Subgroups — C₂×C₁₃×#3400 #15747736

Order 3328.

1970 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#559	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3400	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#497	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#492	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#464	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₃×#461	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#440	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
15	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
16	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
17	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
18	C₁₃×#559	—	2	4	no	—
19	C₁₃×#559	C₂²	1	8	yes	—
20	C₁₃×#557	—	2	4	no	—
21	C₁₃×#557	C₂²	1	8	yes	complemented
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#125	—	2	1	no	—
26	C₂×C₁₃×#125	—	2	2	no	—
27	C₂×C₁₃×#124	—	2	1	no	—
28	C₂×C₁₃×#124	C₂²	1	2	yes	—
29	C₂×C₁₃×#123	—	2	2	no	—
30	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
31	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃	—	2	1	no	—
36	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
37	C₁₃×#497	C₂²	1	16	yes	complemented
38	C₁₃×#492	C₂²	1	8	yes	—
39	C₁₃×#464	C₂²	1	16	yes	complemented
40	C₁₃×#462	C₂²	1	8	yes	complemented
41	C₁₃×#461	C₂²	1	16	yes	complemented
42	C₁₃×#460	C₂²	1	8	yes	—
43	C₁₃×#446	C₂²	1	8	yes	complemented
44	C₁₃×#440	C₂²	1	16	yes	complemented
45	C₄×C₁₃×Q₁₆	C₂²	1	8	yes	complemented
46	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
48	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#103	C₂²	1	2	yes	—
51	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#102	C₂²	1	2	yes	—
53	C₂×C₁₃×#97	C₂²	1	2	yes	—
54	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
55	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
56	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
58	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₁₃	—	2	1	no	—
60	C₂²×D₄×C₁₃	—	2	1	no	—
61	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₃	—	2	2	no	—
63	C₂×C₁₃×Q₁₆	—	2	4	no	—
64	C₂×C₁₃×Q₁₆	—	4	4	no	—
65	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
66	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
67	C₂×C₁₃×SD₁₆	—	2	8	no	—
68	C₂×C₁₃×SD₁₆	—	4	4	no	—
69	C₂×C₁₃×SD₁₆	—	4	4	no	—
70	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
71	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
72	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
75	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×C₄⋊Q₈	—	2	4	no	—
77	C₁₃×C₄⋊Q₈	—	2	2	no	—
78	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
79	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
80	C₁₃×#127	—	2	2	no	—
81	C₁₃×#127	C₂³	1	4	yes	—
82	C₁₃×#125	—	2	8	no	—
83	C₁₃×#125	—	2	16	no	—
84	C₁₃×#124	—	2	8	no	—
85	C₁₃×#124	—	2	4	no	—
86	C₁₃×#124	C₂³	1	8	yes	—
87	C₁₃×#123	—	2	16	no	—
88	C₄×Q₈×C₁₃	—	2	8	no	—
89	C₄×Q₈×C₁₃	—	2	4	no	—
90	C₄×Q₈×C₁₃	—	2	2	no	—
91	C₄×Q₈×C₁₃	—	2	2	no	—
92	C₄×Q₈×C₁₃	D₄	1	4	yes	—
93	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
94	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
95	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
96	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
97	C₄×D₄×C₁₃	—	2	8	no	—
98	C₄×D₄×C₁₃	—	2	4	no	—
99	C₄×D₄×C₁₃	C₂³	1	8	yes	—
100	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
112	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
113	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
114	C₂×C₄²×C₁₃	—	2	1	no	—
