Subgroups — C₁₃×#19836 #15706175

Order 3328.

670 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3366	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3358	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3299	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3287	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1717	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1702	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1683	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1678	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1667	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1641	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1631	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1627	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1622	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1584	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	C₁₃×#550	C₂²	1	1	yes	characteristic
19	C₁₃×#550	C₂²	1	1	yes	characteristic
20	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#493	C₂²	1	1	yes	characteristic
22	C₁₃×#492	C₂²	1	1	yes	characteristic
23	C₁₃×#490	—	2	1	no	—
24	C₁₃×#487	C₂²	1	1	yes	characteristic
25	C₁₃×#486	—	2	1	no	—
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×#476	C₂²	1	1	yes	characteristic
33	C₁₃×#474	—	2	1	no	—
34	C₁₃×#474	C₂²	1	1	yes	characteristic
35	C₁₃×#467	—	2	1	no	—
36	C₁₃×#466	—	2	1	no	—
37	C₁₃×#462	C₂²	1	1	yes	characteristic
38	C₁₃×#460	C₂²	1	1	yes	characteristic
39	C₁₃×#460	C₂²	1	1	yes	characteristic
40	C₁₃×#459	—	2	1	no	—
41	C₁₃×#459	—	2	1	no	—
42	C₁₃×#459	C₂²	1	1	yes	characteristic
43	C₁₃×#459	C₂²	1	1	yes	characteristic
44	C₁₃×#451	—	2	1	no	—
45	C₁₃×#449	—	2	1	no	—
46	C₁₃×#449	—	2	1	no	—
47	C₁₃×#446	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
49	C₁₃×#442	—	2	1	no	—
50	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×D₈	—	2	1	no	—
52	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#103	—	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×#331	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×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	D₄	1	1	yes	characteristic
73	C₂×C₁₃×SD₁₆	—	2	1	no	—
74	C₂×C₁₃×SD₁₆	—	2	1	no	—
75	C₂×C₁₃×SD₁₆	—	4	1	no	—
76	C₂×C₁₃×D₈	—	2	1	no	—
77	C₂×C₁₃×D₈	—	2	1	no	—
78	C₂×C₁₃×D₈	—	2	1	no	—
79	C₂×C₁₃×D₈	—	2	1	no	—
80	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
81	C₂²×C₈×C₁₃	—	2	1	no	—
82	C₂²×C₈×C₁₃	—	2	1	no	—
83	C₁₃×C₄⋊Q₈	—	2	1	no	—
84	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₃×#127	—	2	1	no	—
87	C₁₃×#127	—	2	1	no	—
88	C₁₃×#127	C₂³	1	1	yes	characteristic
89	C₁₃×#127	C₂³	1	1	yes	characteristic
90	C₁₃×#125	—	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	C₁₃×#121	—	4	1	no	—
98	C₁₃×#121	—	4	1	no	—
99	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₁₃	—	2	1	no	—
102	C₄×D₄×C₁₃	—	2	1	no	—
103	C₄×D₄×C₁₃	—	2	1	no	—
