Subgroups — C₂×C₁₃×#3211 #15747115

Order 3328.

2294 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3211	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#495	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#488	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#464	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#463	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#447	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
17	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
18	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
19	C₁₃×#529	—	2	4	no	—
20	C₁₃×#529	C₂²	1	8	yes	complemented
21	C₂×C₁₃×#126	—	2	1	no	—
22	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₃×#124	—	2	1	no	—
24	C₂×C₁₃×#124	—	2	1	no	—
25	C₂×C₁₃×#124	—	2	4	no	—
26	C₂×C₁₃×#124	C₂²	1	2	yes	—
27	C₂×C₁₃×#124	C₂²	1	2	yes	—
28	C₂×C₁₃×#124	C₂²	1	8	yes	complemented
29	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×#123	—	2	1	no	—
31	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄×D₄×C₁₃	—	2	1	no	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₃×#117	—	2	1	no	—
37	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
38	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
39	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#495	C₂²	1	16	yes	complemented
41	C₁₃×#488	C₂²	1	16	yes	complemented
42	C₁₃×#464	C₂²	1	16	yes	complemented
43	C₁₃×#463	C₂²	1	16	yes	complemented
44	C₁₃×#451	C₂²	1	8	yes	complemented
45	C₁₃×#450	C₂²	1	8	yes	complemented
46	C₁₃×#448	C₂²	1	8	yes	complemented
47	C₁₃×#447	C₂²	1	8	yes	—
48	C₁₃×#431	C₂²	1	8	yes	complemented
49	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
50	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
51	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
52	C₂×C₁₃×#102	C₂²	1	2	yes	—
53	C₂×C₁₃×#102	C₂²	1	2	yes	—
54	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	complemented
57	C₂⁵×C₁₃	—	2	1	no	—
58	C₂²×Q₈×C₁₃	—	2	2	no	—
59	C₂²×Q₈×C₁₃	—	2	1	no	—
60	C₂²×Q₈×C₁₃	—	4	4	no	—
61	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
62	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
64	C₂²×D₄×C₁₃	—	2	1	no	—
65	C₂²×D₄×C₁₃	—	2	2	no	—
66	C₂²×D₄×C₁₃	—	2	1	no	—
67	C₂²×D₄×C₁₃	—	4	4	no	—
68	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
71	C₂³×C₄×C₁₃	—	2	1	no	—
72	C₂³×C₄×C₁₃	—	2	1	no	—
73	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×Q₁₆	—	4	4	no	—
77	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	complemented
78	C₂×C₁₃×SD₁₆	—	4	4	no	—
79	C₂×C₁₃×SD₁₆	—	4	4	no	—
80	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
81	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	complemented
82	C₂×C₁₃×D₈	—	4	4	no	—
83	C₂×C₁₃×D₈	C₂³	1	8	yes	—
84	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
85	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
86	C₁₃×#126	—	2	8	no	—
87	C₁₃×#125	—	2	2	no	—
88	C₁₃×#125	C₂³	1	4	yes	complemented
89	C₁₃×#124	—	2	4	no	—
90	C₁₃×#124	—	2	4	no	—
91	C₁₃×#124	—	2	8	no	—
92	C₁₃×#124	—	2	8	no	—
93	C₁₃×#124	—	2	2	no	—
94	C₁₃×#124	C₂³	1	8	yes	—
95	C₁₃×#124	C₂³	1	8	yes	—
96	C₁₃×#124	C₂³	1	4	yes	complemented
97	C₁₃×#123	—	2	8	no	—
