Subgroups — #16769535

Order 3328.

11674 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	H(5,𝔽₂)×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#88256	C₂	1	6	yes	maximal, complemented
4	#13128042	C₂	1	6	yes	maximal, complemented
5	C₄×#88251	C₂	1	9	yes	maximal, complemented
6	#13128040	C₂	1	9	yes	maximal, complemented
7	#13128036	C₂	1	6	yes	maximal, complemented
8	#13128035	C₂	1	6	yes	maximal, complemented
9	C₂×#11719250	C₂	1	9	yes	maximal, complemented
10	D₁₃×#518	C₂	1	9	yes	maximal, complemented
11	C₄×C₁₃×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
13	D₁₃×H(5,𝔽₂)	C₄	1	32	yes	complemented
14	C₂×#88256	C₂²	1	6	yes	—
15	C₂×#41×D₁₃	C₂²	1	6	yes	—
16	C₂×#88251	C₂²	1	9	yes	—
17	C₂²×D₄×D₁₃	C₂²	1	9	yes	—
18	C₁₃×#520	C₂²	1	6	yes	complemented
19	C₁₃×#518	C₂²	1	9	yes	complemented
20	C₄×C₁₃×#41	C₂²	1	6	yes	complemented
21	C₂×C₄×D₄×C₁₃	C₂²	1	9	yes	complemented
22	#11719532	C₂²	1	6	yes	complemented
23	#41×Dic₁₃	C₂²	1	6	yes	complemented
24	#11719503	C₂²	1	9	yes	complemented
25	C₂×D₄×Dic₁₃	C₂²	1	9	yes	complemented
26	C₂×C₄×C₂²⋊D₁₃	C₂²	1	18	yes	complemented
27	C₂²×#6103	C₂²	1	6	yes	complemented
28	#11719279	C₂²	1	6	yes	complemented
29	#11719279	C₂²	1	6	yes	complemented
30	C₄×#6131	C₂²	1	12	yes	complemented
31	#11719277	C₂²	1	2	yes	complemented
32	#11719277	C₂²	1	6	yes	complemented
33	#11719251	C₂²	1	18	yes	complemented
34	#11719251	C₂²	1	18	yes	complemented
35	#11719250	C₂²	1	18	yes	complemented
36	#11719250	C₂²	1	36	yes	complemented
37	#11719250	C₂²	1	18	yes	complemented
38	#11719250	C₂²	1	36	yes	complemented
39	#11719250	C₂²	1	36	yes	complemented
40	C₄×D₄×D₁₃	C₂²	1	36	yes	complemented
41	C₄×D₄×D₁₃	C₂²	1	36	yes	complemented
42	C₄×#6129	C₂²	1	36	yes	complemented
43	#11719228	C₂²	1	18	yes	complemented
44	#11719227	C₂²	1	18	yes	complemented
45	#11719226	C₂²	1	18	yes	complemented
46	D₁₃×#117	C₂²	1	18	yes	complemented
47	#11719209	C₂²	1	18	yes	complemented
48	C₂×#88147	C₂²	1	9	yes	complemented
49	C₂×#88146	C₂²	1	9	yes	complemented
50	#11719191	C₂²	1	36	yes	complemented
51	C₂×#88135	C₂²	1	18	yes	complemented
52	C₂×C₂²⋊C₄×D₁₃	C₂²	1	18	yes	complemented
53	C₄×#6127	C₂²	1	18	yes	complemented
54	C₂×C₄×D₅₂	C₂²	1	9	yes	complemented
55	C₂×#88126	C₂²	1	9	yes	complemented
56	C₂⁴×D₁₃	C₂³	1	6	yes	—
57	C₁₃×H(5,𝔽₂)	C₂×C₄	1	16	yes	complemented
58	C₂×C₁₃×#41	C₂³	1	6	yes	—
59	C₂²×D₄×C₁₃	C₂³	1	9	yes	—
60	C₂³×C₄×C₁₃	C₂³	1	6	yes	complemented
61	C₂²×C₂²⋊D₁₃	C₂³	1	18	yes	—
62	C₂³×Dic₁₃	C₂³	1	6	yes	complemented
63	#88256	C₂×C₄	1	96	yes	complemented
64	#41×D₁₃	C₂×C₄	1	96	yes	complemented
