Subgroups — C₁₃×#19776 #15706115

Order 3328.

630 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3334	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3330	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1718	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1703	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1683	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1679	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1673	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1654	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1654	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1646	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1635	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1581	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1580	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#555	C₂²	1	1	yes	characteristic
17	C₁₃×#547	C₂²	1	1	yes	characteristic
18	C₁₃×#547	C₂²	1	1	yes	characteristic
19	C₁₃×#547	C₂²	1	1	yes	characteristic
20	C₁₃×#500	C₂²	1	1	yes	characteristic
21	C₁₃×#498	C₂²	1	1	yes	characteristic
22	C₁₃×#487	C₂²	1	1	yes	characteristic
23	C₁₃×#487	C₂²	1	1	yes	characteristic
24	C₁₃×#487	C₂²	1	1	yes	characteristic
25	C₁₃×#487	C₂²	1	1	yes	characteristic
26	C₁₃×#485	—	2	1	no	—
27	C₁₃×#485	—	2	1	no	—
28	C₁₃×#484	—	2	1	no	—
29	C₁₃×#480	—	2	1	no	—
30	C₁₃×#480	—	2	1	no	—
31	C₁₃×#476	C₂²	1	1	yes	characteristic
32	C₁₃×#476	C₂²	1	1	yes	characteristic
33	C₁₃×#474	C₂²	1	1	yes	characteristic
34	C₁₃×#474	C₂²	1	1	yes	characteristic
35	C₁₃×#474	C₂²	1	1	yes	characteristic
36	C₁₃×#468	—	2	1	no	—
37	C₁₃×#466	—	2	1	no	—
38	C₁₃×#465	—	2	1	no	—
39	C₁₃×#465	—	2	1	no	—
40	C₁₃×#461	C₂²	1	1	yes	characteristic
41	C₁₃×#461	C₂²	1	1	yes	characteristic
42	C₁₃×#461	C₂²	1	1	yes	characteristic
43	C₁₃×#449	—	2	1	no	—
44	C₁₃×#449	—	2	1	no	—
45	C₁₃×#449	—	2	1	no	—
46	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
48	C₁₃×#436	C₂²	1	1	yes	characteristic
49	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
50	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
51	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#107	—	2	1	no	—
53	C₁₃×#417	—	2	1	no	—
54	C₁₃×#416	—	2	1	no	—
55	C₁₃×#416	—	2	1	no	—
56	C₁₃×#335	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×D₄⋊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	C₂×C₁₃×#41	—	2	1	no	—
70	C₂×C₁₃×SD₁₆	—	2	1	no	—
71	C₂×C₁₃×SD₁₆	—	2	1	no	—
72	C₂×C₁₃×SD₁₆	—	2	1	no	—
73	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
74	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
75	C₂×C₁₃×M₁₆	—	2	1	no	—
76	C₂²×C₈×C₁₃	—	2	1	no	—
77	C₂²×C₈×C₁₃	—	2	1	no	—
78	C₂²×C₈×C₁₃	—	2	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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₃×#124	—	4	1	no	—
84	C₁₃×#123	—	4	1	no	—
85	C₁₃×#123	—	4	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	—	2	1	no	—
90	C₁₃×#121	—	2	1	no	—
91	C₁₃×#121	—	2	1	no	—
92	C₁₃×#121	—	2	1	no	—
93	C₁₃×#121	—	2	1	no	—
94	C₁₃×#121	—	2	1	no	—
95	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₁₃×#117	—	2	1	no	—
100	C₁₃×#117	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₄⋊C₄	—	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×#107	D₄	1	1	yes	characteristic
111	C₁₃×#106	—	2	1	no	—
112	C₁₃×#106	—	2	1	no	—
113	C₁₃×#106	—	4	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	—	2	1	no	—
126	C₁₃×#103	—	2	1	no	—
127	C₁₃×#103	—	4	1	no	—
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	D₄	1	1	yes	characteristic
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	C₁₃×C₂²⋊C₈	—	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	#19776	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₁₃×#41	—	4	2	no	—
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	C₁₃×#41	—	8	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	—	2	1	no	—