115	C₂×C₄²×C₁₃	—	2	2	no	—
116	C₂×C₄²×C₁₃	—	2	1	no	—
117	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
119	C₁₃×#107	C₂³	1	4	yes	—
120	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
121	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
122	C₁₃×#103	C₂³	1	4	yes	—
123	C₁₃×#103	C₂³	1	4	yes	—
124	C₁₃×#103	C₂³	1	8	yes	—
125	C₁₃×#102	C₂³	1	8	yes	—
126	C₁₃×#97	C₂³	1	8	yes	—
127	C₄×C₈×C₁₃	C₂³	1	4	yes	—
128	C₂×#3400	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂⁴×C₁₃	—	2	2	no	—
130	C₂×Q₈×C₁₃	—	2	4	no	—
131	C₂×Q₈×C₁₃	—	2	1	no	—
132	C₂×Q₈×C₁₃	—	2	2	no	—
133	C₂×Q₈×C₁₃	—	2	1	no	—
134	C₂×Q₈×C₁₃	—	2	4	no	—
135	C₂×Q₈×C₁₃	—	2	2	no	—
136	C₂×Q₈×C₁₃	—	2	2	no	—
137	C₂×Q₈×C₁₃	—	2	2	no	—
138	C₂×Q₈×C₁₃	—	2	4	no	—
139	C₂×Q₈×C₁₃	—	2	2	no	—
140	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
141	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
142	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
143	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
144	C₂×D₄×C₁₃	—	2	2	no	—
145	C₂×D₄×C₁₃	—	2	4	no	—
146	C₂×D₄×C₁₃	—	2	4	no	—
147	C₂×D₄×C₁₃	—	2	4	no	—
148	C₂×D₄×C₁₃	—	2	4	no	—
149	C₂×D₄×C₁₃	—	4	4	no	—
150	C₂×D₄×C₁₃	—	8	2	no	—
151	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₁₃	—	2	1	no	—
153	C₂²×C₄×C₁₃	—	2	1	no	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	8	no	—
158	C₂²×C₄×C₁₃	—	8	4	no	—
159	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
164	C₁₃×Q₁₆	—	2	8	no	—
165	C₁₃×Q₁₆	—	4	8	no	—
166	C₁₃×SD₁₆	—	2	16	no	—
167	C₁₃×SD₁₆	—	4	8	no	—
168	C₁₃×SD₁₆	—	4	8	no	—
169	C₂×C₈×C₁₃	—	2	2	no	—
170	C₂×C₈×C₁₃	—	2	4	no	—
171	C₂×C₈×C₁₃	#41	1	4	yes	—
172	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
173	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
174	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
175	C₁₃×C₄⋊C₄	—	2	8	no	—
176	C₁₃×C₄⋊C₄	—	2	4	no	—
177	C₁₃×C₄⋊C₄	—	2	4	no	—
178	C₁₃×C₄⋊C₄	—	2	8	no	—
179	C₁₃×C₄⋊C₄	—	2	4	no	—
180	C₁₃×C₄⋊C₄	—	2	8	no	—
181	C₁₃×C₄⋊C₄	—	2	4	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
185	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
186	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
187	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
188	C₁₃×C₂²⋊C₄	—	2	8	no	—
189	C₁₃×C₂²⋊C₄	—	2	8	no	—
190	C₁₃×C₂²⋊C₄	—	2	8	no	—
191	C₄²×C₁₃	—	2	4	no	—
192	C₄²×C₁₃	—	2	8	no	—
193	C₄²×C₁₃	—	2	4	no	—
194	C₄²×C₁₃	C₂×D₄	1	4	yes	—
195	C₄²×C₁₃	C₂×D₄	1	2	yes	—
196	C₄²×C₁₃	C₂⁴	1	2	yes	—
197	C₄²×C₁₃	C₂⁴	1	4	yes	—
198	C₂×#559	C₂×C₁₃	1	1	yes	characteristic
199	C₂×#557	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#3400	C₂×C₁₃	1	16	yes	direct product factor
201	C₂×#497	C₂×C₁₃	1	2	yes	complemented
202	C₂×#492	C₂×C₁₃	1	1	yes	characteristic
203	C₂×#464	C₂×C₁₃	1	2	yes	complemented
204	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₂×#460	C₂×C₁₃	1	1	yes	characteristic
206	C₂×#461	C₂×C₁₃	1	2	yes	complemented
207	C₂×#446	C₂×C₁₃	1	1	yes	characteristic, complemented
208	C₂×#440	C₂×C₁₃	1	2	yes	complemented
209	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
210	C₂³×C₁₃	—	2	4	no	—
211	C₂³×C₁₃	—	4	4	no	—
212	C₂³×C₁₃	—	4	4	no	—
213	C₂³×C₁₃	—	4	4	no	—
214	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
215	Q₈×C₁₃	—	2	8	no	—
216	Q₈×C₁₃	—	2	4	no	—
217	Q₈×C₁₃	—	2	2	no	—
218	Q₈×C₁₃	—	2	2	no	—
219	Q₈×C₁₃	—	2	2	no	—
220	Q₈×C₁₃	—	2	4	no	—
221	Q₈×C₁₃	—	2	2	no	—
222	Q₈×C₁₃	—	4	2	no	—
223	Q₈×C₁₃	—	4	4	no	—
224	Q₈×C₁₃	—	4	2	no	—
225	D₄×C₁₃	—	2	4	no	—
226	D₄×C₁₃	—	2	4	no	—
227	D₄×C₁₃	—	4	4	no	—
228	D₄×C₁₃	—	4	8	no	—
