Subgroups — C₂×C₁₃×#3394 #15747729

Order 3328.

2022 conjugacy classes of subgroups.

The subgroup lattice has 554 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, complemented
2	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3394	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#495	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#464	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#463	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic
10	C₂×C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
13	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
15	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
17	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
18	C₁₃×#559	—	2	4	no	—
19	C₁₃×#559	C₂²	1	8	yes	complemented
20	C₁₃×#556	—	2	4	no	—
21	C₁₃×#556	C₂²	1	8	yes	complemented
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#126	—	2	2	no	—
25	C₂×C₁₃×#124	—	2	1	no	—
26	C₂×C₁₃×#124	C₂²	1	2	yes	—
27	C₂×C₁₃×#124	C₂²	1	2	yes	—
28	C₂×C₁₃×#123	—	2	2	no	—
29	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
30	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	—	2	1	no	—
34	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
36	C₂×C₁₃×#117	—	2	1	no	—
37	C₁₃×#495	C₂²	1	16	yes	complemented
38	C₁₃×#492	C₂²	1	8	yes	complemented
39	C₁₃×#464	C₂²	1	16	yes	complemented
40	C₁₃×#463	C₂²	1	16	yes	complemented
41	C₁₃×#462	C₂²	1	8	yes	complemented
42	C₁₃×#459	C₂²	1	8	yes	—
43	C₈×Q₈×C₁₃	C₂²	1	8	yes	complemented
44	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
45	C₄×C₁₃×SD₁₆	C₂²	1	16	yes	complemented
46	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
49	C₂×C₁₃×#103	C₂²	1	2	yes	—
50	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#102	C₂²	1	2	yes	—
52	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
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×D₄×C₁₃	—	2	1	no	—
59	C₂²×D₄×C₁₃	—	2	1	no	—
60	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₃	—	2	1	no	—
63	C₂³×C₄×C₁₃	—	2	2	no	—
64	C₂×C₁₃×Q₁₆	—	4	4	no	—
65	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
66	C₂×C₁₃×SD₁₆	—	2	8	no	—
67	C₂×C₁₃×SD₁₆	—	2	4	no	—
68	C₂×C₁₃×SD₁₆	—	4	4	no	—
69	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
70	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
71	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
72	C₂×C₁₃×D₈	—	4	4	no	—
73	C₂×C₁₃×D₈	C₂³	1	8	yes	—
74	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
75	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×C₄⋊Q₈	—	2	2	no	—
78	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
79	C₁₃×#127	—	2	2	no	—
80	C₁₃×#127	C₂³	1	4	yes	—
81	C₁₃×#126	—	2	16	no	—
82	C₁₃×#124	—	2	8	no	—
83	C₁₃×#124	—	2	4	no	—
84	C₁₃×#124	—	2	4	no	—
85	C₁₃×#124	C₂³	1	8	yes	—
86	C₁₃×#124	C₂³	1	8	yes	—
87	C₁₃×#123	—	2	16	no	—
88	C₁₃×C₂²⋊Q₈	—	2	8	no	—
89	C₄×Q₈×C₁₃	—	2	4	no	—
90	C₄×Q₈×C₁₃	—	2	2	no	—
91	C₄×Q₈×C₁₃	D₄	1	4	yes	—
92	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
93	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
94	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
95	C₄×D₄×C₁₃	—	2	8	no	—
96	C₄×D₄×C₁₃	—	2	2	no	—
97	C₄×D₄×C₁₃	—	2	4	no	—
98	C₄×D₄×C₁₃	C₂³	1	4	yes	—
99	C₄×D₄×C₁₃	C₂³	1	8	yes	—
100	C₁₃×#117	—	2	8	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
106	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
111	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
112	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
114	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
115	C₂×C₄²×C₁₃	—	2	2	no	—
116	C₂×C₄²×C₁₃	—	2	1	no	—
117	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
119	C₁₃×#106	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	8	yes	—
123	C₁₃×#103	C₂³	1	4	yes	—
124	C₁₃×#102	C₂³	1	8	yes	—
125	C₁₃×#102	C₂³	1	4	yes	—
126	C₄×C₈×C₁₃	C₂³	1	4	yes	—
127	C₄×C₈×C₁₃	C₂³	1	8	yes	—
128	C₂×#3394	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂⁴×C₁₃	—	2	1	no	—
