Subgroups — #16769536

Order 3328.

11674 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88251	C₂	1	1	yes	maximal, characteristic
2	C₄×#88251	C₂	1	16	yes	maximal, complemented
3	#13128040	C₂	1	16	yes	maximal, complemented
4	#13128037	C₂	1	4	yes	maximal, complemented
5	#13128034	C₂	1	8	yes	maximal, complemented
6	C₂×#11719503	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11719191	C₂	1	8	yes	maximal, complemented
8	D₁₃×#518	C₂	1	8	yes	maximal, complemented
9	C₂×C₁₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂³×C₂²⋊D₁₃	C₂²	1	4	yes	—
12	C₂×#88251	C₄	1	32	yes	complemented
13	C₂×#88251	C₂²	1	8	yes	—
14	C₂×#88251	C₂²	1	8	yes	—
15	C₂²×#6129	C₂²	1	4	yes	—
16	C₂²×D₄×D₁₃	C₂²	1	4	yes	—
17	C₂²×#6127	C₂²	1	2	yes	—
18	C₁₃×#518	C₂²	1	8	yes	complemented
19	C₁₃×#518	C₂²	1	8	yes	complemented
20	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
21	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
23	C₂²×C₂²⋊Dic₁₃	C₂²	1	4	yes	complemented
24	#11719503	C₂²	1	8	yes	complemented
25	#11719503	C₂²	1	8	yes	complemented
26	C₂×D₄×Dic₁₃	C₂²	1	8	yes	complemented
27	C₂×C₄×C₂²⋊D₁₃	C₂²	1	32	yes	complemented
28	C₂×#88180	C₂²	1	2	yes	complemented
29	#11719251	C₂²	1	64	yes	complemented
30	#11719250	C₂²	1	64	yes	complemented
31	C₄×D₄×D₁₃	C₂²	1	64	yes	complemented
32	C₄×#6129	C₂²	1	64	yes	complemented
33	#11719228	C₂²	1	16	yes	complemented
34	#11719227	C₂²	1	16	yes	complemented
35	#11719226	C₂²	1	8	yes	complemented
36	D₁₃×#117	C₂²	1	16	yes	complemented
37	#11719221	C₂²	1	8	yes	complemented
38	#11719209	C₂²	1	16	yes	complemented
39	#11719191	C₂²	1	32	yes	complemented
40	#11719191	C₂²	1	16	yes	complemented
41	#11719191	C₂²	1	32	yes	complemented
42	#11719191	C₂²	1	32	yes	complemented
43	C₂×#88135	C₂²	1	32	yes	complemented
44	C₂×C₂²⋊C₄×D₁₃	C₂²	1	16	yes	complemented
45	C₂×#88131	C₂²	1	16	yes	complemented
46	C₄×#6127	C₂²	1	16	yes	complemented
47	C₂⁵×C₁₃	C₂³	1	2	yes	—
48	C₂⁴×D₁₃	C₂³	1	4	yes	—
49	C₂²×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
50	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
51	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
52	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₃	C₂³	1	8	yes	complemented
55	C₂²×C₂²⋊D₁₃	C₂×C₄	1	64	yes	complemented
56	C₂²×C₂²⋊D₁₃	C₂³	1	16	yes	—
57	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
58	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
59	C₂²×C₂²⋊D₁₃	C₂³	1	16	yes	—
60	C₂³×Dic₁₃	C₂³	1	4	yes	—
61	C₂³×Dic₁₃	C₂³	1	8	yes	complemented
62	#88251	C₂×C₄	1	128	yes	complemented
63	#88251	C₂×C₄	1	128	yes	complemented
