Subgroups — C₂×C₁₃×#3252 #15747241

Order 3328.

1898 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3252	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#479	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#470	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#468	C₂	1	2	yes	maximal
9	C₂×C₁₃×#464	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
15	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
16	C₁₃×#533	—	2	4	no	—
17	C₁₃×#533	C₂²	1	8	yes	complemented
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₁₃×#529	—	2	4	no	—
21	C₁₃×#529	C₂²	1	8	yes	—
22	C₂×C₁₃×#126	—	2	1	no	—
23	C₂×C₁₃×#125	—	2	1	no	—
24	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#123	—	2	1	no	—
27	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
32	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃	—	2	1	no	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#117	—	2	1	no	—
37	C₂×C₁₃×#117	—	2	1	no	—
38	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#479	C₂²	1	16	yes	complemented
40	C₁₃×#477	C₂²	1	8	yes	complemented
41	C₁₃×#476	C₂²	1	8	yes	complemented
42	C₁₃×#470	C₂²	1	16	yes	complemented
43	C₁₃×#468	C₂²	1	16	yes	—
44	C₁₃×#464	C₂²	1	16	yes	complemented
45	C₁₃×#462	C₂²	1	8	yes	complemented
46	C₁₃×#461	C₂²	1	8	yes	complemented
47	C₂×C₁₃×#107	C₂²	1	2	yes	—
48	C₂×C₁₃×#106	C₂²	1	2	yes	—
49	C₁₃×#423	C₂²	1	8	yes	complemented
50	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
53	C₂×C₁₃×#103	C₂²	1	2	yes	—
54	C₂×C₁₃×#103	C₂²	1	2	yes	—
55	C₂×C₁₃×#103	C₂²	1	2	yes	—
56	C₂×C₁₃×#102	C₂²	1	2	yes	—
57	C₂²×Q₈×C₁₃	—	2	1	no	—
58	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
60	C₂²×D₄×C₁₃	—	2	1	no	—
61	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	—	2	1	no	—
63	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×Q₁₆	—	4	4	no	—
67	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
68	C₂×C₁₃×SD₁₆	—	4	4	no	—
69	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
70	C₂×C₁₃×M₁₆	—	4	4	no	—
71	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
72	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
73	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
74	C₁₃×C₄⋊Q₈	—	2	2	no	—
75	C₁₃×C₄⋊Q₈	—	2	2	no	—
76	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
77	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
78	C₁₃×#126	—	2	8	no	—
79	C₁₃×#125	—	2	8	no	—
80	C₁₃×#125	—	2	2	no	—
81	C₁₃×#125	C₂³	1	4	yes	—
82	C₁₃×#124	—	2	2	no	—
83	C₁₃×#124	C₂³	1	4	yes	—
84	C₁₃×#123	—	2	8	no	—
85	C₁₃×C₂²⋊Q₈	—	2	8	no	—
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	—	2	4	no	—
88	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
89	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
90	C₁₃×#121	—	2	2	no	—
91	C₁₃×#121	C₂³	1	4	yes	—
92	C₄×Q₈×C₁₃	—	2	8	no	—
93	C₄×Q₈×C₁₃	—	2	2	no	—
94	C₄×Q₈×C₁₃	—	2	4	no	—
95	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
96	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
97	C₄×D₄×C₁₃	—	2	8	no	—
98	C₄×D₄×C₁₃	—	2	2	no	—
99	C₄×D₄×C₁₃	C₂³	1	4	yes	—
100	C₁₃×#117	—	2	8	no	—
101	C₁₃×#117	—	2	8	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₄²×C₁₃	—	2	1	no	—
121	C₂×C₄²×C₁₃	—	2	2	no	—
122	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
123	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
124	C₂×C₄²×C₁₃	D₄	1	4	yes	—
125	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
128	C₁₃×#107	C₂³	1	8	yes	—
129	C₁₃×#106	C₂³	1	8	yes	—
130	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
131	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
132	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
133	C₁₃×#103	C₂³	1	8	yes	—
134	C₁₃×#103	C₂³	1	8	yes	—