65	C₂×#6131	C₂³	1	6	yes	—
66	C₂×Q₈×D₁₃	C₂³	1	2	yes	—
67	#88251	C₂×C₄	1	144	yes	complemented
68	C₂×#6129	C₂³	1	18	yes	—
69	C₂×D₄×D₁₃	C₂×C₄	1	144	yes	complemented
70	C₂×D₄×D₁₃	C₂³	1	36	yes	—
71	C₂×D₄×D₁₃	C₂³	1	18	yes	—
72	C₂×#6127	C₂³	1	18	yes	—
73	C₂²×D₅₂	C₂³	1	9	yes	—
74	C₂²×C₄×D₁₃	C₂³	1	9	yes	—
75	C₂²×C₄×D₁₃	C₂³	1	18	yes	complemented
76	C₂²×C₄×D₁₃	C₂³	1	18	yes	complemented
77	C₄×Q₈×C₁₃	C₂³	1	6	yes	complemented
78	C₄×Q₈×C₁₃	C₂³	1	2	yes	complemented
79	C₄×D₄×C₁₃	C₂³	1	36	yes	complemented
80	C₄×D₄×C₁₃	C₂³	1	18	yes	complemented
81	C₄×D₄×C₁₃	C₂³	1	18	yes	complemented
82	C₁₃×#117	C₂³	1	18	yes	complemented
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	9	yes	complemented
84	C₂×C₁₃×C₂²⋊C₄	C₂³	1	18	yes	complemented
85	C₂×C₄²×C₁₃	C₂³	1	9	yes	complemented
86	C₂×C₂²⋊Dic₁₃	C₂³	1	18	yes	complemented
87	Q₈×Dic₁₃	C₂³	1	2	yes	complemented
88	Q₈×Dic₁₃	C₂³	1	6	yes	complemented
89	D₄×Dic₁₃	C₂³	1	36	yes	complemented
90	D₄×Dic₁₃	C₂³	1	18	yes	complemented
91	D₄×Dic₁₃	C₂³	1	18	yes	complemented
92	C₄×C₂²⋊D₁₃	C₂³	1	36	yes	complemented
93	C₄×C₂²⋊D₁₃	C₂³	1	36	yes	complemented
94	C₄×C₂²⋊D₁₃	C₂³	1	72	yes	complemented
95	C₂×#6103	C₂³	1	9	yes	—
96	C₂×#6103	C₂³	1	9	yes	—
97	C₂×#6103	C₂³	1	18	yes	—
98	C₂×#6103	C₂³	1	18	yes	complemented
99	C₂×#6103	C₂³	1	18	yes	complemented
100	#88180	C₂³	1	18	yes	complemented
101	C₂×C₄⋊Dic₁₃	C₂³	1	9	yes	complemented
102	C₂×#6101	C₂³	1	9	yes	complemented
103	C₂×#6101	C₂³	1	9	yes	complemented
104	C₂×C₄×Dic₁₃	C₂³	1	9	yes	complemented
105	C₂×C₄×Dic₁₃	C₂³	1	18	yes	complemented
106	#88147	C₂³	1	18	yes	complemented
107	#88147	C₂³	1	36	yes	complemented
108	#88147	C₂³	1	18	yes	complemented
109	#88146	C₂³	1	18	yes	—
110	#88146	C₂³	1	6	yes	—
111	#88146	C₂³	1	36	yes	complemented
112	C₄⋊C₄×D₁₃	C₂³	1	18	yes	complemented
113	C₄⋊C₄×D₁₃	C₂³	1	18	yes	complemented
114	#88141	C₂³	1	18	yes	complemented
115	#88141	C₂³	1	6	yes	complemented
116	#88135	C₂³	1	36	yes	complemented
117	#88135	C₂³	1	72	yes	complemented
118	#88135	C₂³	1	36	yes	complemented
119	C₂²⋊C₄×D₁₃	C₂³	1	36	yes	—
120	C₂²⋊C₄×D₁₃	C₂³	1	72	yes	complemented
121	#88131	C₂³	1	36	yes	complemented
122	C₄×D₅₂	C₂³	1	18	yes	complemented
123	C₄×D₅₂	C₂³	1	36	yes	complemented
124	C₄×D₅₂	C₂³	1	18	yes	complemented
125	#88126	C₂³	1	6	yes	—
126	#88126	C₂³	1	18	yes	—
127	#88126	C₂³	1	18	yes	complemented
128	#88126	C₂³	1	18	yes	complemented
129	C₄²×D₁₃	C₂³	1	36	yes	complemented
130	C₄×Dic₂₆	C₂³	1	6	yes	complemented
131	C₄×Dic₂₆	C₂³	1	18	yes	complemented
132	#62652	—	13	1	no	maximal, Sylow