104	C₄×D₄×C₁₃	—	2	1	no	—
105	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₁₃×#107	—	2	1	no	—
109	C₁₃×#107	—	2	1	no	—
110	C₁₃×#107	D₄	1	1	yes	characteristic
111	C₁₃×#107	D₄	1	1	yes	characteristic
112	C₁₃×#106	—	2	1	no	—
113	C₁₃×C₄⋊C₈	—	2	1	no	—
114	C₁₃×C₄⋊C₈	—	2	1	no	—
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
124	C₁₃×#103	D₄	1	1	yes	characteristic
125	C₁₃×#102	—	2	1	no	—
126	C₁₃×#102	—	2	1	no	—
127	C₁₃×#102	—	2	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	—	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×#102	D₄	1	1	yes	characteristic
138	C₁₃×C₂²⋊C₈	—	2	1	no	—
139	C₁₃×C₂²⋊C₈	—	2	1	no	—
140	C₁₃×#97	—	2	1	no	—
141	C₄×C₈×C₁₃	—	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	#19836	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	—	4	1	no	—
153	C₂×Q₈×C₁₃	—	4	2	no	—
154	C₂×Q₈×C₁₃	—	8	1	no	—
155	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	2	1	no	—
159	C₂×D₄×C₁₃	—	2	1	no	—
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	—	2	1	no	—
162	C₂×D₄×C₁₃	—	2	1	no	—
163	C₂×D₄×C₁₃	—	4	1	no	—
164	C₂×D₄×C₁₃	—	4	1	no	—
165	C₂×D₄×C₁₃	—	4	1	no	—
166	C₂×D₄×C₁₃	—	4	1	no	—
167	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	4	1	no	—
172	C₂²×C₄×C₁₃	—	4	1	no	—
173	C₂²×C₄×C₁₃	—	4	1	no	—
174	C₂²×C₄×C₁₃	—	4	1	no	—
175	C₁₃×Q₁₆	—	2	2	no	—
176	C₁₃×Q₁₆	—	8	1	no	—
177	C₁₃×SD₁₆	—	4	2	no	—
178	C₁₃×SD₁₆	—	4	2	no	—
179	C₁₃×SD₁₆	—	8	2	no	—
180	C₁₃×D₈	—	2	2	no	—
181	C₁₃×D₈	—	4	2	no	—
182	C₁₃×D₈	—	4	2	no	—
183	C₁₃×D₈	—	4	2	no	—
184	C₁₃×D₈	—	8	1	no	—
185	C₂×C₈×C₁₃	—	2	1	no	—
186	C₂×C₈×C₁₃	—	2	1	no	—
187	C₂×C₈×C₁₃	—	2	1	no	—
188	C₂×C₈×C₁₃	—	2	1	no	—
189	C₂×C₈×C₁₃	—	2	1	no	—
190	C₂×C₈×C₁₃	—	4	2	no	—
191	C₂×C₈×C₁₃	—	8	1	no	—
192	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
193	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
194	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₁₃×C₄⋊C₄	—	2	1	no	—
202	C₁₃×C₄⋊C₄	—	4	1	no	—
203	C₁₃×C₄⋊C₄	—	4	1	no	—
204	C₁₃×C₄⋊C₄	—	4	1	no	—
205	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
206	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
207	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
208	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
209	C₁₃×C₂²⋊C₄	—	2	1	no	—
210	C₁₃×C₂²⋊C₄	—	2	1	no	—
211	C₁₃×C₂²⋊C₄	—	4	1	no	—
212	C₁₃×C₂²⋊C₄	—	4	1	no	—
213	C₁₃×C₂²⋊C₄	—	4	1	no	—
214	C₁₃×C₂²⋊C₄	—	4	1	no	—
215	C₄²×C₁₃	—	2	1	no	—
216	C₄²×C₁₃	—	2	1	no	—
217	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