155	C₂×D₄×C₁₃	—	4	1	no	—
156	C₂×D₄×C₁₃	—	4	1	no	—
157	C₂×D₄×C₁₃	—	4	1	no	—
158	C₂×D₄×C₁₃	—	4	1	no	—
159	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	—	2	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×SD₁₆	—	8	1	no	—
171	C₁₃×SD₁₆	—	8	1	no	—
172	C₁₃×SD₁₆	—	8	1	no	—
173	C₁₃×D₈	—	2	2	no	—
174	C₁₃×D₈	—	4	1	no	—
175	C₁₃×M₁₆	—	8	1	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
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	—	4	2	no	—
182	C₂×C₈×C₁₃	—	8	1	no	—
183	C₂×C₈×C₁₃	—	8	1	no	—
184	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₁₃×C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
197	C₁₃×C₄⋊C₄	—	4	1	no	—
198	C₁₃×C₄⋊C₄	—	4	1	no	—
199	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
200	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
201	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
202	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
203	C₁₃×C₂²⋊C₄	—	2	1	no	—
204	C₁₃×C₂²⋊C₄	—	2	1	no	—
205	C₁₃×C₂²⋊C₄	—	2	1	no	—
206	C₁₃×C₂²⋊C₄	—	2	1	no	—
207	C₁₃×C₂²⋊C₄	—	4	1	no	—
208	C₁₃×C₂²⋊C₄	—	4	1	no	—
209	C₁₃×C₂²⋊C₄	—	4	1	no	—
210	C₁₃×C₂²⋊C₄	—	4	1	no	—
211	C₁₃×C₂²⋊C₄	—	4	1	no	—
212	C₄²×C₁₃	—	4	1	no	—
213	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
214	#3334	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#3330	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#3303	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#3303	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1718	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1703	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1683	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1679	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1673	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1654	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1654	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1646	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1635	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1581	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1580	C₂×C₁₃	1	1	yes	characteristic, complemented
229	C₂³×C₁₃	—	2	1	no	—
230	C₂³×C₁₃	—	2	1	no	—
231	C₂³×C₁₃	—	2	1	no	—
232	C₂³×C₁₃	—	2	1	no	—
233	Q₈×C₁₃	—	4	1	no	—
234	Q₈×C₁₃	—	4	1	no	—
235	Q₈×C₁₃	—	4	1	no	—
236	Q₈×C₁₃	—	4	1	no	—
237	Q₈×C₁₃	—	4	1	no	—
238	Q₈×C₁₃	—	4	1	no	—
239	Q₈×C₁₃	—	8	1	no	—
240	D₄×C₁₃	—	2	1	no	—
241	D₄×C₁₃	—	2	1	no	—
242	D₄×C₁₃	—	2	1	no	—
243	D₄×C₁₃	—	2	1	no	—
244	D₄×C₁₃	—	2	1	no	—
245	D₄×C₁₃	—	2	1	no	—
246	D₄×C₁₃	—	2	1	no	—
247	D₄×C₁₃	—	8	2	no	—
248	D₄×C₁₃	—	8	2	no	—
249	D₄×C₁₃	—	8	2	no	—
250	D₄×C₁₃	—	16	1	no	—
251	D₄×C₁₃	#135	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	—	4	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	—	4	1	no	—
268	C₂×C₄×C₁₃	—	8	2	no	—
269	C₂×C₄×C₁₃	—	8	2	no	—
270	C₂×C₄×C₁₃	—	8	2	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	—	2	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	—	4	1	no	—
283	#555	C₂²×C₁₃	1	1	yes	characteristic
284	#547	C₂²×C₁₃	1	1	yes	characteristic
285	#547	C₂²×C₁₃	1	1	yes	characteristic
286	#547	C₂²×C₁₃	1	1	yes	characteristic
287	#500	C₂²×C₁₃	1	1	yes	characteristic
288	#498	C₂²×C₁₃	1	1	yes	characteristic
289	#487	C₂²×C₁₃	1	1	yes	characteristic
290	#487	C₂²×C₁₃	1	1	yes	characteristic
291	#487	C₂²×C₁₃	1	1	yes	characteristic
292	#487	C₂²×C₁₃	1	1	yes	characteristic
293	#485	—	2	1	no	—
294	#485	—	2	1	no	—
295	#484	—	2	1	no	—
296	#480	—	2	1	no	—
297	#480	—	2	1	no	—
298	#476	C₂²×C₁₃	1	1	yes	characteristic
299	#476	C₂²×C₁₃	1	1	yes	characteristic
300	#474	C₂²×C₁₃	1	1	yes	characteristic
301	#474	C₂²×C₁₃	1	1	yes	characteristic
302	#474	C₂²×C₁₃	1	1	yes	characteristic
303	#468	—	2	1	no	—
304	#466	—	2	1	no	—
305	#465	—	2	1	no	—
306	#465	—	2	1	no	—
307	#461	C₂²×C₁₃	1	1	yes	characteristic
