Subgroups — M₁₆×#6106 #15834359

Order 3328.

716 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#6106	C₂	1	1	yes	maximal, characteristic
2	M₁₆×D₅₂	C₂	1	1	yes	maximal, characteristic
3	#13113726	C₂	1	2	yes	maximal, complemented
4	#13113679	C₂	1	2	yes	maximal, complemented
5	#13113670	C₂	1	2	yes	maximal, complemented
6	C₈×#6106	C₂	1	2	yes	maximal, complemented
7	#13113591	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113265	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113260	C₂	1	1	yes	maximal, characteristic
10	M₁₆×#1055	C₂	1	1	yes	maximal, characteristic, complemented
11	Q₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×#6106	C₄	1	1	yes	characteristic
14	C₂×M₁₆×D₁₃	—	2	1	no	—
15	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
16	C₁₃×#446	—	2	2	no	—
17	C₁₃×#446	C₂²	1	2	yes	complemented
18	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
19	C₁₃×#423	—	2	1	no	—
20	C₁₃×#423	C₂²	1	1	yes	characteristic
21	C₄×C₁₃×M₁₆	—	2	1	no	—
22	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
23	C₂×#88075	C₄	1	1	yes	characteristic
24	#11718787	—	2	1	no	—
25	C₄×#6106	C₄	1	1	yes	characteristic
26	C₄×#6106	C₄	1	1	yes	characteristic
27	C₄×#6106	C₄	1	1	yes	characteristic
28	C₄×#6106	C₄	1	1	yes	characteristic
29	C₄×#6106	C₂²	1	1	yes	characteristic
30	C₄×#6106	C₂²	1	1	yes	characteristic
31	C₄×#6106	C₂²	1	1	yes	characteristic
32	C₄×#6106	C₂²	1	1	yes	characteristic
33	C₂×#88049	C₄	1	1	yes	characteristic
34	C₂×#88048	C₄	1	1	yes	characteristic
35	#11718586	C₂²	1	1	yes	characteristic
36	#11718585	C₂²	1	1	yes	characteristic
37	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
38	#11718367	—	2	2	no	—
39	#11718349	C₂²	1	2	yes	—
40	C₈×D₅₂	C₂²	1	2	yes	—
41	Q₈⋊#1055	C₂²	1	2	yes	complemented
42	Q₈⋊#1055	C₂²	1	2	yes	complemented
43	#11718075	C₂²	1	2	yes	—
44	#11718075	C₂²	1	2	yes	—
45	#11718072	C₂²	1	2	yes	complemented
46	#11718072	C₂²	1	2	yes	complemented
47	#11718047	C₂²	1	2	yes	complemented
48	C₈×#1055	C₂²	1	2	yes	complemented
49	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₄×D₁₃	—	2	1	no	—
52	C₂×C₁₃×M₁₆	—	2	1	no	—
53	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
54	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
55	C₄×Q₈×C₁₃	—	2	1	no	—
56	C₄×Q₈×C₁₃	—	2	1	no	—
57	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
58	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	—	2	1	no	—
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×#6106	—	2	4	no	—
66	C₂×#6106	C₂×C₄	1	1	yes	characteristic
67	C₂×#6106	C₂×C₄	1	1	yes	characteristic
68	C₂×#6106	C₂×C₄	1	1	yes	characteristic
69	C₂×#6106	C₂×C₄	1	1	yes	characteristic
70	C₂×#6103	—	2	1	no	—
71	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
72	C₂×#6099	—	2	1	no	—