98	C₁₃×C₂²⋊Q₈	—	2	2	no	—
99	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
100	C₁₃×#121	—	2	2	no	—
101	C₁₃×#121	C₂³	1	4	yes	—
102	C₄×Q₈×C₁₃	—	2	2	no	—
103	C₄×Q₈×C₁₃	C₂³	1	4	yes	complemented
104	C₄×D₄×C₁₃	—	2	8	no	—
105	C₄×D₄×C₁₃	—	2	2	no	—
106	C₄×D₄×C₁₃	C₂³	1	4	yes	complemented
107	C₁₃×#117	—	2	8	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
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	1	no	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
125	C₂×C₄²×C₁₃	—	2	1	no	—
126	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
127	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
128	C₂×C₄²×C₁₃	D₄	1	4	yes	—
129	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
132	C₁₃×C₄⋊C₈	C₂³	1	8	yes	complemented
133	C₁₃×#103	C₂³	1	8	yes	complemented
134	C₁₃×#103	C₂³	1	8	yes	complemented
135	C₁₃×#102	C₂³	1	8	yes	—
136	C₁₃×#102	C₂³	1	8	yes	—
137	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
138	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
139	C₄×C₈×C₁₃	C₂³	1	8	yes	complemented
140	C₂×#3211	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂⁴×C₁₃	—	2	4	no	—
142	C₂⁴×C₁₃	—	2	1	no	—
143	C₂⁴×C₁₃	—	2	2	no	—
144	C₂⁴×C₁₃	—	4	4	no	—
145	C₂⁴×C₁₃	—	4	4	no	—
146	C₂⁴×C₁₃	—	4	4	no	—
147	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	2	4	no	—
150	C₂×Q₈×C₁₃	—	2	2	no	—
151	C₂×Q₈×C₁₃	—	2	4	no	—
152	C₂×Q₈×C₁₃	—	2	4	no	—
153	C₂×Q₈×C₁₃	—	2	4	no	—
154	C₂×Q₈×C₁₃	—	4	8	no	—
155	C₂×Q₈×C₁₃	—	4	4	no	—
156	C₂×Q₈×C₁₃	—	4	8	no	—
157	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
158	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
159	C₂×D₄×C₁₃	—	2	4	no	—
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	—	2	4	no	—
162	C₂×D₄×C₁₃	—	2	2	no	—
163	C₂×D₄×C₁₃	—	2	4	no	—
164	C₂×D₄×C₁₃	—	2	4	no	—
165	C₂×D₄×C₁₃	—	2	4	no	—
166	C₂×D₄×C₁₃	—	4	8	no	—
167	C₂×D₄×C₁₃	—	4	4	no	—
168	C₂×D₄×C₁₃	—	4	8	no	—
169	C₂×D₄×C₁₃	—	4	4	no	—
170	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
171	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₁₃	—	2	4	no	—
173	C₂²×C₄×C₁₃	—	2	4	no	—
174	C₂²×C₄×C₁₃	—	2	4	no	—
175	C₂²×C₄×C₁₃	—	2	1	no	—
176	C₂²×C₄×C₁₃	—	2	1	no	—
177	C₂²×C₄×C₁₃	—	2	2	no	—
178	C₂²×C₄×C₁₃	—	2	1	no	—
179	C₂²×C₄×C₁₃	—	2	4	no	—
180	C₂²×C₄×C₁₃	—	4	2	no	—
181	C₂²×C₄×C₁₃	—	4	4	no	—
182	C₂²×C₄×C₁₃	—	4	4	no	—
183	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
185	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
193	C₁₃×Q₁₆	—	4	8	no	—
194	C₁₃×SD₁₆	—	4	8	no	—
195	C₁₃×SD₁₆	—	4	8	no	—
196	C₁₃×D₈	—	4	8	no	—
197	C₂×C₈×C₁₃	—	2	4	no	—
198	C₂×C₈×C₁₃	—	2	4	no	—
199	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
200	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
201	C₁₃×C₄⋊C₄	—	2	4	no	—
202	C₁₃×C₄⋊C₄	—	2	4	no	—
203	C₁₃×C₄⋊C₄	—	2	4	no	—
204	C₁₃×C₄⋊C₄	—	2	4	no	—
205	C₁₃×C₄⋊C₄	—	2	1	no	—
206	C₁₃×C₄⋊C₄	—	2	1	no	—
207	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
208	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
209	C₁₃×C₂²⋊C₄	—	2	4	no	—
210	C₁₃×C₂²⋊C₄	—	2	8	no	—
211	C₁₃×C₂²⋊C₄	—	2	8	no	—
212	C₁₃×C₂²⋊C₄	—	2	8	no	—
213	C₁₃×C₂²⋊C₄	—	2	8	no	—
214	C₁₃×C₂²⋊C₄	—	2	4	no	—
215	C₁₃×C₂²⋊C₄	—	2	4	no	—