64	C₂×#6129	C₂×C₄	1	64	yes	complemented
65	C₂×#6129	C₂³	1	32	yes	—
66	C₂×D₄×D₁₃	C₂×C₄	1	64	yes	complemented
67	C₂×D₄×D₁₃	C₂³	1	32	yes	—
68	C₂×#6127	C₂×C₄	1	32	yes	complemented
69	C₂×#6127	C₂³	1	8	yes	—
70	C₂×#6127	C₂³	1	8	yes	—
71	C₂²×D₅₂	C₂³	1	2	yes	—
72	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
73	C₂²×C₄×D₁₃	C₂³	1	32	yes	complemented
74	C₂²×Dic₂₆	C₂³	1	2	yes	—
75	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
76	C₁₃×#117	C₂³	1	8	yes	—
77	C₁₃×#117	C₂³	1	8	yes	complemented
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
79	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
80	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
81	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	complemented
82	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
83	C₂×C₄²×C₁₃	C₂³	1	4	yes	complemented
84	C₂×C₂²⋊Dic₁₃	C₂³	1	16	yes	—
85	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
86	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	complemented
87	C₂×C₂²⋊Dic₁₃	C₂³	1	16	yes	complemented
88	D₄×Dic₁₃	C₂³	1	64	yes	complemented
89	C₄×C₂²⋊D₁₃	C₂³	1	64	yes	complemented
90	C₄×C₂²⋊D₁₃	C₂³	1	128	yes	complemented
91	C₂×#6103	C₂³	1	32	yes	complemented
92	#88180	C₂³	1	8	yes	—
93	#88180	C₂³	1	8	yes	complemented
94	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	complemented
95	C₂×#6101	C₂³	1	32	yes	complemented
96	C₂×C₄×Dic₁₃	C₂³	1	32	yes	complemented
97	C₂×C₄×Dic₁₃	C₂³	1	4	yes	complemented
98	#88147	C₂³	1	32	yes	complemented
99	#88146	C₂³	1	32	yes	complemented
100	C₄⋊C₄×D₁₃	C₂³	1	32	yes	complemented
101	#88141	C₂³	1	32	yes	complemented
102	#88135	C₂³	1	64	yes	complemented
103	#88135	C₂³	1	128	yes	complemented
104	C₂²⋊C₄×D₁₃	C₂³	1	32	yes	—
105	C₂²⋊C₄×D₁₃	C₂³	1	64	yes	complemented
106	#88131	C₂³	1	32	yes	—
107	#88131	C₂³	1	64	yes	complemented
108	C₄×D₅₂	C₂³	1	32	yes	complemented
109	#88126	C₂³	1	32	yes	complemented
110	C₄²×D₁₃	C₂³	1	32	yes	complemented
111	C₄×Dic₂₆	C₂³	1	32	yes	complemented
112	#62652	—	13	1	no	maximal, Sylow
113	C₂⁴×C₁₃	—	8	4	no	—
114	C₂⁴×C₁₃	C₂²×C₄	1	16	yes	complemented
115	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
116	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
117	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
118	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
119	C₂³×D₁₃	—	8	8	no	—
120	C₂³×D₁₃	C₂²×C₄	1	32	yes	complemented
121	C₂³×D₁₃	C₂⁴	1	4	yes	—
122	C₂³×D₁₃	C₂⁴	1	16	yes	—
123	C₂×D₄×C₁₃	C₂²×C₄	1	32	yes	complemented
124	C₂×D₄×C₁₃	C₂²×C₄	1	32	yes	complemented
