Subgroups — C₁₃×#19761 #15706100

Order 3328.

694 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3358	C₂	1	1	yes	maximal, characteristic
3	D₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3278	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1722	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1689	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1682	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1674	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1665	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1649	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1649	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1641	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1627	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1581	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1579	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	—	2	1	no	—
17	C₂²×C₁₃×Q₁₆	—	2	1	no	—
18	C₁₃×#550	C₂²	1	1	yes	characteristic
19	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#500	—	2	1	no	—
23	C₁₃×#500	C₂²	1	1	yes	characteristic
24	C₁₃×#500	C₂²	1	1	yes	characteristic
25	C₁₃×#494	C₂²	1	1	yes	characteristic
26	C₁₃×#492	C₂²	1	1	yes	characteristic
27	C₁₃×#486	—	2	1	no	—
28	C₁₃×#486	C₂²	1	1	yes	characteristic
29	C₁₃×#486	C₂²	1	1	yes	characteristic
30	C₁₃×#474	—	2	1	no	—
31	C₁₃×#474	—	2	1	no	—
32	C₁₃×#474	—	2	1	no	—
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×#467	—	2	1	no	—
38	C₁₃×#462	C₂²	1	1	yes	characteristic
39	C₁₃×#462	C₂²	1	1	yes	characteristic
40	C₁₃×#462	C₂²	1	1	yes	characteristic
41	C₁₃×#460	C₂²	1	1	yes	characteristic
42	C₁₃×#459	—	2	1	no	—
43	C₁₃×#459	C₂²	1	1	yes	characteristic
44	C₁₃×#452	—	2	1	no	—
45	C₁₃×#451	—	2	1	no	—
46	C₁₃×#451	—	2	1	no	—
47	C₁₃×#448	—	2	1	no	—
48	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
49	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×D₈	—	2	1	no	—
52	C₄×C₁₃×D₈	—	2	1	no	—
53	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
54	C₁₃×#436	C₂²	1	1	yes	characteristic
55	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
56	C₁₃×#335	C₂²	1	1	yes	characteristic
57	C₁₃×#334	C₂²	1	1	yes	characteristic
58	C₁₃×#332	C₂²	1	1	yes	characteristic
59	C₁₃×#332	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×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	C₂²×Q₈×C₁₃	—	2	1	no	—
69	C₂²×Q₈×C₁₃	—	2	1	no	—
70	C₂²×Q₈×C₁₃	—	2	1	no	—
71	C₁₃×#137	—	4	4	no	—
72	C₂×C₁₃×Q₁₆	—	2	1	no	—
73	C₂×C₁₃×Q₁₆	—	2	1	no	—
74	C₂×C₁₃×Q₁₆	—	2	1	no	—
75	C₂×C₁₃×Q₁₆	—	2	1	no	—
76	C₂×C₁₃×Q₁₆	—	2	1	no	—
77	C₂×C₁₃×Q₁₆	—	4	4	no	—
78	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
79	C₂×C₁₃×SD₁₆	—	2	1	no	—
80	C₂×C₁₃×SD₁₆	—	2	1	no	—
81	C₂×C₁₃×SD₁₆	—	2	1	no	—
82	C₂×C₁₃×D₈	—	2	1	no	—
83	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
84	C₂×C₁₃×M₁₆	—	2	1	no	—
85	C₂²×C₈×C₁₃	—	2	1	no	—
86	C₁₃×C₄⋊Q₈	—	2	1	no	—
87	C₁₃×C₄⋊Q₈	—	2	1	no	—
88	C₁₃×C₄⋊Q₈	—	2	1	no	—