308	#461	C₂²×C₁₃	1	1	yes	characteristic
309	#461	C₂²×C₁₃	1	1	yes	characteristic
310	#449	—	2	1	no	—
311	#449	—	2	1	no	—
312	#449	—	2	1	no	—
313	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
314	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
315	#436	C₂²×C₁₃	1	1	yes	characteristic
316	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
317	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
318	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×#107	—	2	1	no	—
320	#417	—	2	1	no	—
321	#416	—	2	1	no	—
322	#416	—	2	1	no	—
323	#335	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	D₄⋊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	—	4	1	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	—	4	1	no	—
344	C₂²×C₁₃	—	4	1	no	—
345	C₂²×C₁₃	—	4	1	no	—
346	C₂²×C₁₃	D₄²	1	1	yes	characteristic
347	C₄×C₁₃	—	2	1	no	—
348	C₄×C₁₃	—	4	1	no	—
349	C₄×C₁₃	—	4	1	no	—
350	C₄×C₁₃	—	4	1	no	—
351	C₄×C₁₃	—	4	1	no	—
352	C₄×C₁₃	—	8	1	no	—
353	C₄×C₁₃	—	8	1	no	—
354	C₄×C₁₃	—	8	1	no	—
355	C₄×C₁₃	—	8	1	no	—
356	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
357	C₄×C₁₃	#575	1	1	yes	characteristic
358	C₄×C₁₃	#576	1	1	yes	characteristic
359	C₄×C₁₃	#577	1	1	yes	characteristic
360	C₂×#41	—	2	1	no	—
361	C₂×#41	—	2	1	no	—
362	C₂×#41	—	2	1	no	—
363	C₂×SD₁₆	—	2	1	no	—
364	C₂×SD₁₆	—	2	1	no	—
365	C₂×SD₁₆	—	2	1	no	—
366	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
367	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
368	C₂×M₁₆	—	2	1	no	—
369	C₂²×C₈	—	2	1	no	—
370	C₂²×C₈	—	2	1	no	—
371	C₂²×C₈	—	2	1	no	—
372	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
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	#124	—	4	1	no	—
377	#123	—	4	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	#121	—	2	1	no	—
384	#121	—	2	1	no	—
385	#121	—	2	1	no	—
386	#121	—	2	1	no	—
387	#121	—	2	1	no	—
388	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
389	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
390	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
391	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
392	#117	—	2	1	no	—
393	#117	—	2	1	no	—
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	—	2	1	no	—
399	#107	—	2	1	no	—
400	#107	—	2	1	no	—
401	#107	—	2	1	no	—
402	#107	D₄×C₁₃	1	1	yes	characteristic
403	#107	D₄×C₁₃	1	1	yes	characteristic
404	#106	—	2	1	no	—
405	#106	—	2	1	no	—
406	#106	—	4	1	no	—
407	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
408	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
409	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
410	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
411	#103	—	2	1	no	—
412	#103	—	2	1	no	—
413	#103	—	2	1	no	—
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	—	4	1	no	—
421	#102	—	2	1	no	—
422	#102	—	2	1	no	—
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	#102	D₄×C₁₃	1	1	yes	characteristic
430	C₂²⋊C₈	—	2	1	no	—
431	C₂²⋊C₈	—	2	1	no	—
432	C₂²⋊C₈	—	2	1	no	—
433	C₂²⋊C₈	—	2	1	no	—
434	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
435	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
436	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
437	C₂×C₁₃	—	4	2	no	—
438	C₂×C₁₃	—	8	1	no	—
439	C₂×C₁₃	—	8	1	no	—
440	C₂×C₁₃	—	8	1	no	—
441	C₂×C₁₃	#3267	1	1	yes	characteristic
442	C₂×C₁₃	#3280	1	1	yes	characteristic
443	C₂×C₁₃	#3289	1	1	yes	characteristic
444	#41	—	4	2	no	—
445	#41	—	4	2	no	—
446	#41	—	4	2	no	—
447	#41	—	8	1	no	—
448	#41	—	8	1	no	—
449	#41	—	8	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×D₄	—	4	1	no	—
455	C₂×D₄	—	4	1	no	—
456	C₂×D₄	—	4	1	no	—
457	C₂×D₄	—	4	1	no	—
458	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
459	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
460	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