125	C₂×D₄×C₁₃	C₂²×C₄	1	32	yes	complemented
126	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
127	C₂²×C₄×C₁₃	—	8	8	no	—
128	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	complemented
129	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
130	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
134	C₂×C₂²⋊D₁₃	C₂²×C₄	1	32	yes	complemented
135	C₂×C₂²⋊D₁₃	C₂²×C₄	1	64	yes	complemented
136	C₂×C₂²⋊D₁₃	C₂²×C₄	1	128	yes	complemented
137	C₂×C₂²⋊D₁₃	C₂²×C₄	1	128	yes	complemented
138	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
139	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
140	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
141	C₂²×Dic₁₃	—	8	8	no	—
142	C₂²×Dic₁₃	C₂²×C₄	1	32	yes	complemented
143	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
144	C₂²×Dic₁₃	C₂⁴	1	32	yes	—
145	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
146	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
147	#6129	C₂²×C₄	1	256	yes	complemented
148	D₄×D₁₃	C₂²×C₄	1	256	yes	complemented
149	#6127	C₂²×C₄	1	64	yes	complemented
150	#6127	C₂²×C₄	1	64	yes	complemented
151	C₂×D₅₂	C₂²×C₄	1	16	yes	complemented
152	C₂×D₅₂	C₂⁴	1	8	yes	—
153	C₂×C₄×D₁₃	—	8	32	no	—
154	C₂×C₄×D₁₃	C₂²×C₄	1	32	yes	complemented
155	C₂×C₄×D₁₃	C₂⁴	1	64	yes	—
156	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
157	C₂×Dic₂₆	C₂²×C₄	1	16	yes	complemented
158	C₂×Dic₂₆	C₂⁴	1	8	yes	—
159	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
160	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
161	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
162	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
163	C₄²×C₁₃	C₂⁴	1	16	yes	—
164	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
165	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
166	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
167	#6103	C₂⁴	1	64	yes	—
168	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
169	#6101	C₂⁴	1	64	yes	—
170	C₄×Dic₁₃	C₂⁴	1	64	yes	—
171	C₄×Dic₁₃	C₂⁴	1	16	yes	—
172	C₂²×H(5,𝔽₂)	—	13	1	no	—
173	C₄×H(5,𝔽₂)	—	13	16	no	—
174	C₄×H(5,𝔽₂)	—	13	16	no	—
175	#3428	—	13	8	no	—
176	#3428	—	13	4	no	—
177	C₂×#518	—	13	1	no	—
178	C₂×#518	—	13	8	no	—
179	C₂×#518	—	13	8	no	—
180	C₂×#518	D₁₃	1	1	yes	characteristic, complemented
181	C₂³×C₁₃	—	4	8	no	—
182	C₂³×C₁₃	—	4	8	no	—
183	C₂³×C₁₃	—	4	8	no	—
184	C₂³×C₁₃	—	4	2	no	—
185	C₂³×C₁₃	—	8	16	no	—
186	C₂³×C₁₃	C₂³×C₄	1	16	yes	—
187	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
188	C₂³×C₁₃	C₂³×C₄	1	16	yes	—
189	C₂³×C₁₃	C₂³×C₄	1	16	yes	—