216	C₁₃×C₂²⋊C₄	—	2	4	no	—
217	C₁₃×C₂²⋊C₄	—	2	4	no	—
218	C₄²×C₁₃	—	2	4	no	—
219	C₄²×C₁₃	C₂×D₄	1	4	yes	—
220	C₄²×C₁₃	C₂×D₄	1	2	yes	—
221	C₄²×C₁₃	C₂×D₄	1	2	yes	—
222	C₄²×C₁₃	C₂×D₄	1	4	yes	—
223	C₄²×C₁₃	C₂⁴	1	2	yes	—
224	C₄²×C₁₃	C₂⁴	1	2	yes	—
225	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#3211	C₂×C₁₃	1	16	yes	direct product factor
228	C₂×#495	C₂×C₁₃	1	2	yes	complemented
229	C₂×#488	C₂×C₁₃	1	2	yes	complemented
230	C₂×#464	C₂×C₁₃	1	2	yes	complemented
231	C₂×#463	C₂×C₁₃	1	2	yes	complemented
232	C₂×#451	C₂×C₁₃	1	1	yes	characteristic, complemented
233	C₂×#448	C₂×C₁₃	1	1	yes	characteristic, complemented
234	C₂×#450	C₂×C₁₃	1	1	yes	characteristic, complemented
235	C₂×#447	C₂×C₁₃	1	1	yes	characteristic
236	C₂×#431	C₂×C₁₃	1	1	yes	characteristic, complemented
237	C₂³×C₁₃	—	2	2	no	—
238	C₂³×C₁₃	—	2	2	no	—
239	C₂³×C₁₃	—	2	2	no	—
240	C₂³×C₁₃	—	2	4	no	—
241	C₂³×C₁₃	—	4	8	no	—
242	C₂³×C₁₃	—	4	8	no	—
243	C₂³×C₁₃	—	4	4	no	—
244	C₂³×C₁₃	—	4	2	no	—
245	C₂³×C₁₃	—	4	2	no	—
246	C₂³×C₁₃	—	4	8	no	—
247	C₂³×C₁₃	—	4	4	no	—
248	C₂³×C₁₃	—	4	2	no	—
249	C₂³×C₁₃	—	4	4	no	—
250	C₂³×C₁₃	—	8	16	no	—
251	C₂³×C₁₃	#135	1	4	yes	—
252	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
253	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
254	Q₈×C₁₃	—	2	4	no	—
255	Q₈×C₁₃	—	2	4	no	—
256	Q₈×C₁₃	—	2	4	no	—
257	Q₈×C₁₃	—	4	8	no	—
258	Q₈×C₁₃	—	4	2	no	—
259	Q₈×C₁₃	—	4	4	no	—
260	D₄×C₁₃	—	2	4	no	—
261	D₄×C₁₃	—	2	4	no	—
262	D₄×C₁₃	—	2	4	no	—
263	D₄×C₁₃	—	4	8	no	—
264	D₄×C₁₃	—	4	8	no	—
265	D₄×C₁₃	—	4	2	no	—
266	D₄×C₁₃	—	4	4	no	—
267	C₂×C₄×C₁₃	—	2	2	no	—
268	C₂×C₄×C₁₃	—	2	8	no	—
269	C₂×C₄×C₁₃	—	2	2	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	2	2	no	—
273	C₂×C₄×C₁₃	—	2	4	no	—
274	C₂×C₄×C₁₃	—	2	4	no	—
275	C₂×C₄×C₁₃	—	2	2	no	—
276	C₂×C₄×C₁₃	—	2	2	no	—
277	C₂×C₄×C₁₃	—	2	4	no	—
278	C₂×C₄×C₁₃	—	2	2	no	—
279	C₂×C₄×C₁₃	—	4	4	no	—
280	C₂×C₄×C₁₃	—	4	8	no	—
281	C₂×C₄×C₁₃	—	4	8	no	—
282	C₂×C₄×C₁₃	—	4	4	no	—
283	C₂×C₄×C₁₃	—	4	2	no	—
284	C₂×C₄×C₁₃	—	4	2	no	—
285	C₂×C₄×C₁₃	—	4	2	no	—
286	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
287	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
288	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
289	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
290	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
291	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
293	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
294	C₈×C₁₃	—	2	4	no	—
295	C₈×C₁₃	—	2	4	no	—
296	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
297	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
298	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
299	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
300	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
301	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
302	#529	—	2	4	no	—
303	#529	C₂²×C₁₃	1	8	yes	complemented
304	C₂×#126	—	2	1	no	—
305	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
306	C₂×#124	—	2	1	no	—
307	C₂×#124	—	2	1	no	—
308	C₂×#124	—	2	4	no	—
309	C₂×#124	C₂²×C₁₃	1	2	yes	—
310	C₂×#124	C₂²×C₁₃	1	2	yes	—
311	C₂×#124	C₂²×C₁₃	1	8	yes	complemented