229	D₄×C₁₃	—	8	4	no	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	—	4	4	no	—
240	C₂×C₄×C₁₃	—	4	2	no	—
241	C₂×C₄×C₁₃	—	4	2	no	—
242	C₂×C₄×C₁₃	—	4	2	no	—
243	C₂×C₄×C₁₃	—	8	8	no	—
244	C₂×C₄×C₁₃	#137	1	4	yes	—
245	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
246	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
247	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
250	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
251	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
252	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
253	C₈×C₁₃	—	2	2	no	—
254	C₈×C₁₃	—	2	4	no	—
255	C₈×C₁₃	C₂×#41	1	4	yes	—
256	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
257	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
258	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
259	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
260	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
261	#559	—	2	4	no	—
262	#559	C₂²×C₁₃	1	8	yes	—
263	#557	—	2	4	no	—
264	#557	C₂²×C₁₃	1	8	yes	complemented
265	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
267	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×#125	—	2	1	no	—
269	C₂×#125	—	2	2	no	—
270	C₂×#124	—	2	1	no	—
271	C₂×#124	C₂²×C₁₃	1	2	yes	—
272	C₂×#123	—	2	2	no	—
273	C₂×C₄×Q₈	—	2	1	no	—
274	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
277	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×C₄×D₄	—	2	1	no	—
279	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
280	#497	C₂²×C₁₃	1	16	yes	complemented
281	#492	C₂²×C₁₃	1	8	yes	—
282	#464	C₂²×C₁₃	1	16	yes	complemented
283	#462	C₂²×C₁₃	1	8	yes	complemented
284	#461	C₂²×C₁₃	1	16	yes	complemented
285	#460	C₂²×C₁₃	1	8	yes	—
286	#446	C₂²×C₁₃	1	8	yes	complemented
287	#440	C₂²×C₁₃	1	16	yes	complemented
288	C₄×Q₁₆	C₂²×C₁₃	1	8	yes	complemented
289	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
291	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×#103	C₂²×C₁₃	1	2	yes	—
295	C₂×#102	C₂²×C₁₃	1	2	yes	—
296	C₂×#97	C₂²×C₁₃	1	2	yes	—
297	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
298	C₂²×C₁₃	—	4	4	no	—
299	C₂²×C₁₃	—	4	4	no	—
300	C₂²×C₁₃	—	4	4	no	—
301	C₂²×C₁₃	—	8	8	no	—
302	C₂²×C₁₃	#550	1	2	yes	—
303	C₂²×C₁₃	C₂×#137	1	2	yes	—
304	C₂²×C₁₃	#577	1	2	yes	—
305	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
306	C₄×C₁₃	—	2	4	no	—
307	C₄×C₁₃	—	2	4	no	—
308	C₄×C₁₃	—	2	2	no	—
309	C₄×C₁₃	—	4	2	no	—
310	C₄×C₁₃	—	4	4	no	—
311	C₄×C₁₃	—	4	2	no	—
312	C₄×C₁₃	—	4	2	no	—
313	C₄×C₁₃	—	4	2	no	—
314	C₄×C₁₃	#550	1	2	yes	—
315	C₄×C₁₃	C₂×#137	1	4	yes	—
316	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
317	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
318	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
319	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
320	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
321	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
322	C₂²×D₄	—	2	1	no	—
323	C₂²×D₄	—	2	1	no	—
324	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
325	C₂³×C₄	—	2	2	no	—
326	C₂×Q₁₆	—	2	4	no	—
327	C₂×Q₁₆	—	4	4	no	—
328	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
329	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
330	C₂×SD₁₆	—	2	8	no	—
331	C₂×SD₁₆	—	4	4	no	—
332	C₂×SD₁₆	—	4	4	no	—
333	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
334	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
335	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
336	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
337	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