89	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
90	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
91	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
92	C₁₃×#127	—	2	1	no	—
93	C₁₃×#127	C₂³	1	1	yes	characteristic
94	C₁₃×C₂²⋊Q₈	—	2	1	no	—
95	C₁₃×C₂²⋊Q₈	—	2	1	no	—
96	C₁₃×C₂²⋊Q₈	—	2	1	no	—
97	C₁₃×C₂²⋊Q₈	—	4	1	no	—
98	C₁₃×C₂²⋊Q₈	—	4	1	no	—
99	C₁₃×C₂²⋊Q₈	—	4	1	no	—
100	C₁₃×#121	—	2	1	no	—
101	C₁₃×#121	—	4	1	no	—
102	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
104	C₄×D₄×C₁₃	—	2	1	no	—
105	C₄×D₄×C₁₃	—	2	1	no	—
106	C₄×D₄×C₁₃	—	2	1	no	—
107	C₄×D₄×C₁₃	—	2	1	no	—
108	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₁₃×#107	—	2	1	no	—
111	C₁₃×#107	—	2	1	no	—
112	C₁₃×#107	—	2	1	no	—
113	C₁₃×#107	—	2	1	no	—
114	C₁₃×#107	—	2	1	no	—
115	C₁₃×#107	—	4	1	no	—
116	C₁₃×#107	D₄	1	1	yes	characteristic
117	C₁₃×#107	D₄	1	1	yes	characteristic
118	C₁₃×C₄⋊C₈	—	2	1	no	—
119	C₁₃×C₄⋊C₈	—	2	1	no	—
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
124	C₁₃×#103	—	2	1	no	—
125	C₁₃×#103	—	2	1	no	—
126	C₁₃×#103	—	2	1	no	—
127	C₁₃×#103	D₄	1	1	yes	characteristic
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	—	2	1	no	—
135	C₁₃×#102	—	2	1	no	—
136	C₁₃×#102	—	4	1	no	—
137	C₁₃×#102	D₄	1	1	yes	characteristic
138	C₁₃×#102	D₄	1	1	yes	characteristic
139	C₁₃×C₂²⋊C₈	—	2	1	no	—
140	C₁₃×C₂²⋊C₈	—	2	1	no	—
141	C₄×C₈×C₁₃	—	2	1	no	—
142	C₄×C₈×C₁₃	—	2	1	no	—
143	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
145	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
146	#19761	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₁₃×#41	—	4	2	no	—
148	C₁₃×#41	—	8	1	no	—
149	C₂×Q₈×C₁₃	—	2	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	1	no	—
154	C₂×Q₈×C₁₃	—	4	1	no	—
155	C₂×Q₈×C₁₃	—	4	2	no	—
156	C₂×Q₈×C₁₃	—	4	2	no	—
157	C₂×Q₈×C₁₃	—	4	2	no	—
158	C₂×Q₈×C₁₃	—	8	1	no	—
159	C₂×Q₈×C₁₃	—	8	1	no	—
160	C₂×Q₈×C₁₃	—	8	1	no	—
161	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂×D₄×C₁₃	—	2	1	no	—
164	C₂×D₄×C₁₃	—	2	1	no	—
165	C₂×D₄×C₁₃	—	2	1	no	—
166	C₂×D₄×C₁₃	—	4	1	no	—
167	C₂×D₄×C₁₃	—	4	1	no	—
168	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
172	C₂²×C₄×C₁₃	—	4	1	no	—
173	C₂²×C₄×C₁₃	—	4	1	no	—
174	C₂²×C₄×C₁₃	—	4	1	no	—
175	C₂²×C₄×C₁₃	—	4	1	no	—
176	C₁₃×Q₁₆	—	4	2	no	—
177	C₁₃×Q₁₆	—	4	2	no	—
178	C₁₃×Q₁₆	—	4	2	no	—
179	C₁₃×Q₁₆	—	4	2	no	—
180	C₁₃×Q₁₆	—	8	1	no	—
181	C₁₃×Q₁₆	D₈	1	4	yes	complemented
182	C₁₃×SD₁₆	—	4	2	no	—
183	C₁₃×SD₁₆	—	4	2	no	—
184	C₁₃×SD₁₆	—	8	1	no	—
185	C₁₃×D₈	—	2	2	no	—
186	C₁₃×D₈	—	4	2	no	—
187	C₁₃×M₁₆	—	4	2	no	—
188	C₂×C₈×C₁₃	—	2	1	no	—
189	C₂×C₈×C₁₃	—	2	1	no	—
190	C₂×C₈×C₁₃	—	2	1	no	—
191	C₂×C₈×C₁₃	—	2	1	no	—
192	C₂×C₈×C₁₃	—	2	1	no	—
193	C₂×C₈×C₁₃	—	4	2	no	—
194	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
203	C₁₃×C₄⋊C₄	—	2	1	no	—
204	C₁₃×C₄⋊C₄	—	2	1	no	—
205	C₁₃×C₄⋊C₄	—	2	1	no	—
206	C₁₃×C₄⋊C₄	—	4	1	no	—
207	C₁₃×C₄⋊C₄	—	4	1	no	—
208	C₁₃×C₄⋊C₄	—	4	1	no	—
209	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
210	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
