Subgroups — C₁₃×#29174 #15715513

Order 3328.

784 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2628	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2324	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2092	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2058	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2023	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1919	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1918	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1895	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1893	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1809	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1807	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1729	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
30	C₁₃×#400	—	2	1	no	—
31	C₁₃×#399	—	2	1	no	—
32	C₁₃×#395	—	2	1	no	—
33	C₁₃×#393	—	2	1	no	—
34	C₁₃×#390	—	2	1	no	—
35	C₁₃×#390	C₂²	1	1	yes	characteristic
36	C₁₃×#389	C₂²	1	1	yes	characteristic
37	C₁₃×#389	C₂²	1	1	yes	characteristic
38	C₁₃×#389	C₂²	1	1	yes	characteristic
39	C₁₃×#388	—	2	1	no	—
40	C₁₃×#386	—	2	1	no	—
41	C₁₃×#385	—	2	1	no	—
42	C₁₃×#382	C₂²	1	1	yes	characteristic
43	C₁₃×#380	C₂²	1	1	yes	characteristic
44	C₁₃×#380	C₂²	1	1	yes	characteristic
45	C₁₃×#380	C₂²	1	1	yes	characteristic
46	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₁₃×#340	C₂²	1	1	yes	characteristic
48	C₁₃×#340	C₂²	1	1	yes	characteristic
49	C₁₃×#340	C₂²	1	1	yes	characteristic
50	C₁₃×#340	C₂²	1	1	yes	characteristic
51	C₁₃×#340	C₂²	1	1	yes	characteristic
52	C₁₃×#340	C₂²	1	1	yes	characteristic
53	C₁₃×#340	C₂²	1	1	yes	characteristic
54	C₁₃×#340	C₂²	1	1	yes	characteristic
55	C₁₃×#336	C₂²	1	1	yes	characteristic
56	C₁₃×#336	C₂²	1	1	yes	characteristic
57	C₁₃×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₃	—	2	1	no	—
60	C₂²×D₄×C₁₃	—	2	1	no	—
61	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	—	2	1	no	—
63	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×M₁₆	—	2	2	no	—
65	C₂×C₁₃×M₁₆	—	2	2	no	—
66	C₂×C₁₃×M₁₆	—	4	1	no	—
67	C₂²×C₈×C₁₃	—	2	2	no	—
68	C₂²×C₈×C₁₃	—	2	2	no	—
69	C₂²×C₈×C₁₃	—	4	1	no	—
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×C₄⋊Q₈	—	4	1	no	—
75	C₁₃×C₄⋊Q₈	—	4	1	no	—
76	C₁₃×#121	—	2	2	no	—
77	C₁₃×#121	Q₈	1	4	yes	complemented
78	C₄×D₄×C₁₃	—	4	1	no	—
79	C₄×D₄×C₁₃	—	4	1	no	—
80	C₁₃×#117	—	4	1	no	—
81	C₁₃×#117	—	4	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
103	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₁₃	—	2	1	no	—
105	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
107	C₁₃×#107	—	2	2	no	—
108	C₁₃×#106	—	2	2	no	—
109	C₁₃×#106	—	4	1	no	—
110	C₁₃×#106	—	4	1	no	—
111	C₁₃×#102	—	2	2	no	—
112	C₁₃×#102	—	2	2	no	—
113	C₁₃×#102	—	4	1	no	—
114	C₁₃×#102	—	4	1	no	—
115	C₁₃×#95	—	2	1	no	—
116	C₁₃×#95	—	2	1	no	—
117	C₁₃×#95	—	2	1	no	—
118	C₁₃×#95	—	2	1	no	—
119	C₁₃×#95	—	2	1	no	—
120	C₁₃×#95	—	2	1	no	—
121	C₁₃×#95	—	2	1	no	—
122	C₁₃×#95	—	2	1	no	—
123	C₁₃×#95	—	2	1	no	—
124	#29174	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂⁴×C₁₃	—	2	1	no	—
