Subgroups — C₂×C₁₃×#3262 #15747252

Order 3328.

1882 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#542	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3262	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#477	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#474	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#468	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₃×#464	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#463	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
13	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#542	—	2	8	no	—
17	C₁₃×#542	C₂²	1	16	yes	complemented
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#126	—	2	2	no	—
20	C₂×C₁₃×#124	—	2	2	no	—
21	C₂×C₁₃×#124	C₂²	1	2	yes	—
22	C₂×C₁₃×#123	—	2	2	no	—
23	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₁₃×#121	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
28	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
29	C₁₃×#477	C₂²	1	16	yes	complemented
30	C₁₃×#474	C₂²	1	16	yes	complemented
31	C₁₃×#468	C₂²	1	16	yes	complemented
32	C₁₃×#467	C₂²	1	8	yes	complemented
33	C₁₃×#466	C₂²	1	8	yes	—
34	C₁₃×#464	C₂²	1	16	yes	complemented
35	C₁₃×#463	C₂²	1	16	yes	complemented
36	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#107	C₂²	1	2	yes	—
39	C₁₃×#424	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	2	yes	—
43	C₂×C₁₃×#103	C₂²	1	2	yes	—
44	C₂×C₁₃×#102	C₂²	1	2	yes	—
45	C₂×C₁₃×#102	C₂²	1	2	yes	—
46	C₂²×Q₈×C₁₃	—	2	2	no	—
47	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×D₄×C₁₃	—	2	2	no	—
49	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₃	—	2	2	no	—
51	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₁₃×Q₁₆	—	4	2	no	—
53	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
54	C₂×C₁₃×SD₁₆	—	4	4	no	—
55	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
56	C₂×C₁₃×D₈	—	4	2	no	—
57	C₂×C₁₃×D₈	C₂³	1	4	yes	—
58	C₂×C₁₃×M₁₆	—	4	2	no	—
59	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
60	C₂²×C₈×C₁₃	—	4	2	no	—
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
65	C₁₃×C₄⋊Q₈	—	2	4	no	—
66	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
67	C₁₃×#126	—	2	16	no	—
68	C₁₃×#124	—	2	16	no	—
69	C₁₃×#124	—	2	4	no	—
70	C₁₃×#124	C₂³	1	8	yes	—
71	C₁₃×#123	—	2	16	no	—
72	C₁₃×C₂²⋊Q₈	—	2	4	no	—
73	C₁₃×C₂²⋊Q₈	—	2	16	no	—
74	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
75	C₁₃×#121	—	2	4	no	—
76	C₁₃×#121	C₂³	1	8	yes	—
77	C₄×Q₈×C₁₃	—	2	4	no	—
78	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
79	C₄×D₄×C₁₃	—	2	4	no	—
80	C₄×D₄×C₁₃	C₂³	1	8	yes	—
81	C₁₃×#117	D₄	1	4	yes	—
82	C₁₃×#117	C₂³	1	4	yes	—
83	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
86	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
95	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
96	C₂×C₄²×C₁₃	—	2	2	no	—
97	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
98	C₁₃×#107	C₂³	1	4	yes	—
99	C₁₃×#107	C₂³	1	4	yes	—
100	C₁₃×#107	C₂³	1	8	yes	—
101	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
102	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
103	C₁₃×#103	C₂³	1	8	yes	—
104	C₁₃×#103	C₂³	1	8	yes	—
105	C₁₃×#102	C₂³	1	8	yes	—
106	C₁₃×#102	C₂³	1	8	yes	—
107	C₂×#3262	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂⁴×C₁₃	—	2	2	no	—
109	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂×Q₈×C₁₃	—	2	2	no	—
111	C₂×Q₈×C₁₃	—	2	8	no	—
112	C₂×Q₈×C₁₃	—	2	4	no	—
113	C₂×Q₈×C₁₃	—	2	4	no	—
114	C₂×Q₈×C₁₃	—	8	4	no	—
115	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
116	C₂×D₄×C₁₃	—	2	8	no	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	2	4	no	—
119	C₂×D₄×C₁₃	—	2	4	no	—
120	C₂×D₄×C₁₃	—	8	4	no	—
121	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	8	no	—