211	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
212	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
213	C₁₃×C₂²⋊C₄	—	2	1	no	—
214	C₁₃×C₂²⋊C₄	—	2	1	no	—
215	C₁₃×C₂²⋊C₄	—	4	1	no	—
216	C₁₃×C₂²⋊C₄	—	4	1	no	—
217	C₁₃×C₂²⋊C₄	—	4	1	no	—
218	C₁₃×C₂²⋊C₄	—	4	1	no	—
219	C₄²×C₁₃	—	2	1	no	—
220	C₄²×C₁₃	—	2	1	no	—
221	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
222	Q₈×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#3358	C₂×C₁₃	1	1	yes	characteristic
224	D₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#3278	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1722	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1689	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1682	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1674	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#1665	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#1649	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#1649	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#1641	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#1627	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#1581	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#1579	C₂×C₁₃	1	1	yes	characteristic, complemented
237	C₂³×C₁₃	—	2	1	no	—
238	C₂³×C₁₃	—	2	1	no	—
239	C₂³×C₁₃	—	4	1	no	—
240	Q₈×C₁₃	—	2	1	no	—
241	Q₈×C₁₃	—	2	1	no	—
242	Q₈×C₁₃	—	4	1	no	—
243	Q₈×C₁₃	—	4	1	no	—
244	Q₈×C₁₃	—	4	1	no	—
245	Q₈×C₁₃	—	4	1	no	—
246	Q₈×C₁₃	—	4	1	no	—
247	Q₈×C₁₃	—	4	1	no	—
248	Q₈×C₁₃	—	8	2	no	—
249	Q₈×C₁₃	—	8	2	no	—
250	Q₈×C₁₃	—	8	2	no	—
251	Q₈×C₁₃	C₂×D₈	1	2	yes	—
252	Q₈×C₁₃	C₂×D₈	1	2	yes	—
253	D₄×C₁₃	—	2	1	no	—
254	D₄×C₁₃	—	2	1	no	—
255	D₄×C₁₃	—	2	1	no	—
256	D₄×C₁₃	—	4	1	no	—
257	D₄×C₁₃	—	4	1	no	—
258	D₄×C₁₃	—	4	1	no	—
259	D₄×C₁₃	—	4	1	no	—
260	D₄×C₁₃	—	8	2	no	—
261	D₄×C₁₃	—	8	1	no	—
262	D₄×C₁₃	—	16	1	no	—
263	D₄×C₁₃	#137	1	2	yes	complemented
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	—	2	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	—	4	1	no	—
276	C₂×C₄×C₁₃	—	4	1	no	—
277	C₂×C₄×C₁₃	—	8	2	no	—
278	C₂×C₄×C₁₃	—	8	2	no	—
279	C₂×C₄×C₁₃	—	8	2	no	—
280	C₂×C₄×C₁₃	—	8	2	no	—
281	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
284	C₈×C₁₃	—	2	1	no	—
285	C₈×C₁₃	—	2	1	no	—
286	C₈×C₁₃	—	2	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	C₈×C₁₃	—	4	1	no	—
292	C₈×C₁₃	C₂×D₈	1	2	yes	—
293	C₂×#137	—	2	1	no	—
294	C₂²×Q₁₆	—	2	1	no	—
295	#550	C₂²×C₁₃	1	1	yes	characteristic
296	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
297	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
298	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
299	#500	—	2	1	no	—
300	#500	C₂²×C₁₃	1	1	yes	characteristic
301	#500	C₂²×C₁₃	1	1	yes	characteristic
302	#494	C₂²×C₁₃	1	1	yes	characteristic
303	#492	C₂²×C₁₃	1	1	yes	characteristic
304	#486	—	2	1	no	—
305	#486	C₂²×C₁₃	1	1	yes	characteristic
306	#486	C₂²×C₁₃	1	1	yes	characteristic
307	#474	—	2	1	no	—