312	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
313	C₂×#123	—	2	1	no	—
314	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
315	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
317	C₂×C₄×D₄	—	2	1	no	—
318	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
319	C₂×#117	—	2	1	no	—
320	C₂²×C₂²⋊C₄	—	2	1	no	—
321	C₂²×C₂²⋊C₄	—	2	1	no	—
322	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
323	#495	C₂²×C₁₃	1	16	yes	complemented
324	#488	C₂²×C₁₃	1	16	yes	complemented
325	#464	C₂²×C₁₃	1	16	yes	complemented
326	#463	C₂²×C₁₃	1	16	yes	complemented
327	#451	C₂²×C₁₃	1	8	yes	complemented
328	#450	C₂²×C₁₃	1	8	yes	complemented
329	#448	C₂²×C₁₃	1	8	yes	complemented
330	#447	C₂²×C₁₃	1	8	yes	—
331	#431	C₂²×C₁₃	1	8	yes	complemented
332	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
333	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
334	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
335	C₂×#102	C₂²×C₁₃	1	2	yes	—
336	C₂×#102	C₂²×C₁₃	1	2	yes	—
337	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	complemented
340	C₂²×C₁₃	—	2	2	no	—
341	C₂²×C₁₃	—	2	8	no	—
342	C₂²×C₁₃	—	2	2	no	—
343	C₂²×C₁₃	—	4	4	no	—
344	C₂²×C₁₃	—	4	2	no	—
345	C₂²×C₁₃	—	4	2	no	—
346	C₂²×C₁₃	—	4	4	no	—
347	C₂²×C₁₃	—	4	2	no	—
348	C₂²×C₁₃	—	4	4	no	—
349	C₂²×C₁₃	—	8	16	no	—
350	C₂²×C₁₃	—	8	4	no	—
351	C₂²×C₁₃	—	8	8	no	—
352	C₂²×C₁₃	#535	1	2	yes	—
353	C₂²×C₁₃	C₂×#135	1	4	yes	—
354	C₂²×C₁₃	C₂×#135	1	2	yes	—
355	C₂²×C₁₃	#575	1	2	yes	—
356	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
357	C₄×C₁₃	—	2	2	no	—
358	C₄×C₁₃	—	2	2	no	—
359	C₄×C₁₃	—	2	2	no	—
360	C₄×C₁₃	—	2	2	no	—
361	C₄×C₁₃	—	2	2	no	—
362	C₄×C₁₃	—	4	4	no	—
363	C₄×C₁₃	—	4	2	no	—
364	C₄×C₁₃	—	4	2	no	—
365	C₄×C₁₃	—	4	2	no	—
366	C₄×C₁₃	#535	1	2	yes	—
367	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
368	C₂⁵	—	2	1	no	—
369	C₂²×Q₈	—	2	1	no	—
370	C₂²×Q₈	—	2	2	no	—
371	C₂²×Q₈	—	4	4	no	—
372	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
373	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
374	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
375	C₂²×D₄	—	2	1	no	—
376	C₂²×D₄	—	2	1	no	—
377	C₂²×D₄	—	2	2	no	—
378	C₂²×D₄	—	4	4	no	—
379	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
380	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
381	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
382	C₂³×C₄	—	2	1	no	—
383	C₂³×C₄	—	2	1	no	—
384	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
385	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
387	C₂×Q₁₆	—	4	4	no	—
388	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	complemented
389	C₂×SD₁₆	—	4	4	no	—
390	C₂×SD₁₆	—	4	4	no	—
391	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
392	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	complemented
393	C₂×D₈	—	4	4	no	—
394	C₂×D₈	C₂³×C₁₃	1	8	yes	—
395	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
396	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
397	#126	—	2	8	no	—
398	#125	—	2	2	no	—
399	#125	C₂³×C₁₃	1	4	yes	complemented
400	#124	—	2	4	no	—
401	#124	—	2	4	no	—
402	#124	—	2	8	no	—
403	#124	—	2	8	no	—
404	#124	—	2	2	no	—
405	#124	C₂³×C₁₃	1	8	yes	—