133	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
134	C₂³×D₁₃	—	8	6	no	—
135	C₂³×D₁₃	—	8	6	no	—
136	C₂³×D₁₃	C₂²×C₄	1	48	yes	complemented
137	C₂³×D₁₃	C₂⁴	1	9	yes	—
138	C₂³×D₁₃	C₂⁴	1	18	yes	—
139	C₁₃×#41	C₂²×C₄	1	48	yes	complemented
140	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
141	C₂×D₄×C₁₃	C₂²×C₄	1	72	yes	complemented
142	C₂×D₄×C₁₃	C₂⁴	1	18	yes	—
143	C₂²×C₄×C₁₃	—	8	6	no	—
144	C₂²×C₄×C₁₃	C₂⁴	1	18	yes	—
145	C₂²×C₄×C₁₃	C₂⁴	1	9	yes	—
146	C₂²×C₄×C₁₃	C₂⁴	1	9	yes	—
147	C₂²×C₄×C₁₃	C₂⁴	1	9	yes	—
148	C₂×C₂²⋊D₁₃	C₂²×C₄	1	144	yes	complemented
149	C₂×C₂²⋊D₁₃	C₂⁴	1	36	yes	—
150	C₂²×Dic₁₃	—	8	6	no	—
151	C₂²×Dic₁₃	C₂⁴	1	9	yes	—
152	C₂²×Dic₁₃	C₂⁴	1	9	yes	—
153	C₂²×Dic₁₃	C₂⁴	1	18	yes	—
154	C₂²×Dic₁₃	C₂⁴	1	9	yes	—
155	#6131	C₂²×C₄	1	48	yes	complemented
156	Q₈×D₁₃	C₂²×C₄	1	16	yes	complemented
157	#6129	C₂²×C₄	1	144	yes	complemented
158	D₄×D₁₃	C₂²×C₄	1	144	yes	complemented
159	D₄×D₁₃	C₂²×C₄	1	288	yes	complemented
160	#6127	C₂²×C₄	1	144	yes	complemented
161	C₂×D₅₂	C₂²×C₄	1	72	yes	complemented
162	C₂×D₅₂	C₂⁴	1	18	yes	—
163	C₂×C₄×D₁₃	—	8	18	no	—
164	C₂×C₄×D₁₃	—	8	18	no	—
165	C₂×C₄×D₁₃	C₂²×C₄	1	72	yes	complemented
166	C₂×C₄×D₁₃	C₂⁴	1	36	yes	—
167	C₂×C₄×D₁₃	C₂⁴	1	36	yes	—
168	C₂×C₄×D₁₃	C₂⁴	1	18	yes	—
169	C₂×C₄×D₁₃	C₂⁴	1	6	yes	—
170	C₂×Dic₂₆	C₂⁴	1	6	yes	—
171	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
172	C₁₃×C₄⋊C₄	C₂⁴	1	18	yes	—
173	C₁₃×C₂²⋊C₄	C₂⁴	1	36	yes	—
174	C₄²×C₁₃	C₂⁴	1	18	yes	—
175	C₄²×C₁₃	C₂⁴	1	6	yes	—
176	C₂²⋊Dic₁₃	C₂⁴	1	36	yes	—
177	#6103	C₂⁴	1	1	yes	characteristic
178	#6103	C₂⁴	1	6	yes	—
179	#6103	C₂⁴	1	9	yes	—
180	#6103	C₂⁴	1	9	yes	—
181	#6103	C₂⁴	1	18	yes	—
182	#6103	C₂⁴	1	9	yes	—
183	#6103	C₂⁴	1	36	yes	—
184	C₄⋊Dic₁₃	C₂⁴	1	6	yes	—
185	C₄⋊Dic₁₃	C₂⁴	1	18	yes	—
186	#6101	C₂⁴	1	6	yes	—
187	#6101	C₂⁴	1	18	yes	—
188	#6101	C₂⁴	1	6	yes	—
189	#6101	C₂⁴	1	18	yes	—
190	C₄×Dic₁₃	C₂⁴	1	12	yes	—
191	C₄×Dic₁₃	C₂⁴	1	36	yes	—
192	C₄×Dic₁₃	C₂⁴	1	18	yes	—
193	C₄×Dic₁₃	C₂⁴	1	6	yes	—
194	C₂²×H(5,𝔽₂)	—	13	1	no	—
195	C₄×H(5,𝔽₂)	—	13	1	no	—
196	C₄×H(5,𝔽₂)	—	13	6	no	—
197	C₄×H(5,𝔽₂)	—	13	9	no	—
198	C₄×H(5,𝔽₂)	—	13	6	no	—
199	C₄×H(5,𝔽₂)	—	13	9	no	—
200	C₄×H(5,𝔽₂)	D₁₃	1	1	yes	characteristic, complemented
201	#3428	—	13	6	no	—
202	#3428	—	13	6	no	—
203	C₂×#518	—	13	9	no	—
204	C₂×#518	—	13	9	no	—
205	C₂³×C₁₃	—	4	6	no	—
206	C₂³×C₁₃	—	4	6	no	—
207	C₂³×C₁₃	C₂³×C₄	1	24	yes	—
208	C₂³×C₁₃	C₂⁵	1	9	yes	—
209	C₂²×D₁₃	—	4	18	no	—
210	C₂²×D₁₃	—	4	18	no	—
211	C₂²×D₁₃	—	4	9	no	—
212	C₂²×D₁₃	—	4	9	no	—
213	C₂²×D₁₃	—	8	48	no	—
214	C₂²×D₁₃	C₂³×C₄	1	36	yes	—
215	C₂²×D₁₃	C₂³×C₄	1	72	yes	—
