Subgroups — C₂×C₁₃×#3357 #15747589

Order 3328.

1930 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#555	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3357	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#485	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#480	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#468	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#428	C₂	1	2	yes	maximal, complemented
13	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
15	C₁₃×#555	—	2	4	no	—
16	C₁₃×#555	C₂²	1	8	yes	—
17	C₁₃×#554	—	2	4	no	—
18	C₁₃×#554	C₂²	1	8	yes	complemented
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#125	—	2	1	no	—
22	C₂×C₁₃×#124	—	2	2	no	—
23	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₁₃×#121	—	2	1	no	—
26	C₂×C₁₃×#121	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	—	2	1	no	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#117	—	2	1	no	—
32	C₂×C₁₃×#117	C₂²	1	2	yes	—
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
34	C₁₃×#500	C₂²	1	8	yes	complemented
35	C₁₃×#485	C₂²	1	16	yes	complemented
36	C₁₃×#480	C₂²	1	16	yes	complemented
37	C₁₃×#477	C₂²	1	8	yes	complemented
38	C₁₃×#476	C₂²	1	8	yes	complemented
39	C₁₃×#468	C₂²	1	16	yes	complemented
40	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
41	C₁₃×#436	C₂²	1	8	yes	complemented
42	C₁₃×#428	C₂²	1	16	yes	complemented
43	C₂×C₁₃×#107	C₂²	1	2	yes	—
44	C₂×C₁₃×#107	C₂²	1	2	yes	—
45	C₂×C₁₃×#107	C₂²	1	2	yes	—
46	C₂×C₁₃×#106	C₂²	1	2	yes	—
47	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#103	C₂²	1	2	yes	—
50	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#102	C₂²	1	2	yes	—
52	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
54	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
55	C₂²×Q₈×C₁₃	—	2	1	no	—
56	C₂²×Q₈×C₁₃	—	2	1	no	—
57	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₁₃	—	2	2	no	—
59	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
60	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	—	2	2	no	—
62	C₂³×C₄×C₁₃	—	2	1	no	—
63	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
64	C₂×C₁₃×SD₁₆	—	2	4	no	—
65	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
66	C₂×C₁₃×M₁₆	—	2	8	no	—
67	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×C₄⋊Q₈	—	2	2	no	—
72	C₁₃×C₄⋊Q₈	—	2	2	no	—
73	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
74	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
75	C₁₃×#125	—	2	8	no	—
76	C₁₃×#124	—	2	16	no	—
77	C₁₃×C₂²⋊Q₈	—	2	4	no	—
78	C₁₃×C₂²⋊Q₈	—	2	16	no	—
79	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
80	C₁₃×#121	—	2	8	no	—
81	C₁₃×#121	—	2	4	no	—
82	C₁₃×#121	C₂³	1	8	yes	—
83	C₄×Q₈×C₁₃	—	2	2	no	—
84	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
85	C₄×D₄×C₁₃	—	2	8	no	—
86	C₄×D₄×C₁₃	—	2	2	no	—
87	C₄×D₄×C₁₃	D₄	1	4	yes	—
88	C₄×D₄×C₁₃	C₂³	1	4	yes	—
89	C₄×D₄×C₁₃	C₂³	1	4	yes	—
90	C₁₃×#117	—	2	4	no	—
91	C₁₃×#117	—	2	8	no	—
92	C₁₃×#117	C₂³	1	8	yes	—
93	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
99	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
105	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
108	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
110	C₂×C₄²×C₁₃	—	2	2	no	—
111	C₂×C₄²×C₁₃	—	2	1	no	—
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₁₃×#107	C₂³	1	8	yes	—
114	C₁₃×#107	C₂³	1	8	yes	—
115	C₁₃×#107	C₂³	1	8	yes	—
116	C₁₃×#106	C₂³	1	4	yes	—
117	C₁₃×#106	C₂³	1	8	yes	—
118	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
119	C₁₃×#103	C₂³	1	4	yes	—
120	C₁₃×#103	C₂³	1	8	yes	—
121	C₁₃×#102	C₂³	1	4	yes	—
122	C₁₃×#102	C₂³	1	8	yes	—
