Subgroups — #16797159

Order 3328.

1242 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	C₄×D₁₃⋊M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×#261	C₂	1	2	yes	maximal
3	C₂×C₄×C₄⋊#261	C₂	1	1	yes	maximal, characteristic
4	#13130637	C₂	1	4	yes	maximal, complemented
5	#13130633	C₂	1	2	yes	maximal, complemented
6	#13130629	C₂	1	2	yes	maximal, complemented
7	#13130498	C₂	1	2	yes	maximal
8	D₁₃×#423	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄⋊#261	C₄	1	2	yes	—
10	C₂²×C₄×#261	C₂²	1	2	yes	—
11	C₂×D₁₃⋊M₁₆	C₂²	1	1	yes	characteristic
12	C₂×D₁₃⋊M₁₆	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×D₁₃	C₂²	1	2	yes	—
14	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
15	C₂×(C₂×#261)⋊C₄	C₄	1	2	yes	—
16	C₄×#6122	C₄	1	2	yes	complemented
17	C₄×#6122	C₄	1	2	yes	complemented
18	M₁₆×#261	—	2	8	no	—
19	C₂×#88100	C₂²	1	4	yes	—
20	C₂×C₈×#261	C₂²	1	4	yes	—
21	C₄×C₄⋊#261	C₄	1	2	yes	—
22	C₄×C₄⋊#261	C₄	1	2	yes	—
23	C₄×C₄⋊#261	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊#261	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊#261	C₂²	1	2	yes	—
26	C₄×#6118	C₄	1	2	yes	complemented
27	C₄×#6118	C₄	1	2	yes	complemented
28	#11719047	C₂²	1	2	yes	—
29	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
30	C₁₃×#423	C₄	1	1	yes	characteristic, complemented
31	#11718779	C₄	1	2	yes	complemented
32	#11718585	C₄	1	1	yes	characteristic, complemented
33	#11718498	C₄	1	2	yes	complemented
34	#11718498	C₄	1	2	yes	complemented
35	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
36	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
37	(C₂×#261)⋊C₈	C₂²	1	4	yes	—
38	(C₂×#261)⋊C₈	C₂²	1	4	yes	—
39	C₂³×#261	C₂×C₄	1	4	yes	—
40	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
43	C₂×#6122	C₂×C₄	1	2	yes	—
44	C₂×#6122	C₂×C₄	1	2	yes	—
45	C₂×C₄⋊#261	—	2	8	no	—
46	C₂×C₄⋊#261	C₂×C₄	1	4	yes	—
47	C₂×C₄⋊#261	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊#261	C₂×C₄	1	2	yes	—
49	C₂×C₄×#261	—	2	4	no	—
50	C₂×C₄×#261	—	2	4	no	—
51	C₂×C₄×#261	C₂×C₄	1	4	yes	—
52	C₂×C₄×#261	C₂³	1	2	yes	—
53	C₂×C₄×#261	C₂³	1	2	yes	—
54	D₁₃⋊M₁₆	—	2	2	no	—
55	D₁₃⋊M₁₆	—	2	2	no	—
56	D₁₃⋊M₁₆	D₄	1	4	yes	—
57	D₁₃⋊M₁₆	Q₈	1	4	yes	—
58	C₂×#6118	C₂×C₄	1	2	yes	—
59	C₂×#6118	C₂×C₄	1	2	yes	—
60	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
61	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
62	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
63	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
67	C₂×#6099	C₂×C₄	1	2	yes	—
68	M₁₆×D₁₃	—	2	4	no	—
69	M₁₆×D₁₃	—	2	4	no	—
70	C₂×#6094	C₂×C₄	1	4	yes	—
71	C₂×C₈×D₁₃	C₂³	1	4	yes	—
72	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
73	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
74	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