406	#124	C₂³×C₁₃	1	8	yes	—
407	#124	C₂³×C₁₃	1	4	yes	complemented
408	#123	—	2	8	no	—
409	C₂²⋊Q₈	—	2	2	no	—
410	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
411	#121	—	2	2	no	—
412	#121	C₂³×C₁₃	1	4	yes	—
413	C₄×Q₈	—	2	2	no	—
414	C₄×Q₈	C₂³×C₁₃	1	4	yes	complemented
415	C₄×D₄	—	2	8	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	C₂³×C₁₃	1	4	yes	complemented
418	#117	—	2	8	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	—	2	1	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₂²⋊C₄	—	2	2	no	—
427	C₂×C₂²⋊C₄	—	2	2	no	—
428	C₂×C₂²⋊C₄	—	2	2	no	—
429	C₂×C₂²⋊C₄	—	2	2	no	—
430	C₂×C₂²⋊C₄	—	2	8	no	—
431	C₂×C₂²⋊C₄	—	2	8	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₄²	—	2	1	no	—
437	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
438	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
439	C₂×C₄²	D₄×C₁₃	1	4	yes	—
440	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
441	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
442	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
443	C₄⋊C₈	C₂³×C₁₃	1	8	yes	complemented
444	#103	C₂³×C₁₃	1	8	yes	complemented
445	#103	C₂³×C₁₃	1	8	yes	complemented
446	#102	C₂³×C₁₃	1	8	yes	—
447	#102	C₂³×C₁₃	1	8	yes	—
448	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
449	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
450	C₄×C₈	C₂³×C₁₃	1	8	yes	complemented
451	C₂×C₁₃	—	2	4	no	—
452	C₂×C₁₃	—	8	2	no	—
453	C₂×C₁₃	—	8	4	no	—
454	C₂×C₁₃	#3211	1	4	yes	direct product factor
455	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
456	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
457	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
458	C₂⁴	—	2	1	no	—
459	C₂⁴	—	2	4	no	—
460	C₂⁴	—	2	2	no	—
461	C₂⁴	—	4	4	no	—
462	C₂⁴	—	4	4	no	—
463	C₂⁴	—	4	4	no	—
464	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	4	no	—
467	C₂×Q₈	—	2	2	no	—
468	C₂×Q₈	—	2	4	no	—
469	C₂×Q₈	—	2	4	no	—
470	C₂×Q₈	—	2	4	no	—
471	C₂×Q₈	—	4	8	no	—
472	C₂×Q₈	—	4	4	no	—
473	C₂×Q₈	—	4	8	no	—
474	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
475	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	4	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	2	4	no	—
481	C₂×D₄	—	2	4	no	—
482	C₂×D₄	—	2	4	no	—
483	C₂×D₄	—	4	8	no	—
484	C₂×D₄	—	4	4	no	—
485	C₂×D₄	—	4	8	no	—
486	C₂×D₄	—	4	4	no	—
487	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
488	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
489	C₂²×C₄	—	2	4	no	—
490	C₂²×C₄	—	2	4	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	4	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	4	no	—
497	C₂²×C₄	—	4	2	no	—
498	C₂²×C₄	—	4	4	no	—
499	C₂²×C₄	—	4	4	no	—
500	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
501	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
502	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
503	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
504	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
505	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
507	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
508	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