123	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
124	C₄×C₈×C₁₃	C₂³	1	4	yes	—
125	C₂×#3357	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂⁴×C₁₃	—	2	1	no	—
127	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
128	C₂×Q₈×C₁₃	—	2	1	no	—
129	C₂×Q₈×C₁₃	—	2	4	no	—
130	C₂×Q₈×C₁₃	—	2	4	no	—
131	C₂×Q₈×C₁₃	—	2	2	no	—
132	C₂×Q₈×C₁₃	—	2	2	no	—
133	C₂×Q₈×C₁₃	—	8	2	no	—
134	C₂×Q₈×C₁₃	—	8	2	no	—
135	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
136	C₂×D₄×C₁₃	—	2	8	no	—
137	C₂×D₄×C₁₃	—	2	4	no	—
138	C₂×D₄×C₁₃	—	2	1	no	—
139	C₂×D₄×C₁₃	—	2	2	no	—
140	C₂×D₄×C₁₃	—	2	2	no	—
141	C₂×D₄×C₁₃	—	8	4	no	—
142	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
143	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₁₃	—	2	4	no	—
145	C₂²×C₄×C₁₃	—	2	4	no	—
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	2	2	no	—
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂²×C₄×C₁₃	—	2	2	no	—
151	C₂²×C₄×C₁₃	—	2	8	no	—
152	C₂²×C₄×C₁₃	—	2	4	no	—
153	C₂²×C₄×C₁₃	—	4	4	no	—
154	C₂²×C₄×C₁₃	—	8	4	no	—
155	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
156	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₁₃×SD₁₆	—	2	8	no	—
162	C₁₃×M₁₆	—	2	16	no	—
163	C₂×C₈×C₁₃	—	2	4	no	—
164	C₂×C₈×C₁₃	—	2	2	no	—
165	C₂×C₈×C₁₃	#41	1	4	yes	—
166	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
167	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
168	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
169	C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₁₃×C₄⋊C₄	—	2	8	no	—
171	C₁₃×C₄⋊C₄	—	2	2	no	—
172	C₁₃×C₄⋊C₄	—	2	4	no	—
173	C₁₃×C₄⋊C₄	—	2	4	no	—
174	C₁₃×C₄⋊C₄	—	2	4	no	—
175	C₁₃×C₄⋊C₄	—	2	8	no	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
179	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
180	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
181	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
182	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
183	C₁₃×C₂²⋊C₄	—	2	8	no	—
184	C₁₃×C₂²⋊C₄	—	2	8	no	—
185	C₁₃×C₂²⋊C₄	—	2	8	no	—
186	C₁₃×C₂²⋊C₄	—	2	4	no	—
187	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
188	C₄²×C₁₃	—	2	8	no	—
189	C₄²×C₁₃	—	2	4	no	—
190	C₄²×C₁₃	C₂×D₄	1	2	yes	—
191	C₄²×C₁₃	C₂⁴	1	2	yes	—
192	C₂×#555	C₂×C₁₃	1	1	yes	characteristic
193	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#3357	C₂×C₁₃	1	16	yes	direct product factor
195	C₂×#500	C₂×C₁₃	1	1	yes	characteristic, complemented
196	C₂×#485	C₂×C₁₃	1	2	yes	complemented
197	C₂×#480	C₂×C₁₃	1	2	yes	complemented
198	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
199	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
200	C₂×#468	C₂×C₁₃	1	2	yes	complemented
201	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
202	C₂×#436	C₂×C₁₃	1	1	yes	characteristic, complemented
203	C₂×#428	C₂×C₁₃	1	2	yes	complemented
204	C₂³×C₁₃	—	2	4	no	—
205	C₂³×C₁₃	—	2	4	no	—
206	C₂³×C₁₃	—	2	4	no	—
207	C₂³×C₁₃	—	2	2	no	—
208	C₂³×C₁₃	—	4	2	no	—
209	C₂³×C₁₃	—	4	2	no	—
210	C₂³×C₁₃	—	4	2	no	—
211	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
212	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
213	Q₈×C₁₃	—	2	2	no	—
214	Q₈×C₁₃	—	2	2	no	—
215	Q₈×C₁₃	—	4	2	no	—
216	Q₈×C₁₃	—	8	4	no	—
217	Q₈×C₁₃	—	8	4	no	—
218	D₄×C₁₃	—	2	8	no	—
219	D₄×C₁₃	—	2	2	no	—
220	D₄×C₁₃	—	2	2	no	—
221	D₄×C₁₃	—	4	2	no	—
222	D₄×C₁₃	—	8	8	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	8	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	4	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	4	no	—
233	C₂×C₄×C₁₃	—	4	2	no	—
234	C₂×C₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	—	4	2	no	—