75	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
76	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
77	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
78	C₄²×D₁₃	C₂³	1	1	yes	characteristic
79	C₄²×D₁₃	C₂³	1	1	yes	characteristic
80	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
81	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
82	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
83	#88110	C₂×C₄	1	4	yes	complemented
84	#88110	C₂×C₄	1	4	yes	complemented
85	C₄×#1057	C₂×C₄	1	4	yes	complemented
86	C₄×#1057	C₂×C₄	1	4	yes	complemented
87	#88100	—	2	8	no	—
88	C₈×#261	—	2	8	no	—
89	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	complemented
90	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	complemented
91	#88054	C₂×C₄	1	4	yes	complemented
92	#88054	C₂×C₄	1	4	yes	complemented
93	C₄⋊#1055	C₂×C₄	1	2	yes	complemented
94	C₄⋊#1055	C₂×C₄	1	2	yes	complemented
95	C₄⋊C₄×M₁₆	—	13	1	no	maximal, Sylow
96	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×#261	—	2	8	no	—
98	C₂²×#261	—	2	8	no	—
99	C₂²×#261	—	4	4	no	—
100	C₂²×#261	C₂²×C₄	1	4	yes	—
101	C₂²×#261	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
106	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
107	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₁₃	—	2	4	no	—
109	C₂×C₄×D₁₃	—	4	2	no	—
110	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
112	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
113	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
114	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
122	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
123	C₂×C₄×D₁₃	#41	1	2	yes	—
124	C₂×C₄×D₁₃	#41	1	2	yes	—
125	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
126	#6122	—	2	4	no	—
127	#6122	C₄⋊C₄	1	8	yes	complemented
128	C₂×#1057	C₂²×C₄	1	4	yes	—
129	C₂×#1057	C₂²×C₄	1	4	yes	—
130	C₄⋊#261	—	2	8	no	—
131	C₄⋊#261	—	2	4	no	—
132	C₄⋊#261	M₁₆	1	8	yes	complemented
133	C₄×#261	—	2	8	no	—
134	C₄×#261	—	2	2	no	—
135	C₄×#261	—	2	2	no	—
136	C₄×#261	—	2	2	no	—
137	C₄×#261	—	2	2	no	—
138	#6118	—	2	4	no	—
139	#6118	C₄⋊C₄	1	8	yes	complemented
140	D₁₃⋊C₈	—	2	2	no	—
141	D₁₃⋊C₈	—	2	2	no	—
142	D₁₃⋊C₈	C₂×D₄	1	4	yes	—
143	D₁₃⋊C₈	C₂×Q₈	1	4	yes	—
144	C₁₃×M₁₆	—	2	4	no	—
145	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
146	C₄²×C₁₃	C₄²	1	1	yes	characteristic
147	C₄²×C₁₃	C₄²	1	1	yes	characteristic
148	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
151	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
152	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
153	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
154	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
155	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
