Subgroups — C₂×C₁₃×#3254 #15747243

Order 3328.

2146 conjugacy classes of subgroups.

The subgroup lattice has 498 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×#532	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3254	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#477	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#474	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#468	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#460	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#461	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	—	2	1	no	—
11	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	—
12	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
13	C₁₃×#533	—	2	4	no	—
14	C₁₃×#533	C₂²	1	8	yes	complemented
15	C₁₃×#532	—	2	4	no	—
16	C₁₃×#532	C₂²	1	8	yes	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#125	—	2	1	no	—
22	C₂×C₁₃×#124	—	2	1	no	—
23	C₂×C₁₃×C₂²⋊Q₈	—	2	1	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	—	2	1	no	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃	—	2	1	no	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
31	C₂×C₁₃×#117	—	2	1	no	—
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#477	C₂²	1	16	yes	complemented
34	C₁₃×#474	C₂²	1	16	yes	complemented
35	C₁₃×#468	C₂²	1	32	yes	complemented
36	C₁₃×#461	C₂²	1	16	yes	complemented
37	C₁₃×#460	C₂²	1	16	yes	complemented
38	C₂×C₁₃×#107	C₂²	1	4	yes	—
39	C₁₃×#423	C₂²	1	8	yes	complemented
40	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
41	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
42	C₂×C₁₃×#103	C₂²	1	4	yes	—
43	C₂×C₁₃×#102	C₂²	1	4	yes	—
44	C₂×C₁₃×#41	—	2	8	no	—
45	C₂×C₁₃×#41	—	4	8	no	—
46	C₂²×Q₈×C₁₃	—	2	1	no	—
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
49	C₂²×D₄×C₁₃	—	2	2	no	—
50	C₂²×D₄×C₁₃	—	2	1	no	—
51	C₂²×D₄×C₁₃	—	2	1	no	—
52	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₃	—	2	2	no	—
54	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₁₃×SD₁₆	—	4	8	no	—
58	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
59	C₂×C₁₃×M₁₆	—	4	4	no	—
60	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
61	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
62	C₁₃×C₄⋊Q₈	—	2	2	no	—
63	C₁₃×C₄⋊Q₈	—	2	2	no	—
64	C₁₃×C₄⋊Q₈	—	2	2	no	—
65	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
66	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
67	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
68	C₁₃×#127	—	2	2	no	—
69	C₁₃×#127	C₂³	1	4	yes	—
70	C₁₃×#125	—	2	8	no	—
71	C₁₃×#124	—	2	8	no	—
72	C₁₃×C₂²⋊Q₈	—	2	8	no	—
73	C₁₃×C₂²⋊Q₈	—	2	4	no	—
74	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
75	C₁₃×#121	—	2	8	no	—
76	C₁₃×#121	—	2	4	no	—
77	C₁₃×#121	C₂³	1	8	yes	—
78	C₄×Q₈×C₁₃	—	2	8	no	—
79	C₄×Q₈×C₁₃	—	2	4	no	—
80	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
81	C₄×D₄×C₁₃	—	2	8	no	—
82	C₄×D₄×C₁₃	—	2	4	no	—
83	C₄×D₄×C₁₃	C₂³	1	8	yes	—
84	C₁₃×#117	—	2	8	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
96	C₂×C₄²×C₁₃	—	2	2	no	—
97	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	D₄	1	4	yes	—
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
103	C₁₃×#107	C₂³	1	16	yes	—
104	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
105	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
106	C₁₃×#103	C₂³	1	16	yes	—
107	C₁₃×#102	C₂³	1	16	yes	—
108	C₂×#3254	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂⁴×C₁₃	—	2	2	no	—
110	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₁₃×#41	—	4	32	no	—
112	C₂×Q₈×C₁₃	—	2	2	no	—
113	C₂×Q₈×C₁₃	—	2	4	no	—
114	C₂×Q₈×C₁₃	—	2	4	no	—
115	C₂×Q₈×C₁₃	—	2	4	no	—
116	C₂×Q₈×C₁₃	—	2	4	no	—
117	C₂×Q₈×C₁₃	—	4	4	no	—
118	C₂×Q₈×C₁₃	—	4	4	no	—
119	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
120	C₂×D₄×C₁₃	—	2	8	no	—
121	C₂×D₄×C₁₃	—	2	2	no	—
122	C₂×D₄×C₁₃	—	2	4	no	—
123	C₂×D₄×C₁₃	—	2	4	no	—
124	C₂×D₄×C₁₃	—	2	4	no	—