73	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
74	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
75	M₁₆×D₁₃	—	4	4	no	—
76	C₂×#6094	—	2	2	no	—
77	C₂×C₈×D₁₃	—	2	2	no	—
78	C₄×D₅₂	—	2	1	no	—
79	C₄×D₅₂	—	2	1	no	—
80	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
81	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
82	C₄×D₅₂	C₂³	1	1	yes	characteristic
83	C₄×D₅₂	C₂³	1	1	yes	characteristic
84	C₁₃×C₄⋊C₈	—	2	2	no	—
85	C₁₃×C₄⋊C₈	—	2	2	no	—
86	C₁₃×C₄⋊C₈	—	2	1	no	—
87	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
88	C₁₃×#97	—	2	2	no	—
89	C₁₃×#97	D₄	1	2	yes	—
90	C₄×C₈×C₁₃	—	2	2	no	—
91	C₄×C₈×C₁₃	C₂³	1	2	yes	—
92	#88075	C₂×C₄	1	1	yes	characteristic
93	#88075	C₂×C₄	1	1	yes	characteristic
94	#88075	C₂×C₄	1	1	yes	characteristic
95	#88075	C₂×C₄	1	1	yes	characteristic
96	C₂²⋊#1055	—	2	1	no	—
97	#88060	—	2	2	no	—
98	#88060	—	2	2	no	—
99	#88049	C₂×C₄	1	1	yes	characteristic
100	#88049	C₂×C₄	1	1	yes	characteristic
101	#88049	C₂×C₄	1	1	yes	characteristic
102	#88049	C₂×C₄	1	1	yes	characteristic
103	#88048	C₂×C₄	1	1	yes	characteristic
104	#88048	C₂×C₄	1	1	yes	characteristic
105	#88048	C₂×C₄	1	1	yes	characteristic
106	#88048	C₂×C₄	1	1	yes	characteristic
107	C₄⋊#1055	—	2	1	no	—
108	C₄⋊#1055	—	2	1	no	—
109	C₄⋊#1055	C₂³	1	2	yes	—
110	C₄×#1055	C₂×C₄	1	1	yes	characteristic
111	C₄×#1055	C₂×C₄	1	1	yes	characteristic
112	C₄×#1055	C₂³	1	2	yes	—
113	C₄×#1055	C₂³	1	1	yes	characteristic
114	C₄×#1055	C₂³	1	1	yes	characteristic
115	M₁₆×SD₁₆	—	13	1	no	maximal, Sylow
116	C₂³×D₁₃	—	2	1	no	—
117	C₂×Q₈×C₁₃	—	2	1	no	—
118	C₂×Q₈×C₁₃	—	2	2	no	—
119	C₂×Q₈×C₁₃	—	4	1	no	—
120	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
127	C₂²×Dic₁₃	—	2	1	no	—
128	C₂×D₅₂	—	2	2	no	—
129	C₂×D₅₂	—	2	1	no	—
130	C₂×D₅₂	—	4	1	no	—
131	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
132	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄×D₁₃	—	2	1	no	—
134	C₂×C₄×D₁₃	—	2	1	no	—
135	C₂×C₄×D₁₃	—	2	1	no	—
136	C₂×C₄×D₁₃	—	2	1	no	—
137	C₂×C₄×D₁₃	—	4	2	no	—
138	C₂×C₄×D₁₃	—	4	2	no	—
139	C₁₃×M₁₆	—	2	2	no	—
140	C₁₃×M₁₆	—	4	2	no	—
141	C₁₃×M₁₆	SD₁₆	1	4	yes	complemented
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
145	C₁₃×C₄⋊C₄	—	2	1	no	—
146	C₁₃×C₄⋊C₄	—	2	1	no	—
147	C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
151	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₁₃	—	2	1	no	—
153	C₄²×C₁₃	—	2	1	no	—
154	C₄²×C₁₃	—	2	1	no	—
155	C₄²×C₁₃	—	2	1	no	—
156	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₁₃	#41	1	1	yes	characteristic
159	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
160	#6106	—	2	2	no	—
161	#6106	—	2	2	no	—
162	#6106	—	2	2	no	—
163	#6106	M₁₆	1	4	yes	direct product factor
164	#6103	—	2	1	no	—
165	#6103	—	2	1	no	—
166	#6103	—	2	1	no	—
167	#6103	—	2	1	no	—