216	C₂²×D₁₃	C₂⁵	1	1	yes	characteristic
217	C₂²×D₁₃	C₂⁵	1	9	yes	—
218	Q₈×C₁₃	C₂³×C₄	1	8	yes	—
219	D₄×C₁₃	C₂³×C₄	1	72	yes	—
220	C₂×C₄×C₁₃	—	4	9	no	—
221	C₂×C₄×C₁₃	—	4	18	no	—
222	C₂×C₄×C₁₃	—	4	9	no	—
223	C₂×C₄×C₁₃	C₂³×C₄	1	36	yes	—
224	C₂×C₄×C₁₃	C₂⁵	1	9	yes	—
225	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
226	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
228	C₂²⋊D₁₃	C₂³×C₄	1	144	yes	—
229	C₂×Dic₁₃	—	4	9	no	—
230	C₂×Dic₁₃	—	4	18	no	—
231	C₂×Dic₁₃	—	4	9	no	—
232	C₂×Dic₁₃	C₂³×C₄	1	36	yes	—
233	C₂×Dic₁₃	C₂⁵	1	1	yes	characteristic
234	C₂×Dic₁₃	C₂⁵	1	6	yes	—
235	C₂×Dic₁₃	C₂⁵	1	9	yes	—
236	C₂×Dic₁₃	C₂⁵	1	6	yes	—
237	D₅₂	C₂³×C₄	1	72	yes	—
238	C₄×D₁₃	—	4	36	no	—
239	C₄×D₁₃	—	4	36	no	—
240	C₄×D₁₃	C₂³×C₄	1	24	yes	—
241	C₄×D₁₃	C₂³×C₄	1	72	yes	—
242	Dic₂₆	C₂³×C₄	1	24	yes	—
243	C₂×H(5,𝔽₂)	—	13	32	no	—
244	C₂×H(5,𝔽₂)	—	13	6	no	—
245	C₂×H(5,𝔽₂)	—	13	9	no	—
246	C₂×H(5,𝔽₂)	C₂×D₁₃	1	1	yes	characteristic
247	C₂²×#41	—	13	6	no	—
248	C₂³×D₄	—	13	9	no	—
249	#520	—	13	6	no	—
250	#520	—	13	6	no	—
251	#520	—	13	6	no	—
252	#520	—	13	18	no	—
253	#520	—	13	18	no	—
254	#520	—	13	18	no	—
255	#520	—	13	18	no	—
256	#520	C₂×D₁₃	1	6	yes	complemented
257	#519	—	13	6	no	—
258	#519	—	13	2	no	—
259	#518	—	13	9	no	—
260	#518	—	13	18	no	—
261	#518	—	13	36	no	—
262	#518	—	13	18	no	—
263	#518	—	13	36	no	—
264	#518	—	13	36	no	—
265	#518	—	13	18	no	—
266	#518	—	13	36	no	—
267	#518	C₂×D₁₃	1	9	yes	complemented
268	C₄×#41	—	13	6	no	—
269	C₄×#41	—	13	12	no	—
270	C₄×#41	—	13	36	no	—
271	C₄×#41	—	13	18	no	—
272	C₄×#41	—	13	18	no	—
273	C₄×#41	C₂×D₁₃	1	6	yes	complemented
274	C₂×C₄×D₄	—	13	9	no	—
275	C₂×C₄×D₄	—	13	18	no	—
276	C₂×C₄×D₄	—	13	36	no	—
277	C₂×C₄×D₄	—	13	36	no	—
278	C₂×C₄×D₄	—	13	9	no	—
279	C₂×C₄×D₄	—	13	18	no	—
280	C₂×C₄×D₄	—	13	9	no	—
281	C₂×C₄×D₄	C₂×D₁₃	1	9	yes	complemented
282	C₂×#117	—	13	18	no	—
283	C₂×#117	—	13	9	no	—
284	C₂×#117	—	13	9	no	—
285	C₂²×C₂²⋊C₄	—	13	6	no	—
286	C₂²×C₂²⋊C₄	—	13	18	no	—
287	C₂²×C₁₃	—	2	9	no	—
288	C₂²×C₁₃	—	2	9	no	—
289	C₂²×C₁₃	—	4	24	no	—
290	C₂²×C₁₃	C₂⁴×C₄	1	18	yes	—
291	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
292	C₂×D₁₃	—	2	9	no	—
293	C₂×D₁₃	—	2	9	no	—
294	C₂×D₁₃	—	2	1	no	—
295	C₂×D₁₃	—	2	1	no	—
296	C₂×D₁₃	—	4	36	no	—
297	C₂×D₁₃	—	4	72	no	—
298	C₂×D₁₃	C₂⁴×C₄	1	2	yes	—
299	C₂×D₁₃	C₂⁴×C₄	1	18	yes	—
300	C₄×C₁₃	—	2	6	no	—
301	C₄×C₁₃	—	2	9	no	—
302	C₄×C₁₃	—	2	1	no	—
303	C₄×C₁₃	C₂⁴×C₄	1	12	yes	—
304	Dic₁₃	—	2	6	no	—
305	Dic₁₃	—	2	9	no	—
306	Dic₁₃	—	2	1	no	—
307	Dic₁₃	C₂⁴×C₄	1	12	yes	—
308	C₂⁵	—	13	6	no	—
309	H(5,𝔽₂)	—	13	96	no	—