190	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
191	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
192	C₂³×C₁₃	C₂⁵	1	8	yes	—
193	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
194	C₂²×D₁₃	—	4	32	no	—
195	C₂²×D₁₃	—	4	8	no	—
196	C₂²×D₁₃	—	8	32	no	—
197	C₂²×D₁₃	C₂³×C₄	1	16	yes	—
198	C₂²×D₁₃	C₂³×C₄	1	64	yes	—
199	C₂²×D₁₃	C₂⁵	1	8	yes	—
200	D₄×C₁₃	C₂³×C₄	1	64	yes	—
201	C₂×C₄×C₁₃	—	4	32	no	—
202	C₂×C₄×C₁₃	—	4	8	no	—
203	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
204	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
205	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
206	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
207	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
208	C₂²⋊D₁₃	C₂³×C₄	1	32	yes	—
209	C₂²⋊D₁₃	C₂³×C₄	1	32	yes	—
210	C₂²⋊D₁₃	C₂³×C₄	1	128	yes	—
211	C₂×Dic₁₃	—	4	32	no	—
212	C₂×Dic₁₃	—	4	8	no	—
213	C₂×Dic₁₃	C₂³×C₄	1	16	yes	—
214	C₂×Dic₁₃	C₂³×C₄	1	64	yes	—
215	C₂×Dic₁₃	C₂⁵	1	16	yes	—
216	C₂×Dic₁₃	C₂⁵	1	8	yes	—
217	D₅₂	C₂³×C₄	1	32	yes	—
218	C₄×D₁₃	—	4	64	no	—
219	C₄×D₁₃	C₂³×C₄	1	64	yes	—
220	Dic₂₆	C₂³×C₄	1	32	yes	—
221	C₂×H(5,𝔽₂)	—	13	32	no	—
222	C₂×H(5,𝔽₂)	—	13	8	no	—
223	C₂×H(5,𝔽₂)	—	13	8	no	—
224	C₂²×#41	—	13	4	no	—
225	C₂²×#41	—	13	2	no	—
226	C₂³×D₄	—	13	4	no	—
227	C₂³×D₄	—	13	4	no	—
228	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
229	#520	—	13	64	no	—
230	#520	—	13	16	no	—
231	#520	—	13	16	no	—
232	#519	—	13	8	no	—
233	#518	—	13	8	no	—
234	#518	—	13	8	no	—
235	#518	—	13	64	no	—
236	#518	—	13	8	no	—
237	#518	—	13	32	no	—
238	#518	—	13	16	no	—
239	#518	—	13	32	no	—
240	#518	—	13	32	no	—
241	#518	C₂×D₁₃	1	8	yes	complemented
242	#518	C₂×D₁₃	1	8	yes	complemented
243	C₄×#41	—	13	64	no	—
244	C₄×#41	—	13	16	no	—
245	C₄×#41	—	13	16	no	—
246	C₂×C₄×D₄	—	13	8	no	—
247	C₂×C₄×D₄	—	13	32	no	—
248	C₂×C₄×D₄	—	13	64	no	—
249	C₂×C₄×D₄	—	13	32	no	—
250	C₂×C₄×D₄	C₂×D₁₃	1	8	yes	complemented
251	C₂×#117	—	13	2	no	—
252	C₂×#117	—	13	16	no	—
253	C₂×#117	—	13	16	no	—
254	C₂×#117	C₂×D₁₃	1	2	yes	complemented
255	C₂²×C₂²⋊C₄	—	13	4	no	—
256	C₂²×C₂²⋊C₄	—	13	16	no	—
257	C₂²×C₂²⋊C₄	C₂×D₁₃	1	4	yes	complemented
258	C₂²×C₁₃	—	2	2	no	—
259	C₂²×C₁₃	—	2	16	no	—
260	C₂²×C₁₃	—	2	2	no	—
261	C₂²×C₁₃	—	2	2	no	—
262	C₂²×C₁₃	—	4	16	no	—
263	C₂²×C₁₃	—	4	4	no	—
264	C₂²×C₁₃	—	4	16	no	—
265	C₂²×C₁₃	—	4	16	no	—
266	C₂²×C₁₃	C₂⁴×C₄	1	2	yes	—
267	C₂²×C₁₃	C₂⁴×C₄	1	16	yes	—
268	C₂²×C₁₃	C₂⁴×C₄	1	2	yes	—
269	C₂²×C₁₃	C₂⁴×C₄	1	2	yes	—
270	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
271	C₂×D₁₃	—	2	16	no	—
272	C₂×D₁₃	—	4	16	no	—
273	C₂×D₁₃	—	4	64	no	—
