes	characteristic
442	#41	—	4	2	no	—
443	#41	—	4	2	no	—
444	#41	—	8	1	no	—
445	#41	—	8	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	4	1	no	—
451	C₂×Q₈	—	4	2	no	—
452	C₂×Q₈	—	8	1	no	—
453	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
454	C₂×D₄	—	4	1	no	—
455	C₂×D₄	—	4	1	no	—
456	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
457	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
458	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	4	1	no	—
463	C₂²×C₄	—	4	1	no	—
464	C₂²×C₄	—	4	1	no	—
465	C₂²×C₄	—	4	1	no	—
466	Q₁₆	—	4	2	no	—
467	Q₁₆	—	8	1	no	—
468	SD₁₆	—	4	1	no	—
469	SD₁₆	—	4	2	no	—
470	SD₁₆	—	4	2	no	—
471	SD₁₆	—	8	1	no	—
472	D₈	C₁₃×SD₁₆	1	4	yes	complemented
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	4	2	no	—
479	C₂×C₈	—	4	2	no	—
480	C₂×C₈	—	8	1	no	—
481	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
482	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
483	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
484	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	4	1	no	—
495	C₄⋊C₄	—	4	1	no	—
496	C₄⋊C₄	—	4	1	no	—
497	C₄⋊C₄	—	4	1	no	—
498	C₄⋊C₄	—	4	1	no	—
499	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
500	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
501	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
502	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	2	1	no	—
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	4	1	no	—
507	C₂²⋊C₄	—	4	1	no	—
508	C₂²⋊C₄	—	4	1	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
512	C₁₃	#19766	1	1	yes	characteristic, direct product factor, Sylow
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	Q₈	—	2	1	no	—
517	Q₈	—	2	1	no	—
518	Q₈	—	4	1	no	—
519	Q₈	—	4	1	no	—
520	Q₈	—	4	1	no	—
521	Q₈	—	4	1	no	—
522	Q₈	—	4	1	no	—
523	Q₈	—	4	1	no	—
524	Q₈	—	8	1	no	—
525	Q₈	—	8	2	no	—
526	D₄	—	2	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	8	2	no	—
531	D₄	—	8	2	no	—
532	D₄	C₂×C₁₃×SD₁₆	1	2	yes	—
533	D₄	C₂×C₁₃×SD₁₆	1	2	yes	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	8	2	no	—
550	C₂×C₄	—	8	2	no	—
551	C₂×C₄	—	8	2	no	—
552	C₂×C₄	—	16	1	no	—
553	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
554	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
555	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
556	C₈	—	2	1	no	—
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	4	1	no	—
562	C₈	—	4	1	no	—
563	C₈	—	4	1	no	—
564	C₈	C₂×C₁₃×SD₁₆	1	2	yes	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	D₄²×C₁₃	1	1	yes	characteristic
575	C₄	—	2	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	8	1	no	—
582	C₄	—	8	1	no	—
583	C₄	—	8	1	no	—
584	C₄	—	8	1	no	—
585	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
586	C₄	C₁₃×#575	1	1	yes	characteristic
587	C₄	C₁₃×#577	1	1	yes	characteristic
588	C₄	C₁₃×#577	1	1	yes	characteristic
589	C₂	—	4	2	no	—
590	C₂	—	4	2	no	—
591	C₂	—	8	1	no	—
592	C₂	C₁₃×#3267	1	1	yes	characteristic
593	C₂	D₄×C₁₃×SD₁₆	1	1	yes	characteristic
594	C₂	C₁₃×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3283	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×#3384	C₂	semidirect
2. C₁₃×#3335	C₂	semidirect
3. C₁₃×#3298	C₂	semidirect
5. C₁₃×#1716	C₂	semidirect
6. C₁₃×#1690	C₂	semidirect
7. C₁₃×#1679	C₂	semidirect
8. C₁₃×#1671	C₂	semidirect
9. C₁₃×#1671	C₂	semidirect
10. C₁₃×#1654	C₂	semidirect
11. C₁₃×#1651	C₂	semidirect
12. C₁₃×#1643	C₂	semidirect
13. C₁₃×#1635	C₂	semidirect
14. C₁₃×#1582	C₂	semidirect
15. C₁₃×#1580	C₂	semidirect
145. #19766	C₁₃	direct (N × H)
176. C₁₃×D₈	SD₁₆	semidirect
216. #3384	C₂×C₁₃	semidirect
217. #3335	C₂×C₁₃	semidirect
218. #3298	C₂×C₁₃	semidirect
220. #1716	C₂×C₁₃	semidirect
221. #1690	C₂×C₁₃	semidirect
222. #1679	C₂×C₁₃	semidirect
223. #1671	C₂×C₁₃	semidirect
224. #1671	C₂×C₁₃	semidirect
225. #1654	C₂×C₁₃	semidirect
226. #1651	C₂×C₁₃	semidirect
227. #1643	C₂×C₁₃	semidirect
228. #1635	C₂×C₁₃	semidirect
229. #1582	C₂×C₁₃	semidirect
230. #1580	C₂×C₁₃	semidirect
472. D₈	C₁₃×SD₁₆	semidirect
512. C₁₃	#19766	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×#3384	2
C₁₃×#3335	2
C₁₃×#3298	2
C₁₃×#3283	2
C₁₃×#1716	2
C₁₃×#1690	2
C₁₃×#1679	2
C₁₃×#1671	2
C₁₃×#1654	2
C₁₃×#1651	2
C₁₃×#1643	2
C₁₃×#1635	2
C₁₃×#1582	2
C₁₃×#1580	2
#19766	13

Subgroups — C13×#19766 #15706105

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19766 #15706105