156	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
162	#6099	—	2	4	no	—
163	C₂×#1055	C₂²×C₄	1	4	yes	—
164	#6094	—	2	8	no	—
165	C₈×D₁₃	—	2	4	no	—
166	C₈×D₁₃	—	2	4	no	—
167	C₂×#423	—	13	1	no	—
168	C₂×C₄×M₁₆	—	13	1	no	—
169	C₂×C₄×M₁₆	—	13	2	no	—
170	C₂×C₄×C₄⋊C₄	—	13	1	no	—
171	#1771	—	13	4	no	—
172	#1770	—	13	2	no	—
173	C₈×C₄⋊C₄	—	13	2	no	—
174	#1728	—	13	2	no	—
175	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
176	C₂²×D₁₃	—	2	2	no	—
177	C₂²×D₁₃	—	2	2	no	—
178	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
179	C₂²×D₁₃	C₄×D₄	1	2	yes	—
180	C₂²×D₁₃	C₄×Q₈	1	2	yes	—
181	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
182	C₂×#261	—	2	4	no	—
183	C₂×#261	—	2	4	no	—
184	C₂×#261	—	2	4	no	—
185	C₂×#261	—	2	4	no	—
186	C₂×#261	—	2	4	no	—
187	C₂×#261	—	4	16	no	—
188	C₂×#261	C₂×M₁₆	1	8	yes	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
197	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
198	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
199	C₂×Dic₁₃	—	2	2	no	—
200	C₂×Dic₁₃	—	4	1	no	—
201	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
202	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
203	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
204	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
205	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
206	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
207	C₂×Dic₁₃	#117	1	2	yes	—
208	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
209	C₄×D₁₃	—	2	2	no	—
210	C₄×D₁₃	—	2	2	no	—
211	C₄×D₁₃	—	2	2	no	—
212	C₄×D₁₃	—	2	2	no	—
213	C₄×D₁₃	—	2	2	no	—
214	C₄×D₁₃	—	4	1	no	—
215	C₄×D₁₃	—	4	1	no	—
216	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
217	C₄×D₁₃	#117	1	2	yes	—
218	C₄×D₁₃	C₄×D₄	1	2	yes	—
219	C₄×D₁₃	C₄×D₄	1	2	yes	—
220	C₄×D₁₃	C₄×Q₈	1	2	yes	—
221	C₄×D₁₃	C₄×Q₈	1	2	yes	—
222	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
223	C₄×D₁₃	C₂²×D₄	1	1	yes	characteristic
224	C₄×D₁₃	C₂²×Q₈	1	1	yes	characteristic
225	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
226	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
227	#1057	—	2	4	no	—
228	#1057	C₂×C₄⋊C₄	1	8	yes	complemented
229	C₈×C₁₃	—	2	4	no	—
230	#1055	—	2	4	no	—
231	C₂²×M₁₆	—	13	1	no	—
232	C₂²×M₁₆	—	13	1	no	—
233	C₂²×M₁₆	—	13	2	no	—
234	C₂²×C₄⋊C₄	—	13	2	no	—
235	C₂²×C₄²	—	13	1	no	—
236	C₂²×C₄²	—	13	2	no	—
237	#423	—	13	2	no	—
238	#423	—	13	1	no	—
239	#423	—	13	2	no	—
240	#423	—	13	2	no	—
241	#423	#261	1	1	yes	characteristic, complemented
242	C₂×C₄⋊C₈	—	13	2	no	—
243	C₂×C₄⋊C₈	—	13	2	no	—
244	C₄×M₁₆	—	13	2	no	—
245	C₄×M₁₆	—	13	2	no	—
246	C₄×M₁₆	—	13	2	no	—
247	C₄×M₁₆	—	13	2	no	—
248	C₄×M₁₆	—	26	8	no	—
249	C₂×#97	—	13	2	no	—
250	C₂×#97	—	13	4	no	—
251	C₂×C₄×C₈	—	13	2	no	—
252	C₂×C₄×C₈	—	13	4	no	—
253	C₄×C₄⋊C₄	—	13	2	no	—