236	C₂×C₄×C₁₃	—	4	4	no	—
237	C₂×C₄×C₁₃	—	4	4	no	—
238	C₂×C₄×C₁₃	—	4	8	no	—
239	C₂×C₄×C₁₃	—	8	8	no	—
240	C₂×C₄×C₁₃	#137	1	4	yes	—
241	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
242	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
243	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
245	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
246	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
247	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
248	C₈×C₁₃	—	2	4	no	—
249	C₈×C₁₃	—	2	2	no	—
250	C₈×C₁₃	C₂×#41	1	4	yes	—
251	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
252	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
253	#555	—	2	4	no	—
254	#555	C₂²×C₁₃	1	8	yes	—
255	#554	—	2	4	no	—
256	#554	C₂²×C₁₃	1	8	yes	complemented
257	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
258	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
259	C₂×#125	—	2	1	no	—
260	C₂×#124	—	2	2	no	—
261	C₂×C₂²⋊Q₈	—	2	2	no	—
262	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
263	C₂×#121	—	2	1	no	—
264	C₂×#121	C₂²×C₁₃	1	2	yes	—
265	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×C₄×D₄	—	2	1	no	—
267	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
269	C₂×#117	—	2	1	no	—
270	C₂×#117	C₂²×C₁₃	1	2	yes	—
271	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
272	#500	C₂²×C₁₃	1	8	yes	complemented
273	#485	C₂²×C₁₃	1	16	yes	complemented
274	#480	C₂²×C₁₃	1	16	yes	complemented
275	#477	C₂²×C₁₃	1	8	yes	complemented
276	#476	C₂²×C₁₃	1	8	yes	complemented
277	#468	C₂²×C₁₃	1	16	yes	complemented
278	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
279	#436	C₂²×C₁₃	1	8	yes	complemented
280	#428	C₂²×C₁₃	1	16	yes	complemented
281	C₂×#107	C₂²×C₁₃	1	2	yes	—
282	C₂×#107	C₂²×C₁₃	1	2	yes	—
283	C₂×#107	C₂²×C₁₃	1	2	yes	—
284	C₂×#106	C₂²×C₁₃	1	2	yes	—
285	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×#103	C₂²×C₁₃	1	2	yes	—
288	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×#102	C₂²×C₁₃	1	2	yes	—
291	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
292	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
293	C₂²×C₁₃	—	2	4	no	—
294	C₂²×C₁₃	—	2	4	no	—
295	C₂²×C₁₃	—	2	4	no	—
296	C₂²×C₁₃	—	4	8	no	—
297	C₂²×C₁₃	—	4	2	no	—
298	C₂²×C₁₃	—	4	2	no	—
299	C₂²×C₁₃	—	4	2	no	—
300	C₂²×C₁₃	—	8	4	no	—
301	C₂²×C₁₃	#547	1	2	yes	—
302	C₂²×C₁₃	C₂×#137	1	2	yes	—
303	C₂²×C₁₃	#576	1	2	yes	—
304	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
305	C₄×C₁₃	—	2	4	no	—
306	C₄×C₁₃	—	2	2	no	—
307	C₄×C₁₃	—	4	2	no	—
308	C₄×C₁₃	—	4	2	no	—
309	C₄×C₁₃	—	4	2	no	—
310	C₄×C₁₃	—	4	4	no	—
311	C₄×C₁₃	—	4	4	no	—
312	C₄×C₁₃	#547	1	2	yes	—
313	C₄×C₁₃	C₂×#137	1	4	yes	—
314	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
315	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
316	C₂²×Q₈	—	2	1	no	—
317	C₂²×Q₈	—	2	1	no	—
318	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
319	C₂²×D₄	—	2	2	no	—
320	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
321	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
322	C₂³×C₄	—	2	2	no	—
323	C₂³×C₄	—	2	1	no	—
324	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
325	C₂×SD₁₆	—	2	4	no	—
326	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
327	C₂×M₁₆	—	2	8	no	—
328	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
329	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
330	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
331	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
332	C₄⋊Q₈	—	2	2	no	—
333	C₄⋊Q₈	—	2	2	no	—
334	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