126	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂×Q₈×C₁₃	—	4	2	no	—
128	C₂×Q₈×C₁₃	—	8	1	no	—
129	C₂×Q₈×C₁₃	—	8	1	no	—
130	C₂×D₄×C₁₃	—	2	4	no	—
131	C₂×D₄×C₁₃	—	2	1	no	—
132	C₂×D₄×C₁₃	—	2	1	no	—
133	C₂×D₄×C₁₃	—	2	1	no	—
134	C₂×D₄×C₁₃	—	2	1	no	—
135	C₂×D₄×C₁₃	—	2	1	no	—
136	C₂×D₄×C₁₃	—	8	1	no	—
137	C₂×D₄×C₁₃	—	8	1	no	—
138	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	1	no	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂²×C₄×C₁₃	—	4	2	no	—
151	C₂²×C₄×C₁₃	—	8	1	no	—
152	C₂²×C₄×C₁₃	—	8	1	no	—
153	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
159	C₂²×C₄×C₁₃	#41	1	2	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₁₃×M₁₆	—	4	4	no	—
162	C₂×C₈×C₁₃	—	2	1	no	—
163	C₂×C₈×C₁₃	—	2	1	no	—
164	C₂×C₈×C₁₃	—	2	1	no	—
165	C₂×C₈×C₁₃	—	2	1	no	—
166	C₂×C₈×C₁₃	—	2	1	no	—
167	C₂×C₈×C₁₃	—	2	1	no	—
168	C₂×C₈×C₁₃	—	2	1	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	—	4	4	no	—
173	C₂×C₈×C₁₃	#41	1	2	yes	—
174	C₂×C₈×C₁₃	#41	1	2	yes	—
175	C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
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	2	no	—
191	C₁₃×C₄⋊C₄	—	8	1	no	—
192	C₁₃×C₄⋊C₄	—	8	1	no	—
193	C₁₃×C₄⋊C₄	—	8	1	no	—
194	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
195	C₁₃×C₂²⋊C₄	—	2	4	no	—
196	C₁₃×C₂²⋊C₄	—	4	1	no	—
197	C₁₃×C₂²⋊C₄	—	4	1	no	—
198	C₁₃×C₂²⋊C₄	—	4	2	no	—
199	C₁₃×C₂²⋊C₄	—	8	1	no	—
200	C₁₃×C₂²⋊C₄	—	8	1	no	—
201	C₁₃×C₂²⋊C₄	—	8	1	no	—
202	C₁₃×C₂²⋊C₄	—	8	1	no	—
203	C₁₃×C₂²⋊C₄	—	8	1	no	—
204	C₄²×C₁₃	—	2	1	no	—
205	C₄²×C₁₃	—	2	1	no	—
206	C₄²×C₁₃	—	2	1	no	—
207	C₄²×C₁₃	—	2	1	no	—
208	C₄²×C₁₃	—	8	1	no	—
209	#2628	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#2324	C₂×C₁₃	1	1	yes	characteristic
211	#2101	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#2092	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#2058	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#2023	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1919	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1918	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1895	C₂×C₁₃	1	1	yes	characteristic
218	#1893	C₂×C₁₃	1	1	yes	characteristic
219	#1864	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1864	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1809	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1807	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1729	C₂×C₁₃	1	1	yes	characteristic, complemented
224	C₂³×C₁₃	—	2	1	no	—
225	C₂³×C₁₃	—	2	1	no	—
226	C₂³×C₁₃	—	2	1	no	—
227	C₂³×C₁₃	—	2	1	no	—
228	C₂³×C₁₃	—	2	1	no	—
229	C₂³×C₁₃	—	2	1	no	—
230	C₂³×C₁₃	—	2	2	no	—
231	C₂³×C₁₃	—	4	1	no	—
232	C₂³×C₁₃	—	4	1	no	—
233	C₂³×C₁₃	—	4	1	no	—
234	C₂³×C₁₃	—	4	1	no	—
235	C₂³×C₁₃	—	4	1	no	—
236	C₂³×C₁₃	—	4	1	no	—
237	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
238	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
239	Q₈×C₁₃	—	8	4	no	—
240	D₄×C₁₃	—	2	2	no	—
241	D₄×C₁₃	—	2	2	no	—
242	D₄×C₁₃	—	4	1	no	—
243	D₄×C₁₃	—	4	1	no	—
244	D₄×C₁₃	—	8	4	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
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	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	1	no	—