218	#3366	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#3358	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#3299	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#3287	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1717	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1702	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1683	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1678	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1667	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1641	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1631	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1627	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#1622	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#1584	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#1580	C₂×C₁₃	1	1	yes	characteristic, complemented
233	C₂³×C₁₃	—	2	1	no	—
234	C₂³×C₁₃	—	2	1	no	—
235	C₂³×C₁₃	—	4	1	no	—
236	C₂³×C₁₃	—	4	1	no	—
237	Q₈×C₁₃	—	2	1	no	—
238	Q₈×C₁₃	—	2	1	no	—
239	Q₈×C₁₃	—	2	1	no	—
240	Q₈×C₁₃	—	4	1	no	—
241	Q₈×C₁₃	—	4	1	no	—
242	Q₈×C₁₃	—	8	2	no	—
243	Q₈×C₁₃	—	8	1	no	—
244	Q₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
245	D₄×C₁₃	—	2	1	no	—
246	D₄×C₁₃	—	2	1	no	—
247	D₄×C₁₃	—	2	1	no	—
248	D₄×C₁₃	—	4	1	no	—
249	D₄×C₁₃	—	4	1	no	—
250	D₄×C₁₃	—	4	1	no	—
251	D₄×C₁₃	—	4	1	no	—
252	D₄×C₁₃	—	4	1	no	—
253	D₄×C₁₃	—	4	1	no	—
254	D₄×C₁₃	—	4	1	no	—
255	D₄×C₁₃	—	4	1	no	—
256	D₄×C₁₃	—	8	2	no	—
257	D₄×C₁₃	—	8	1	no	—
258	D₄×C₁₃	—	8	1	no	—
259	D₄×C₁₃	—	8	2	no	—
260	D₄×C₁₃	—	16	1	no	—
261	D₄×C₁₃	—	16	1	no	—
262	D₄×C₁₃	#135	1	2	yes	complemented
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	2	1	no	—
268	C₂×C₄×C₁₃	—	2	1	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	4	1	no	—
271	C₂×C₄×C₁₃	—	4	1	no	—
272	C₂×C₄×C₁₃	—	4	1	no	—
273	C₂×C₄×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	8	2	no	—
276	C₂×C₄×C₁₃	—	8	2	no	—
277	C₂×C₄×C₁₃	—	8	2	no	—
278	C₂×C₄×C₁₃	—	16	1	no	—
279	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
282	C₈×C₁₃	—	2	1	no	—
283	C₈×C₁₃	—	2	1	no	—
284	C₈×C₁₃	—	2	1	no	—
285	C₈×C₁₃	—	2	1	no	—
286	C₈×C₁₃	—	4	1	no	—
287	C₈×C₁₃	—	4	1	no	—
288	C₈×C₁₃	—	4	1	no	—
289	C₈×C₁₃	—	4	1	no	—
290	C₈×C₁₃	—	4	1	no	—
291	C₂×#135	—	2	1	no	—
292	#554	C₂²×C₁₃	1	1	yes	characteristic
293	#550	C₂²×C₁₃	1	1	yes	characteristic
294	#550	C₂²×C₁₃	1	1	yes	characteristic
295	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
296	#493	C₂²×C₁₃	1	1	yes	characteristic
297	#492	C₂²×C₁₃	1	1	yes	characteristic
298	#490	—	2	1	no	—
299	#487	C₂²×C₁₃	1	1	yes	characteristic
300	#486	—	2	1	no	—
301	#486	C₂²×C₁₃	1	1	yes	characteristic
302	#486	C₂²×C₁₃	1	1	yes	characteristic
303	#486	C₂²×C₁₃	1	1	yes	characteristic
304	#484	—	2	1	no	—
305	#478	—	2	1	no	—
306	#477	C₂²×C₁₃	1	1	yes	characteristic
307	#476	C₂²×C₁₃	1	1	yes	characteristic
308	#474	—	2	1	no	—
309	#474	C₂²×C₁₃	1	1	yes	characteristic
310	#467	—	2	1	no	—
311	#466	—	2	1	no	—
312	#462	C₂²×C₁₃	1	1	yes	characteristic
313	#460	C₂²×C₁₃	1	1	yes	characteristic
314	#460	C₂²×C₁₃	1	1	yes	characteristic
315	#459	—	2	1	no	—
316	#459	—	2	1	no	—
317	#459	C₂²×C₁₃	1	1	yes	characteristic
318	#459	C₂²×C₁₃	1	1	yes	characteristic
319	#451	—	2	1	no	—
320	#449	—	2	1	no	—
321	#449	—	2	1	no	—
322	#446	C₂²×C₁₃	1	1	yes	characteristic
323	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
