Subgroups — M₁₆×#6099 #15828629

Order 3328.

900 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123469	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#6099	C₂	1	1	yes	maximal, characteristic
3	#13113139	C₂	1	4	yes	maximal, complemented
4	#13113125	C₂	1	2	yes	maximal, complemented
5	#13113123	C₂	1	2	yes	maximal, complemented
6	C₈×#6099	C₂	1	2	yes	maximal, complemented
7	M₁₆×#1055	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₁₃×M₁₆	C₄	1	2	yes	—
10	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×#6099	C₄	1	2	yes	—
12	C₄×C₁₃×M₁₆	C₄	1	2	yes	—
13	C₄×C₁₃×M₁₆	C₄	1	2	yes	—
14	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
15	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
16	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
17	C₂×C₁₃×#97	C₄	1	2	yes	—
18	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
19	#11718868	C₄	1	2	yes	—
20	#11718587	C₄	1	2	yes	—
21	#11718587	C₄	1	2	yes	—
22	#11718586	C₂²	1	2	yes	—
23	#11718586	C₂²	1	2	yes	—
24	#11718585	C₄	1	2	yes	—
25	C₄×#6099	C₄	1	2	yes	—
26	C₄×#6099	C₄	1	2	yes	—
27	C₄×#6099	C₂²	1	1	yes	characteristic
28	C₄×#6099	C₂²	1	1	yes	characteristic
29	C₄×#6099	C₂²	1	2	yes	—
30	C₄×#6099	C₂²	1	2	yes	—
31	C₂×#88043	C₄	1	2	yes	—
32	C₂×C₄×#1055	C₂²	1	2	yes	—
33	#11718047	C₂²	1	4	yes	complemented
34	#11718046	C₂²	1	4	yes	complemented
35	#11718046	C₂²	1	4	yes	complemented
36	C₈×#1055	C₂²	1	4	yes	complemented
37	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₁₃×M₁₆	—	2	8	no	—
41	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
42	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
43	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
44	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
45	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
57	C₂×#6099	—	2	8	no	—
58	C₂×#6099	C₂×C₄	1	2	yes	—
59	C₂×#6099	C₂×C₄	1	4	yes	—
60	C₂×#6099	C₂×C₄	1	4	yes	—
61	C₂×#6099	C₂×C₄	1	2	yes	—
62	C₂²×#1055	C₂×C₄	1	4	yes	—
63	C₁₃×#97	C₂×C₄	1	2	yes	—
64	C₁₃×#97	C₂×C₄	1	4	yes	—
65	C₁₃×#97	C₂×C₄	1	2	yes	—
66	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
67	C₄×C₈×C₁₃	C₂³	1	2	yes	—
68	C₄×C₈×C₁₃	C₂³	1	2	yes	—
69	C₂²⋊#1055	C₂×C₄	1	4	yes	—
70	C₂²⋊#1055	C₂×C₄	1	4	yes	—
71	C₄⋊#1055	C₂×C₄	1	4	yes	—
72	C₄⋊#1055	C₂×C₄	1	4	yes	—
73	#88043	C₂×C₄	1	2	yes	—
74	#88043	C₂×C₄	1	4	yes	—
75	#88043	C₂×C₄	1	2	yes	—
76	#88043	C₂×C₄	1	4	yes	—
77	C₄×#1055	C₂×C₄	1	4	yes	—
78	C₄×#1055	C₂³	1	2	yes	—
79	C₄×#1055	C₂³	1	4	yes	—
80	C₄×#1055	C₂³	1	2	yes	—
81	M₁₆²	—	13	1	no	maximal, Sylow
82	C₂⁴×C₁₃	C₄²	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	—	2	4	no	—
84	C₂²×C₄×C₁₃	—	2	4	no	—
85	C₂²×C₄×C₁₃	—	4	2	no	—
86	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂²×C₄	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×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₁₃×M₁₆	—	2	4	no	—
105	C₁₃×M₁₆	—	2	8	no	—
106	C₁₃×M₁₆	M₁₆	1	8	yes	complemented
107	C₂×C₈×C₁₃	—	2	8	no	—
108	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
109	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
110	C₄²×C₁₃	C₄²	1	1	yes	characteristic
111	C₄²×C₁₃	C₄²	1	1	yes	characteristic
112	C₄²×C₁₃	C₄²	1	1	yes	characteristic
113	C₄²×C₁₃	C₄²	1	1	yes	characteristic
114	C₄²×C₁₃	C₄²	1	1	yes	characteristic
115	C₄²×C₁₃	C₄²	1	1	yes	characteristic
116	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
126	#6099	—	2	4	no	—
127	#6099	—	2	8	no	—
128	#6099	—	4	4	no	—
129	#6099	M₁₆	1	8	yes	direct product factor
130	C₂×#1055	—	2	8	no	—
131	C₂×#1055	C₂²×C₄	1	8	yes	—
132	C₂×#1055	C₂²×C₄	1	4	yes	—
133	C₂×#1055	C₂²×C₄	1	4	yes	—
134	#2920	—	13	1	no	—
135	C₂×C₄×M₁₆	—	13	1	no	—
136	C₂×C₄×M₁₆	D₁₃	1	1	yes	characteristic
137	#1455	—	13	4	no	—
138	#1451	—	13	2	no	—
139	#1451	—	13	2	no	—
140	C₈×M₁₆	—	13	2	no	—
141	C₈×M₁₆	—	13	2	no	—
142	C₂³×C₁₃	—	2	2	no	—
143	C₂³×C₁₃	—	2	2	no	—
144	C₂³×C₁₃	—	4	1	no	—
145	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
146	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
147	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	4	1	no	—
162	C₂×C₄×C₁₃	—	4	1	no	—
163	C₂×C₄×C₁₃	—	4	1	no	—
164	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