168	C₄⋊Dic₁₃	—	2	1	no	—
169	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
170	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
171	#6099	—	4	2	no	—
172	C₂×#1055	—	2	2	no	—
173	C₂×#1055	—	2	2	no	—
174	C₂×#1055	—	2	2	no	—
175	C₂×#1055	—	4	1	no	—
176	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
177	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
178	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
179	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
180	#6094	—	4	4	no	—
181	C₈×D₁₃	—	4	4	no	—
182	Q₈×M₁₆	D₁₃	1	1	yes	characteristic, complemented
183	C₂×C₄×SD₁₆	—	13	1	no	—
184	D₄×M₁₆	—	13	1	no	—
185	#1590	—	13	2	no	—
186	#1583	—	13	2	no	—
187	#1582	—	13	2	no	—
188	C₈×SD₁₆	—	13	2	no	—
189	#1566	—	13	1	no	—
190	#1487	—	13	1	no	—
191	#1486	—	13	1	no	—
192	C₈×M₁₆	—	13	1	no	—
193	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
194	C₂²×D₁₃	—	2	1	no	—
195	C₂²×D₁₃	—	2	1	no	—
196	C₂²×D₁₃	—	4	2	no	—
197	C₂²×D₁₃	—	4	2	no	—
198	C₂²×D₁₃	—	8	1	no	—
199	Q₈×C₁₃	—	2	1	no	—
200	Q₈×C₁₃	—	2	1	no	—
201	Q₈×C₁₃	—	2	1	no	—
202	Q₈×C₁₃	—	4	2	no	—
203	Q₈×C₁₃	C₂×M₁₆	1	2	yes	complemented
204	C₂×C₄×C₁₃	—	2	1	no	—
205	C₂×C₄×C₁₃	—	2	1	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	4	1	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	8	1	no	—
213	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
217	C₂×C₄×C₁₃	#135	1	2	yes	—
218	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
221	C₂×Dic₁₃	—	2	1	no	—
222	C₂×Dic₁₃	—	2	1	no	—
223	C₂×Dic₁₃	—	4	2	no	—
224	D₅₂	—	2	1	no	—
225	D₅₂	—	2	1	no	—
226	D₅₂	—	2	1	no	—
227	D₅₂	—	4	2	no	—
228	D₅₂	C₂×M₁₆	1	2	yes	—
229	C₄×D₁₃	—	4	1	no	—
230	C₄×D₁₃	—	4	1	no	—
231	C₄×D₁₃	—	4	1	no	—
232	C₄×D₁₃	—	4	1	no	—
233	C₄×D₁₃	—	4	2	no	—
234	C₄×D₁₃	—	4	2	no	—
235	C₈×C₁₃	—	2	2	no	—
236	C₈×C₁₃	—	4	2	no	—
237	C₈×C₁₃	C₂×SD₁₆	1	4	yes	complemented
238	#1055	—	2	1	no	—
239	#1055	—	2	1	no	—
240	#1055	—	2	1	no	—
241	#1055	—	4	2	no	—
242	#1055	—	4	2	no	—
243	#1055	C₂×M₁₆	1	2	yes	complemented
244	C₂²×SD₁₆	—	13	1	no	—
245	C₂²×M₁₆	—	26	1	no	—
246	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
247	C₂×C₄×D₄	—	13	1	no	—
248	#446	—	2	2	no	—
249	#446	C₂×D₁₃	1	2	yes	complemented
250	C₈×Q₈	C₂×D₁₃	1	2	yes	complemented
251	C₄×SD₁₆	—	13	1	no	—
252	C₄×SD₁₆	—	13	1	no	—
253	C₄×SD₁₆	—	13	1	no	—
254	C₄×SD₁₆	—	13	1	no	—
255	C₄×SD₁₆	—	13	1	no	—
256	C₄×SD₁₆	—	13	1	no	—
257	C₄×SD₁₆	—	13	1	no	—
258	C₄×SD₁₆	—	13	1	no	—
259	#436	—	13	2	no	—
260	#435	—	26	2	no	—
261	C₈×D₄	—	13	2	no	—
262	#431	—	13	1	no	—
263	C₂×#106	—	13	1	no	—
264	#423	—	2	1	no	—
265	#423	—	13	1	no	—
266	#423	C₂×D₁₃	1	1	yes	characteristic
267	C₂×#103	—	13	1	no	—
268	C₂×#102	—	13	1	no	—
269	#407	—	26	1	no	—
270	C₄×M₁₆	—	2	1	no	—
271	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