324	#442	—	2	1	no	—
325	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
326	C₄×D₈	—	2	1	no	—
327	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
328	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
329	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×#103	—	2	1	no	—
331	#335	C₂²×C₁₃	1	1	yes	characteristic
332	#334	C₂²×C₁₃	1	1	yes	characteristic
333	#333	C₂²×C₁₃	1	1	yes	characteristic
334	#332	C₂²×C₁₃	1	1	yes	characteristic
335	#331	C₂²×C₁₃	1	1	yes	characteristic
336	#331	C₂²×C₁₃	1	1	yes	characteristic
337	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
338	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
339	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
340	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
341	#322	C₂²×C₁₃	1	1	yes	characteristic
342	C₂²×C₁₃	—	2	2	no	—
343	C₂²×C₁₃	—	4	1	no	—
344	C₂²×C₁₃	—	4	1	no	—
345	C₂²×C₁₃	—	4	1	no	—
346	C₂²×C₁₃	—	4	1	no	—
347	C₂²×C₁₃	—	4	1	no	—
348	C₂²×C₁₃	—	8	1	no	—
349	C₂²×C₁₃	—	8	1	no	—
350	C₂²×C₁₃	—	8	1	no	—
351	C₂²×C₁₃	—	8	1	no	—
352	C₂²×C₁₃	—	8	1	no	—
353	C₂²×C₁₃	—	8	1	no	—
354	C₂²×C₁₃	D₄²	1	1	yes	characteristic
355	C₄×C₁₃	—	2	2	no	—
356	C₄×C₁₃	—	2	1	no	—
357	C₄×C₁₃	—	4	1	no	—
358	C₄×C₁₃	—	4	1	no	—
359	C₄×C₁₃	—	4	1	no	—
360	C₄×C₁₃	—	4	1	no	—
361	C₄×C₁₃	—	4	1	no	—
362	C₄×C₁₃	—	8	1	no	—
363	C₄×C₁₃	—	8	1	no	—
364	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
365	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
366	C₄×C₁₃	#576	1	1	yes	characteristic
367	C₄×C₁₃	#578	1	1	yes	characteristic
368	C₂×#41	—	2	1	no	—
369	C₂×#41	—	2	1	no	—
370	C₂²×Q₈	—	2	1	no	—
371	#135	—	4	4	no	—
372	C₂×Q₁₆	—	2	1	no	—
373	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
374	C₂×SD₁₆	—	2	1	no	—
375	C₂×SD₁₆	—	2	1	no	—
376	C₂×SD₁₆	—	4	1	no	—
377	C₂×D₈	—	2	1	no	—
378	C₂×D₈	—	2	1	no	—
379	C₂×D₈	—	2	1	no	—
380	C₂×D₈	—	2	1	no	—
381	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
382	C₂²×C₈	—	2	1	no	—
383	C₂²×C₈	—	2	1	no	—
384	C₄⋊Q₈	—	2	1	no	—
385	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
386	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
387	#127	—	2	1	no	—
388	#127	—	2	1	no	—
389	#127	C₂³×C₁₃	1	1	yes	characteristic
390	#127	C₂³×C₁₃	1	1	yes	characteristic
391	#125	—	2	1	no	—
392	C₂²⋊Q₈	—	2	1	no	—
393	C₂²⋊Q₈	—	2	1	no	—
394	C₂²⋊Q₈	—	4	1	no	—
395	C₂²⋊Q₈	—	4	1	no	—
396	#121	—	2	1	no	—
397	#121	—	2	1	no	—
398	#121	—	4	1	no	—
399	#121	—	4	1	no	—
400	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
401	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	—	2	1	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
407	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
408	C₂×C₄⋊C₄	—	2	1	no	—
409	#107	—	2	1	no	—
410	#107	—	2	1	no	—
411	#107	D₄×C₁₃	1	1	yes	characteristic
412	#107	D₄×C₁₃	1	1	yes	characteristic
413	#106	—	2	1	no	—