310	H(5,𝔽₂)	—	13	144	no	—
311	H(5,𝔽₂)	C₄×D₁₃	1	16	yes	complemented
312	C₂×#41	—	13	96	no	—
313	C₂×#41	—	13	6	no	—
314	C₂×#41	—	13	18	no	—
315	C₂×#41	—	13	18	no	—
316	C₂×#41	C₂²×D₁₃	1	6	yes	—
317	C₂²×Q₈	—	13	2	no	—
318	C₂²×D₄	—	13	18	no	—
319	C₂²×D₄	—	13	144	no	—
320	C₂²×D₄	—	13	36	no	—
321	C₂²×D₄	—	13	18	no	—
322	C₂²×D₄	—	13	9	no	—
323	C₂²×D₄	C₂²×D₁₃	1	9	yes	—
324	C₂³×C₄	—	13	9	no	—
325	C₂³×C₄	—	13	6	no	—
326	C₂³×C₄	—	13	18	no	—
327	C₂³×C₄	—	13	18	no	—
328	C₂³×C₄	C₂²×D₁₃	1	6	yes	complemented
329	C₄×Q₈	—	13	2	no	—
330	C₄×Q₈	—	13	6	no	—
331	C₄×Q₈	—	13	6	no	—
332	C₄×Q₈	—	13	18	no	—
333	C₄×Q₈	—	13	18	no	—
334	C₄×Q₈	—	13	6	no	—
335	C₄×Q₈	C₂²×D₁₃	1	6	yes	complemented
336	C₄×Q₈	C₂²×D₁₃	1	2	yes	complemented
337	C₄×D₄	—	13	18	no	—
338	C₄×D₄	—	13	36	no	—
339	C₄×D₄	—	13	18	no	—
340	C₄×D₄	—	13	72	no	—
341	C₄×D₄	—	13	36	no	—
342	C₄×D₄	—	13	36	no	—
343	C₄×D₄	—	13	18	no	—
344	C₄×D₄	—	13	36	no	—
345	C₄×D₄	—	13	18	no	—
346	C₄×D₄	—	13	36	no	—
347	C₄×D₄	—	13	72	no	—
348	C₄×D₄	—	13	36	no	—
349	C₄×D₄	—	13	18	no	—
350	C₄×D₄	—	13	36	no	—
351	C₄×D₄	—	13	18	no	—
352	C₄×D₄	C₂²×D₁₃	1	18	yes	complemented
353	C₄×D₄	C₂²×D₁₃	1	36	yes	complemented
354	C₄×D₄	C₂²×D₁₃	1	18	yes	complemented
355	#117	—	13	18	no	—
356	#117	—	13	6	no	—
357	#117	—	13	18	no	—
358	#117	—	13	36	no	—
359	#117	—	13	36	no	—
360	#117	—	13	18	no	—
361	#117	—	13	6	no	—
362	#117	—	13	18	no	—
363	#117	—	13	18	no	—
364	#117	C₂²×D₁₃	1	18	yes	complemented
365	C₂×C₄⋊C₄	—	13	9	no	—
366	C₂×C₄⋊C₄	—	13	9	no	—
367	C₂×C₄⋊C₄	—	13	9	no	—
368	C₂×C₄⋊C₄	—	13	18	no	—
369	C₂×C₄⋊C₄	—	13	18	no	—
370	C₂×C₄⋊C₄	C₂²×D₁₃	1	9	yes	complemented
371	C₂×C₂²⋊C₄	—	13	18	no	—
372	C₂×C₂²⋊C₄	—	13	18	no	—
373	C₂×C₂²⋊C₄	—	13	9	no	—
374	C₂×C₂²⋊C₄	—	13	9	no	—
375	C₂×C₂²⋊C₄	—	13	18	no	—
376	C₂×C₂²⋊C₄	—	13	18	no	—
377	C₂×C₂²⋊C₄	—	13	36	no	—
378	C₂×C₂²⋊C₄	—	13	72	no	—
379	C₂×C₂²⋊C₄	C₂²×D₁₃	1	18	yes	complemented
380	C₂×C₄²	—	13	18	no	—
381	C₂×C₄²	—	13	9	no	—
382	C₂×C₄²	—	13	36	no	—
383	C₂×C₄²	C₂²×D₁₃	1	9	yes	complemented
384	C₂×C₁₃	—	2	18	no	—
385	C₂×C₁₃	C₂⁵×C₄	1	1	yes	characteristic
386	C₂×C₁₃	H(7,𝔽₂)	1	1	yes	characteristic
387	C₂×C₁₃	H(7,𝔽₂)	1	1	yes	characteristic
388	D₁₃	—	2	2	no	—
389	D₁₃	—	2	18	no	—
390	C₂⁴	—	13	9	no	—
391	C₂⁴	—	13	18	no	—
392	C₂⁴	—	13	48	no	—
393	C₂⁴	—	104	6	no	—
394	C₂⁴	—	104	6	no	—
395	C₂⁴	C₂³×D₁₃	1	6	yes	—
396	#41	—	13	48	no	—
397	#41	—	13	144	no	—
398	#41	—	13	144	no	—
399	#41	C₂×C₄×D₁₃	1	48	yes	complemented
400	C₂×Q₈	—	13	16	no	—
401	C₂×Q₈	—	13	6	no	—
402	C₂×Q₈	C₂³×D₁₃	1	2	yes	—
403	C₂×D₄	—	13	144	no	—
404	C₂×D₄	—	13	36	no	—
405	C₂×D₄	—	13	144	no	—