274	C₂×D₁₃	C₂⁴×C₄	1	16	yes	—
275	C₄×C₁₃	—	2	16	no	—
276	C₄×C₁₃	C₂⁴×C₄	1	8	yes	—
277	Dic₁₃	—	2	16	no	—
278	Dic₁₃	C₂⁴×C₄	1	16	yes	—
279	C₂⁵	—	13	4	no	—
280	C₂⁵	C₂²×D₁₃	1	2	yes	—
281	H(5,𝔽₂)	—	13	128	no	—
282	H(5,𝔽₂)	—	13	128	no	—
283	C₂×#41	—	13	64	no	—
284	C₂×#41	—	13	32	no	—
285	C₂×#41	—	13	32	no	—
286	C₂×#41	—	13	8	no	—
287	C₂×#41	—	13	8	no	—
288	C₂²×Q₈	—	13	2	no	—
289	C₂²×D₄	—	13	64	no	—
290	C₂²×D₄	—	13	16	no	—
291	C₂²×D₄	—	13	16	no	—
292	C₂²×D₄	—	13	8	no	—
293	C₂²×D₄	—	13	4	no	—
294	C₂²×D₄	—	13	64	no	—
295	C₂²×D₄	—	13	32	no	—
296	C₂²×D₄	—	13	2	no	—
297	C₂²×D₄	C₄×D₁₃	1	16	yes	complemented
298	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
299	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
300	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
301	C₂³×C₄	—	13	4	no	—
302	C₂³×C₄	—	13	4	no	—
303	C₂³×C₄	—	13	8	no	—
304	C₂³×C₄	—	13	32	no	—
305	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
306	C₂³×C₄	C₂²×D₁₃	1	8	yes	complemented
307	C₄×Q₈	—	13	32	no	—
308	C₄×Q₈	—	13	32	no	—
309	C₄×D₄	—	13	64	no	—
310	C₄×D₄	—	13	128	no	—
311	C₄×D₄	—	13	64	no	—
312	C₄×D₄	—	13	32	no	—
313	C₄×D₄	—	13	128	no	—
314	C₄×D₄	—	13	64	no	—
315	C₄×D₄	—	13	32	no	—
316	C₄×D₄	C₂²×D₁₃	1	64	yes	complemented
317	#117	—	13	8	no	—
318	#117	—	13	8	no	—
319	#117	—	13	32	no	—
320	#117	—	13	32	no	—
321	#117	—	13	64	no	—
322	#117	—	13	32	no	—
323	#117	C₂²×D₁₃	1	8	yes	—
324	#117	C₂²×D₁₃	1	8	yes	complemented
325	C₂×C₄⋊C₄	—	13	32	no	—
326	C₂×C₄⋊C₄	—	13	4	no	—
327	C₂×C₄⋊C₄	—	13	32	no	—
328	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	complemented
329	C₂×C₂²⋊C₄	—	13	16	no	—
330	C₂×C₂²⋊C₄	—	13	4	no	—
331	C₂×C₂²⋊C₄	—	13	16	no	—
332	C₂×C₂²⋊C₄	—	13	8	no	—
333	C₂×C₂²⋊C₄	—	13	32	no	—
334	C₂×C₂²⋊C₄	—	13	32	no	—
335	C₂×C₂²⋊C₄	—	13	64	no	—
336	C₂×C₂²⋊C₄	C₂²×D₁₃	1	16	yes	—
337	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
338	C₂×C₂²⋊C₄	C₂²×D₁₃	1	16	yes	complemented
339	C₂×C₂²⋊C₄	C₂²×D₁₃	1	8	yes	complemented
340	C₂×C₄²	—	13	32	no	—
341	C₂×C₄²	—	13	4	no	—
342	C₂×C₄²	—	13	32	no	—
343	C₂×C₄²	C₂²×D₁₃	1	4	yes	complemented
344	C₂×C₁₃	—	2	2	no	—
345	C₂×C₁₃	—	2	16	no	—
346	C₂×C₁₃	—	2	2	no	—
347	C₂×C₁₃	—	2	2	no	—
348	C₂×C₁₃	C₂⁵×C₄	1	1	yes	characteristic
349	C₂×C₁₃	H(7,𝔽₂)	1	2	yes	—
350	D₁₃	—	2	16	no	—
351	C₂⁴	—	8	4	no	—
352	C₂⁴	—	13	4	no	—
353	C₂⁴	—	13	16	no	—
354	C₂⁴	—	13	32	no	—
355	C₂⁴	—	104	8	no	—
356	C₂⁴	C₂×C₄×D₁₃	1	16	yes	complemented
357	C₂⁴	C₂³×D₁₃	1	4	yes	—
358	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
359	C₂⁴	C₂³×D₁₃	1	4	yes	—
360	C₂⁴	C₂³×D₁₃	1	4	yes	—
361	#41	—	13	256	no	—