263	C₂×C₄×C₁₃	—	2	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	—	4	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	—	4	1	no	—
276	C₂×C₄×C₁₃	—	4	1	no	—
277	C₂×C₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	—	4	1	no	—
279	C₂×C₄×C₁₃	—	4	1	no	—
280	C₂×C₄×C₁₃	—	4	1	no	—
281	C₂×C₄×C₁₃	—	4	1	no	—
282	C₂×C₄×C₁₃	—	4	1	no	—
283	C₂×C₄×C₁₃	—	4	1	no	—
284	C₂×C₄×C₁₃	—	8	4	no	—
285	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
286	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
287	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
289	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
291	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
292	C₈×C₁₃	—	2	2	no	—
293	C₈×C₁₃	—	2	2	no	—
294	C₈×C₁₃	—	4	1	no	—
295	C₈×C₁₃	—	4	1	no	—
296	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
297	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
310	#400	—	2	1	no	—
311	#399	—	2	1	no	—
312	#395	—	2	1	no	—
313	#393	—	2	1	no	—
314	#390	—	2	1	no	—
315	#390	C₂²×C₁₃	1	1	yes	characteristic
316	#389	C₂²×C₁₃	1	1	yes	characteristic
317	#389	C₂²×C₁₃	1	1	yes	characteristic
318	#389	C₂²×C₁₃	1	1	yes	characteristic
319	#388	—	2	1	no	—
320	#386	—	2	1	no	—
321	#385	—	2	1	no	—
322	#382	C₂²×C₁₃	1	1	yes	characteristic
323	#380	C₂²×C₁₃	1	1	yes	characteristic
324	#380	C₂²×C₁₃	1	1	yes	characteristic
325	#380	C₂²×C₁₃	1	1	yes	characteristic
326	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
327	#340	C₂²×C₁₃	1	1	yes	characteristic
328	#340	C₂²×C₁₃	1	1	yes	characteristic
329	#340	C₂²×C₁₃	1	1	yes	characteristic
330	#340	C₂²×C₁₃	1	1	yes	characteristic
331	#340	C₂²×C₁₃	1	1	yes	characteristic
332	#340	C₂²×C₁₃	1	1	yes	characteristic
333	#340	C₂²×C₁₃	1	1	yes	characteristic
334	#340	C₂²×C₁₃	1	1	yes	characteristic
335	#336	C₂²×C₁₃	1	1	yes	characteristic
336	#336	C₂²×C₁₃	1	1	yes	characteristic
337	#336	C₂²×C₁₃	1	1	yes	characteristic
338	#336	C₂²×C₁₃	1	1	yes	characteristic
339	C₂²×C₁₃	—	2	2	no	—
340	C₂²×C₁₃	—	2	2	no	—
341	C₂²×C₁₃	—	2	2	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	—	4	2	no	—
347	C₂²×C₁₃	—	4	2	no	—
348	C₂²×C₁₃	—	4	2	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	C₂×C₂²⋊Q₈	1	1	yes	characteristic
354	C₂²×C₁₃	#532	1	1	yes	characteristic
355	C₂²×C₁₃	#534	1	1	yes	characteristic
356	C₂²×C₁₃	#576	1	1	yes	characteristic
357	C₂²×C₁₃	#577	1	1	yes	characteristic
358	C₂²×C₁₃	#577	1	1	yes	characteristic
359	C₂²×C₁₃	#577	1	1	yes	characteristic
360	C₄×C₁₃	—	2	2	no	—
361	C₄×C₁₃	—	4	2	no	—
362	C₄×C₁₃	—	4	1	no	—
363	C₄×C₁₃	—	4	1	no	—
364	C₄×C₁₃	—	4	1	no	—
365	C₄×C₁₃	—	4	1	no	—
366	C₄×C₁₃	—	8	1	no	—
367	C₄×C₁₃	—	8	1	no	—
368	C₄×C₁₃	—	8	1	no	—
369	C₄×C₁₃	—	8	1	no	—
370	C₄×C₁₃	—	8	1	no	—
371	C₄×C₁₃	—	8	1	no	—
372	C₄×C₁₃	#551	1	1	yes	characteristic
373	C₄×C₁₃	#551	1	1	yes	characteristic
374	C₄×C₁₃	#554	1	1	yes	characteristic
375	C₄×C₁₃	#554	1	1	yes	characteristic
376	C₂²×Q₈	—	2	1	no	—
377	C₂²×D₄	—	2	1	no	—
378	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
379	C₂³×C₄	—	2	1	no	—
380	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
381	C₂×M₁₆	—	2	2	no	—
382	C₂×M₁₆	—	2	2	no	—