125	C₂×D₄×C₁₃	—	2	4	no	—
126	C₂×D₄×C₁₃	—	4	4	no	—
127	C₂×D₄×C₁₃	—	4	8	no	—
128	C₂×D₄×C₁₃	—	4	4	no	—
129	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	2	4	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	8	no	—
138	C₂²×C₄×C₁₃	—	4	8	no	—
139	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₁₃×SD₁₆	—	4	16	no	—
150	C₁₃×M₁₆	—	4	8	no	—
151	C₂×C₈×C₁₃	—	2	8	no	—
152	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
153	C₁₃×C₄⋊C₄	—	2	4	no	—
154	C₁₃×C₄⋊C₄	—	2	4	no	—
155	C₁₃×C₄⋊C₄	—	2	4	no	—
156	C₁₃×C₄⋊C₄	—	2	4	no	—
157	C₁₃×C₄⋊C₄	—	2	8	no	—
158	C₁₃×C₄⋊C₄	—	2	8	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
162	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
163	C₁₃×C₂²⋊C₄	—	2	8	no	—
164	C₁₃×C₂²⋊C₄	—	2	8	no	—
165	C₁₃×C₂²⋊C₄	—	2	8	no	—
166	C₄²×C₁₃	—	2	8	no	—
167	C₄²×C₁₃	C₂×D₄	1	4	yes	—
168	C₄²×C₁₃	C₂×D₄	1	2	yes	—
169	C₄²×C₁₃	C₂×D₄	1	2	yes	—
170	C₄²×C₁₃	C₂×D₄	1	4	yes	—
171	C₄²×C₁₃	C₂⁴	1	2	yes	—
172	C₄²×C₁₃	C₂⁴	1	2	yes	—
173	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
174	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
175	#3254	C₂×C₁₃	1	16	yes	direct product factor
176	C₂×#477	C₂×C₁₃	1	2	yes	complemented
177	C₂×#474	C₂×C₁₃	1	2	yes	complemented
178	C₂×#468	C₂×C₁₃	1	4	yes	complemented
179	C₂×#460	C₂×C₁₃	1	2	yes	complemented
180	C₂×#461	C₂×C₁₃	1	2	yes	complemented
181	C₂×#423	C₂×C₁₃	1	1	yes	characteristic, complemented
182	C₂³×C₁₃	—	2	2	no	—
183	C₂³×C₁₃	—	2	2	no	—
184	C₂³×C₁₃	—	2	2	no	—
185	C₂³×C₁₃	—	2	4	no	—
186	C₂³×C₁₃	—	4	4	no	—
187	C₂³×C₁₃	—	4	4	no	—
188	C₂³×C₁₃	—	4	4	no	—
189	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
190	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	Q₈×C₁₃	—	2	4	no	—
192	Q₈×C₁₃	—	2	4	no	—
193	Q₈×C₁₃	—	4	8	no	—
194	Q₈×C₁₃	—	4	4	no	—
195	Q₈×C₁₃	—	4	8	no	—
196	D₄×C₁₃	—	2	4	no	—
197	D₄×C₁₃	—	2	4	no	—
198	D₄×C₁₃	—	4	8	no	—
199	D₄×C₁₃	—	4	16	no	—
200	D₄×C₁₃	—	4	4	no	—
201	D₄×C₁₃	—	4	8	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	4	no	—
206	C₂×C₄×C₁₃	—	2	8	no	—
207	C₂×C₄×C₁₃	—	2	8	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	4	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	4	4	no	—
214	C₂×C₄×C₁₃	—	4	4	no	—
215	C₂×C₄×C₁₃	—	4	4	no	—
216	C₂×C₄×C₁₃	—	4	16	no	—
217	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
218	C₂×C₄×C₁₃	#137	1	4	yes	—
219	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
224	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
225	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
226	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
227	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
228	C₈×C₁₃	—	2	8	no	—
229	C₂²×#41	—	2	1	no	—
230	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	—
231	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
232	#533	—	2	4	no	—
233	#533	C₂²×C₁₃	1	8	yes	complemented
234	#532	—	2	4	no	—
235	#532	C₂²×C₁₃	1	8	yes	—
236	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
238	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×#125	—	2	1	no	—
241	C₂×#124	—	2	1	no	—
242	C₂×C₂²⋊Q₈	—	2	1	no	—
243	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
244	C₂×#121	—	2	1	no	—
245	C₂×#121	C₂²×C₁₃	1	2	yes	—
246	C₂×C₄×Q₈	—	2	1	no	—
247	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
248	C₂×C₄×D₄	—	2	1	no	—
249	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
250	C₂×#117	—	2	1	no	—
251	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
252	#477	C₂²×C₁₃	1	16	yes	complemented
253	#474	C₂²×C₁₃	1	16	yes	complemented
254	#468	C₂²×C₁₃	1	32	yes	complemented
255	#461	C₂²×C₁₃	1	16	yes	complemented
256	#460	C₂²×C₁₃	1	16	yes	complemented
257	C₂×#107	C₂²×C₁₃	1	4	yes	—
258	#423	C₂²×C₁₃	1	8	yes	complemented
259	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
260	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
261	C₂×#103	C₂²×C₁₃	1	4	yes	—