135	C₁₃×#103	C₂³	1	8	yes	—
136	C₁₃×#102	C₂³	1	8	yes	—
137	C₂×#3252	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂⁴×C₁₃	—	2	1	no	—
139	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂×Q₈×C₁₃	—	2	1	no	—
141	C₂×Q₈×C₁₃	—	2	2	no	—
142	C₂×Q₈×C₁₃	—	2	4	no	—
143	C₂×Q₈×C₁₃	—	2	4	no	—
144	C₂×Q₈×C₁₃	—	2	2	no	—
145	C₂×Q₈×C₁₃	—	2	2	no	—
146	C₂×Q₈×C₁₃	—	2	4	no	—
147	C₂×Q₈×C₁₃	—	4	4	no	—
148	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
149	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
150	C₂×D₄×C₁₃	—	2	4	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	2	2	no	—
153	C₂×D₄×C₁₃	—	2	2	no	—
154	C₂×D₄×C₁₃	—	4	4	no	—
155	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₁₃	—	2	4	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	2	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	2	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	4	2	no	—
166	C₂²×C₄×C₁₃	—	4	4	no	—
167	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
174	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₁₃×Q₁₆	—	4	8	no	—
178	C₁₃×SD₁₆	—	4	8	no	—
179	C₁₃×M₁₆	—	4	8	no	—
180	C₂×C₈×C₁₃	—	2	4	no	—
181	C₂×C₈×C₁₃	—	2	4	no	—
182	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
183	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
184	C₁₃×C₄⋊C₄	—	2	4	no	—
185	C₁₃×C₄⋊C₄	—	2	4	no	—
186	C₁₃×C₄⋊C₄	—	2	4	no	—
187	C₁₃×C₄⋊C₄	—	2	4	no	—
188	C₁₃×C₄⋊C₄	—	2	4	no	—
189	C₁₃×C₄⋊C₄	—	2	4	no	—
190	C₁₃×C₄⋊C₄	—	2	8	no	—
191	C₁₃×C₄⋊C₄	—	2	8	no	—
192	C₁₃×C₄⋊C₄	—	2	4	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
197	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
198	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
199	C₁₃×C₂²⋊C₄	—	2	8	no	—
200	C₁₃×C₂²⋊C₄	—	2	4	no	—
201	C₁₃×C₂²⋊C₄	—	2	4	no	—
202	C₁₃×C₂²⋊C₄	—	2	4	no	—
203	C₁₃×C₂²⋊C₄	—	2	4	no	—
204	C₁₃×C₂²⋊C₄	—	2	4	no	—
205	C₄²×C₁₃	—	2	4	no	—
206	C₄²×C₁₃	—	2	8	no	—
207	C₄²×C₁₃	C₂×D₄	1	4	yes	—
208	C₄²×C₁₃	C₂×D₄	1	2	yes	—
209	C₄²×C₁₃	C₂×D₄	1	2	yes	—
210	C₄²×C₁₃	C₂×D₄	1	4	yes	—
211	C₄²×C₁₃	C₂⁴	1	2	yes	—
212	C₄²×C₁₃	C₂⁴	1	2	yes	—
213	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
214	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
215	#3252	C₂×C₁₃	1	16	yes	direct product factor
216	C₂×#479	C₂×C₁₃	1	2	yes	complemented
217	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
218	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
219	C₂×#470	C₂×C₁₃	1	2	yes	complemented
220	C₂×#468	C₂×C₁₃	1	2	yes	—
221	C₂×#464	C₂×C₁₃	1	2	yes	complemented
222	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
224	C₂×#423	C₂×C₁₃	1	1	yes	characteristic, complemented
225	C₂³×C₁₃	—	2	2	no	—
226	C₂³×C₁₃	—	2	2	no	—
227	C₂³×C₁₃	—	2	2	no	—
228	C₂³×C₁₃	—	2	2	no	—
229	C₂³×C₁₃	—	4	2	no	—
230	C₂³×C₁₃	—	4	2	no	—
231	C₂³×C₁₃	—	4	2	no	—
232	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
233	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
234	Q₈×C₁₃	—	2	4	no	—
235	Q₈×C₁₃	—	2	2	no	—
236	Q₈×C₁₃	—	2	2	no	—
237	Q₈×C₁₃	—	2	4	no	—
238	Q₈×C₁₃	—	4	8	no	—
239	Q₈×C₁₃	—	4	2	no	—
240	Q₈×C₁₃	—	4	4	no	—
241	D₄×C₁₃	—	2	2	no	—
242	D₄×C₁₃	—	2	2	no	—
243	D₄×C₁₃	—	4	8	no	—
244	D₄×C₁₃	—	4	2	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	2	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	4	no	—
250	C₂×C₄×C₁₃	—	2	8	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	4	4	no	—
259	C₂×C₄×C₁₃	—	4	2	no	—
260	C₂×C₄×C₁₃	—	4	4	no	—
261	C₂×C₄×C₁₃	—	4	2	no	—
262	C₂×C₄×C₁₃	—	4	2	no	—
263	C₂×C₄×C₁₃	—	4	4	no	—
264	C₂×C₄×C₁₃	—	4	8	no	—
265	C₂×C₄×C₁₃	#137	1	4	yes	—
266	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
268	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