509	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
510	Q₁₆	—	4	8	no	—
511	SD₁₆	—	4	8	no	—
512	SD₁₆	—	4	8	no	—
513	D₈	—	4	8	no	—
514	C₂×C₈	—	2	4	no	—
515	C₂×C₈	—	2	4	no	—
516	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
517	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
518	C₄⋊C₄	—	2	4	no	—
519	C₄⋊C₄	—	2	4	no	—
520	C₄⋊C₄	—	2	4	no	—
521	C₄⋊C₄	—	2	4	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
525	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
526	C₂²⋊C₄	—	2	4	no	—
527	C₂²⋊C₄	—	2	8	no	—
528	C₂²⋊C₄	—	2	8	no	—
529	C₂²⋊C₄	—	2	8	no	—
530	C₂²⋊C₄	—	2	8	no	—
531	C₂²⋊C₄	—	2	4	no	—
532	C₂²⋊C₄	—	2	4	no	—
533	C₂²⋊C₄	—	2	4	no	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₄²	—	2	4	no	—
536	C₄²	C₂×D₄×C₁₃	1	4	yes	—
537	C₄²	C₂×D₄×C₁₃	1	2	yes	—
538	C₄²	C₂×D₄×C₁₃	1	2	yes	—
539	C₄²	C₂×D₄×C₁₃	1	4	yes	—
540	C₄²	C₂⁴×C₁₃	1	2	yes	—
541	C₄²	C₂⁴×C₁₃	1	2	yes	—
542	C₁₃	C₂×#3211	1	1	yes	characteristic, direct product factor, Sylow
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	4	no	—
547	C₂³	—	4	8	no	—
548	C₂³	—	4	8	no	—
549	C₂³	—	4	4	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	4	2	no	—
552	C₂³	—	4	8	no	—
553	C₂³	—	4	4	no	—
554	C₂³	—	4	2	no	—
555	C₂³	—	4	4	no	—
556	C₂³	—	8	16	no	—
557	C₂³	C₁₃×#135	1	4	yes	—
558	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
559	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
560	Q₈	—	2	4	no	—
561	Q₈	—	2	4	no	—
562	Q₈	—	2	4	no	—
563	Q₈	—	4	8	no	—
564	Q₈	—	4	4	no	—
565	Q₈	—	4	2	no	—
566	D₄	—	2	4	no	—
567	D₄	—	2	4	no	—
568	D₄	—	2	4	no	—
569	D₄	—	4	8	no	—
570	D₄	—	4	8	no	—
571	D₄	—	4	4	no	—
572	D₄	—	4	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	8	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	4	4	no	—
586	C₂×C₄	—	4	8	no	—
587	C₂×C₄	—	4	8	no	—
588	C₂×C₄	—	4	4	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
593	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
594	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
595	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
596	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
597	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
598	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
599	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
600	C₈	—	2	4	no	—
601	C₈	—	2	4	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	8	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	4	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	4	no	—
609	C₂²	—	4	4	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	8	16	no	—
612	C₂²	—	8	4	no	—
613	C₂²	—	8	8	no	—
614	C₂²	C₁₃×#535	1	2	yes	—
615	C₂²	C₂×C₁₃×#135	1	4	yes	—
616	C₂²	C₂×C₁₃×#135	1	2	yes	—
617	C₂²	C₁₃×#575	1	2	yes	—
618	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	2	no	—
626	C₄	—	4	4	no	—
627	C₄	—	4	2	no	—
628	C₄	C₁₃×#535	1	2	yes	—
629	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
630	C₂	—	2	4	no	—
631	C₂	—	8	4	no	—
632	C₂	—	8	2	no	—
633	C₂	C₁₃×#3211	1	4	yes	direct product factor
634	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
635	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