383	C₂×M₁₆	—	4	1	no	—
384	C₂²×C₈	—	2	2	no	—
385	C₂²×C₈	—	2	2	no	—
386	C₂²×C₈	—	4	1	no	—
387	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
388	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
389	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
390	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
391	C₄⋊Q₈	—	4	1	no	—
392	C₄⋊Q₈	—	4	1	no	—
393	#121	—	2	2	no	—
394	#121	Q₈×C₁₃	1	4	yes	complemented
395	C₄×D₄	—	4	1	no	—
396	C₄×D₄	—	4	1	no	—
397	#117	—	4	1	no	—
398	#117	—	4	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
404	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
421	C₂×C₄²	—	2	1	no	—
422	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
424	#107	—	2	2	no	—
425	#106	—	2	2	no	—
426	#106	—	4	1	no	—
427	#106	—	4	1	no	—
428	#102	—	2	2	no	—
429	#102	—	2	2	no	—
430	#102	—	4	1	no	—
431	#102	—	4	1	no	—
432	#95	—	2	1	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	#95	—	2	1	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	C₂×C₁₃	—	4	2	no	—
442	C₂×C₁₃	—	8	2	no	—
443	C₂×C₁₃	#2564	1	1	yes	characteristic
444	C₂×C₁₃	#3081	1	1	yes	characteristic
445	C₂×C₁₃	#3084	1	1	yes	characteristic
446	C₂×C₁₃	#3173	1	1	yes	characteristic
447	C₂×C₁₃	#3179	1	1	yes	characteristic
448	C₂×C₁₃	#3198	1	1	yes	characteristic
449	C₂×C₁₃	#3200	1	1	yes	characteristic
450	C₂⁴	—	2	1	no	—
451	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
452	C₂×Q₈	—	4	2	no	—
453	C₂×Q₈	—	8	1	no	—
454	C₂×Q₈	—	8	1	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	8	1	no	—
462	C₂×D₄	—	8	1	no	—
463	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	4	2	no	—
476	C₂²×C₄	—	8	1	no	—
477	C₂²×C₄	—	8	1	no	—
478	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
483	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
484	C₂²×C₄	C₁₃×#41	1	2	yes	—
485	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
486	M₁₆	—	4	4	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	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	4	no	—
498	C₂×C₈	C₁₃×#41	1	2	yes	—
499	C₂×C₈	C₁₃×#41	1	2	yes	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
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	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	4	1	no	—
514	C₄⋊C₄	—	4	1	no	—
515	C₄⋊C₄	—	4	2	no	—
516	C₄⋊C₄	—	8	1	no	—
517	C₄⋊C₄	—	8	1	no	—
518	C₄⋊C₄	—	8	1	no	—
519	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
520	C₂²⋊C₄	—	2	4	no	—
521	C₂²⋊C₄	—	4	1	no	—
522	C₂²⋊C₄	—	4	1	no	—
523	C₂²⋊C₄	—	4	2	no	—
524	C₂²⋊C₄	—	8	1	no	—
525	C₂²⋊C₄	—	8	1	no	—
526	C₂²⋊C₄	—	8	1	no	—
527	C₂²⋊C₄	—	8	1	no	—
528	C₂²⋊C₄	—	8	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	2	1	no	—
533	C₄²	—	8	1	no	—
534	C₁₃	#29174	1	1	yes	characteristic, direct product factor, Sylow
535	C₂³	—	2	1	no	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	1	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	4	1	no	—
543	C₂³	—	4	1	no	—
544	C₂³	—	4	1	no	—
545	C₂³	—	4	1	no	—
546	C₂³	—	4	1	no	—
547	C₂³	—	4	1	no	—
548	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
549	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