269	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
270	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
272	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
273	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
274	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
275	C₈×C₁₃	—	2	4	no	—
276	C₈×C₁₃	—	2	4	no	—
277	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
278	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
279	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
280	#533	—	2	4	no	—
281	#533	C₂²×C₁₃	1	8	yes	complemented
282	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
284	#529	—	2	4	no	—
285	#529	C₂²×C₁₃	1	8	yes	—
286	C₂×#126	—	2	1	no	—
287	C₂×#125	—	2	1	no	—
288	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×#123	—	2	1	no	—
291	C₂×C₂²⋊Q₈	—	2	1	no	—
292	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
294	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×C₄×Q₈	—	2	1	no	—
296	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
298	C₂×C₄×D₄	—	2	1	no	—
299	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×#117	—	2	1	no	—
301	C₂×#117	—	2	1	no	—
302	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
303	#479	C₂²×C₁₃	1	16	yes	complemented
304	#477	C₂²×C₁₃	1	8	yes	complemented
305	#476	C₂²×C₁₃	1	8	yes	complemented
306	#470	C₂²×C₁₃	1	16	yes	complemented
307	#468	C₂²×C₁₃	1	16	yes	—
308	#464	C₂²×C₁₃	1	16	yes	complemented
309	#462	C₂²×C₁₃	1	8	yes	complemented
310	#461	C₂²×C₁₃	1	8	yes	complemented
311	C₂×#107	C₂²×C₁₃	1	2	yes	—
312	C₂×#106	C₂²×C₁₃	1	2	yes	—
313	#423	C₂²×C₁₃	1	8	yes	complemented
314	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
315	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
316	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×#103	C₂²×C₁₃	1	2	yes	—
318	C₂×#103	C₂²×C₁₃	1	2	yes	—
319	C₂×#103	C₂²×C₁₃	1	2	yes	—
320	C₂×#102	C₂²×C₁₃	1	2	yes	—
321	C₂²×C₁₃	—	2	2	no	—
322	C₂²×C₁₃	—	2	2	no	—
323	C₂²×C₁₃	—	2	2	no	—
324	C₂²×C₁₃	—	4	4	no	—
325	C₂²×C₁₃	—	4	2	no	—
326	C₂²×C₁₃	—	4	2	no	—
327	C₂²×C₁₃	—	4	2	no	—
328	C₂²×C₁₃	—	8	4	no	—
329	C₂²×C₁₃	#537	1	2	yes	—
330	C₂²×C₁₃	C₂×#137	1	2	yes	—
331	C₂²×C₁₃	#575	1	2	yes	—
332	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
333	C₄×C₁₃	—	2	2	no	—
334	C₄×C₁₃	—	2	2	no	—
335	C₄×C₁₃	—	2	2	no	—
336	C₄×C₁₃	—	2	2	no	—
337	C₄×C₁₃	—	4	2	no	—
338	C₄×C₁₃	—	4	4	no	—
339	C₄×C₁₃	—	4	2	no	—
340	C₄×C₁₃	—	4	2	no	—
341	C₄×C₁₃	—	4	4	no	—
342	C₄×C₁₃	#537	1	2	yes	—
343	C₄×C₁₃	C₂×#137	1	4	yes	—
344	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
345	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
346	C₂²×Q₈	—	2	1	no	—
347	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
348	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
349	C₂²×D₄	—	2	1	no	—
350	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
351	C₂³×C₄	—	2	1	no	—
352	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
353	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
354	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
355	C₂×Q₁₆	—	4	4	no	—
356	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
357	C₂×SD₁₆	—	4	4	no	—
358	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
359	C₂×M₁₆	—	4	4	no	—
360	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
361	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
362	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
363	C₄⋊Q₈	—	2	2	no	—
364	C₄⋊Q₈	—	2	2	no	—
365	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
366	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
367	#126	—	2	8	no	—
368	#125	—	2	8	no	—
369	#125	—	2	2	no	—
370	#125	C₂³×C₁₃	1	4	yes	—
371	#124	—	2	2	no	—