308	#474	—	2	1	no	—
309	#474	—	2	1	no	—
310	#474	C₂²×C₁₃	1	1	yes	characteristic
311	#474	C₂²×C₁₃	1	1	yes	characteristic
312	#474	C₂²×C₁₃	1	1	yes	characteristic
313	#468	—	2	1	no	—
314	#467	—	2	1	no	—
315	#462	C₂²×C₁₃	1	1	yes	characteristic
316	#462	C₂²×C₁₃	1	1	yes	characteristic
317	#462	C₂²×C₁₃	1	1	yes	characteristic
318	#460	C₂²×C₁₃	1	1	yes	characteristic
319	#459	—	2	1	no	—
320	#459	C₂²×C₁₃	1	1	yes	characteristic
321	#452	—	2	1	no	—
322	#451	—	2	1	no	—
323	#451	—	2	1	no	—
324	#448	—	2	1	no	—
325	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
326	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
327	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
328	C₄×D₈	—	2	1	no	—
329	C₄×D₈	—	2	1	no	—
330	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
331	#436	C₂²×C₁₃	1	1	yes	characteristic
332	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
333	#335	C₂²×C₁₃	1	1	yes	characteristic
334	#334	C₂²×C₁₃	1	1	yes	characteristic
335	#332	C₂²×C₁₃	1	1	yes	characteristic
336	#332	C₂²×C₁₃	1	1	yes	characteristic
337	#332	C₂²×C₁₃	1	1	yes	characteristic
338	#331	C₂²×C₁₃	1	1	yes	characteristic
339	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
340	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
341	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
342	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
343	#322	C₂²×C₁₃	1	1	yes	characteristic
344	C₂²×C₁₃	—	2	2	no	—
345	C₂²×C₁₃	—	4	1	no	—
346	C₂²×C₁₃	—	4	1	no	—
347	C₂²×C₁₃	—	4	1	no	—
348	C₂²×C₁₃	—	4	1	no	—
349	C₂²×C₁₃	—	4	1	no	—
350	C₂²×C₁₃	—	8	1	no	—
351	C₂²×C₁₃	—	8	1	no	—
352	C₂²×C₁₃	—	8	1	no	—
353	C₂²×C₁₃	D₄²	1	1	yes	characteristic
354	C₄×C₁₃	—	2	2	no	—
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	—	8	1	no	—
362	C₄×C₁₃	—	8	1	no	—
363	C₄×C₁₃	—	8	1	no	—
364	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
365	C₄×C₁₃	C₂×#137	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	C₂²×Q₈	—	2	1	no	—
370	C₂²×Q₈	—	2	1	no	—
371	C₂²×Q₈	—	2	1	no	—
372	#137	—	4	4	no	—
373	C₂×Q₁₆	—	2	1	no	—
374	C₂×Q₁₆	—	2	1	no	—
375	C₂×Q₁₆	—	2	1	no	—
376	C₂×Q₁₆	—	2	1	no	—
377	C₂×Q₁₆	—	2	1	no	—
378	C₂×Q₁₆	—	4	4	no	—
379	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
380	C₂×SD₁₆	—	2	1	no	—
381	C₂×SD₁₆	—	2	1	no	—
382	C₂×SD₁₆	—	2	1	no	—
383	C₂×D₈	—	2	1	no	—
384	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
385	C₂×M₁₆	—	2	1	no	—
386	C₂²×C₈	—	2	1	no	—
387	C₄⋊Q₈	—	2	1	no	—
388	C₄⋊Q₈	—	2	1	no	—
389	C₄⋊Q₈	—	2	1	no	—
390	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
391	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
392	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
393	#127	—	2	1	no	—
394	#127	C₂³×C₁₃	1	1	yes	characteristic
395	C₂²⋊Q₈	—	2	1	no	—
396	C₂²⋊Q₈	—	2	1	no	—
397	C₂²⋊Q₈	—	2	1	no	—
398	C₂²⋊Q₈	—	4	1	no	—
399	C₂²⋊Q₈	—	4	1	no	—
400	C₂²⋊Q₈	—	4	1	no	—
401	#121	—	2	1	no	—
402	#121	—	4	1	no	—
403	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