335	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
336	#125	—	2	8	no	—
337	#124	—	2	16	no	—
338	C₂²⋊Q₈	—	2	4	no	—
339	C₂²⋊Q₈	—	2	16	no	—
340	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
341	#121	—	2	8	no	—
342	#121	—	2	4	no	—
343	#121	C₂³×C₁₃	1	8	yes	—
344	C₄×Q₈	—	2	2	no	—
345	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
346	C₄×D₄	—	2	8	no	—
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	D₄×C₁₃	1	4	yes	—
349	C₄×D₄	C₂³×C₁₃	1	4	yes	—
350	C₄×D₄	C₂³×C₁₃	1	4	yes	—
351	#117	—	2	4	no	—
352	#117	—	2	8	no	—
353	#117	C₂³×C₁₃	1	8	yes	—
354	C₂×C₄⋊C₄	—	2	2	no	—
355	C₂×C₄⋊C₄	—	2	4	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
371	C₂×C₄²	—	2	2	no	—
372	C₂×C₄²	—	2	1	no	—
373	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
374	#107	C₂³×C₁₃	1	8	yes	—
375	#107	C₂³×C₁₃	1	8	yes	—
376	#107	C₂³×C₁₃	1	8	yes	—
377	#106	C₂³×C₁₃	1	4	yes	—
378	#106	C₂³×C₁₃	1	8	yes	—
379	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
380	#103	C₂³×C₁₃	1	4	yes	—
381	#103	C₂³×C₁₃	1	8	yes	—
382	#102	C₂³×C₁₃	1	4	yes	—
383	#102	C₂³×C₁₃	1	8	yes	—
384	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
385	C₄×C₈	C₂³×C₁₃	1	4	yes	—
386	C₂×C₁₃	—	4	4	no	—
387	C₂×C₁₃	—	8	2	no	—
388	C₂×C₁₃	#3357	1	4	yes	direct product factor
389	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
390	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
391	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
392	C₂⁴	—	2	1	no	—
393	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	4	no	—
396	C₂×Q₈	—	2	4	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	8	2	no	—
400	C₂×Q₈	—	8	2	no	—
401	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
402	C₂×D₄	—	2	8	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	8	4	no	—
408	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
409	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	8	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	4	4	no	—
420	C₂²×C₄	—	8	4	no	—
421	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
422	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
423	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
424	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
425	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
426	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
427	SD₁₆	—	2	8	no	—
428	M₁₆	—	2	16	no	—
429	C₂×C₈	—	2	4	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	C₁₃×#41	1	4	yes	—
432	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
433	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
434	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	8	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	4	no	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	8	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
445	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
446	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
447	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
448	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
449	C₂²⋊C₄	—	2	8	no	—
450	C₂²⋊C₄	—	2	8	no	—
451	C₂²⋊C₄	—	2	8	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
454	C₄²	—	2	8	no	—
455	C₄²	—	2	4	no	—
456	C₄²	C₂×D₄×C₁₃	1	2	yes	—
457	C₄²	C₂⁴×C₁₃	1	2	yes	—
458	C₁₃	C₂×#3357	1	1	yes	characteristic, direct product factor, Sylow
459	C₂³	—	2	4	no	—
460	C₂³	—	2	4	no	—
461	C₂³	—	2	4	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	2	no	—
465	C₂³	—	4	2	no	—
466	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
467	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