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×M₁₆	1	4	yes	—
174	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
175	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
178	C₈×C₁₃	—	2	4	no	—
179	C₈×C₁₃	C₂×M₁₆	1	8	yes	complemented
180	#1055	—	2	4	no	—
181	#1055	—	2	8	no	—
182	#1055	C₂×M₁₆	1	8	yes	complemented
183	C₂²×M₁₆	—	13	2	no	—
184	C₂²×M₁₆	Dic₁₃	1	2	yes	—
185	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
186	#432	—	13	2	no	—
187	#432	—	13	2	no	—
188	#431	—	13	2	no	—
189	#431	—	13	2	no	—
190	#423	—	13	2	no	—
191	#407	—	13	2	no	—
192	C₄×M₁₆	—	13	2	no	—
193	C₄×M₁₆	—	13	2	no	—
194	C₄×M₁₆	—	13	1	no	—
195	C₄×M₁₆	—	13	1	no	—
196	C₄×M₁₆	—	13	2	no	—
197	C₄×M₁₆	—	13	2	no	—
198	C₄×M₁₆	Dic₁₃	1	2	yes	—
199	C₄×M₁₆	Dic₁₃	1	2	yes	—
200	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
201	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
202	C₄×M₁₆	C₂×D₁₃	1	2	yes	—
203	C₂×#97	—	13	2	no	—
204	C₂×#97	Dic₁₃	1	2	yes	—
205	C₂×C₄×C₈	—	13	2	no	—
206	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
207	#322	—	13	4	no	—
208	#322	—	13	4	no	—
209	#322	—	13	4	no	—
210	C₈²	—	13	4	no	—
211	C₂²×C₁₃	—	2	1	no	—
212	C₂²×C₁₃	—	2	1	no	—
213	C₂²×C₁₃	—	2	1	no	—
214	C₂²×C₁₃	—	2	1	no	—
215	C₂²×C₁₃	—	2	1	no	—
216	C₂²×C₁₃	—	2	1	no	—
217	C₂²×C₁₃	—	2	1	no	—
218	C₂²×C₁₃	—	4	4	no	—
219	C₂²×C₁₃	C₄×M₁₆	1	2	yes	—
220	C₂²×C₁₃	C₄×M₁₆	1	2	yes	—
221	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
222	C₄×C₁₃	—	2	1	no	—
223	C₄×C₁₃	—	2	1	no	—
224	C₄×C₁₃	—	2	1	no	—
225	C₄×C₁₃	—	2	1	no	—
226	C₄×C₁₃	—	2	1	no	—
227	C₄×C₁₃	—	2	1	no	—
228	C₄×C₁₃	—	2	1	no	—
229	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
230	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
231	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
232	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
233	C₄×C₁₃	#568	1	2	yes	—
234	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
235	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
236	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
237	C₂×M₁₆	—	2	8	no	—
238	C₂×M₁₆	—	13	2	no	—
239	C₂×M₁₆	—	13	4	no	—
240	C₂×M₁₆	—	13	2	no	—
241	C₂×M₁₆	—	13	4	no	—
242	C₂×M₁₆	—	26	8	no	—
243	C₂×M₁₆	C₂×Dic₁₃	1	2	yes	—
244	C₂×M₁₆	C₂×Dic₁₃	1	4	yes	—
245	C₂×M₁₆	C₂×Dic₁₃	1	2	yes	—
246	C₂²×C₈	—	13	4	no	—
247	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
248	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
249	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
250	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
251	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
252	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
253	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
254	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
255	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
256	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
257	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
258	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
259	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
260	C₄⋊C₈	—	13	4	no	—
261	C₄⋊C₈	—	13	4	no	—
262	C₂²⋊C₈	—	13	4	no	—
263	C₂²⋊C₈	—	13	4	no	—
264	#97	—	13	2	no	—
265	#97	—	13	4	no	—
266	#97	—	13	2	no	—
267	#97	—	13	4	no	—
268	#97	C₂×Dic₁₃	1	2	yes	—
269	#97	C₂×Dic₁₃	1	4	yes	—
270	#97	C₂×Dic₁₃	1	2	yes	—
271	C₄×C₈	—	13	4	no	—
272	C₄×C₈	—	13	2	no	—
273	C₄×C₈	—	13	4	no	—
274	C₄×C₈	—	13	2	no	—
275	C₄×C₈	C₂×Dic₁₃	1	4	yes	—
276	C₄×C₈	C₂²×D₁₃	1	2	yes	—
277	C₄×C₈	C₂²×D₁₃	1	2	yes	—
278	C₂×C₁₃	—	2	2	no	—
279	C₂×C₁₃	—	2	2	no	—
280	C₂×C₁₃	—	4	1	no	—
281	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
282	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
283	C₂×C₁₃	#2873	1	1	yes	characteristic
284	C₂⁴	C₄×Dic₁₃	1	1	yes	characteristic
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
289	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
290	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
291	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
292	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
293	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
294	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