128	C₂²×C₄×C₁₃	—	8	4	no	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₁₃×Q₁₆	—	4	4	no	—
136	C₁₃×SD₁₆	—	4	8	no	—
137	C₁₃×D₈	—	4	4	no	—
138	C₁₃×M₁₆	—	4	4	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₂×C₈×C₁₃	—	2	4	no	—
142	C₂×C₈×C₁₃	—	4	4	no	—
143	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
144	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
145	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
146	C₁₃×C₄⋊C₄	—	2	8	no	—
147	C₁₃×C₄⋊C₄	—	2	8	no	—
148	C₁₃×C₄⋊C₄	—	2	8	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
152	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
153	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
154	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
155	C₁₃×C₂²⋊C₄	—	2	8	no	—
156	C₁₃×C₂²⋊C₄	—	2	8	no	—
157	C₁₃×C₂²⋊C₄	—	2	8	no	—
158	C₁₃×C₂²⋊C₄	—	2	8	no	—
159	C₁₃×C₂²⋊C₄	—	2	8	no	—
160	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
161	C₄²×C₁₃	—	2	8	no	—
162	C₄²×C₁₃	C₂×D₄	1	4	yes	—
163	C₄²×C₁₃	C₂⁴	1	4	yes	—
164	C₂×#542	C₂×C₁₃	1	2	yes	complemented
165	#3262	C₂×C₁₃	1	16	yes	direct product factor
166	C₂×#477	C₂×C₁₃	1	2	yes	complemented
167	C₂×#474	C₂×C₁₃	1	2	yes	complemented
168	C₂×#468	C₂×C₁₃	1	2	yes	complemented
169	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
170	C₂×#466	C₂×C₁₃	1	1	yes	characteristic
171	C₂×#464	C₂×C₁₃	1	2	yes	complemented
172	C₂×#463	C₂×C₁₃	1	2	yes	complemented
173	C₂×#424	C₂×C₁₃	1	1	yes	characteristic, complemented
174	C₂³×C₁₃	—	2	2	no	—
175	C₂³×C₁₃	—	2	2	no	—
176	C₂³×C₁₃	—	2	2	no	—
177	C₂³×C₁₃	—	2	4	no	—
178	C₂³×C₁₃	—	4	4	no	—
179	C₂³×C₁₃	—	4	4	no	—
180	C₂³×C₁₃	—	4	4	no	—
181	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
182	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
183	Q₈×C₁₃	—	2	4	no	—
184	Q₈×C₁₃	—	2	4	no	—
185	Q₈×C₁₃	—	4	4	no	—
186	Q₈×C₁₃	—	8	8	no	—
187	D₄×C₁₃	—	2	4	no	—
188	D₄×C₁₃	—	2	4	no	—
189	D₄×C₁₃	—	4	4	no	—
190	D₄×C₁₃	—	8	8	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	2	4	no	—
194	C₂×C₄×C₁₃	—	2	4	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	4	no	—
198	C₂×C₄×C₁₃	—	2	4	no	—
199	C₂×C₄×C₁₃	—	2	4	no	—
200	C₂×C₄×C₁₃	—	4	4	no	—
201	C₂×C₄×C₁₃	—	4	4	no	—
202	C₂×C₄×C₁₃	—	4	4	no	—
203	C₂×C₄×C₁₃	—	8	8	no	—
204	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
205	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
206	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
207	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
209	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
210	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
211	C₈×C₁₃	—	2	2	no	—
212	C₈×C₁₃	—	2	2	no	—
213	C₈×C₁₃	—	2	4	no	—
214	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
215	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
216	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
217	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
218	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
219	#542	—	2	8	no	—
220	#542	C₂²×C₁₃	1	16	yes	complemented
221	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
222	C₂×#126	—	2	2	no	—
223	C₂×#124	—	2	2	no	—
224	C₂×#124	C₂²×C₁₃	1	2	yes	—
225	C₂×#123	—	2	2	no	—
226	C₂×C₂²⋊Q₈	—	2	2	no	—
227	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
228	C₂×#121	C₂²×C₁₃	1	2	yes	—
229	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
230	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
231	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
232	#477	C₂²×C₁₃	1	16	yes	complemented
233	#474	C₂²×C₁₃	1	16	yes	complemented
234	#468	C₂²×C₁₃	1	16	yes	complemented
235	#467	C₂²×C₁₃	1	8	yes	complemented
236	#466	C₂²×C₁₃	1	8	yes	—
237	#464	C₂²×C₁₃	1	16	yes	complemented
238	#463	C₂²×C₁₃	1	16	yes	complemented
239	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×#107	C₂²×C₁₃	1	2	yes	—