468	Q₈	—	2	2	no	—
469	Q₈	—	2	2	no	—
470	Q₈	—	4	2	no	—
471	Q₈	—	8	4	no	—
472	Q₈	—	8	4	no	—
473	D₄	—	2	8	no	—
474	D₄	—	2	2	no	—
475	D₄	—	2	2	no	—
476	D₄	—	4	2	no	—
477	D₄	—	8	8	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	8	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	4	no	—
493	C₂×C₄	—	4	8	no	—
494	C₂×C₄	—	8	8	no	—
495	C₂×C₄	C₁₃×#137	1	4	yes	—
496	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
497	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
498	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
499	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
500	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
501	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
502	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
503	C₈	—	2	4	no	—
504	C₈	—	2	2	no	—
505	C₈	C₂×C₁₃×#41	1	4	yes	—
506	C₂²	—	2	4	no	—
507	C₂²	—	2	4	no	—
508	C₂²	—	2	4	no	—
509	C₂²	—	4	8	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	8	4	no	—
514	C₂²	C₁₃×#547	1	2	yes	—
515	C₂²	C₂×C₁₃×#137	1	2	yes	—
516	C₂²	C₁₃×#576	1	2	yes	—
517	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
518	C₄	—	2	2	no	—
519	C₄	—	2	4	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	4	no	—
523	C₄	—	4	4	no	—
524	C₄	—	4	2	no	—
525	C₄	C₁₃×#547	1	2	yes	—
526	C₄	C₂×C₁₃×#137	1	4	yes	—
527	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
528	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
529	C₂	—	4	4	no	—
530	C₂	—	8	2	no	—
531	C₂	C₁₃×#3357	1	4	yes	direct product factor
532	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
533	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
534	C₂	C₂×C₁₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#555	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#554	C₂	semidirect
3. C₁₃×#3357	C₂	direct (N × H)
4. C₂×C₁₃×#500	C₂	semidirect
5. C₂×C₁₃×#485	C₂	semidirect
6. C₂×C₁₃×#480	C₂	semidirect
7. C₂×C₁₃×#477	C₂	semidirect
8. C₂×C₁₃×#476	C₂	semidirect
9. C₂×C₁₃×#468	C₂	semidirect
10. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
11. C₂×C₁₃×#436	C₂	semidirect
12. C₂×C₁₃×#428	C₂	semidirect
18. C₁₃×#554	C₂²	semidirect
34. C₁₃×#500	C₂²	semidirect
35. C₁₃×#485	C₂²	semidirect
36. C₁₃×#480	C₂²	semidirect
37. C₁₃×#477	C₂²	semidirect
38. C₁₃×#476	C₂²	semidirect
39. C₁₃×#468	C₂²	semidirect
40. C₄×C₁₃×SD₁₆	C₂²	semidirect
41. C₁₃×#436	C₂²	semidirect
42. C₁₃×#428	C₂²	semidirect
125. C₂×#3357	C₁₃	direct (N × H)
193. C₂×#554	C₂×C₁₃	semidirect
194. #3357	C₂×C₁₃	direct (N × H)
195. C₂×#500	C₂×C₁₃	semidirect
196. C₂×#485	C₂×C₁₃	semidirect
197. C₂×#480	C₂×C₁₃	semidirect
198. C₂×#477	C₂×C₁₃	semidirect
199. C₂×#476	C₂×C₁₃	semidirect
200. C₂×#468	C₂×C₁₃	semidirect
201. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
202. C₂×#436	C₂×C₁₃	semidirect
203. C₂×#428	C₂×C₁₃	semidirect
256. #554	C₂²×C₁₃	semidirect
272. #500	C₂²×C₁₃	semidirect
273. #485	C₂²×C₁₃	semidirect
274. #480	C₂²×C₁₃	semidirect
275. #477	C₂²×C₁₃	semidirect
276. #476	C₂²×C₁₃	semidirect
277. #468	C₂²×C₁₃	semidirect
278. C₄×SD₁₆	C₂²×C₁₃	semidirect
279. #436	C₂²×C₁₃	semidirect
280. #428	C₂²×C₁₃	semidirect
388. C₂×C₁₃	#3357	direct (N × H)
458. C₁₃	C₂×#3357	direct (N × H)
531. C₂	C₁₃×#3357	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#555	2
C₂×C₁₃×#554	2
C₁₃×#3357	2
C₂×C₁₃×#500	2
C₂×C₁₃×#485	2
C₂×C₁₃×#480	2
C₂×C₁₃×#477	2
C₂×C₁₃×#476	2
C₂×C₁₃×#468	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×C₁₃×#436	2
C₂×C₁₃×#428	2
C₂×#3357	13

Subgroups — C2×C13×#3357 #15747589

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3357 #15747589