254	C₄×C₄⋊C₄	—	13	2	no	—
255	C₄×C₄⋊C₄	—	13	1	no	—
256	C₄×C₄⋊C₄	—	13	1	no	—
257	C₄×C₄⋊C₄	—	13	2	no	—
258	C₂×#95	—	13	2	no	—
259	#336	—	13	4	no	—
260	#336	—	13	4	no	—
261	C₂²×C₁₃	—	2	1	no	—
262	C₂²×C₁₃	—	2	1	no	—
263	C₂²×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
264	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
265	C₂×D₁₃	—	2	1	no	—
266	C₂×D₁₃	—	2	1	no	—
267	C₂×D₁₃	—	2	4	no	—
268	C₂×D₁₃	—	2	4	no	—
269	C₂×D₁₃	C₄×C₄⋊C₄	1	2	yes	—
270	C₂×D₁₃	C₂×C₄×D₄	1	1	yes	characteristic
271	C₂×D₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
272	C₂×D₁₃	C₂²×M₁₆	1	2	yes	—
273	C₂×D₁₃	#568	1	2	yes	—
274	#261	—	2	8	no	—
275	#261	—	4	4	no	—
276	C₄×C₁₃	—	2	1	no	—
277	C₄×C₁₃	—	2	1	no	—
278	C₄×C₁₃	—	2	1	no	—
279	C₄×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
280	C₄×C₁₃	C₄×M₁₆	1	2	yes	complemented
281	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
282	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
283	Dic₁₃	—	2	1	no	—
284	Dic₁₃	—	2	1	no	—
285	Dic₁₃	—	2	1	no	—
286	Dic₁₃	C₄×C₄⋊C₄	1	2	yes	—
287	Dic₁₃	C₄×M₁₆	1	2	yes	complemented
288	Dic₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
289	Dic₁₃	C₂×#117	1	1	yes	characteristic
290	C₂³×C₄	—	13	1	no	—
291	C₂³×C₄	—	13	1	no	—
292	C₂³×C₄	—	13	1	no	—
293	C₂³×C₄	—	13	4	no	—
294	C₂×M₁₆	—	13	2	no	—
295	C₂×M₁₆	—	13	2	no	—
296	C₂×M₁₆	—	13	4	no	—
297	C₂×M₁₆	—	13	4	no	—
298	C₂×M₁₆	—	13	2	no	—
299	C₂×M₁₆	—	13	2	no	—
300	C₂×M₁₆	—	13	2	no	—
301	C₂×M₁₆	—	13	4	no	—
302	C₂×M₁₆	—	26	4	no	—
303	C₂×M₁₆	—	26	4	no	—
304	C₂×M₁₆	—	26	2	no	—
305	C₂×M₁₆	—	26	2	no	—
306	C₂×M₁₆	C₂×#261	1	2	yes	—
307	C₂²×C₈	—	13	2	no	—
308	C₂²×C₈	—	13	2	no	—
309	C₂²×C₈	—	13	4	no	—
310	C₂×C₄⋊C₄	—	13	2	no	—
311	C₂×C₄⋊C₄	—	13	2	no	—
312	C₂×C₄⋊C₄	—	13	4	no	—
313	C₂×C₄⋊C₄	—	26	8	no	—
314	C₂×C₄²	—	13	1	no	—
315	C₂×C₄²	—	13	1	no	—
316	C₂×C₄²	—	13	1	no	—
317	C₂×C₄²	—	13	1	no	—
318	C₂×C₄²	—	13	1	no	—
319	C₂×C₄²	—	13	1	no	—
320	C₂×C₄²	—	13	1	no	—
321	C₂×C₄²	—	13	1	no	—
322	C₂×C₄²	—	13	1	no	—
323	C₂×C₄²	—	13	1	no	—
324	C₂×C₄²	—	13	1	no	—
325	C₂×C₄²	—	13	2	no	—
326	C₂×C₄²	—	13	2	no	—
327	C₂×C₄²	—	13	4	no	—
328	C₂×C₄²	—	26	4	no	—
329	C₂×C₄²	—	26	4	no	—
330	C₂×C₄²	C₂×#261	1	1	yes	characteristic
331	C₄⋊C₈	—	13	4	no	—
332	C₄⋊C₈	—	13	4	no	—
333	C₄⋊C₈	—	13	2	no	—
334	C₄⋊C₈	—	13	2	no	—
335	C₄⋊C₈	C₂×#261	1	2	yes	complemented
336	C₄⋊C₈	C₂×#261	1	2	yes	complemented
337	#97	—	13	4	no	—
338	#97	—	13	4	no	—
339	#97	—	26	8	no	—
340	C₄×C₈	—	13	4	no	—
341	C₄×C₈	—	13	4	no	—
342	C₄×C₈	—	26	8	no	—
343	#95	—	13	2	no	—
344	#95	—	13	4	no	—
345	#95	—	13	2	no	—
346	C₂×C₁₃	—	2	2	no	—
347	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
348	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
349	C₂×C₁₃	#2873	1	1	yes	characteristic
350	D₁₃	—	2	2	no	—
351	D₁₃	D₄×M₁₆	1	2	yes	—