241	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
242	#424	C₂²×C₁₃	1	8	yes	complemented
243	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
244	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
245	C₂×#103	C₂²×C₁₃	1	2	yes	—
246	C₂×#103	C₂²×C₁₃	1	2	yes	—
247	C₂×#102	C₂²×C₁₃	1	2	yes	—
248	C₂×#102	C₂²×C₁₃	1	2	yes	—
249	C₂²×C₁₃	—	2	2	no	—
250	C₂²×C₁₃	—	2	2	no	—
251	C₂²×C₁₃	—	2	2	no	—
252	C₂²×C₁₃	—	4	4	no	—
253	C₂²×C₁₃	—	4	4	no	—
254	C₂²×C₁₃	—	4	4	no	—
255	C₂²×C₁₃	—	4	4	no	—
256	C₂²×C₁₃	—	8	8	no	—
257	C₂²×C₁₃	#537	1	2	yes	—
258	C₂²×C₁₃	#576	1	2	yes	—
259	C₂²×C₁₃	#578	1	2	yes	—
260	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
261	C₄×C₁₃	—	2	2	no	—
262	C₄×C₁₃	—	2	4	no	—
263	C₄×C₁₃	—	2	4	no	—
264	C₄×C₁₃	—	4	4	no	—
265	C₄×C₁₃	—	4	4	no	—
266	C₄×C₁₃	—	4	4	no	—
267	C₄×C₁₃	#537	1	2	yes	—
268	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
269	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
270	C₂²×Q₈	—	2	2	no	—
271	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
272	C₂²×D₄	—	2	2	no	—
273	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
274	C₂³×C₄	—	2	2	no	—
275	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
276	C₂×Q₁₆	—	4	2	no	—
277	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
278	C₂×SD₁₆	—	4	4	no	—
279	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
280	C₂×D₈	—	4	2	no	—
281	C₂×D₈	C₂³×C₁₃	1	4	yes	—
282	C₂×M₁₆	—	4	2	no	—
283	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
284	C₂²×C₈	—	4	2	no	—
285	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
287	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
288	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
289	C₄⋊Q₈	—	2	4	no	—
290	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
291	#126	—	2	16	no	—
292	#124	—	2	16	no	—
293	#124	—	2	4	no	—
294	#124	C₂³×C₁₃	1	8	yes	—
295	#123	—	2	16	no	—
296	C₂²⋊Q₈	—	2	4	no	—
297	C₂²⋊Q₈	—	2	16	no	—
298	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
299	#121	—	2	4	no	—
300	#121	C₂³×C₁₃	1	8	yes	—
301	C₄×Q₈	—	2	4	no	—
302	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
303	C₄×D₄	—	2	4	no	—
304	C₄×D₄	C₂³×C₁₃	1	8	yes	—
305	#117	D₄×C₁₃	1	4	yes	—
306	#117	C₂³×C₁₃	1	4	yes	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
311	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
322	#107	C₂³×C₁₃	1	4	yes	—
323	#107	C₂³×C₁₃	1	4	yes	—
324	#107	C₂³×C₁₃	1	8	yes	—
325	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
326	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
327	#103	C₂³×C₁₃	1	8	yes	—
328	#103	C₂³×C₁₃	1	8	yes	—
329	#102	C₂³×C₁₃	1	8	yes	—
330	#102	C₂³×C₁₃	1	8	yes	—
331	C₂×C₁₃	—	4	2	no	—
332	C₂×C₁₃	—	8	4	no	—
333	C₂×C₁₃	#3262	1	4	yes	direct product factor
334	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
335	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
336	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
337	C₂⁴	—	2	2	no	—
338	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	8	no	—
341	C₂×Q₈	—	2	4	no	—
342	C₂×Q₈	—	2	4	no	—
343	C₂×Q₈	—	8	4	no	—
344	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
345	C₂×D₄	—	2	8	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	8	4	no	—
350	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	8	no	—
357	C₂²×C₄	—	8	4	no	—
358	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
359	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
362	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
363	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
364	Q₁₆	—	4	4	no	—
365	SD₁₆	—	4	8	no	—
366	D₈	—	4	4	no	—
367	M₁₆	—	4	4	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	4	no	—
371	C₂×C₈	—	4	4	no	—
372	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