295	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
296	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
303	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
304	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
305	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
306	M₁₆	—	2	4	no	—
307	M₁₆	—	2	8	no	—
308	M₁₆	—	13	8	no	—
309	M₁₆	—	26	8	no	—
310	M₁₆	—	26	4	no	—
311	M₁₆	—	52	4	no	—
312	M₁₆	#6099	1	8	yes	direct product factor
313	C₂×C₈	—	2	8	no	—
314	C₂×C₈	—	13	4	no	—
315	C₂×C₈	—	13	4	no	—
316	C₂×C₈	—	13	8	no	—
317	C₂×C₈	—	26	8	no	—
318	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
319	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
320	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
321	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
322	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
323	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
324	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
325	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
326	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
327	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
328	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
329	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
330	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
331	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
332	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
333	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
334	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
335	C₄²	C₂³×D₁₃	1	1	yes	characteristic
336	C₁₃	M₁₆²	1	1	yes	characteristic, complemented, Sylow
337	C₂³	—	2	2	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	4	1	no	—
340	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
341	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
342	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	M₁₆×D₁₃	1	4	yes	—
360	C₂×C₄	C₂×#6099	1	4	yes	—
361	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
362	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
364	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
365	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
366	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
367	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
368	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
369	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
371	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
372	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
373	C₈	—	2	4	no	—
374	C₈	—	13	8	no	—
375	C₈	—	26	4	no	—
376	C₈	—	26	8	no	—
377	C₈	C₂×#6099	1	8	yes	complemented
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	4	4	no	—
386	C₂²	C₄×#6099	1	2	yes	—
387	C₂²	M₁₆×Dic₁₃	1	2	yes	—
388	C₂²	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	C₄×#6099	1	2	yes	—
397	C₄	M₁₆×Dic₁₃	1	2	yes	—
398	C₄	C₂×M₁₆×D₁₃	1	2	yes	—
399	C₄	#11719450	1	2	yes	—
400	C₄	C₂²×#6099	1	2	yes	—
401	C₂	—	2	2	no	—
402	C₂	—	2	2	no	—
403	C₂	—	4	1	no	—
404	C₂	C₂×M₁₆×Dic₁₃	1	1	yes	characteristic
405	C₂	C₂×C₄×#6099	1	1	yes	characteristic
406	C₂	#13123254	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₂×C₄×C₁₃×M₁₆	C₂
prime radical	C₂⁴×C₁₃	C₄²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₂×C₄×M₁₆	D₁₃
hypocenter	C₁₃	M₁₆²
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #13113139	C₂	semidirect
4. #13113125	C₂	semidirect
5. #13113123	C₂	semidirect
6. C₈×#6099	C₂	semidirect
7. M₁₆×#1055	C₂	semidirect
33. #11718047	C₂²	semidirect
34. #11718046	C₂²	semidirect
35. #11718046	C₂²	semidirect
36. C₈×#1055	C₂²	semidirect
106. C₁₃×M₁₆	M₁₆	semidirect
129. #6099	M₁₆	direct (N × H)
179. C₈×C₁₃	C₂×M₁₆	semidirect
182. #1055	C₂×M₁₆	semidirect
312. M₁₆	#6099	direct (N × H)
336. C₁₃	M₁₆²	semidirect
377. C₈	C₂×#6099	semidirect

Maximal subgroups

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

subgroup	index
#13123469	2
C₂×C₄×#6099	2
#13113139	2
#13113125	2
#13113123	2
C₈×#6099	2
M₁₆×#1055	2
C₂×C₄×C₁₃×M₁₆	2
M₁₆²	13

Subgroups — M16×#6099 #15828629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×#6099 #15828629