272	C₂×C₄×C₈	—	13	1	no	—
273	#334	—	13	2	no	—
274	#334	—	13	2	no	—
275	Q₈⋊C₈	—	13	2	no	—
276	Q₈⋊C₈	—	13	2	no	—
277	D₄⋊C₈	—	13	2	no	—
278	D₄⋊C₈	—	13	2	no	—
279	#322	—	13	2	no	—
280	C₈²	—	13	2	no	—
281	C₂²×C₁₃	—	2	1	no	—
282	C₂²×C₁₃	—	2	1	no	—
283	C₂²×C₁₃	C₄×SD₁₆	1	2	yes	—
284	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
285	C₂×D₁₃	—	2	2	no	—
286	C₂×D₁₃	—	4	1	no	—
287	C₂×D₁₃	—	4	1	no	—
288	C₂×D₁₃	—	4	1	no	—
289	C₂×D₁₃	—	4	1	no	—
290	C₂×D₁₃	—	4	1	no	—
291	C₂×D₁₃	—	8	4	no	—
292	C₄×C₁₃	—	2	1	no	—
293	C₄×C₁₃	—	2	2	no	—
294	C₄×C₁₃	—	2	1	no	—
295	C₄×C₁₃	—	2	1	no	—
296	C₄×C₁₃	—	4	1	no	—
297	C₄×C₁₃	—	4	1	no	—
298	C₄×C₁₃	—	4	1	no	—
299	C₄×C₁₃	C₄×SD₁₆	1	2	yes	—
300	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
301	C₄×C₁₃	#568	1	1	yes	characteristic
302	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
303	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
304	Dic₁₃	—	4	1	no	—
305	Dic₁₃	—	4	1	no	—
306	C₂²×Q₈	C₄×D₁₃	1	1	yes	characteristic
307	C₂²×D₄	—	13	1	no	—
308	C₂³×C₄	—	26	1	no	—
309	C₂×SD₁₆	—	13	1	no	—
310	C₂×SD₁₆	—	13	1	no	—
311	C₂×SD₁₆	—	13	1	no	—
312	C₂×SD₁₆	—	13	1	no	—
313	C₂×SD₁₆	—	26	4	no	—
314	C₂×M₁₆	—	2	1	no	—
315	C₂×M₁₆	—	26	1	no	—
316	C₂×M₁₆	—	26	2	no	—
317	C₂×M₁₆	—	52	4	no	—
318	C₂×M₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
319	C₂×M₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
320	C₂²×C₈	—	13	1	no	—
321	C₂²×C₈	—	13	1	no	—
322	C₂²×C₈	—	26	2	no	—
323	C₄×Q₈	—	2	1	no	—
324	C₄×Q₈	—	2	1	no	—
325	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
326	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
327	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
328	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
329	C₄×D₄	—	13	1	no	—
330	C₄×D₄	—	13	1	no	—
331	C₄×D₄	—	13	1	no	—
332	C₄×D₄	—	13	1	no	—
333	C₄×D₄	—	26	1	no	—
334	C₄×D₄	—	26	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	13	1	no	—
337	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
338	C₂×C₂²⋊C₄	—	26	1	no	—
339	C₂×C₄²	—	2	1	no	—
340	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
341	#106	—	13	1	no	—
342	#106	—	13	1	no	—
343	#106	—	13	1	no	—
344	#106	—	13	1	no	—
345	C₄⋊C₈	—	2	2	no	—
346	C₄⋊C₈	—	2	2	no	—
347	C₄⋊C₈	—	2	1	no	—
348	C₄⋊C₈	—	13	2	no	—
349	C₄⋊C₈	—	26	1	no	—
350	C₄⋊C₈	—	26	1	no	—
351	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
352	#103	—	13	1	no	—
353	#103	—	13	1	no	—
354	#103	—	13	1	no	—
355	#103	—	13	1	no	—
356	#102	—	13	1	no	—
357	#102	—	13	1	no	—
358	#102	—	13	1	no	—
359	#102	—	13	1	no	—
360	C₂²⋊C₈	—	26	1	no	—
361	C₂²⋊C₈	—	26	2	no	—
362	C₂²⋊C₈	—	26	2	no	—
363	#97	—	2	2	no	—
364	#97	C₂²⋊D₁₃	1	2	yes	—
365	C₄×C₈	—	2	2	no	—
366	C₄×C₈	—	13	1	no	—
367	C₄×C₈	—	13	1	no	—
368	C₄×C₈	—	13	1	no	—
369	C₄×C₈	—	13	1	no	—
