Subgroups — M₁₆×#6122 #16792723

Order 3328.

900 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131512	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#6122	C₂	1	1	yes	maximal, characteristic
3	#13130059	C₂	1	4	yes	maximal, complemented
4	#13130045	C₂	1	2	yes	maximal, complemented
5	#13130043	C₂	1	2	yes	maximal, complemented
6	C₈×#6122	C₂	1	2	yes	maximal, complemented
7	M₁₆×#1057	C₂	1	2	yes	maximal, complemented
8	C₂×M₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic
9	C₂²×#6122	C₄	1	2	yes	—
10	C₂²×C₁₃×M₁₆	C₄	1	1	yes	characteristic
11	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
12	C₂²×#6099	C₄	1	1	yes	characteristic
13	#11719169	C₄	1	2	yes	—
14	#11719130	C₄	1	2	yes	—
15	#11719129	C₄	1	2	yes	—
16	#11719128	C₄	1	2	yes	—
17	#11719125	C₂²	1	2	yes	—
18	C₄×#6122	C₄	1	2	yes	—
19	C₄×#6122	C₄	1	2	yes	—
20	C₄×#6122	C₂²	1	1	yes	characteristic
21	C₄×#6122	C₂²	1	1	yes	characteristic
22	C₄×#6122	C₂²	1	2	yes	—
23	C₄×#6122	C₂²	1	2	yes	—
24	C₂×#88110	C₄	1	2	yes	—
25	#11719119	C₂²	1	2	yes	—
26	C₂×C₄×#1057	C₂²	1	2	yes	—
27	M₁₆×Dic₁₃	C₄	1	2	yes	—
28	M₁₆×Dic₁₃	C₄	1	1	yes	characteristic
29	M₁₆×Dic₁₃	C₄	1	1	yes	characteristic
30	M₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
31	M₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
32	M₁₆×Dic₁₃	C₂²	1	2	yes	—
33	C₂×#88055	C₄	1	2	yes	—
34	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
35	#1057⋊C₈	C₂²	1	4	yes	complemented
36	#1057⋊C₈	C₂²	1	4	yes	complemented
37	#11718251	C₂²	1	4	yes	complemented
38	C₈×#1057	C₂²	1	4	yes	complemented
39	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂³×Dic₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂³×Dic₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂×#6122	—	2	8	no	—
43	C₂×#6122	C₂×C₄	1	2	yes	—
44	C₂×#6122	C₂×C₄	1	4	yes	—
45	C₂×#6122	C₂×C₄	1	4	yes	—
46	C₂×#6122	C₂×C₄	1	2	yes	—
47	C₂²×#1057	C₂×C₄	1	4	yes	—
48	C₂×C₁₃×M₁₆	—	2	4	no	—
49	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
51	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
53	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
65	C₂×#6099	—	2	4	no	—
66	C₂×#6099	C₂×C₄	1	1	yes	characteristic
67	C₂×#6099	C₂×C₄	1	2	yes	—
68	C₂×#6099	C₂×C₄	1	1	yes	characteristic
69	C₂²×#1055	C₂×C₄	1	2	yes	—
70	C₂²⋊#1057	C₂×C₄	1	4	yes	—
71	C₂²⋊#1057	C₂×C₄	1	4	yes	—
72	#88112	C₂×C₄	1	4	yes	—
73	#88110	C₂×C₄	1	2	yes	—
74	#88110	C₂×C₄	1	4	yes	—
75	#88110	C₂×C₄	1	2	yes	—
76	#88110	C₂×C₄	1	4	yes	—
77	C₄⋊#1057	C₂×C₄	1	4	yes	—
78	C₄×#1057	C₂×C₄	1	4	yes	—
79	C₄×#1057	C₂³	1	2	yes	—
80	C₄×#1057	C₂³	1	4	yes	—
81	C₄×#1057	C₂³	1	2	yes	—
82	#88055	C₂×C₄	1	2	yes	—
83	#88055	C₂×C₄	1	2	yes	—
84	#88055	C₂×C₄	1	2	yes	—
85	#88055	C₂×C₄	1	2	yes	—
86	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
87	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
88	C₈×Dic₁₃	C₂³	1	2	yes	—
89	C₈×Dic₁₃	C₂³	1	2	yes	—
90	M₁₆²	—	13	1	no	maximal, Sylow
91	C₂⁴×C₁₃	C₄²	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×Dic₁₃	—	2	4	no	—
101	C₂²×Dic₁₃	—	4	2	no	—
102	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