130	C₂⁴×C₁₃	—	2	2	no	—
131	C₂×Q₈×C₁₃	—	2	4	no	—
132	C₂×Q₈×C₁₃	—	2	1	no	—
133	C₂×Q₈×C₁₃	—	2	2	no	—
134	C₂×Q₈×C₁₃	—	2	2	no	—
135	C₂×Q₈×C₁₃	—	2	4	no	—
136	C₂×Q₈×C₁₃	—	2	4	no	—
137	C₂×Q₈×C₁₃	—	2	2	no	—
138	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
139	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
140	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	—	2	2	no	—
143	C₂×D₄×C₁₃	—	2	4	no	—
144	C₂×D₄×C₁₃	—	2	4	no	—
145	C₂×D₄×C₁₃	—	2	2	no	—
146	C₂×D₄×C₁₃	—	2	4	no	—
147	C₂×D₄×C₁₃	—	2	2	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	2	yes	—
152	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
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	4	no	—
158	C₂²×C₄×C₁₃	—	2	8	no	—
159	C₂²×C₄×C₁₃	—	4	4	no	—
160	C₂²×C₄×C₁₃	—	8	4	no	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₁₃×Q₁₆	—	4	8	no	—
167	C₁₃×SD₁₆	—	2	16	no	—
168	C₁₃×SD₁₆	—	2	8	no	—
169	C₁₃×SD₁₆	—	4	8	no	—
170	C₁₃×D₈	—	4	8	no	—
171	C₂×C₈×C₁₃	—	2	4	no	—
172	C₂×C₈×C₁₃	—	2	2	no	—
173	C₂×C₈×C₁₃	#41	1	4	yes	—
174	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
175	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
176	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
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	4	no	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
184	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
185	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
186	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
187	C₁₃×C₂²⋊C₄	—	2	8	no	—
188	C₁₃×C₂²⋊C₄	—	2	8	no	—
189	C₁₃×C₂²⋊C₄	—	2	8	no	—
190	C₁₃×C₂²⋊C₄	—	2	4	no	—
191	C₁₃×C₂²⋊C₄	—	2	8	no	—
192	C₁₃×C₂²⋊C₄	—	2	8	no	—
193	C₄²×C₁₃	—	2	8	no	—
194	C₄²×C₁₃	—	2	4	no	—
195	C₄²×C₁₃	C₂×D₄	1	4	yes	—
196	C₄²×C₁₃	C₂×D₄	1	2	yes	—
197	C₄²×C₁₃	C₂⁴	1	4	yes	—
198	C₄²×C₁₃	C₂⁴	1	2	yes	—
199	C₂×#559	C₂×C₁₃	1	1	yes	characteristic, complemented
200	C₂×#556	C₂×C₁₃	1	1	yes	characteristic, complemented
201	#3394	C₂×C₁₃	1	16	yes	direct product factor
202	C₂×#495	C₂×C₁₃	1	2	yes	complemented
203	C₂×#492	C₂×C₁₃	1	1	yes	characteristic, complemented
204	C₂×#464	C₂×C₁₃	1	2	yes	complemented
205	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
206	C₂×#463	C₂×C₁₃	1	2	yes	complemented
207	C₂×#459	C₂×C₁₃	1	1	yes	characteristic
208	C₂×C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
209	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
210	C₂×C₄×SD₁₆	C₂×C₁₃	1	2	yes	complemented
211	C₂³×C₁₃	—	2	2	no	—
212	C₂³×C₁₃	—	2	4	no	—
213	C₂³×C₁₃	—	4	2	no	—
214	C₂³×C₁₃	—	4	4	no	—
215	C₂³×C₁₃	—	4	2	no	—
216	C₂³×C₁₃	—	4	4	no	—
217	C₂³×C₁₃	—	4	4	no	—
218	C₂³×C₁₃	—	4	2	no	—
219	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
220	Q₈×C₁₃	—	2	8	no	—
221	Q₈×C₁₃	—	2	2	no	—
222	Q₈×C₁₃	—	2	4	no	—
223	Q₈×C₁₃	—	2	4	no	—
224	Q₈×C₁₃	—	2	2	no	—
225	Q₈×C₁₃	—	4	2	no	—
226	Q₈×C₁₃	—	4	4	no	—
227	D₄×C₁₃	—	2	2	no	—
228	D₄×C₁₃	—	2	4	no	—
229	D₄×C₁₃	—	2	2	no	—
230	D₄×C₁₃	—	2	4	no	—
231	D₄×C₁₃	—	4	2	no	—
232	D₄×C₁₃	—	4	4	no	—
233	D₄×C₁₃	—	4	8	no	—
234	D₄×C₁₃	—	8	4	no	—
235	C₂×C₄×C₁₃	—	2	4	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	4	2	no	—
243	C₂×C₄×C₁₃	—	4	4	no	—
244	C₂×C₄×C₁₃	—	4	2	no	—
245	C₂×C₄×C₁₃	—	4	2	no	—
246	C₂×C₄×C₁₃	—	4	8	no	—
247	C₂×C₄×C₁₃	—	8	8	no	—
248	C₂×C₄×C₁₃	#135	1	4	yes	—
249	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
250	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
251	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
252	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
254	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
255	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
256	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
257	C₈×C₁₃	—	2	4	no	—
258	C₈×C₁₃	—	2	2	no	—
259	C₈×C₁₃	C₂×#41	1	4	yes	—
260	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
261	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
262	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
263	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