550	Q₈	—	8	4	no	—
551	D₄	—	2	2	no	—
552	D₄	—	2	2	no	—
553	D₄	—	4	1	no	—
554	D₄	—	4	1	no	—
555	D₄	—	8	4	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	8	4	no	—
596	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
597	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
598	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
599	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
600	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
601	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
602	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
603	C₈	—	2	2	no	—
604	C₈	—	2	2	no	—
605	C₈	—	4	1	no	—
606	C₈	—	4	1	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	4	1	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	4	1	no	—
613	C₂²	—	4	1	no	—
614	C₂²	—	4	2	no	—
615	C₂²	—	4	2	no	—
616	C₂²	—	4	2	no	—
617	C₂²	—	8	1	no	—
618	C₂²	—	8	1	no	—
619	C₂²	—	8	1	no	—
620	C₂²	—	8	1	no	—
621	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
622	C₂²	C₁₃×#532	1	1	yes	characteristic
623	C₂²	C₁₃×#534	1	1	yes	characteristic
624	C₂²	C₁₃×#576	1	1	yes	characteristic
625	C₂²	C₁₃×#577	1	1	yes	characteristic
626	C₂²	C₁₃×#577	1	1	yes	characteristic
627	C₂²	C₁₃×#577	1	1	yes	characteristic
628	C₄	—	2	2	no	—
629	C₄	—	4	2	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	1	no	—
632	C₄	—	4	1	no	—
633	C₄	—	4	1	no	—
634	C₄	—	8	1	no	—
635	C₄	—	8	1	no	—
636	C₄	—	8	1	no	—
637	C₄	—	8	1	no	—
638	C₄	—	8	1	no	—
639	C₄	—	8	1	no	—
640	C₄	C₁₃×#551	1	1	yes	characteristic
641	C₄	C₁₃×#551	1	1	yes	characteristic
642	C₄	C₁₃×#554	1	1	yes	characteristic
643	C₄	C₁₃×#554	1	1	yes	characteristic
644	C₂	—	4	2	no	—
645	C₂	—	8	2	no	—
646	C₂	C₁₃×#2564	1	1	yes	characteristic
647	C₂	C₁₃×#3081	1	1	yes	characteristic
648	C₂	C₁₃×#3084	1	1	yes	characteristic
649	C₂	C₁₃×#3173	1	1	yes	characteristic
650	C₂	C₁₃×#3179	1	1	yes	characteristic
651	C₂	C₁₃×#3198	1	1	yes	characteristic
652	C₂	C₁₃×#3200	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃×#2628	C₂	semidirect
3. C₁₃×#2101	C₂	semidirect
4. C₁₃×#2092	C₂	semidirect
5. C₁₃×#2058	C₂	semidirect
6. C₁₃×#2023	C₂	semidirect
7. C₁₃×#1919	C₂	semidirect
8. C₁₃×#1918	C₂	semidirect
11. C₁₃×#1864	C₂	semidirect
12. C₁₃×#1864	C₂	semidirect
13. C₁₃×#1809	C₂	semidirect
14. C₁₃×#1807	C₂	semidirect
15. C₁₃×#1729	C₂	semidirect
77. C₁₃×#121	Q₈	semidirect
124. #29174	C₁₃	direct (N × H)
209. #2628	C₂×C₁₃	semidirect
211. #2101	C₂×C₁₃	semidirect
212. #2092	C₂×C₁₃	semidirect
213. #2058	C₂×C₁₃	semidirect
214. #2023	C₂×C₁₃	semidirect
215. #1919	C₂×C₁₃	semidirect
216. #1918	C₂×C₁₃	semidirect
219. #1864	C₂×C₁₃	semidirect
220. #1864	C₂×C₁₃	semidirect
221. #1809	C₂×C₁₃	semidirect
222. #1807	C₂×C₁₃	semidirect
223. #1729	C₂×C₁₃	semidirect
394. #121	Q₈×C₁₃	semidirect
534. C₁₃	#29174	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×#2628	2
C₁₃×#2324	2
C₁₃×#2101	2
C₁₃×#2092	2
C₁₃×#2058	2
C₁₃×#2023	2
C₁₃×#1919	2
C₁₃×#1918	2
C₁₃×#1895	2
C₁₃×#1893	2
C₁₃×#1864	2
C₁₃×#1809	2
C₁₃×#1807	2
C₁₃×#1729	2
#29174	13

Subgroups — C13×#29174 #15715513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29174 #15715513