103	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
104	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
105	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
106	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
107	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
108	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
114	#6122	—	2	4	no	—
115	#6122	—	2	8	no	—
116	#6122	—	4	4	no	—
117	#6122	M₁₆	1	8	yes	direct product factor
118	C₂×#1057	—	2	8	no	—
119	C₂×#1057	C₂²×C₄	1	4	yes	—
120	C₂×#1057	C₂²×C₄	1	8	yes	—
121	C₂×#1057	C₂²×C₄	1	4	yes	—
122	C₁₃×M₁₆	—	2	2	no	—
123	C₁₃×M₁₆	—	2	4	no	—
124	C₁₃×M₁₆	M₁₆	1	4	yes	complemented
125	C₂×C₈×C₁₃	—	2	4	no	—
126	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
128	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
129	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
130	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
131	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
132	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
133	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
134	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
144	#6099	—	2	2	no	—
145	#6099	—	2	4	no	—
146	#6099	M₁₆	1	4	yes	complemented
147	C₂×#1055	—	2	4	no	—
148	C₂×#1055	C₂²×C₄	1	2	yes	—
149	C₂×#1055	C₂²×C₄	1	2	yes	—
150	#2920	—	13	1	no	—
151	C₂×C₄×M₁₆	—	13	1	no	—
152	C₂×C₄×M₁₆	—	13	1	no	—
153	#1455	—	13	4	no	—
154	#1451	—	13	2	no	—
155	#1451	—	13	2	no	—
156	C₈×M₁₆	—	13	2	no	—
157	C₈×M₁₆	—	13	2	no	—
158	C₂³×C₁₃	—	2	2	no	—
159	C₂³×C₁₃	—	2	2	no	—
160	C₂³×C₁₃	—	4	1	no	—
161	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
162	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
163	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
175	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
176	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
177	C₂×Dic₁₃	—	2	2	no	—
178	C₂×Dic₁₃	—	2	2	no	—
179	C₂×Dic₁₃	—	2	2	no	—
180	C₂×Dic₁₃	—	2	2	no	—
181	C₂×Dic₁₃	—	2	2	no	—
182	C₂×Dic₁₃	—	2	2	no	—
183	C₂×Dic₁₃	—	2	2	no	—
184	C₂×Dic₁₃	—	2	2	no	—
185	C₂×Dic₁₃	—	4	1	no	—
186	C₂×Dic₁₃	—	4	1	no	—
187	C₂×Dic₁₃	—	4	1	no	—
188	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
189	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
190	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
191	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
192	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
193	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
194	C₂×Dic₁₃	C₂×M₁₆	1	4	yes	—
195	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
196	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
197	#1057	—	2	4	no	—
198	#1057	—	2	8	no	—
199	#1057	C₂×M₁₆	1	8	yes	complemented
200	C₈×C₁₃	—	2	2	no	—
201	C₈×C₁₃	C₂×M₁₆	1	4	yes	complemented
202	#1055	—	2	2	no	—
203	#1055	C₂×M₁₆	1	4	yes	complemented
204	C₂²×M₁₆	—	13	2	no	—
205	C₂²×M₁₆	—	13	1	no	—
206	C₂²×M₁₆	#261	1	1	yes	characteristic
207	C₂²×C₄²	—	13	1	no	—
208	#432	—	13	2	no	—
209	#432	—	13	2	no	—
210	#431	—	13	2	no	—
211	#431	—	13	2	no	—
212	#423	—	13	2	no	—
213	#407	—	13	2	no	—
214	C₄×M₁₆	—	13	1	no	—