636	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×#447	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×#529	C₂	semidirect
2. C₂²×C₁₃×#124	C₂	semidirect
3. C₁₃×#3211	C₂	direct (N × H)
4. C₂×C₁₃×#495	C₂	semidirect
5. C₂×C₁₃×#488	C₂	semidirect
6. C₂×C₁₃×#464	C₂	semidirect
7. C₂×C₁₃×#463	C₂	semidirect
8. C₂×C₁₃×#451	C₂	semidirect
9. C₂×C₁₃×#448	C₂	semidirect
10. C₂×C₁₃×#450	C₂	semidirect
12. C₂×C₁₃×#431	C₂	semidirect
15. C₂²×C₁₃×Q₁₆	C₂²	semidirect
17. C₂²×C₁₃×SD₁₆	C₂²	semidirect
20. C₁₃×#529	C₂²	semidirect
22. C₂×C₁₃×#125	C₂²	semidirect
28. C₂×C₁₃×#124	C₂²	semidirect
29. C₂×C₁₃×#124	C₂²	semidirect
33. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
35. C₂×C₄×D₄×C₁₃	C₂²	semidirect
40. C₁₃×#495	C₂²	semidirect
41. C₁₃×#488	C₂²	semidirect
42. C₁₃×#464	C₂²	semidirect
43. C₁₃×#463	C₂²	semidirect
44. C₁₃×#451	C₂²	semidirect
45. C₁₃×#450	C₂²	semidirect
46. C₁₃×#448	C₂²	semidirect
48. C₁₃×#431	C₂²	semidirect
49. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
50. C₂×C₁₃×#103	C₂²	semidirect
51. C₂×C₁₃×#103	C₂²	semidirect
56. C₂×C₄×C₈×C₁₃	C₂²	semidirect
77. C₂×C₁₃×Q₁₆	C₂³	semidirect
81. C₂×C₁₃×SD₁₆	C₂³	semidirect
88. C₁₃×#125	C₂³	semidirect
96. C₁₃×#124	C₂³	semidirect
103. C₄×Q₈×C₁₃	C₂³	semidirect
106. C₄×D₄×C₁₃	C₂³	semidirect
132. C₁₃×C₄⋊C₈	C₂³	semidirect
133. C₁₃×#103	C₂³	semidirect
134. C₁₃×#103	C₂³	semidirect
139. C₄×C₈×C₁₃	C₂³	semidirect
140. C₂×#3211	C₁₃	direct (N × H)
225. C₂×#529	C₂×C₁₃	semidirect
226. C₂²×#124	C₂×C₁₃	semidirect
227. #3211	C₂×C₁₃	direct (N × H)
228. C₂×#495	C₂×C₁₃	semidirect
229. C₂×#488	C₂×C₁₃	semidirect
230. C₂×#464	C₂×C₁₃	semidirect
231. C₂×#463	C₂×C₁₃	semidirect
232. C₂×#451	C₂×C₁₃	semidirect
233. C₂×#448	C₂×C₁₃	semidirect
234. C₂×#450	C₂×C₁₃	semidirect
236. C₂×#431	C₂×C₁₃	semidirect
298. C₂²×Q₁₆	C₂²×C₁₃	semidirect
300. C₂²×SD₁₆	C₂²×C₁₃	semidirect
303. #529	C₂²×C₁₃	semidirect
305. C₂×#125	C₂²×C₁₃	semidirect
311. C₂×#124	C₂²×C₁₃	semidirect
312. C₂×#124	C₂²×C₁₃	semidirect
316. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
318. C₂×C₄×D₄	C₂²×C₁₃	semidirect
323. #495	C₂²×C₁₃	semidirect
324. #488	C₂²×C₁₃	semidirect
325. #464	C₂²×C₁₃	semidirect
326. #463	C₂²×C₁₃	semidirect
327. #451	C₂²×C₁₃	semidirect
328. #450	C₂²×C₁₃	semidirect
329. #448	C₂²×C₁₃	semidirect
331. #431	C₂²×C₁₃	semidirect
332. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
333. C₂×#103	C₂²×C₁₃	semidirect
334. C₂×#103	C₂²×C₁₃	semidirect
339. C₂×C₄×C₈	C₂²×C₁₃	semidirect
388. C₂×Q₁₆	C₂³×C₁₃	semidirect
392. C₂×SD₁₆	C₂³×C₁₃	semidirect
399. #125	C₂³×C₁₃	semidirect
407. #124	C₂³×C₁₃	semidirect
414. C₄×Q₈	C₂³×C₁₃	semidirect
417. C₄×D₄	C₂³×C₁₃	semidirect
443. C₄⋊C₈	C₂³×C₁₃	semidirect
444. #103	C₂³×C₁₃	semidirect
445. #103	C₂³×C₁₃	semidirect
450. C₄×C₈	C₂³×C₁₃	semidirect
454. C₂×C₁₃	#3211	direct (N × H)
542. C₁₃	C₂×#3211	direct (N × H)
633. C₂	C₁₃×#3211	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×#529	2
C₂²×C₁₃×#124	2
C₁₃×#3211	2
C₂×C₁₃×#495	2
C₂×C₁₃×#488	2
C₂×C₁₃×#464	2
C₂×C₁₃×#463	2
C₂×C₁₃×#451	2
C₂×C₁₃×#448	2
C₂×C₁₃×#450	2
C₂×C₁₃×#447	2
C₂×C₁₃×#431	2
C₂×#3211	13

Subgroups — C2×C13×#3211 #15747115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3211 #15747115