370	C₄×C₈	—	13	2	no	—
371	C₄×C₈	C₂²×D₁₃	1	2	yes	—
372	C₂×C₁₃	—	2	2	no	—
373	C₂×C₁₃	D₄×M₁₆	1	1	yes	characteristic
374	C₂×C₁₃	C₂×C₄×SD₁₆	1	1	yes	characteristic
375	C₂×C₁₃	#2957	1	1	yes	characteristic
376	D₁₃	—	4	2	no	—
377	D₁₃	—	8	1	no	—
378	C₂⁴	—	26	1	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	4	1	no	—
382	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
383	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
384	C₂×D₄	—	13	1	no	—
385	C₂×D₄	—	13	1	no	—
386	C₂×D₄	—	26	2	no	—
387	C₂×D₄	—	26	1	no	—
388	C₂×D₄	—	52	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	26	1	no	—
392	C₂²×C₄	—	26	1	no	—
393	C₂²×C₄	—	26	1	no	—
394	C₂²×C₄	—	26	1	no	—
395	C₂²×C₄	—	26	1	no	—
396	C₂²×C₄	—	52	2	no	—
397	C₂²×C₄	—	52	2	no	—
398	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
399	C₂²×C₄	#6127	1	1	yes	characteristic
400	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
401	SD₁₆	—	13	4	no	—
402	SD₁₆	—	26	2	no	—
403	SD₁₆	—	26	2	no	—
404	SD₁₆	—	26	2	no	—
405	M₁₆	—	2	2	no	—
406	M₁₆	—	4	2	no	—
407	M₁₆	—	52	2	no	—
408	M₁₆	—	52	4	no	—
409	M₁₆	#6106	1	4	yes	direct product factor
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	13	1	no	—
412	C₂×C₈	—	13	1	no	—
413	C₂×C₈	—	13	1	no	—
414	C₂×C₈	—	13	1	no	—
415	C₂×C₈	—	26	2	no	—
416	C₂×C₈	—	26	2	no	—
417	C₂×C₈	—	26	2	no	—
418	C₂×C₈	—	52	1	no	—
419	C₂×C₈	—	52	4	no	—
420	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
421	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	13	1	no	—
428	C₄⋊C₄	—	13	1	no	—
429	C₄⋊C₄	—	26	1	no	—
430	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
431	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
432	C₂²⋊C₄	—	26	1	no	—
433	C₂²⋊C₄	—	26	1	no	—
434	C₂²⋊C₄	—	26	1	no	—
435	C₂²⋊C₄	—	26	1	no	—
436	C₄²	—	2	1	no	—
437	C₄²	—	2	1	no	—
438	C₄²	—	2	1	no	—
439	C₄²	—	2	1	no	—
440	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
441	C₄²	#6127	1	1	yes	characteristic
442	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
443	C₄²	C₂³×D₁₃	1	1	yes	characteristic
444	C₁₃	M₁₆×SD₁₆	1	1	yes	characteristic, complemented, Sylow
445	C₂³	—	26	1	no	—
446	C₂³	—	26	1	no	—
447	C₂³	—	52	2	no	—
448	C₂³	—	52	2	no	—
449	C₂³	—	104	1	no	—
450	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
451	Q₈	—	2	1	no	—
452	Q₈	—	2	1	no	—
453	Q₈	—	2	1	no	—
454	Q₈	—	4	2	no	—
455	Q₈	M₁₆×D₁₃	1	2	yes	complemented
456	D₄	—	13	2	no	—
457	D₄	—	26	1	no	—
458	D₄	—	26	1	no	—
459	D₄	—	26	1	no	—
460	D₄	—	52	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	8	1	no	—
470	C₂×C₄	—	26	1	no	—
471	C₂×C₄	—	26	1	no	—
472	C₂×C₄	—	52	2	no	—
473	C₂×C₄	—	52	2	no	—
474	C₂×C₄	—	52	2	no	—
475	C₂×C₄	—	52	1	no	—
476	C₂×C₄	—	52	1	no	—
477	C₂×C₄	—	52	1	no	—
478	C₂×C₄	—	52	1	no	—
479	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