215	C₄×M₁₆	—	13	1	no	—
216	C₄×M₁₆	—	13	2	no	—
217	C₄×M₁₆	—	13	2	no	—
218	C₄×M₁₆	—	13	2	no	—
219	C₄×M₁₆	—	13	2	no	—
220	C₄×M₁₆	—	13	1	no	—
221	C₄×M₁₆	—	13	2	no	—
222	C₄×M₁₆	—	13	1	no	—
223	C₄×M₁₆	—	13	1	no	—
224	C₄×M₁₆	—	13	1	no	—
225	C₄×M₁₆	—	13	2	no	—
226	C₂×#97	—	13	2	no	—
227	C₂×#97	—	13	2	no	—
228	C₂×C₄×C₈	—	13	2	no	—
229	C₂×C₄×C₈	—	13	2	no	—
230	#322	—	13	4	no	—
231	#322	—	13	4	no	—
232	#322	—	13	4	no	—
233	C₈²	—	13	4	no	—
234	C₂²×C₁₃	—	2	1	no	—
235	C₂²×C₁₃	—	2	1	no	—
236	C₂²×C₁₃	—	2	1	no	—
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	—	2	1	no	—
239	C₂²×C₁₃	—	2	1	no	—
240	C₂²×C₁₃	—	2	1	no	—
241	C₂²×C₁₃	—	4	4	no	—
242	C₂²×C₁₃	C₄×M₁₆	1	2	yes	—
243	C₂²×C₁₃	C₄×M₁₆	1	2	yes	—
244	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
245	C₄×C₁₃	—	2	1	no	—
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
248	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
249	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
250	Dic₁₃	—	2	1	no	—
251	Dic₁₃	—	2	1	no	—
252	Dic₁₃	—	2	1	no	—
253	Dic₁₃	—	2	1	no	—
254	Dic₁₃	—	2	1	no	—
255	Dic₁₃	C₄×M₁₆	1	2	yes	—
256	Dic₁₃	C₂²×M₁₆	1	2	yes	—
257	Dic₁₃	#568	1	2	yes	—
258	C₂³×C₄	—	13	1	no	—
259	C₂³×C₄	—	13	1	no	—
260	C₂³×C₄	C₂×#261	1	1	yes	characteristic
261	C₂×M₁₆	—	2	4	no	—
262	C₂×M₁₆	—	13	2	no	—
263	C₂×M₁₆	—	13	1	no	—
264	C₂×M₁₆	—	13	4	no	—
265	C₂×M₁₆	—	13	2	no	—
266	C₂×M₁₆	—	13	2	no	—
267	C₂×M₁₆	—	13	1	no	—
268	C₂×M₁₆	—	13	4	no	—
269	C₂×M₁₆	—	26	4	no	—
270	C₂×M₁₆	—	26	8	no	—
271	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
272	C₂×M₁₆	C₂×#261	1	2	yes	—
273	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
274	C₂²×C₈	—	13	4	no	—
275	C₂²×C₈	—	13	2	no	—
276	C₂²×C₈	C₂×#261	1	2	yes	—
277	C₂×C₄²	—	13	1	no	—
278	C₂×C₄²	—	13	1	no	—
279	C₂×C₄²	—	13	1	no	—
280	C₂×C₄²	—	13	1	no	—
281	C₂×C₄²	—	13	1	no	—
282	C₂×C₄²	—	13	1	no	—
283	C₂×C₄²	—	13	1	no	—
284	C₂×C₄²	—	13	1	no	—
285	C₂×C₄²	—	13	1	no	—
286	C₂×C₄²	—	13	1	no	—
287	C₂×C₄²	—	13	1	no	—
288	C₂×C₄²	—	13	1	no	—
289	C₄⋊C₈	—	13	4	no	—
290	C₄⋊C₈	—	13	4	no	—
291	C₂²⋊C₈	—	13	4	no	—
292	C₂²⋊C₈	—	13	4	no	—
293	#97	—	13	2	no	—
294	#97	—	13	4	no	—
295	#97	—	13	2	no	—
296	#97	—	13	4	no	—
297	#97	—	13	2	no	—
298	#97	—	13	2	no	—
299	#97	—	13	2	no	—
300	#97	—	13	2	no	—
301	C₄×C₈	—	13	4	no	—
302	C₄×C₈	—	13	2	no	—
303	C₄×C₈	—	13	4	no	—
304	C₄×C₈	—	13	2	no	—
305	C₄×C₈	—	13	2	no	—
306	C₄×C₈	—	13	2	no	—
307	C₄×C₈	—	13	2	no	—
308	C₄×C₈	—	13	2	no	—
309	C₂×C₁₃	—	2	2	no	—
310	C₂×C₁₃	—	2	2	no	—
311	C₂×C₁₃	—	4	1	no	—
312	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
313	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
314	C₂×C₁₃	#2873	1	1	yes	characteristic
315	C₂⁴	C₄×#261	1	1	yes	characteristic
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	13	1	no	—
319	C₂²×C₄	—	13	1	no	—
320	C₂²×C₄	—	13	1	no	—
321	C₂²×C₄	—	13	1	no	—
322	C₂²×C₄	—	13	1	no	—
323	C₂²×C₄	—	13	1	no	—
324	C₂²×C₄	—	13	1	no	—
325	C₂²×C₄	—	13	1	no	—
326	C₂²×C₄	—	13	1	no	—
327	C₂²×C₄	—	13	1	no	—
328	C₂²×C₄	—	13	1	no	—
329	C₂²×C₄	—	13	1	no	—
330	C₂²×C₄	—	26	4	no	—
331	C₂²×C₄	—	52	2	no	—
332	C₂²×C₄	C₄×#261	1	1	yes	characteristic