406	C₂×D₄	—	13	288	no	—
407	C₂×D₄	—	13	72	no	—
408	C₂×D₄	—	13	18	no	—
409	C₂×D₄	C₂×C₄×D₁₃	1	72	yes	complemented
410	C₂×D₄	C₂³×D₁₃	1	18	yes	—
411	C₂²×C₄	—	8	6	no	—
412	C₂²×C₄	—	13	9	no	—
413	C₂²×C₄	—	13	72	no	—
414	C₂²×C₄	—	13	18	no	—
415	C₂²×C₄	—	13	6	no	—
416	C₂²×C₄	—	13	9	no	—
417	C₂²×C₄	—	13	18	no	—
418	C₂²×C₄	—	13	9	no	—
419	C₂²×C₄	—	13	36	no	—
420	C₂²×C₄	—	13	36	no	—
421	C₂²×C₄	—	104	18	no	—
422	C₂²×C₄	—	104	18	no	—
423	C₂²×C₄	—	104	6	no	—
424	C₂²×C₄	C₂³×D₁₃	1	18	yes	—
425	C₂²×C₄	C₂³×D₁₃	1	9	yes	—
426	C₂²×C₄	C₂³×D₁₃	1	9	yes	—
427	C₂²×C₄	C₂³×D₁₃	1	9	yes	—
428	C₄⋊C₄	—	13	18	no	—
429	C₄⋊C₄	—	13	6	no	—
430	C₄⋊C₄	—	13	18	no	—
431	C₄⋊C₄	—	13	6	no	—
432	C₄⋊C₄	—	13	18	no	—
433	C₄⋊C₄	—	13	6	no	—
434	C₄⋊C₄	C₂³×D₁₃	1	6	yes	—
435	C₄⋊C₄	C₂³×D₁₃	1	18	yes	—
436	C₂²⋊C₄	—	13	36	no	—
437	C₂²⋊C₄	—	13	9	no	—
438	C₂²⋊C₄	—	13	6	no	—
439	C₂²⋊C₄	—	13	1	no	—
440	C₂²⋊C₄	—	13	9	no	—
441	C₂²⋊C₄	—	13	36	no	—
442	C₂²⋊C₄	—	13	18	no	—
443	C₂²⋊C₄	—	13	9	no	—
444	C₂²⋊C₄	C₂³×D₁₃	1	36	yes	—
445	C₄²	—	13	36	no	—
446	C₄²	—	13	12	no	—
447	C₄²	—	13	6	no	—
448	C₄²	—	13	18	no	—
449	C₄²	C₂³×D₁₃	1	18	yes	—
450	C₄²	C₂³×D₁₃	1	6	yes	—
451	C₁₃	#62652	1	1	yes	characteristic, complemented, Sylow
452	C₂³	—	4	6	no	—
453	C₂³	—	4	6	no	—
454	C₂³	—	13	1	no	—
455	C₂³	—	13	9	no	—
456	C₂³	—	13	36	no	—
457	C₂³	—	13	72	no	—
458	C₂³	—	52	18	no	—
459	C₂³	—	52	18	no	—
460	C₂³	—	52	9	no	—
461	C₂³	—	52	9	no	—
462	C₂³	—	104	48	no	—
463	C₂³	C₂²×C₄×D₁₃	1	24	yes	—
464	C₂³	C₂⁴×D₁₃	1	9	yes	—
465	Q₈	—	13	24	no	—
466	Q₈	C₂²×C₄×D₁₃	1	8	yes	—
467	D₄	—	13	144	no	—
468	D₄	—	13	72	no	—
469	D₄	C₂²×C₄×D₁₃	1	72	yes	—
470	C₂×C₄	—	4	9	no	—
471	C₂×C₄	—	4	18	no	—
472	C₂×C₄	—	4	9	no	—
473	C₂×C₄	—	13	36	no	—
474	C₂×C₄	—	13	6	no	—
475	C₂×C₄	—	13	24	no	—
476	C₂×C₄	—	13	72	no	—
477	C₂×C₄	—	13	6	no	—
478	C₂×C₄	—	13	9	no	—
479	C₂×C₄	—	13	1	no	—
480	C₂×C₄	—	52	36	no	—
481	C₂×C₄	—	52	36	no	—
482	C₂×C₄	—	52	9	no	—
483	C₂×C₄	—	52	18	no	—
484	C₂×C₄	—	52	9	no	—
485	C₂×C₄	C₂²×C₄×D₁₃	1	36	yes	—
486	C₂×C₄	C₂⁴×D₁₃	1	9	yes	—
487	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
488	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
489	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
490	C₂²	—	2	9	no	—
491	C₂²	—	2	9	no	—
492	C₂²	—	4	24	no	—
493	C₂²	—	13	2	no	—
494	C₂²	—	13	18	no	—
495	C₂²	—	26	9	no	—
496	C₂²	—	26	1	no	—
497	C₂²	—	26	9	no	—
498	C₂²	—	26	1	no	—
499	C₂²	—	52	72	no	—
500	C₂²	—	52	36	no	—
501	C₂²	C₂³×C₄×D₁₃	1	18	yes	—
502	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
503	C₄	—	2	1	no	—
504	C₄	—	2	9	no	—