480	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
481	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
482	C₂×C₄	C₂×#6106	1	2	yes	—
483	C₂×C₄	#88204	1	2	yes	—
484	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
485	C₂×C₄	C₂×#6127	1	1	yes	characteristic
486	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
487	C₈	—	2	2	no	—
488	C₈	—	4	2	no	—
489	C₈	—	13	2	no	—
490	C₈	—	26	1	no	—
491	C₈	—	26	1	no	—
492	C₈	—	26	1	no	—
493	C₈	—	52	2	no	—
494	C₈	—	52	2	no	—
495	C₈	C₂×#6106	1	4	yes	complemented
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	26	2	no	—
499	C₂²	—	52	1	no	—
500	C₂²	—	52	1	no	—
501	C₂²	—	52	1	no	—
502	C₂²	—	52	1	no	—
503	C₂²	—	52	1	no	—
504	C₂²	—	104	4	no	—
505	C₂²	C₄×#6106	1	2	yes	—
506	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	2	2	no	—
511	C₄	—	4	1	no	—
512	C₄	—	4	1	no	—
513	C₄	—	4	1	no	—
514	C₄	—	52	1	no	—
515	C₄	—	52	1	no	—
516	C₄	C₄×#6106	1	2	yes	—
517	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
518	C₄	#11719450	1	1	yes	characteristic
519	C₄	C₂²×#6106	1	1	yes	characteristic
520	C₄	C₂×#88204	1	1	yes	characteristic
521	C₂	—	2	2	no	—
522	C₂	—	52	2	no	—
523	C₂	—	104	1	no	—
524	C₂	M₁₆×C₂²⋊D₁₃	1	1	yes	characteristic
525	C₂	C₂×C₄×#6106	1	1	yes	characteristic
526	C₂	#13123751	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	Q₈×C₁₃×M₁₆	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂²×D₅₂	C₂×C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	Q₈×M₁₆	D₁₃
hypocenter	C₁₃	M₁₆×SD₁₆
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ Q₈×M₁₆

Complements

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

N	H ≅ G/N	type
3. #13113726	C₂	semidirect
4. #13113679	C₂	semidirect
5. #13113670	C₂	semidirect
6. C₈×#6106	C₂	semidirect
7. #13113591	C₂	semidirect
8. #13113265	C₂	semidirect
10. M₁₆×#1055	C₂	semidirect
11. Q₈×C₁₃×M₁₆	C₂	semidirect
17. C₁₃×#446	C₂²	semidirect
18. C₈×Q₈×C₁₃	C₂²	semidirect
41. Q₈⋊#1055	C₂²	semidirect
42. Q₈⋊#1055	C₂²	semidirect
45. #11718072	C₂²	semidirect
46. #11718072	C₂²	semidirect
47. #11718047	C₂²	semidirect
48. C₈×#1055	C₂²	semidirect
141. C₁₃×M₁₆	SD₁₆	semidirect
163. #6106	M₁₆	direct (N × H)
182. Q₈×M₁₆	D₁₃	semidirect
203. Q₈×C₁₃	C₂×M₁₆	semidirect
237. C₈×C₁₃	C₂×SD₁₆	semidirect
243. #1055	C₂×M₁₆	semidirect
249. #446	C₂×D₁₃	semidirect
250. C₈×Q₈	C₂×D₁₃	semidirect
409. M₁₆	#6106	direct (N × H)
444. C₁₃	M₁₆×SD₁₆	semidirect
455. Q₈	M₁₆×D₁₃	semidirect
495. C₈	C₂×#6106	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#6106	2
M₁₆×D₅₂	2
#13113726	2
#13113679	2
#13113670	2
C₈×#6106	2
#13113591	2
#13113265	2
#13113260	2
M₁₆×#1055	2
Q₈×C₁₃×M₁₆	2
M₁₆×SD₁₆	13

Subgroups — M16×#6106 #15834359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×#6106 #15834359