333	C₂²×C₄	C₄×#261	1	1	yes	characteristic
334	C₂²×C₄	C₄×#261	1	1	yes	characteristic
335	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
336	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
337	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
338	M₁₆	—	2	2	no	—
339	M₁₆	—	2	4	no	—
340	M₁₆	—	13	8	no	—
341	M₁₆	—	13	4	no	—
342	M₁₆	—	26	4	no	—
343	M₁₆	—	26	8	no	—
344	M₁₆	—	26	4	no	—
345	M₁₆	—	26	2	no	—
346	M₁₆	—	52	4	no	—
347	M₁₆	#6122	1	4	yes	direct product factor
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	—	13	4	no	—
350	C₂×C₈	—	13	2	no	—
351	C₂×C₈	—	13	4	no	—
352	C₂×C₈	—	13	8	no	—
353	C₂×C₈	—	13	2	no	—
354	C₂×C₈	—	26	4	no	—
355	C₂×C₈	—	26	8	no	—
356	C₂×C₈	C₂²×#261	1	2	yes	—
357	C₂×C₈	C₂²×#261	1	2	yes	—
358	C₄²	—	13	1	no	—
359	C₄²	—	13	1	no	—
360	C₄²	—	13	1	no	—
361	C₄²	—	13	1	no	—
362	C₄²	—	13	1	no	—
363	C₄²	—	13	1	no	—
364	C₄²	—	13	1	no	—
365	C₄²	—	13	1	no	—
366	C₄²	—	13	1	no	—
367	C₄²	—	13	1	no	—
368	C₄²	—	13	1	no	—
369	C₄²	—	13	1	no	—
370	C₄²	—	13	1	no	—
371	C₄²	—	13	1	no	—
372	C₄²	—	13	1	no	—
373	C₄²	—	13	1	no	—
374	C₁₃	M₁₆²	1	1	yes	characteristic, complemented, Sylow
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	4	1	no	—
378	C₂³	C₂×C₄×#261	1	1	yes	characteristic
379	C₂³	C₂×C₄×#261	1	1	yes	characteristic
380	C₂³	C₂×C₄×#261	1	1	yes	characteristic
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	13	4	no	—
389	C₂×C₄	—	13	1	no	—
390	C₂×C₄	—	13	1	no	—
391	C₂×C₄	—	13	1	no	—
392	C₂×C₄	—	13	1	no	—
393	C₂×C₄	—	13	1	no	—
394	C₂×C₄	—	13	1	no	—
395	C₂×C₄	—	13	1	no	—
396	C₂×C₄	—	13	1	no	—
397	C₂×C₄	—	26	2	no	—
398	C₂×C₄	—	26	2	no	—
399	C₂×C₄	—	26	2	no	—
400	C₂×C₄	—	26	2	no	—
401	C₂×C₄	—	26	2	no	—
402	C₂×C₄	—	26	2	no	—
403	C₂×C₄	—	26	2	no	—
404	C₂×C₄	—	26	2	no	—
405	C₂×C₄	—	52	1	no	—
406	C₂×C₄	—	52	1	no	—
407	C₂×C₄	—	52	1	no	—
408	C₂×C₄	D₁₃⋊M₁₆	1	2	yes	—
409	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
410	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
411	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
412	C₂×C₄	C₂×#6122	1	2	yes	—
413	C₂×C₄	C₂³×#261	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	13	8	no	—
416	C₈	—	13	4	no	—
417	C₈	—	26	4	no	—
418	C₈	—	26	8	no	—
419	C₈	—	26	2	no	—
420	C₈	C₂×#6122	1	4	yes	complemented
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	4	4	no	—
429	C₂²	M₁₆×#261	1	2	yes	—
430	C₂²	C₄×#6122	1	2	yes	—
431	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	13	2	no	—
435	C₄	—	13	2	no	—
436	C₄	—	13	2	no	—
437	C₄	—	26	1	no	—
438	C₄	—	26	1	no	—
439	C₄	—	26	1	no	—
440	C₄	—	26	1	no	—
441	C₄	—	26	1	no	—
442	C₄	C₄×#6122	1	2	yes	—
443	C₄	C₂×D₁₃⋊M₁₆	1	1	yes	characteristic
444	C₄	C₂²×#6122	1	1	yes	characteristic
445	C₂	—	2	2	no	—
446	C₂	—	2	2	no	—
447	C₂	—	4	1	no	—
448	C₂	C₂×M₁₆×#261	1	1	yes	characteristic
449	C₂	C₂×C₄×#6122	1	1	yes	characteristic
450	C₂	#13131399	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₂²×C₁₃×M₁₆	C₄
prime radical	C₂⁴×C₁₃	C₄²
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	C₂²×M₁₆	#261
hypocenter	C₁₃	M₁₆²
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×M₁₆