352	D₁₃	Q₈×M₁₆	1	2	yes	—
353	C₂⁴	—	13	1	no	—
354	C₂²×C₄	—	13	1	no	—
355	C₂²×C₄	—	13	1	no	—
356	C₂²×C₄	—	13	1	no	—
357	C₂²×C₄	—	13	1	no	—
358	C₂²×C₄	—	13	2	no	—
359	C₂²×C₄	—	13	2	no	—
360	C₂²×C₄	—	13	2	no	—
361	C₂²×C₄	—	13	2	no	—
362	C₂²×C₄	—	13	1	no	—
363	C₂²×C₄	—	13	1	no	—
364	C₂²×C₄	—	13	4	no	—
365	C₂²×C₄	—	13	1	no	—
366	C₂²×C₄	—	13	1	no	—
367	C₂²×C₄	—	13	1	no	—
368	C₂²×C₄	—	13	1	no	—
369	C₂²×C₄	—	13	1	no	—
370	C₂²×C₄	—	13	1	no	—
371	C₂²×C₄	—	13	1	no	—
372	C₂²×C₄	—	13	1	no	—
373	C₂²×C₄	—	13	1	no	—
374	C₂²×C₄	—	13	4	no	—
375	C₂²×C₄	—	26	4	no	—
376	C₂²×C₄	—	26	8	no	—
377	C₂²×C₄	—	26	8	no	—
378	C₂²×C₄	—	52	2	no	—
379	C₂²×C₄	—	52	4	no	—
380	C₂²×C₄	C₄×#261	1	1	yes	characteristic
381	C₂²×C₄	C₄×#261	1	1	yes	characteristic
382	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
383	M₁₆	—	2	4	no	—
384	M₁₆	—	13	8	no	—
385	M₁₆	—	13	8	no	—
386	M₁₆	—	26	8	no	—
387	M₁₆	—	26	4	no	—
388	M₁₆	—	26	4	no	—
389	M₁₆	—	26	4	no	—
390	C₂×C₈	—	13	4	no	—
391	C₂×C₈	—	13	4	no	—
392	C₂×C₈	—	13	4	no	—
393	C₂×C₈	—	13	4	no	—
394	C₂×C₈	—	13	4	no	—
395	C₂×C₈	—	26	4	no	—
396	C₂×C₈	—	26	4	no	—
397	C₂×C₈	—	26	2	no	—
398	C₂×C₈	—	26	2	no	—
399	C₂×C₈	C₂²×#261	1	4	yes	—
400	C₄⋊C₄	—	13	8	no	—
401	C₄⋊C₄	—	26	4	no	—
402	C₄⋊C₄	—	26	8	no	—
403	C₄²	—	13	1	no	—
404	C₄²	—	13	1	no	—
405	C₄²	—	13	1	no	—
406	C₄²	—	13	1	no	—
407	C₄²	—	13	1	no	—
408	C₄²	—	13	1	no	—
409	C₄²	—	13	1	no	—
410	C₄²	—	13	1	no	—
411	C₄²	—	13	1	no	—
412	C₄²	—	13	1	no	—
413	C₄²	—	13	1	no	—
414	C₄²	—	13	1	no	—
415	C₄²	—	26	2	no	—
416	C₄²	—	26	2	no	—
417	C₄²	—	26	8	no	—
418	C₄²	—	26	2	no	—
419	C₄²	—	26	2	no	—
420	C₄²	C₄×#261	1	1	yes	characteristic
421	C₄²	C₄×#261	1	1	yes	characteristic
422	C₄²	C₂²×#261	1	1	yes	characteristic
423	C₄²	C₂²×#261	1	1	yes	characteristic
424	C₁₃	C₄⋊C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
425	C₂³	—	13	1	no	—
426	C₂³	—	13	2	no	—
427	C₂³	—	13	2	no	—
428	C₂³	—	13	1	no	—
429	C₂³	—	26	2	no	—
430	C₂³	—	26	2	no	—
431	C₂³	C₂×C₄×#261	1	1	yes	characteristic
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	13	2	no	—
435	C₂×C₄	—	13	2	no	—
436	C₂×C₄	—	13	1	no	—
437	C₂×C₄	—	13	1	no	—
438	C₂×C₄	—	13	1	no	—
439	C₂×C₄	—	13	2	no	—
440	C₂×C₄	—	13	2	no	—
441	C₂×C₄	—	13	2	no	—
442	C₂×C₄	—	13	2	no	—
443	C₂×C₄	—	13	4	no	—
444	C₂×C₄	—	13	1	no	—
445	C₂×C₄	—	13	1	no	—
446	C₂×C₄	—	13	2	no	—
447	C₂×C₄	—	13	1	no	—
448	C₂×C₄	—	13	1	no	—
449	C₂×C₄	—	13	2	no	—
450	C₂×C₄	—	13	8	no	—
451	C₂×C₄	—	13	1	no	—
452	C₂×C₄	—	13	1	no	—
453	C₂×C₄	—	13	1	no	—
454	C₂×C₄	—	26	2	no	—
455	C₂×C₄	—	26	2	no	—
456	C₂×C₄	—	26	2	no	—
457	C₂×C₄	—	26	2	no	—
458	C₂×C₄	—	26	2	no	—
459	C₂×C₄	—	26	4	no	—
460	C₂×C₄	—	26	4	no	—
461	C₂×C₄	—	26	2	no	—
462	C₂×C₄	—	26	4	no	—
463	C₂×C₄	—	26	4	no	—
464	C₂×C₄	—	26	4	no	—
465	C₂×C₄	—	52	1	no	—
466	C₂×C₄	—	52	1	no	—
467	C₂×C₄	—	52	1	no	—
