Subgroups — C₁₃×M₁₆×SD₁₆ #15704375

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

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂²×D₄×C₁₃	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₄×C₁₃×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
1. Q₈×C₁₃×M₁₆	C₂	semidirect
4. C₁₃×#1590	C₂	semidirect
5. C₁₃×#1583	C₂	semidirect
6. C₁₃×#1582	C₂	semidirect
7. C₈×C₁₃×SD₁₆	C₂	semidirect
8. C₁₃×#1566	C₂	semidirect
9. C₁₃×#1487	C₂	semidirect
11. C₈×C₁₃×M₁₆	C₂	semidirect
17. C₁₃×#446	C₂²	semidirect
18. C₈×Q₈×C₁₃	C₂²	semidirect
41. C₁₃×#334	C₂²	semidirect
42. C₁₃×#334	C₂²	semidirect
43. C₁₃×Q₈⋊C₈	C₂²	semidirect
44. C₁₃×Q₈⋊C₈	C₂²	semidirect
47. C₁₃×#322	C₂²	semidirect
48. C₈²×C₁₃	C₂²	semidirect
115. M₁₆×SD₁₆	C₁₃	direct (N × H)
142. C₁₃×SD₁₆	M₁₆	direct (N × H)
147. C₁₃×M₁₆	SD₁₆	direct (N × H)
182. Q₈×M₁₆	C₂×C₁₃	semidirect
185. #1590	C₂×C₁₃	semidirect
186. #1583	C₂×C₁₃	semidirect
187. #1582	C₂×C₁₃	semidirect
188. C₈×SD₁₆	C₂×C₁₃	semidirect
189. #1566	C₂×C₁₃	semidirect
190. #1487	C₂×C₁₃	semidirect
192. C₈×M₁₆	C₂×C₁₃	semidirect
203. Q₈×C₁₃	C₂×M₁₆	semidirect
242. C₈×C₁₃	C₂×M₁₆	semidirect
243. C₈×C₁₃	C₂×SD₁₆	semidirect
249. #446	C₂²×C₁₃	semidirect
250. C₈×Q₈	C₂²×C₁₃	semidirect
273. #334	C₂²×C₁₃	semidirect
274. #334	C₂²×C₁₃	semidirect
275. Q₈⋊C₈	C₂²×C₁₃	semidirect
276. Q₈⋊C₈	C₂²×C₁₃	semidirect
279. #322	C₂²×C₁₃	semidirect
280. C₈²	C₂²×C₁₃	semidirect
404. SD₁₆	C₁₃×M₁₆	direct (N × H)
409. M₁₆	C₁₃×SD₁₆	direct (N × H)
444. C₁₃	M₁₆×SD₁₆	direct (N × H)
455. Q₈	C₂×C₁₃×M₁₆	semidirect
494. C₈	C₂×C₁₃×M₁₆	semidirect
495. C₈	C₂×C₁₃×SD₁₆	semidirect

Maximal subgroups

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

subgroup	index
Q₈×C₁₃×M₁₆	2
C₂×C₄×C₁₃×SD₁₆	2
D₄×C₁₃×M₁₆	2
C₁₃×#1590	2
C₁₃×#1583	2
C₁₃×#1582	2
C₈×C₁₃×SD₁₆	2
C₁₃×#1566	2
C₁₃×#1487	2
C₁₃×#1486	2
C₈×C₁₃×M₁₆	2
M₁₆×SD₁₆	13

Subgroups — C13×M16×SD16 #15704375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×M₁₆×SD₁₆ #15704375