505	C₄	—	2	6	no	—
506	C₄	—	13	12	no	—
507	C₄	—	26	6	no	—
508	C₄	—	26	9	no	—
509	C₄	—	26	1	no	—
510	C₄	C₂³×C₄×D₁₃	1	12	yes	—
511	C₂	—	2	18	no	—
512	C₂	—	26	2	no	—
513	C₂	—	26	18	no	—
514	C₂	C₂⁴×C₄×D₁₃	1	1	yes	characteristic
515	C₂	#13129646	1	1	yes	characteristic
516	C₂	#13129647	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₁₃
commutator	C₂×C₁₃	C₂⁵×C₄
Fitting	C₄×C₁₃×H(5,𝔽₂)	C₂
socle, cosocle	C₂²×C₁₃	C₂⁶
prime radical	C₂×D₁₃×H(5,𝔽₂)	C₂
hypercenter	C₄×H(5,𝔽₂)	D₁₃
hypocenter	C₁₃	#62652
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄×H(5,𝔽₂)

Complements

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

N	H ≅ G/N	type
2. H(5,𝔽₂)×Dic₁₃	C₂	semidirect
3. C₄×#88256	C₂	semidirect
4. #13128042	C₂	semidirect
5. C₄×#88251	C₂	semidirect
6. #13128040	C₂	semidirect
7. #13128036	C₂	semidirect
8. #13128035	C₂	semidirect
9. C₂×#11719250	C₂	semidirect
10. D₁₃×#518	C₂	semidirect
11. C₄×C₁₃×H(5,𝔽₂)	C₂	semidirect
13. D₁₃×H(5,𝔽₂)	C₄	semidirect
18. C₁₃×#520	C₂²	semidirect
19. C₁₃×#518	C₂²	semidirect
20. C₄×C₁₃×#41	C₂²	semidirect
21. C₂×C₄×D₄×C₁₃	C₂²	semidirect
22. #11719532	C₂²	semidirect
23. #41×Dic₁₃	C₂²	semidirect
24. #11719503	C₂²	semidirect
25. C₂×D₄×Dic₁₃	C₂²	semidirect
26. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
27. C₂²×#6103	C₂²	semidirect
28. #11719279	C₂²	semidirect
29. #11719279	C₂²	semidirect
30. C₄×#6131	C₂²	semidirect
31. #11719277	C₂²	semidirect
32. #11719277	C₂²	semidirect
33. #11719251	C₂²	semidirect
34. #11719251	C₂²	semidirect
35. #11719250	C₂²	semidirect
36. #11719250	C₂²	semidirect
37. #11719250	C₂²	semidirect
38. #11719250	C₂²	semidirect
39. #11719250	C₂²	semidirect
40. C₄×D₄×D₁₃	C₂²	semidirect
41. C₄×D₄×D₁₃	C₂²	semidirect
42. C₄×#6129	C₂²	semidirect
43. #11719228	C₂²	semidirect
44. #11719227	C₂²	semidirect
45. #11719226	C₂²	semidirect
46. D₁₃×#117	C₂²	semidirect
47. #11719209	C₂²	semidirect
48. C₂×#88147	C₂²	semidirect
49. C₂×#88146	C₂²	semidirect
50. #11719191	C₂²	semidirect
51. C₂×#88135	C₂²	semidirect
52. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
53. C₄×#6127	C₂²	semidirect
54. C₂×C₄×D₅₂	C₂²	semidirect
55. C₂×#88126	C₂²	semidirect
57. C₁₃×H(5,𝔽₂)	C₂×C₄	semidirect
60. C₂³×C₄×C₁₃	C₂³	semidirect
62. C₂³×Dic₁₃	C₂³	semidirect
63. #88256	C₂×C₄	semidirect
64. #41×D₁₃	C₂×C₄	semidirect
67. #88251	C₂×C₄	semidirect
69. C₂×D₄×D₁₃	C₂×C₄	semidirect
75. C₂²×C₄×D₁₃	C₂³	semidirect
76. C₂²×C₄×D₁₃	C₂³	semidirect
77. C₄×Q₈×C₁₃	C₂³	semidirect
78. C₄×Q₈×C₁₃	C₂³	semidirect
79. C₄×D₄×C₁₃	C₂³	semidirect
80. C₄×D₄×C₁₃	C₂³	semidirect