404	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
410	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
411	#107	—	2	1	no	—
412	#107	—	2	1	no	—
413	#107	—	2	1	no	—
414	#107	—	2	1	no	—
415	#107	—	2	1	no	—
416	#107	—	4	1	no	—
417	#107	D₄×C₁₃	1	1	yes	characteristic
418	#107	D₄×C₁₃	1	1	yes	characteristic
419	C₄⋊C₈	—	2	1	no	—
420	C₄⋊C₈	—	2	1	no	—
421	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
422	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
423	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
424	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
425	#103	—	2	1	no	—
426	#103	—	2	1	no	—
427	#103	—	2	1	no	—
428	#103	D₄×C₁₃	1	1	yes	characteristic
429	#103	D₄×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
437	#102	—	4	1	no	—
438	#102	D₄×C₁₃	1	1	yes	characteristic
439	#102	D₄×C₁₃	1	1	yes	characteristic
440	C₂²⋊C₈	—	2	1	no	—
441	C₂²⋊C₈	—	2	1	no	—
442	C₄×C₈	—	2	1	no	—
443	C₄×C₈	—	2	1	no	—
444	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
445	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
446	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
447	C₂×C₁₃	—	4	2	no	—
448	C₂×C₁₃	—	8	1	no	—
449	C₂×C₁₃	—	16	1	no	—
450	C₂×C₁₃	#3270	1	1	yes	characteristic
451	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
452	C₂×C₁₃	#3289	1	1	yes	characteristic
453	#41	—	4	2	no	—
454	#41	—	8	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	4	1	no	—
459	C₂×Q₈	—	4	1	no	—
460	C₂×Q₈	—	4	1	no	—
461	C₂×Q₈	—	4	2	no	—
462	C₂×Q₈	—	4	2	no	—
463	C₂×Q₈	—	4	2	no	—
464	C₂×Q₈	—	8	1	no	—
465	C₂×Q₈	—	8	1	no	—
466	C₂×Q₈	—	8	1	no	—
467	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
468	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	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	—	4	2	no	—
483	Q₁₆	—	4	2	no	—
484	Q₁₆	—	4	2	no	—
485	Q₁₆	—	4	2	no	—
486	Q₁₆	—	8	1	no	—
487	Q₁₆	C₁₃×D₈	1	4	yes	complemented
488	SD₁₆	—	4	2	no	—
489	SD₁₆	—	4	2	no	—
490	SD₁₆	—	8	1	no	—
491	D₈	—	2	2	no	—
492	D₈	—	4	2	no	—
493	M₁₆	—	4	2	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	4	2	no	—
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	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	4	1	no	—
513	C₄⋊C₄	—	4	1	no	—
514	C₄⋊C₄	—	4	1	no	—
515	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
516	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
517	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
518	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
519	C₂²⋊C₄	—	2	1	no	—
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	4	1	no	—
522	C₂²⋊C₄	—	4	1	no	—
523	C₂²⋊C₄	—	4	1	no	—
524	C₂²⋊C₄	—	4	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	2	1	no	—
527	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
528	C₁₃	#19761	1	1	yes	characteristic, direct product factor, Sylow
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	4	1	no	—
532	Q₈	—	2	1	no	—
533	Q₈	—	2	1	no	—
534	Q₈	—	4	1	no	—
535	Q₈	—	4	1	no	—
536	Q₈	—	4	1	no	—