362	#41	—	13	64	no	—
363	#41	—	13	64	no	—
364	C₂×Q₈	—	13	16	no	—
365	C₂×Q₈	—	13	8	no	—
366	C₂×D₄	—	13	64	no	—
367	C₂×D₄	—	13	32	no	—
368	C₂×D₄	—	13	128	no	—
369	C₂×D₄	—	13	128	no	—
370	C₂×D₄	—	13	8	no	—
371	C₂×D₄	—	13	32	no	—
372	C₂×D₄	—	13	8	no	—
373	C₂×D₄	—	13	256	no	—
374	C₂×D₄	—	13	16	no	—
375	C₂×D₄	—	13	8	no	—
376	C₂×D₄	C₂×C₄×D₁₃	1	32	yes	complemented
377	C₂×D₄	C₂×C₄×D₁₃	1	32	yes	complemented
378	C₂×D₄	C₂×C₄×D₁₃	1	32	yes	complemented
379	C₂×D₄	C₂³×D₁₃	1	16	yes	—
380	C₂²×C₄	—	8	8	no	—
381	C₂²×C₄	—	13	32	no	—
382	C₂²×C₄	—	13	16	no	—
383	C₂²×C₄	—	13	4	no	—
384	C₂²×C₄	—	13	32	no	—
385	C₂²×C₄	—	13	16	no	—
386	C₂²×C₄	—	13	32	no	—
387	C₂²×C₄	—	13	8	no	—
388	C₂²×C₄	—	13	64	no	—
389	C₂²×C₄	—	104	32	no	—
390	C₂²×C₄	—	104	8	no	—
391	C₂²×C₄	C₂×C₄×D₁₃	1	8	yes	complemented
392	C₂²×C₄	C₂³×D₁₃	1	32	yes	—
393	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
394	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
395	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
396	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
397	C₄⋊C₄	—	13	64	no	—
398	C₄⋊C₄	—	13	16	no	—
399	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
400	C₂²⋊C₄	—	13	8	no	—
401	C₂²⋊C₄	—	13	8	no	—
402	C₂²⋊C₄	—	13	32	no	—
403	C₂²⋊C₄	—	13	64	no	—
404	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
405	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	—
406	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
407	C₄²	—	13	64	no	—
408	C₄²	—	13	16	no	—
409	C₄²	C₂³×D₁₃	1	16	yes	—
410	C₁₃	#62652	1	1	yes	characteristic, complemented, Sylow
411	C₂³	—	4	8	no	—
412	C₂³	—	4	8	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	8	no	—
415	C₂³	—	8	16	no	—
416	C₂³	—	13	8	no	—
417	C₂³	—	13	16	no	—
418	C₂³	—	13	64	no	—
419	C₂³	—	52	32	no	—
420	C₂³	—	52	8	no	—
421	C₂³	—	104	32	no	—
422	C₂³	C₂²×C₄×D₁₃	1	16	yes	—
423	C₂³	C₂²×C₄×D₁₃	1	4	yes	—
424	C₂³	C₂²×C₄×D₁₃	1	16	yes	—
425	C₂³	C₂²×C₄×D₁₃	1	16	yes	—
426	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
427	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
428	C₂³	C₂⁴×D₁₃	1	8	yes	—
429	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
430	Q₈	—	13	32	no	—
431	D₄	—	13	128	no	—
432	D₄	—	13	32	no	—
433	D₄	—	13	32	no	—
434	D₄	—	13	32	no	—
435	D₄	C₂²×C₄×D₁₃	1	64	yes	—
436	C₂×C₄	—	4	8	no	—
437	C₂×C₄	—	4	32	no	—
438	C₂×C₄	—	13	16	no	—
439	C₂×C₄	—	13	64	no	—
440	C₂×C₄	—	13	8	no	—
441	C₂×C₄	—	13	64	no	—
442	C₂×C₄	—	13	16	no	—
443	C₂×C₄	—	52	64	no	—
444	C₂×C₄	—	52	32	no	—
445	C₂×C₄	—	52	8	no	—
446	C₂×C₄	C₂²×C₄×D₁₃	1	8	yes	—
447	C₂×C₄	C₂²×C₄×D₁₃	1	8	yes	—