461	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	4	1	no	—
467	C₂²×C₄	—	4	1	no	—
468	C₂²×C₄	—	4	1	no	—
469	SD₁₆	—	8	1	no	—
470	SD₁₆	—	8	1	no	—
471	SD₁₆	—	8	1	no	—
472	D₈	—	2	2	no	—
473	D₈	—	4	1	no	—
474	M₁₆	—	8	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	4	2	no	—
481	C₂×C₈	—	8	1	no	—
482	C₂×C₈	—	8	1	no	—
483	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
484	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
485	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
486	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
495	C₄⋊C₄	—	4	1	no	—
496	C₄⋊C₄	—	4	1	no	—
497	C₄⋊C₄	—	4	1	no	—
498	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
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	C₂²⋊C₄	—	2	1	no	—
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	C₂²⋊C₄	—	4	1	no	—
511	C₄²	—	4	1	no	—
512	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
513	C₁₃	#19776	1	1	yes	characteristic, direct product factor, Sylow
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	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	D₄	—	2	1	no	—
526	D₄	—	2	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	2	1	no	—
531	D₄	—	2	1	no	—
532	D₄	—	8	2	no	—
533	D₄	—	8	2	no	—
534	D₄	—	8	2	no	—
535	D₄	—	16	1	no	—
536	D₄	C₁₃×#135	1	2	yes	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	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	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	8	2	no	—
554	C₂×C₄	—	8	2	no	—
555	C₂×C₄	—	8	2	no	—
556	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
557	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
558	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	2	1	no	—
562	C₈	—	2	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	1	no	—
565	C₈	—	4	1	no	—
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₂²	—	2	2	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	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	D₄²×C₁₃	1	1	yes	characteristic
581	C₄	—	2	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	8	1	no	—
587	C₄	—	8	1	no	—
588	C₄	—	8	1	no	—
589	C₄	—	8	1	no	—
590	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
591	C₄	C₁₃×#575	1	1	yes	characteristic
592	C₄	C₁₃×#576	1	1	yes	characteristic
593	C₄	C₁₃×#577	1	1	yes	characteristic
594	C₂	—	4	2	no	—
595	C₂	—	8	1	no	—
596	C₂	—	8	1	no	—
597	C₂	—	8	1	no	—
598	C₂	C₁₃×#3267	1	1	yes	characteristic
599	C₂	C₁₃×#3280	1	1	yes	characteristic
600	C₂	C₁₃×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
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×#3334	C₂	semidirect
2. C₁₃×#3330	C₂	semidirect
3. C₁₃×#3303	C₂	semidirect
4. C₁₃×#3303	C₂	semidirect
5. C₁₃×#1718	C₂	semidirect
6. C₁₃×#1703	C₂	semidirect
7. C₁₃×#1683	C₂	semidirect
8. C₁₃×#1679	C₂	semidirect
9. C₁₃×#1673	C₂	semidirect
10. C₁₃×#1654	C₂	semidirect
11. C₁₃×#1654	C₂	semidirect
12. C₁₃×#1646	C₂	semidirect
13. C₁₃×#1635	C₂	semidirect
14. C₁₃×#1581	C₂	semidirect
15. C₁₃×#1580	C₂	semidirect
144. #19776	C₁₃	direct (N × H)
214. #3334	C₂×C₁₃	semidirect
215. #3330	C₂×C₁₃	semidirect
216. #3303	C₂×C₁₃	semidirect
217. #3303	C₂×C₁₃	semidirect
218. #1718	C₂×C₁₃	semidirect
219. #1703	C₂×C₁₃	semidirect
220. #1683	C₂×C₁₃	semidirect
221. #1679	C₂×C₁₃	semidirect
222. #1673	C₂×C₁₃	semidirect
223. #1654	C₂×C₁₃	semidirect
224. #1654	C₂×C₁₃	semidirect
225. #1646	C₂×C₁₃	semidirect
226. #1635	C₂×C₁₃	semidirect
227. #1581	C₂×C₁₃	semidirect
228. #1580	C₂×C₁₃	semidirect
513. C₁₃	#19776	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×#3334	2
C₁₃×#3330	2
C₁₃×#3303	2
C₁₃×#1718	2
C₁₃×#1703	2
C₁₃×#1683	2
C₁₃×#1679	2
C₁₃×#1673	2
C₁₃×#1654	2
C₁₃×#1646	2
C₁₃×#1635	2
C₁₃×#1581	2
C₁₃×#1580	2
#19776	13

Subgroups — C13×#19776 #15706115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19776 #15706115