373	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
374	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	—	2	8	no	—
377	C₄⋊C₄	—	2	8	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
381	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
382	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
383	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₂²⋊C₄	—	2	8	no	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
390	C₄²	—	2	8	no	—
391	C₄²	C₂×D₄×C₁₃	1	4	yes	—
392	C₄²	C₂⁴×C₁₃	1	4	yes	—
393	C₁₃	C₂×#3262	1	1	yes	characteristic, direct product factor, Sylow
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	4	no	—
398	C₂³	—	4	4	no	—
399	C₂³	—	4	4	no	—
400	C₂³	—	4	4	no	—
401	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
402	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
403	Q₈	—	2	4	no	—
404	Q₈	—	2	4	no	—
405	Q₈	—	4	4	no	—
406	Q₈	—	8	8	no	—
407	D₄	—	2	4	no	—
408	D₄	—	2	4	no	—
409	D₄	—	4	4	no	—
410	D₄	—	8	8	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	8	8	no	—
424	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
425	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
426	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
427	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
428	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
429	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
430	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	2	4	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	4	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	8	8	no	—
442	C₂²	C₁₃×#537	1	2	yes	—
443	C₂²	C₁₃×#576	1	2	yes	—
444	C₂²	C₁₃×#578	1	2	yes	—
445	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
446	C₄	—	2	4	no	—
447	C₄	—	2	4	no	—
448	C₄	—	2	2	no	—
449	C₄	—	4	4	no	—
450	C₄	—	4	4	no	—
451	C₄	—	4	4	no	—
452	C₄	C₁₃×#537	1	2	yes	—
453	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
454	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
455	C₂	—	4	2	no	—
456	C₂	—	8	4	no	—
457	C₂	C₁₃×#3262	1	4	yes	direct product factor
458	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
459	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
460	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#466	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#542	C₂	semidirect
2. C₁₃×#3262	C₂	direct (N × H)
3. C₂×C₁₃×#477	C₂	semidirect
4. C₂×C₁₃×#474	C₂	semidirect
5. C₂×C₁₃×#468	C₂	semidirect
6. C₂×C₁₃×#467	C₂	semidirect
8. C₂×C₁₃×#464	C₂	semidirect
9. C₂×C₁₃×#463	C₂	semidirect
10. C₂×C₁₃×#424	C₂	semidirect
17. C₁₃×#542	C₂²	semidirect
29. C₁₃×#477	C₂²	semidirect
30. C₁₃×#474	C₂²	semidirect
31. C₁₃×#468	C₂²	semidirect
32. C₁₃×#467	C₂²	semidirect
34. C₁₃×#464	C₂²	semidirect
35. C₁₃×#463	C₂²	semidirect
39. C₁₃×#424	C₂²	semidirect
107. C₂×#3262	C₁₃	direct (N × H)
164. C₂×#542	C₂×C₁₃	semidirect
165. #3262	C₂×C₁₃	direct (N × H)
166. C₂×#477	C₂×C₁₃	semidirect
167. C₂×#474	C₂×C₁₃	semidirect
168. C₂×#468	C₂×C₁₃	semidirect
169. C₂×#467	C₂×C₁₃	semidirect
171. C₂×#464	C₂×C₁₃	semidirect
172. C₂×#463	C₂×C₁₃	semidirect
173. C₂×#424	C₂×C₁₃	semidirect
220. #542	C₂²×C₁₃	semidirect
232. #477	C₂²×C₁₃	semidirect
233. #474	C₂²×C₁₃	semidirect
234. #468	C₂²×C₁₃	semidirect
235. #467	C₂²×C₁₃	semidirect
237. #464	C₂²×C₁₃	semidirect
238. #463	C₂²×C₁₃	semidirect
242. #424	C₂²×C₁₃	semidirect
333. C₂×C₁₃	#3262	direct (N × H)
393. C₁₃	C₂×#3262	direct (N × H)
457. C₂	C₁₃×#3262	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×#542	2
C₁₃×#3262	2
C₂×C₁₃×#477	2
C₂×C₁₃×#474	2
C₂×C₁₃×#468	2
C₂×C₁₃×#467	2
C₂×C₁₃×#466	2
C₂×C₁₃×#464	2
C₂×C₁₃×#463	2
C₂×C₁₃×#424	2
C₂×#3262	13

Subgroups — C2×C13×#3262 #15747252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3262 #15747252