372	#124	C₂³×C₁₃	1	4	yes	—
373	#123	—	2	8	no	—
374	C₂²⋊Q₈	—	2	8	no	—
375	C₂²⋊Q₈	—	2	2	no	—
376	C₂²⋊Q₈	—	2	4	no	—
377	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
378	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
379	#121	—	2	2	no	—
380	#121	C₂³×C₁₃	1	4	yes	—
381	C₄×Q₈	—	2	8	no	—
382	C₄×Q₈	—	2	2	no	—
383	C₄×Q₈	—	2	4	no	—
384	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
385	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
386	C₄×D₄	—	2	8	no	—
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	C₂³×C₁₃	1	4	yes	—
389	#117	—	2	8	no	—
390	#117	—	2	8	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	2	no	—
398	C₂×C₄⋊C₄	—	2	2	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
403	C₂×C₂²⋊C₄	—	2	2	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₄²	—	2	1	no	—
410	C₂×C₄²	—	2	2	no	—
411	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
412	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
413	C₂×C₄²	D₄×C₁₃	1	4	yes	—
414	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
415	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
416	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
417	#107	C₂³×C₁₃	1	8	yes	—
418	#106	C₂³×C₁₃	1	8	yes	—
419	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
420	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
421	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
422	#103	C₂³×C₁₃	1	8	yes	—
423	#103	C₂³×C₁₃	1	8	yes	—
424	#103	C₂³×C₁₃	1	8	yes	—
425	#102	C₂³×C₁₃	1	8	yes	—
426	C₂×C₁₃	—	4	2	no	—
427	C₂×C₁₃	—	8	2	no	—
428	C₂×C₁₃	#3252	1	4	yes	direct product factor
429	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
430	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
431	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
432	C₂⁴	—	2	1	no	—
433	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	—	2	4	no	—
437	C₂×Q₈	—	2	4	no	—
438	C₂×Q₈	—	2	2	no	—
439	C₂×Q₈	—	2	2	no	—
440	C₂×Q₈	—	2	4	no	—
441	C₂×Q₈	—	4	4	no	—
442	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
443	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	4	4	no	—
449	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	4	2	no	—
460	C₂²×C₄	—	4	4	no	—
461	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
462	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
464	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
467	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
468	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
469	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
470	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
471	Q₁₆	—	4	8	no	—
472	SD₁₆	—	4	8	no	—
473	M₁₆	—	4	8	no	—
474	C₂×C₈	—	2	4	no	—
475	C₂×C₈	—	2	4	no	—
476	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
477	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
478	C₄⋊C₄	—	2	4	no	—
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	—	2	4	no	—
481	C₄⋊C₄	—	2	4	no	—
482	C₄⋊C₄	—	2	4	no	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	—	2	8	no	—
485	C₄⋊C₄	—	2	8	no	—
486	C₄⋊C₄	—	2	4	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
491	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
492	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
493	C₂²⋊C₄	—	2	8	no	—
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	2	4	no	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₂²⋊C₄	—	2	4	no	—
498	C₂²⋊C₄	—	2	4	no	—
499	C₄²	—	2	4	no	—
500	C₄²	—	2	8	no	—
501	C₄²	C₂×D₄×C₁₃	1	4	yes	—
502	C₄²	C₂×D₄×C₁₃	1	2	yes	—
503	C₄²	C₂×D₄×C₁₃	1	2	yes	—
504	C₄²	C₂×D₄×C₁₃	1	4	yes	—
505	C₄²	C₂⁴×C₁₃	1	2	yes	—
506	C₄²	C₂⁴×C₁₃	1	2	yes	—
507	C₁₃	C₂×#3252	1	1	yes	characteristic, direct product factor, Sylow