338	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
339	C₄⋊Q₈	—	2	4	no	—
340	C₄⋊Q₈	—	2	2	no	—
341	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
342	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
343	#127	—	2	2	no	—
344	#127	C₂³×C₁₃	1	4	yes	—
345	#125	—	2	8	no	—
346	#125	—	2	16	no	—
347	#124	—	2	8	no	—
348	#124	—	2	4	no	—
349	#124	C₂³×C₁₃	1	8	yes	—
350	#123	—	2	16	no	—
351	C₄×Q₈	—	2	8	no	—
352	C₄×Q₈	—	2	4	no	—
353	C₄×Q₈	—	2	2	no	—
354	C₄×Q₈	—	2	2	no	—
355	C₄×Q₈	D₄×C₁₃	1	4	yes	—
356	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
357	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
358	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
359	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
360	C₄×D₄	—	2	8	no	—
361	C₄×D₄	—	2	4	no	—
362	C₄×D₄	C₂³×C₁₃	1	8	yes	—
363	C₂×C₄⋊C₄	—	2	2	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	2	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	2	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
371	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
374	C₂×C₂²⋊C₄	—	2	2	no	—
375	C₂×C₂²⋊C₄	—	2	2	no	—
376	C₂×C₂²⋊C₄	—	2	2	no	—
377	C₂×C₄²	—	2	1	no	—
378	C₂×C₄²	—	2	2	no	—
379	C₂×C₄²	—	2	1	no	—
380	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
381	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
382	#107	C₂³×C₁₃	1	4	yes	—
383	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
384	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
385	#103	C₂³×C₁₃	1	4	yes	—
386	#103	C₂³×C₁₃	1	4	yes	—
387	#103	C₂³×C₁₃	1	8	yes	—
388	#102	C₂³×C₁₃	1	8	yes	—
389	#97	C₂³×C₁₃	1	8	yes	—
390	C₄×C₈	C₂³×C₁₃	1	4	yes	—
391	C₂×C₁₃	—	8	4	no	—
392	C₂×C₁₃	#3400	1	4	yes	direct product factor
393	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
394	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
395	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
396	C₂⁴	—	2	2	no	—
397	C₂×Q₈	—	2	4	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	4	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	4	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
408	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
409	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
410	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	4	no	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	4	4	no	—
417	C₂×D₄	—	8	2	no	—
418	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	8	no	—
425	C₂²×C₄	—	8	4	no	—
426	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
427	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
428	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
430	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
431	Q₁₆	—	2	8	no	—
432	Q₁₆	—	4	8	no	—
433	SD₁₆	—	2	16	no	—
434	SD₁₆	—	4	8	no	—
435	SD₁₆	—	4	8	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	4	no	—
438	C₂×C₈	C₁₃×#41	1	4	yes	—
439	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
440	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
441	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
442	C₄⋊C₄	—	2	8	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	2	8	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	8	no	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
452	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
453	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
454	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
455	C₂²⋊C₄	—	2	8	no	—
456	C₂²⋊C₄	—	2	8	no	—
457	C₂²⋊C₄	—	2	8	no	—
458	C₄²	—	2	4	no	—
459	C₄²	—	2	8	no	—
460	C₄²	—	2	4	no	—