262	C₂×#102	C₂²×C₁₃	1	4	yes	—
263	C₂²×C₁₃	—	2	2	no	—
264	C₂²×C₁₃	—	2	2	no	—
265	C₂²×C₁₃	—	2	2	no	—
266	C₂²×C₁₃	—	4	4	no	—
267	C₂²×C₁₃	—	4	4	no	—
268	C₂²×C₁₃	—	4	4	no	—
269	C₂²×C₁₃	—	4	4	no	—
270	C₂²×C₁₃	—	8	8	no	—
271	C₂²×C₁₃	#537	1	2	yes	—
272	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
273	C₂²×C₁₃	C₂×#137	1	2	yes	—
274	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
275	C₄×C₁₃	—	2	2	no	—
276	C₄×C₁₃	—	2	2	no	—
277	C₄×C₁₃	—	2	2	no	—
278	C₄×C₁₃	—	4	4	no	—
279	C₄×C₁₃	—	4	4	no	—
280	C₄×C₁₃	—	4	4	no	—
281	C₄×C₁₃	#537	1	2	yes	—
282	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
283	C₄×C₁₃	C₂×#137	1	4	yes	—
284	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
285	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
286	C₂×#41	—	2	8	no	—
287	C₂×#41	—	4	8	no	—
288	C₂²×Q₈	—	2	1	no	—
289	C₂²×Q₈	—	2	1	no	—
290	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
291	C₂²×D₄	—	2	2	no	—
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	—	2	1	no	—
294	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
295	C₂³×C₄	—	2	2	no	—
296	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
297	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
298	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
299	C₂×SD₁₆	—	4	8	no	—
300	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
301	C₂×M₁₆	—	4	4	no	—
302	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
303	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
304	C₄⋊Q₈	—	2	2	no	—
305	C₄⋊Q₈	—	2	2	no	—
306	C₄⋊Q₈	—	2	2	no	—
307	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
308	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
309	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
310	#127	—	2	2	no	—
311	#127	C₂³×C₁₃	1	4	yes	—
312	#125	—	2	8	no	—
313	#124	—	2	8	no	—
314	C₂²⋊Q₈	—	2	8	no	—
315	C₂²⋊Q₈	—	2	4	no	—
316	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
317	#121	—	2	8	no	—
318	#121	—	2	4	no	—
319	#121	C₂³×C₁₃	1	8	yes	—
320	C₄×Q₈	—	2	8	no	—
321	C₄×Q₈	—	2	4	no	—
322	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
323	C₄×D₄	—	2	8	no	—
324	C₄×D₄	—	2	4	no	—
325	C₄×D₄	C₂³×C₁₃	1	8	yes	—
326	#117	—	2	8	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	2	no	—
333	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₄²	—	2	2	no	—
339	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
340	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
341	C₂×C₄²	D₄×C₁₃	1	4	yes	—
342	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
345	#107	C₂³×C₁₃	1	16	yes	—
346	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
347	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
348	#103	C₂³×C₁₃	1	16	yes	—
349	#102	C₂³×C₁₃	1	16	yes	—
350	C₂×C₁₃	—	4	2	no	—
351	C₂×C₁₃	—	8	4	no	—
352	C₂×C₁₃	#3254	1	4	yes	direct product factor
353	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
354	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
355	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
356	C₂⁴	—	2	2	no	—
357	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
358	#41	—	4	32	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	—	2	4	no	—
362	C₂×Q₈	—	2	4	no	—
363	C₂×Q₈	—	2	4	no	—
364	C₂×Q₈	—	4	4	no	—
365	C₂×Q₈	—	4	4	no	—
366	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
367	C₂×D₄	—	2	8	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	—	4	4	no	—
374	C₂×D₄	—	4	8	no	—
375	C₂×D₄	—	4	4	no	—
376	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	8	no	—
385	C₂²×C₄	—	4	8	no	—
386	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
388	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
391	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
392	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
395	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
396	SD₁₆	—	4	16	no	—
397	M₁₆	—	4	8	no	—
398	C₂×C₈	—	2	8	no	—