414	C₄⋊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	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
420	#103	—	2	1	no	—
421	#103	—	2	1	no	—
422	#103	—	2	1	no	—
423	#103	—	2	1	no	—
424	#103	D₄×C₁₃	1	1	yes	characteristic
425	#103	D₄×C₁₃	1	1	yes	characteristic
426	#102	—	2	1	no	—
427	#102	—	2	1	no	—
428	#102	—	2	1	no	—
429	#102	—	2	1	no	—
430	#102	—	2	1	no	—
431	#102	—	2	1	no	—
432	#102	—	2	1	no	—
433	#102	—	2	1	no	—
434	#102	—	2	1	no	—
435	#102	—	2	1	no	—
436	#102	—	4	1	no	—
437	#102	D₄×C₁₃	1	1	yes	characteristic
438	#102	D₄×C₁₃	1	1	yes	characteristic
439	C₂²⋊C₈	—	2	1	no	—
440	C₂²⋊C₈	—	2	1	no	—
441	#97	—	2	1	no	—
442	C₄×C₈	—	2	1	no	—
443	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
444	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
445	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
446	C₂×C₁₃	—	4	2	no	—
447	C₂×C₁₃	—	8	1	no	—
448	C₂×C₁₃	—	16	1	no	—
449	C₂×C₁₃	—	16	1	no	—
450	C₂×C₁₃	#3264	1	1	yes	characteristic
451	C₂×C₁₃	#3285	1	1	yes	characteristic
452	C₂×C₁₃	#3288	1	1	yes	characteristic
453	#41	—	4	2	no	—
454	#41	—	4	2	no	—
455	#41	—	8	1	no	—
456	#41	—	8	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	4	1	no	—
460	C₂×Q₈	—	4	2	no	—
461	C₂×Q₈	—	8	1	no	—
462	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
463	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	4	1	no	—
471	C₂×D₄	—	4	1	no	—
472	C₂×D₄	—	4	1	no	—
473	C₂×D₄	—	4	1	no	—
474	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
475	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	4	1	no	—
479	C₂²×C₄	—	4	1	no	—
480	C₂²×C₄	—	4	1	no	—
481	C₂²×C₄	—	4	1	no	—
482	Q₁₆	—	2	2	no	—
483	Q₁₆	—	8	1	no	—
484	SD₁₆	—	4	2	no	—
485	SD₁₆	—	4	2	no	—
486	SD₁₆	—	8	2	no	—
487	D₈	—	2	2	no	—
488	D₈	—	4	2	no	—
489	D₈	—	4	2	no	—
490	D₈	—	4	2	no	—
491	D₈	—	8	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	4	2	no	—
498	C₂×C₈	—	8	1	no	—
499	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
500	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
501	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
502	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	4	1	no	—
510	C₄⋊C₄	—	4	1	no	—
511	C₄⋊C₄	—	4	1	no	—
512	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
513	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
514	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
515	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	2	1	no	—
518	C₂²⋊C₄	—	4	1	no	—
519	C₂²⋊C₄	—	4	1	no	—
520	C₂²⋊C₄	—	4	1	no	—
521	C₂²⋊C₄	—	4	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	1	no	—
524	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
525	C₁₃	#19836	1	1	yes	characteristic, direct product factor, Sylow
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	4	1	no	—
530	Q₈	—	2	1	no	—
531	Q₈	—	2	1	no	—
532	Q₈	—	2	1	no	—
533	Q₈	—	4	1	no	—
534	Q₈	—	4	1	no	—
535	Q₈	—	8	2	no	—
536	Q₈	—	8	1	no	—
537	Q₈	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