81. C₄×D₄×C₁₃	C₂³	semidirect
82. C₁₃×#117	C₂³	semidirect
83. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
84. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
85. C₂×C₄²×C₁₃	C₂³	semidirect
86. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
87. Q₈×Dic₁₃	C₂³	semidirect
88. Q₈×Dic₁₃	C₂³	semidirect
89. D₄×Dic₁₃	C₂³	semidirect
90. D₄×Dic₁₃	C₂³	semidirect
91. D₄×Dic₁₃	C₂³	semidirect
92. C₄×C₂²⋊D₁₃	C₂³	semidirect
93. C₄×C₂²⋊D₁₃	C₂³	semidirect
94. C₄×C₂²⋊D₁₃	C₂³	semidirect
98. C₂×#6103	C₂³	semidirect
99. C₂×#6103	C₂³	semidirect
100. #88180	C₂³	semidirect
101. C₂×C₄⋊Dic₁₃	C₂³	semidirect
102. C₂×#6101	C₂³	semidirect
103. C₂×#6101	C₂³	semidirect
104. C₂×C₄×Dic₁₃	C₂³	semidirect
105. C₂×C₄×Dic₁₃	C₂³	semidirect
106. #88147	C₂³	semidirect
107. #88147	C₂³	semidirect
108. #88147	C₂³	semidirect
111. #88146	C₂³	semidirect
112. C₄⋊C₄×D₁₃	C₂³	semidirect
113. C₄⋊C₄×D₁₃	C₂³	semidirect
114. #88141	C₂³	semidirect
115. #88141	C₂³	semidirect
116. #88135	C₂³	semidirect
117. #88135	C₂³	semidirect
118. #88135	C₂³	semidirect
120. C₂²⋊C₄×D₁₃	C₂³	semidirect
121. #88131	C₂³	semidirect
122. C₄×D₅₂	C₂³	semidirect
123. C₄×D₅₂	C₂³	semidirect
124. C₄×D₅₂	C₂³	semidirect
127. #88126	C₂³	semidirect
128. #88126	C₂³	semidirect
129. C₄²×D₁₃	C₂³	semidirect
130. C₄×Dic₂₆	C₂³	semidirect
131. C₄×Dic₂₆	C₂³	semidirect
136. C₂³×D₁₃	C₂²×C₄	semidirect
139. C₁₃×#41	C₂²×C₄	semidirect
141. C₂×D₄×C₁₃	C₂²×C₄	semidirect
148. C₂×C₂²⋊D₁₃	C₂²×C₄	semidirect
155. #6131	C₂²×C₄	semidirect
156. Q₈×D₁₃	C₂²×C₄	semidirect
157. #6129	C₂²×C₄	semidirect
158. D₄×D₁₃	C₂²×C₄	semidirect
159. D₄×D₁₃	C₂²×C₄	semidirect
160. #6127	C₂²×C₄	semidirect
161. C₂×D₅₂	C₂²×C₄	semidirect
165. C₂×C₄×D₁₃	C₂²×C₄	semidirect
200. C₄×H(5,𝔽₂)	D₁₃	semidirect
256. #520	C₂×D₁₃	semidirect
267. #518	C₂×D₁₃	semidirect
273. C₄×#41	C₂×D₁₃	semidirect
281. C₂×C₄×D₄	C₂×D₁₃	semidirect
311. H(5,𝔽₂)	C₄×D₁₃	semidirect
328. C₂³×C₄	C₂²×D₁₃	semidirect
335. C₄×Q₈	C₂²×D₁₃	semidirect
336. C₄×Q₈	C₂²×D₁₃	semidirect
352. C₄×D₄	C₂²×D₁₃	semidirect
353. C₄×D₄	C₂²×D₁₃	semidirect
354. C₄×D₄	C₂²×D₁₃	semidirect
364. #117	C₂²×D₁₃	semidirect
370. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
379. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
383. C₂×C₄²	C₂²×D₁₃	semidirect
399. #41	C₂×C₄×D₁₃	semidirect
409. C₂×D₄	C₂×C₄×D₁₃	semidirect
451. C₁₃	#62652	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₃×H(5,𝔽₂)	2
H(5,𝔽₂)×Dic₁₃	2
C₄×#88256	2
#13128042	2
C₄×#88251	2
#13128040	2
#13128036	2
#13128035	2
C₂×#11719250	2
D₁₃×#518	2
C₄×C₁₃×H(5,𝔽₂)	2
#62652	13