399	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	8	no	—
405	C₄⋊C₄	—	2	8	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
409	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
410	C₂²⋊C₄	—	2	8	no	—
411	C₂²⋊C₄	—	2	8	no	—
412	C₂²⋊C₄	—	2	8	no	—
413	C₄²	—	2	8	no	—
414	C₄²	C₂×D₄×C₁₃	1	4	yes	—
415	C₄²	C₂×D₄×C₁₃	1	2	yes	—
416	C₄²	C₂×D₄×C₁₃	1	2	yes	—
417	C₄²	C₂×D₄×C₁₃	1	4	yes	—
418	C₄²	C₂⁴×C₁₃	1	2	yes	—
419	C₄²	C₂⁴×C₁₃	1	2	yes	—
420	C₁₃	C₂×#3254	1	1	yes	characteristic, direct product factor, Sylow
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	4	no	—
425	C₂³	—	4	4	no	—
426	C₂³	—	4	4	no	—
427	C₂³	—	4	4	no	—
428	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
429	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
430	Q₈	—	2	4	no	—
431	Q₈	—	2	4	no	—
432	Q₈	—	4	8	no	—
433	Q₈	—	4	4	no	—
434	Q₈	—	4	8	no	—
435	D₄	—	2	4	no	—
436	D₄	—	2	4	no	—
437	D₄	—	4	8	no	—
438	D₄	—	4	16	no	—
439	D₄	—	4	4	no	—
440	D₄	—	4	8	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	8	no	—
446	C₂×C₄	—	2	8	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	4	16	no	—
456	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
457	C₂×C₄	C₁₃×#137	1	4	yes	—
458	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
459	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
460	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
461	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
463	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
464	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
465	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
466	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
467	C₈	—	2	8	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	4	4	no	—
473	C₂²	—	4	4	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	8	8	no	—
476	C₂²	C₁₃×#537	1	2	yes	—
477	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
478	C₂²	C₂×C₁₃×#137	1	2	yes	—
479	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	2	2	no	—
483	C₄	—	4	4	no	—
484	C₄	—	4	4	no	—
485	C₄	—	4	4	no	—
486	C₄	C₁₃×#537	1	2	yes	—
487	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
488	C₄	C₂×C₁₃×#137	1	4	yes	—
489	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
490	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
491	C₂	—	4	2	no	—
492	C₂	—	8	4	no	—
493	C₂	C₁₃×#3254	1	4	yes	direct product factor
494	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
495	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
496	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#532	C₂
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×#3254	C₂	direct (N × H)
4. C₂×C₁₃×#477	C₂	semidirect
5. C₂×C₁₃×#474	C₂	semidirect
6. C₂×C₁₃×#468	C₂	semidirect
7. C₂×C₁₃×#460	C₂	semidirect
8. C₂×C₁₃×#461	C₂	semidirect
9. C₂×C₁₃×#423	C₂	semidirect
14. C₁₃×#533	C₂²	semidirect
33. C₁₃×#477	C₂²	semidirect
34. C₁₃×#474	C₂²	semidirect
35. C₁₃×#468	C₂²	semidirect
36. C₁₃×#461	C₂²	semidirect
37. C₁₃×#460	C₂²	semidirect
39. C₁₃×#423	C₂²	semidirect
108. C₂×#3254	C₁₃	direct (N × H)
173. C₂×#533	C₂×C₁₃	semidirect
175. #3254	C₂×C₁₃	direct (N × H)
176. C₂×#477	C₂×C₁₃	semidirect
177. C₂×#474	C₂×C₁₃	semidirect
178. C₂×#468	C₂×C₁₃	semidirect
179. C₂×#460	C₂×C₁₃	semidirect
180. C₂×#461	C₂×C₁₃	semidirect
181. C₂×#423	C₂×C₁₃	semidirect
233. #533	C₂²×C₁₃	semidirect
252. #477	C₂²×C₁₃	semidirect
253. #474	C₂²×C₁₃	semidirect
254. #468	C₂²×C₁₃	semidirect
255. #461	C₂²×C₁₃	semidirect
256. #460	C₂²×C₁₃	semidirect
258. #423	C₂²×C₁₃	semidirect
352. C₂×C₁₃	#3254	direct (N × H)
420. C₁₃	C₂×#3254	direct (N × H)
493. C₂	C₁₃×#3254	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×#532	2
C₁₃×#3254	2
C₂×C₁₃×#477	2
C₂×C₁₃×#474	2
C₂×C₁₃×#468	2
C₂×C₁₃×#460	2
C₂×C₁₃×#461	2
C₂×C₁₃×#423	2
C₂×#3254	13

Subgroups — C2×C13×#3254 #15747243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3254 #15747243