448	C₂×C₄	C₂²×C₄×D₁₃	1	8	yes	—
449	C₂×C₄	C₂⁴×D₁₃	1	16	yes	—
450	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	16	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	16	no	—
457	C₂²	—	4	16	no	—
458	C₂²	—	4	16	no	—
459	C₂²	—	13	16	no	—
460	C₂²	—	26	16	no	—
461	C₂²	—	52	64	no	—
462	C₂²	—	52	16	no	—
463	C₂²	C₂³×C₄×D₁₃	1	2	yes	—
464	C₂²	C₂³×C₄×D₁₃	1	16	yes	—
465	C₂²	C₂³×C₄×D₁₃	1	2	yes	—
466	C₂²	C₂³×C₄×D₁₃	1	2	yes	—
467	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
468	C₄	—	2	16	no	—
469	C₄	—	13	16	no	—
470	C₄	—	26	16	no	—
471	C₄	C₂³×C₄×D₁₃	1	8	yes	—
472	C₂	—	2	2	no	—
473	C₂	—	2	2	no	—
474	C₂	—	2	2	no	—
475	C₂	—	2	16	no	—
476	C₂	—	26	16	no	—
477	C₂	C₂⁴×C₄×D₁₃	1	1	yes	characteristic
478	C₂	#13129646	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₁₃
commutator	C₂×C₁₃	C₂⁵×C₄
Fitting	C₂×C₁₃×#518	C₂
socle, cosocle	C₂²×C₁₃	C₂⁶
prime radical	C₂²×#88251	C₂
hypercenter	C₂×#518	D₁₃
hypocenter	C₁₃	#62652
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×#518

Complements

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

N	H ≅ G/N	type
2. C₄×#88251	C₂	semidirect
3. #13128040	C₂	semidirect
4. #13128037	C₂	semidirect
5. #13128034	C₂	semidirect
6. C₂×#11719503	C₂	semidirect
7. C₂×#11719191	C₂	semidirect
8. D₁₃×#518	C₂	semidirect
9. C₂×C₁₃×#518	C₂	semidirect
12. C₂×#88251	C₄	semidirect
18. C₁₃×#518	C₂²	semidirect
19. C₁₃×#518	C₂²	semidirect
20. C₂×C₄×D₄×C₁₃	C₂²	semidirect
21. C₂×C₁₃×#117	C₂²	semidirect
22. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
23. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
24. #11719503	C₂²	semidirect
25. #11719503	C₂²	semidirect
26. C₂×D₄×Dic₁₃	C₂²	semidirect
27. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
28. C₂×#88180	C₂²	semidirect
29. #11719251	C₂²	semidirect
30. #11719250	C₂²	semidirect
31. C₄×D₄×D₁₃	C₂²	semidirect
32. C₄×#6129	C₂²	semidirect
33. #11719228	C₂²	semidirect
34. #11719227	C₂²	semidirect
35. #11719226	C₂²	semidirect
36. D₁₃×#117	C₂²	semidirect
37. #11719221	C₂²	semidirect
38. #11719209	C₂²	semidirect
39. #11719191	C₂²	semidirect
40. #11719191	C₂²	semidirect
41. #11719191	C₂²	semidirect
42. #11719191	C₂²	semidirect
43. C₂×#88135	C₂²	semidirect
44. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
45. C₂×#88131	C₂²	semidirect
46. C₄×#6127	C₂²	semidirect
49. C₂²×D₄×C₁₃	C₂×C₄	semidirect
54. C₂³×C₄×C₁₃	C₂³	semidirect
55. C₂²×C₂²⋊D₁₃	C₂×C₄	semidirect
61. C₂³×Dic₁₃	C₂³	semidirect
62. #88251	C₂×C₄	semidirect
63. #88251	C₂×C₄	semidirect
64. C₂×#6129	C₂×C₄	semidirect
66. C₂×D₄×D₁₃	C₂×C₄	semidirect