508	C₂³	—	2	2	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	4	2	no	—
514	C₂³	—	4	2	no	—
515	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
516	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
517	Q₈	—	2	4	no	—
518	Q₈	—	2	2	no	—
519	Q₈	—	2	2	no	—
520	Q₈	—	2	4	no	—
521	Q₈	—	4	8	no	—
522	Q₈	—	4	2	no	—
523	Q₈	—	4	4	no	—
524	D₄	—	2	2	no	—
525	D₄	—	2	2	no	—
526	D₄	—	4	8	no	—
527	D₄	—	4	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	8	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	4	4	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	4	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	4	no	—
547	C₂×C₄	—	4	8	no	—
548	C₂×C₄	C₁₃×#137	1	4	yes	—
549	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
550	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
551	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
552	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
553	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
554	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
555	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
556	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
557	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
558	C₈	—	2	4	no	—
559	C₈	—	2	4	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	4	4	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	8	4	no	—
568	C₂²	C₁₃×#537	1	2	yes	—
569	C₂²	C₂×C₁₃×#137	1	2	yes	—
570	C₂²	C₁₃×#575	1	2	yes	—
571	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	4	2	no	—
577	C₄	—	4	2	no	—
578	C₄	—	4	4	no	—
579	C₄	—	4	2	no	—
580	C₄	—	4	4	no	—
581	C₄	C₁₃×#537	1	2	yes	—
582	C₄	C₂×C₁₃×#137	1	4	yes	—
583	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
584	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
585	C₂	—	4	2	no	—
586	C₂	—	8	2	no	—
587	C₂	C₁₃×#3252	1	4	yes	direct product factor
588	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
589	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
590	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#533	C₂	semidirect
3. C₁₃×#3252	C₂	direct (N × H)
4. C₂×C₁₃×#479	C₂	semidirect
5. C₂×C₁₃×#477	C₂	semidirect
6. C₂×C₁₃×#476	C₂	semidirect
7. C₂×C₁₃×#470	C₂	semidirect
9. C₂×C₁₃×#464	C₂	semidirect
10. C₂×C₁₃×#462	C₂	semidirect
11. C₂×C₁₃×#461	C₂	semidirect
12. C₂×C₁₃×#423	C₂	semidirect
17. C₁₃×#533	C₂²	semidirect
39. C₁₃×#479	C₂²	semidirect
40. C₁₃×#477	C₂²	semidirect
41. C₁₃×#476	C₂²	semidirect
42. C₁₃×#470	C₂²	semidirect
44. C₁₃×#464	C₂²	semidirect
45. C₁₃×#462	C₂²	semidirect
46. C₁₃×#461	C₂²	semidirect
49. C₁₃×#423	C₂²	semidirect
137. C₂×#3252	C₁₃	direct (N × H)
213. C₂×#533	C₂×C₁₃	semidirect
215. #3252	C₂×C₁₃	direct (N × H)
216. C₂×#479	C₂×C₁₃	semidirect
217. C₂×#477	C₂×C₁₃	semidirect
218. C₂×#476	C₂×C₁₃	semidirect
219. C₂×#470	C₂×C₁₃	semidirect
221. C₂×#464	C₂×C₁₃	semidirect
222. C₂×#462	C₂×C₁₃	semidirect
223. C₂×#461	C₂×C₁₃	semidirect
224. C₂×#423	C₂×C₁₃	semidirect
281. #533	C₂²×C₁₃	semidirect
303. #479	C₂²×C₁₃	semidirect
304. #477	C₂²×C₁₃	semidirect
305. #476	C₂²×C₁₃	semidirect
306. #470	C₂²×C₁₃	semidirect
308. #464	C₂²×C₁₃	semidirect
309. #462	C₂²×C₁₃	semidirect
310. #461	C₂²×C₁₃	semidirect
313. #423	C₂²×C₁₃	semidirect
428. C₂×C₁₃	#3252	direct (N × H)
507. C₁₃	C₂×#3252	direct (N × H)
587. C₂	C₁₃×#3252	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×#533	2
C₂×C₁₃×#529	2
C₁₃×#3252	2
C₂×C₁₃×#479	2
C₂×C₁₃×#477	2
C₂×C₁₃×#476	2
C₂×C₁₃×#470	2
C₂×C₁₃×#468	2
C₂×C₁₃×#464	2
C₂×C₁₃×#462	2
C₂×C₁₃×#461	2
C₂×C₁₃×#423	2
C₂×#3252	13

Subgroups — C2×C13×#3252 #15747241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3252 #15747241