538	D₄	—	2	1	no	—
539	D₄	—	2	1	no	—
540	D₄	—	2	1	no	—
541	D₄	—	4	1	no	—
542	D₄	—	4	1	no	—
543	D₄	—	4	1	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	1	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	1	no	—
549	D₄	—	8	2	no	—
550	D₄	—	8	1	no	—
551	D₄	—	8	1	no	—
552	D₄	—	8	2	no	—
553	D₄	—	16	1	no	—
554	D₄	—	16	1	no	—
555	D₄	C₁₃×#135	1	2	yes	complemented
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	8	2	no	—
569	C₂×C₄	—	8	2	no	—
570	C₂×C₄	—	8	2	no	—
571	C₂×C₄	—	16	1	no	—
572	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
573	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
574	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
575	C₈	—	2	1	no	—
576	C₈	—	2	1	no	—
577	C₈	—	2	1	no	—
578	C₈	—	2	1	no	—
579	C₈	—	4	1	no	—
580	C₈	—	4	1	no	—
581	C₈	—	4	1	no	—
582	C₈	—	4	1	no	—
583	C₈	—	4	1	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	8	1	no	—
591	C₂²	—	8	1	no	—
592	C₂²	—	8	1	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	—	8	1	no	—
596	C₂²	D₄²×C₁₃	1	1	yes	characteristic
597	C₄	—	2	2	no	—
598	C₄	—	2	1	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	8	1	no	—
605	C₄	—	8	1	no	—
606	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
607	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
608	C₄	C₁₃×#576	1	1	yes	characteristic
609	C₄	C₁₃×#578	1	1	yes	characteristic
610	C₂	—	4	2	no	—
611	C₂	—	8	1	no	—
612	C₂	—	16	1	no	—
613	C₂	—	16	1	no	—
614	C₂	C₁₃×#3264	1	1	yes	characteristic
615	C₂	C₁₃×#3285	1	1	yes	characteristic
616	C₂	C₁₃×#3288	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×#3366	C₂	semidirect
2. C₁₃×#3358	C₂	semidirect
3. C₁₃×#3299	C₂	semidirect
4. C₁₃×#3287	C₂	semidirect
5. C₁₃×#1717	C₂	semidirect
6. C₁₃×#1702	C₂	semidirect
7. C₁₃×#1683	C₂	semidirect
8. C₁₃×#1678	C₂	semidirect
9. C₁₃×#1667	C₂	semidirect
10. C₁₃×#1641	C₂	semidirect
11. C₁₃×#1631	C₂	semidirect
12. C₁₃×#1627	C₂	semidirect
13. C₁₃×#1622	C₂	semidirect
14. C₁₃×#1584	C₂	semidirect
15. C₁₃×#1580	C₂	semidirect
145. #19836	C₁₃	direct (N × H)
218. #3366	C₂×C₁₃	semidirect
219. #3358	C₂×C₁₃	semidirect
220. #3299	C₂×C₁₃	semidirect
221. #3287	C₂×C₁₃	semidirect
222. #1717	C₂×C₁₃	semidirect
223. #1702	C₂×C₁₃	semidirect
224. #1683	C₂×C₁₃	semidirect
225. #1678	C₂×C₁₃	semidirect
226. #1667	C₂×C₁₃	semidirect
227. #1641	C₂×C₁₃	semidirect
228. #1631	C₂×C₁₃	semidirect
229. #1627	C₂×C₁₃	semidirect
230. #1622	C₂×C₁₃	semidirect
231. #1584	C₂×C₁₃	semidirect
232. #1580	C₂×C₁₃	semidirect
262. D₄×C₁₃	#135	semidirect
525. C₁₃	#19836	direct (N × H)
555. D₄	C₁₃×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3366	2
C₁₃×#3358	2
C₁₃×#3299	2
C₁₃×#3287	2
C₁₃×#1717	2
C₁₃×#1702	2
C₁₃×#1683	2
C₁₃×#1678	2
C₁₃×#1667	2
C₁₃×#1641	2
C₁₃×#1631	2
C₁₃×#1627	2
C₁₃×#1622	2
C₁₃×#1584	2
C₁₃×#1580	2
#19836	13

Subgroups — C13×#19836 #15706175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19836 #15706175