468	C₂×C₄	—	52	16	no	—
469	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
470	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
471	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
472	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
473	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
474	C₂×C₄	D₄×#261	1	2	yes	—
475	C₂×C₄	Q₈×#261	1	2	yes	—
476	C₂×C₄	C₂³×#261	1	1	yes	characteristic
477	C₈	—	2	4	no	—
478	C₈	—	13	8	no	—
479	C₈	—	26	4	no	—
480	C₈	—	26	4	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	13	1	no	—
484	C₂²	—	13	1	no	—
485	C₂²	—	13	2	no	—
486	C₂²	—	13	2	no	—
487	C₂²	—	13	2	no	—
488	C₂²	—	26	4	no	—
489	C₂²	—	26	4	no	—
490	C₂²	—	26	1	no	—
491	C₂²	—	26	1	no	—
492	C₂²	C₄⋊C₄×#261	1	2	yes	—
493	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	13	1	no	—
498	C₄	—	13	1	no	—
499	C₄	—	13	2	no	—
500	C₄	—	13	2	no	—
501	C₄	—	26	8	no	—
502	C₄	—	26	1	no	—
503	C₄	—	26	1	no	—
504	C₄	—	26	1	no	—
505	C₄	—	52	4	no	—
506	C₄	C₄⋊C₄×#261	1	2	yes	—
507	C₄	M₁₆×#261	1	2	yes	complemented
508	C₄	C₂×D₄×#261	1	1	yes	characteristic
509	C₄	C₂×Q₈×#261	1	1	yes	characteristic
510	C₂	—	2	2	no	—
511	C₂	—	13	2	no	—
512	C₂	—	13	2	no	—
513	C₂	—	26	2	no	—
514	C₂	C₂×C₄⋊C₄×#261	1	1	yes	characteristic
515	C₂	C₂×M₁₆×#261	1	1	yes	characteristic
516	C₂	#13131399	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#423	C₄
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#423	#261
hypocenter	C₁₃	C₄⋊C₄×M₁₆
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #423

Complements

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

N	H ≅ G/N	type
4. #13130637	C₂	semidirect
5. #13130633	C₂	semidirect
6. #13130629	C₂	semidirect
16. C₄×#6122	C₄	semidirect
17. C₄×#6122	C₄	semidirect
26. C₄×#6118	C₄	semidirect
27. C₄×#6118	C₄	semidirect
30. C₁₃×#423	C₄	semidirect
31. #11718779	C₄	semidirect
32. #11718585	C₄	semidirect
33. #11718498	C₄	semidirect
34. #11718498	C₄	semidirect
83. #88110	C₂×C₄	semidirect
84. #88110	C₂×C₄	semidirect
85. C₄×#1057	C₂×C₄	semidirect
86. C₄×#1057	C₂×C₄	semidirect
89. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
90. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
91. #88054	C₂×C₄	semidirect
92. #88054	C₂×C₄	semidirect
93. C₄⋊#1055	C₂×C₄	semidirect
94. C₄⋊#1055	C₂×C₄	semidirect
127. #6122	C₄⋊C₄	semidirect
132. C₄⋊#261	M₁₆	semidirect
139. #6118	C₄⋊C₄	semidirect
228. #1057	C₂×C₄⋊C₄	semidirect
241. #423	#261	semidirect
280. C₄×C₁₃	C₄×M₁₆	semidirect
287. Dic₁₃	C₄×M₁₆	semidirect
335. C₄⋊C₈	C₂×#261	semidirect
336. C₄⋊C₈	C₂×#261	semidirect
424. C₁₃	C₄⋊C₄×M₁₆	semidirect
507. C₄	M₁₆×#261	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₁₃⋊M₁₆	2
C₂×M₁₆×#261	2
C₂×C₄×C₄⋊#261	2
#13130637	2
#13130633	2
#13130629	2
#13130498	2
D₁₃×#423	2
C₄⋊C₄×M₁₆	13