Complements

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

N	H ≅ G/N	type
3. #13130059	C₂	semidirect
4. #13130045	C₂	semidirect
5. #13130043	C₂	semidirect
6. C₈×#6122	C₂	semidirect
7. M₁₆×#1057	C₂	semidirect
35. #1057⋊C₈	C₂²	semidirect
36. #1057⋊C₈	C₂²	semidirect
37. #11718251	C₂²	semidirect
38. C₈×#1057	C₂²	semidirect
117. #6122	M₁₆	direct (N × H)
124. C₁₃×M₁₆	M₁₆	semidirect
146. #6099	M₁₆	semidirect
199. #1057	C₂×M₁₆	semidirect
201. C₈×C₁₃	C₂×M₁₆	semidirect
203. #1055	C₂×M₁₆	semidirect
347. M₁₆	#6122	direct (N × H)
374. C₁₃	M₁₆²	semidirect
420. C₈	C₂×#6122	semidirect

Maximal subgroups

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

subgroup	index
#13131512	2
C₂×C₄×#6122	2
#13130059	2
#13130045	2
#13130043	2
C₈×#6122	2
M₁₆×#1057	2
C₂×M₁₆×Dic₁₃	2
M₁₆²	13

Subgroups — M16×#6122 #16792723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×#6122 #16792723