68. C₂×#6127	C₂×C₄	semidirect
73. C₂²×C₄×D₁₃	C₂³	semidirect
75. C₄×D₄×C₁₃	C₂³	semidirect
77. C₁₃×#117	C₂³	semidirect
78. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
81. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
82. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
83. C₂×C₄²×C₁₃	C₂³	semidirect
86. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
87. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
88. D₄×Dic₁₃	C₂³	semidirect
89. C₄×C₂²⋊D₁₃	C₂³	semidirect
90. C₄×C₂²⋊D₁₃	C₂³	semidirect
91. C₂×#6103	C₂³	semidirect
93. #88180	C₂³	semidirect
94. C₂×C₄⋊Dic₁₃	C₂³	semidirect
95. C₂×#6101	C₂³	semidirect
96. C₂×C₄×Dic₁₃	C₂³	semidirect
97. C₂×C₄×Dic₁₃	C₂³	semidirect
98. #88147	C₂³	semidirect
99. #88146	C₂³	semidirect
100. C₄⋊C₄×D₁₃	C₂³	semidirect
101. #88141	C₂³	semidirect
102. #88135	C₂³	semidirect
103. #88135	C₂³	semidirect
105. C₂²⋊C₄×D₁₃	C₂³	semidirect
107. #88131	C₂³	semidirect
108. C₄×D₅₂	C₂³	semidirect
109. #88126	C₂³	semidirect
110. C₄²×D₁₃	C₂³	semidirect
111. C₄×Dic₂₆	C₂³	semidirect
114. C₂⁴×C₁₃	C₂²×C₄	semidirect
120. C₂³×D₁₃	C₂²×C₄	semidirect
123. C₂×D₄×C₁₃	C₂²×C₄	semidirect
124. C₂×D₄×C₁₃	C₂²×C₄	semidirect
125. C₂×D₄×C₁₃	C₂²×C₄	semidirect
128. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
134. C₂×C₂²⋊D₁₃	C₂²×C₄	semidirect
135. C₂×C₂²⋊D₁₃	C₂²×C₄	semidirect
136. C₂×C₂²⋊D₁₃	C₂²×C₄	semidirect
137. C₂×C₂²⋊D₁₃	C₂²×C₄	semidirect
142. C₂²×Dic₁₃	C₂²×C₄	semidirect
147. #6129	C₂²×C₄	semidirect
148. D₄×D₁₃	C₂²×C₄	semidirect
149. #6127	C₂²×C₄	semidirect
150. #6127	C₂²×C₄	semidirect
151. C₂×D₅₂	C₂²×C₄	semidirect
154. C₂×C₄×D₁₃	C₂²×C₄	semidirect
157. C₂×Dic₂₆	C₂²×C₄	semidirect
180. C₂×#518	D₁₃	semidirect
241. #518	C₂×D₁₃	semidirect
242. #518	C₂×D₁₃	semidirect
250. C₂×C₄×D₄	C₂×D₁₃	semidirect
254. C₂×#117	C₂×D₁₃	semidirect
257. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
297. C₂²×D₄	C₄×D₁₃	semidirect
306. C₂³×C₄	C₂²×D₁₃	semidirect
316. C₄×D₄	C₂²×D₁₃	semidirect
324. #117	C₂²×D₁₃	semidirect
328. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
338. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
339. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
343. C₂×C₄²	C₂²×D₁₃	semidirect
356. C₂⁴	C₂×C₄×D₁₃	semidirect
376. C₂×D₄	C₂×C₄×D₁₃	semidirect
377. C₂×D₄	C₂×C₄×D₁₃	semidirect
378. C₂×D₄	C₂×C₄×D₁₃	semidirect
391. C₂²×C₄	C₂×C₄×D₁₃	semidirect
410. C₁₃	#62652	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#88251	2
C₄×#88251	2
#13128040	2
#13128037	2
#13128034	2
C₂×#11719503	2
C₂×#11719191	2
D₁₃×#518	2
C₂×C₁₃×#518	2
#62652	13