537	Q₈	—	4	1	no	—
538	Q₈	—	4	1	no	—
539	Q₈	—	4	1	no	—
540	Q₈	—	8	2	no	—
541	Q₈	—	8	2	no	—
542	Q₈	—	8	2	no	—
543	Q₈	C₂×C₁₃×D₈	1	2	yes	—
544	Q₈	C₂×C₁₃×D₈	1	2	yes	—
545	D₄	—	2	1	no	—
546	D₄	—	2	1	no	—
547	D₄	—	2	1	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	1	no	—
550	D₄	—	4	1	no	—
551	D₄	—	4	1	no	—
552	D₄	—	8	2	no	—
553	D₄	—	8	1	no	—
554	D₄	—	16	1	no	—
555	D₄	C₁₃×#137	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	—	4	1	no	—
569	C₂×C₄	—	8	2	no	—
570	C₂×C₄	—	8	2	no	—
571	C₂×C₄	—	8	2	no	—
572	C₂×C₄	—	8	2	no	—
573	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
574	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
575	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
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	C₈	C₂×C₁₃×D₈	1	2	yes	—
585	C₂²	—	2	2	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	8	1	no	—
592	C₂²	—	8	1	no	—
593	C₂²	—	8	1	no	—
594	C₂²	D₄²×C₁₃	1	1	yes	characteristic
595	C₄	—	2	2	no	—
596	C₄	—	2	2	no	—
597	C₄	—	2	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	1	no	—
602	C₄	—	8	1	no	—
603	C₄	—	8	1	no	—
604	C₄	—	8	1	no	—
605	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
606	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
607	C₄	C₁₃×#576	1	1	yes	characteristic
608	C₄	C₁₃×#578	1	1	yes	characteristic
609	C₂	—	4	2	no	—
610	C₂	—	8	1	no	—
611	C₂	—	16	1	no	—
612	C₂	C₁₃×#3270	1	1	yes	characteristic
613	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
614	C₂	C₁₃×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3358	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. Q₈×C₁₃×D₈	C₂	semidirect
3. D₄×C₁₃×Q₁₆	C₂	semidirect
4. C₁₃×#3278	C₂	semidirect
5. C₁₃×#1722	C₂	semidirect
6. C₁₃×#1689	C₂	semidirect
7. C₁₃×#1682	C₂	semidirect
8. C₁₃×#1674	C₂	semidirect
9. C₁₃×#1665	C₂	semidirect
10. C₁₃×#1649	C₂	semidirect
11. C₁₃×#1649	C₂	semidirect
12. C₁₃×#1641	C₂	semidirect
13. C₁₃×#1627	C₂	semidirect
14. C₁₃×#1581	C₂	semidirect
15. C₁₃×#1579	C₂	semidirect
146. #19761	C₁₃	direct (N × H)
181. C₁₃×Q₁₆	D₈	semidirect
222. Q₈×D₈	C₂×C₁₃	semidirect
224. D₄×Q₁₆	C₂×C₁₃	semidirect
225. #3278	C₂×C₁₃	semidirect
226. #1722	C₂×C₁₃	semidirect
227. #1689	C₂×C₁₃	semidirect
228. #1682	C₂×C₁₃	semidirect
229. #1674	C₂×C₁₃	semidirect
230. #1665	C₂×C₁₃	semidirect
231. #1649	C₂×C₁₃	semidirect
232. #1649	C₂×C₁₃	semidirect
233. #1641	C₂×C₁₃	semidirect
234. #1627	C₂×C₁₃	semidirect
235. #1581	C₂×C₁₃	semidirect
236. #1579	C₂×C₁₃	semidirect
263. D₄×C₁₃	#137	semidirect
487. Q₁₆	C₁₃×D₈	semidirect
528. C₁₃	#19761	direct (N × H)
555. D₄	C₁₃×#137	semidirect

Maximal subgroups

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

subgroup	index
Q₈×C₁₃×D₈	2
C₁₃×#3358	2
D₄×C₁₃×Q₁₆	2
C₁₃×#3278	2
C₁₃×#1722	2
C₁₃×#1689	2
C₁₃×#1682	2
C₁₃×#1674	2
C₁₃×#1665	2
C₁₃×#1649	2
C₁₃×#1641	2
C₁₃×#1627	2
C₁₃×#1581	2
C₁₃×#1579	2
#19761	13

Subgroups — C13×#19761 #15706100

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19761 #15706100