461	C₄²	C₂×D₄×C₁₃	1	4	yes	—
462	C₄²	C₂×D₄×C₁₃	1	2	yes	—
463	C₄²	C₂⁴×C₁₃	1	2	yes	—
464	C₄²	C₂⁴×C₁₃	1	4	yes	—
465	C₁₃	C₂×#3400	1	1	yes	characteristic, direct product factor, Sylow
466	C₂³	—	2	4	no	—
467	C₂³	—	4	4	no	—
468	C₂³	—	4	4	no	—
469	C₂³	—	4	4	no	—
470	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
471	Q₈	—	2	8	no	—
472	Q₈	—	2	4	no	—
473	Q₈	—	2	2	no	—
474	Q₈	—	2	2	no	—
475	Q₈	—	2	2	no	—
476	Q₈	—	2	4	no	—
477	Q₈	—	2	2	no	—
478	Q₈	—	4	2	no	—
479	Q₈	—	4	4	no	—
480	Q₈	—	4	2	no	—
481	D₄	—	2	4	no	—
482	D₄	—	2	4	no	—
483	D₄	—	4	4	no	—
484	D₄	—	4	8	no	—
485	D₄	—	8	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	8	8	no	—
500	C₂×C₄	C₁₃×#137	1	4	yes	—
501	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
502	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
503	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
504	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
505	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
506	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
507	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
508	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
509	C₈	—	2	2	no	—
510	C₈	—	2	4	no	—
511	C₈	C₂×C₁₃×#41	1	4	yes	—
512	C₂²	—	4	4	no	—
513	C₂²	—	4	4	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	8	8	no	—
516	C₂²	C₁₃×#550	1	2	yes	—
517	C₂²	C₂×C₁₃×#137	1	2	yes	—
518	C₂²	C₁₃×#577	1	2	yes	—
519	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
520	C₄	—	2	4	no	—
521	C₄	—	2	4	no	—
522	C₄	—	2	2	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	4	no	—
527	C₄	—	4	2	no	—
528	C₄	C₁₃×#550	1	2	yes	—
529	C₄	C₂×C₁₃×#137	1	4	yes	—
530	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
531	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
532	C₂	—	8	4	no	—
533	C₂	C₁₃×#3400	1	4	yes	direct product factor
534	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
535	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
536	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#557	C₂	semidirect
3. C₁₃×#3400	C₂	direct (N × H)
4. C₂×C₁₃×#497	C₂	semidirect
6. C₂×C₁₃×#464	C₂	semidirect
7. C₂×C₁₃×#462	C₂	semidirect
9. C₂×C₁₃×#461	C₂	semidirect
10. C₂×C₁₃×#446	C₂	semidirect
11. C₂×C₁₃×#440	C₂	semidirect
12. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
21. C₁₃×#557	C₂²	semidirect
37. C₁₃×#497	C₂²	semidirect
39. C₁₃×#464	C₂²	semidirect
40. C₁₃×#462	C₂²	semidirect
41. C₁₃×#461	C₂²	semidirect
43. C₁₃×#446	C₂²	semidirect
44. C₁₃×#440	C₂²	semidirect
45. C₄×C₁₃×Q₁₆	C₂²	semidirect
128. C₂×#3400	C₁₃	direct (N × H)
199. C₂×#557	C₂×C₁₃	semidirect
200. #3400	C₂×C₁₃	direct (N × H)
201. C₂×#497	C₂×C₁₃	semidirect
203. C₂×#464	C₂×C₁₃	semidirect
204. C₂×#462	C₂×C₁₃	semidirect
206. C₂×#461	C₂×C₁₃	semidirect
207. C₂×#446	C₂×C₁₃	semidirect
208. C₂×#440	C₂×C₁₃	semidirect
209. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
264. #557	C₂²×C₁₃	semidirect
280. #497	C₂²×C₁₃	semidirect
282. #464	C₂²×C₁₃	semidirect
283. #462	C₂²×C₁₃	semidirect
284. #461	C₂²×C₁₃	semidirect
286. #446	C₂²×C₁₃	semidirect
287. #440	C₂²×C₁₃	semidirect
288. C₄×Q₁₆	C₂²×C₁₃	semidirect
392. C₂×C₁₃	#3400	direct (N × H)
465. C₁₃	C₂×#3400	direct (N × H)
533. C₂	C₁₃×#3400	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×#559	2
C₂×C₁₃×#557	2
C₁₃×#3400	2
C₂×C₁₃×#497	2
C₂×C₁₃×#492	2
C₂×C₁₃×#464	2
C₂×C₁₃×#462	2
C₂×C₁₃×#460	2
C₂×C₁₃×#461	2
C₂×C₁₃×#446	2
C₂×C₁₃×#440	2
C₂×C₄×C₁₃×Q₁₆	2
C₂×#3400	13

Subgroups — C2×C13×#3400 #15747736

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3400 #15747736