264	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
265	#559	—	2	4	no	—
266	#559	C₂²×C₁₃	1	8	yes	complemented
267	#556	—	2	4	no	—
268	#556	C₂²×C₁₃	1	8	yes	complemented
269	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×#126	—	2	2	no	—
272	C₂×#124	—	2	1	no	—
273	C₂×#124	C₂²×C₁₃	1	2	yes	—
274	C₂×#124	C₂²×C₁₃	1	2	yes	—
275	C₂×#123	—	2	2	no	—
276	C₂×C₂²⋊Q₈	—	2	1	no	—
277	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
278	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×C₄×D₄	—	2	1	no	—
281	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
283	C₂×#117	—	2	1	no	—
284	#495	C₂²×C₁₃	1	16	yes	complemented
285	#492	C₂²×C₁₃	1	8	yes	complemented
286	#464	C₂²×C₁₃	1	16	yes	complemented
287	#463	C₂²×C₁₃	1	16	yes	complemented
288	#462	C₂²×C₁₃	1	8	yes	complemented
289	#459	C₂²×C₁₃	1	8	yes	—
290	C₈×Q₈	C₂²×C₁₃	1	8	yes	complemented
291	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
292	C₄×SD₁₆	C₂²×C₁₃	1	16	yes	complemented
293	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
296	C₂×#103	C₂²×C₁₃	1	2	yes	—
297	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×#102	C₂²×C₁₃	1	2	yes	—
299	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
302	C₂²×C₁₃	—	4	2	no	—
303	C₂²×C₁₃	—	4	4	no	—
304	C₂²×C₁₃	—	4	2	no	—
305	C₂²×C₁₃	—	4	4	no	—
306	C₂²×C₁₃	—	4	4	no	—
307	C₂²×C₁₃	—	4	2	no	—
308	C₂²×C₁₃	—	8	4	no	—
309	C₂²×C₁₃	—	8	8	no	—
310	C₂²×C₁₃	#550	1	2	yes	—
311	C₂²×C₁₃	C₂×#135	1	2	yes	—
312	C₂²×C₁₃	#577	1	2	yes	—
313	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
314	C₄×C₁₃	—	2	4	no	—
315	C₄×C₁₃	—	2	4	no	—
316	C₄×C₁₃	—	2	2	no	—
317	C₄×C₁₃	—	4	2	no	—
318	C₄×C₁₃	—	4	4	no	—
319	C₄×C₁₃	—	4	2	no	—
320	C₄×C₁₃	—	4	2	no	—
321	C₄×C₁₃	#550	1	2	yes	—
322	C₄×C₁₃	C₂×#135	1	4	yes	—
323	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
324	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
325	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
326	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
327	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
328	C₂²×D₄	—	2	1	no	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
331	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
332	C₂³×C₄	—	2	1	no	—
333	C₂³×C₄	—	2	2	no	—
334	C₂×Q₁₆	—	4	4	no	—
335	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
336	C₂×SD₁₆	—	2	8	no	—
337	C₂×SD₁₆	—	2	4	no	—
338	C₂×SD₁₆	—	4	4	no	—
339	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
340	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
341	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
342	C₂×D₈	—	4	4	no	—
343	C₂×D₈	C₂³×C₁₃	1	8	yes	—
344	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
345	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
346	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
347	C₄⋊Q₈	—	2	2	no	—
348	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
349	#127	—	2	2	no	—
350	#127	C₂³×C₁₃	1	4	yes	—
351	#126	—	2	16	no	—
352	#124	—	2	8	no	—
353	#124	—	2	4	no	—
354	#124	—	2	4	no	—
355	#124	C₂³×C₁₃	1	8	yes	—
356	#124	C₂³×C₁₃	1	8	yes	—
357	#123	—	2	16	no	—
358	C₂²⋊Q₈	—	2	8	no	—
359	C₄×Q₈	—	2	4	no	—
360	C₄×Q₈	—	2	2	no	—
361	C₄×Q₈	D₄×C₁₃	1	4	yes	—
362	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
363	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
364	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
365	C₄×D₄	—	2	8	no	—
366	C₄×D₄	—	2	2	no	—
367	C₄×D₄	—	2	4	no	—
368	C₄×D₄	C₂³×C₁₃	1	4	yes	—
369	C₄×D₄	C₂³×C₁₃	1	8	yes	—
370	#117	—	2	8	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	2	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
376	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	2	no	—
381	C₂×C₂²⋊C₄	—	2	2	no	—
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₂²⋊C₄	—	2	2	no	—
384	C₂×C₂²⋊C₄	—	2	2	no	—
385	C₂×C₄²	—	2	2	no	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
388	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
389	#106	C₂³×C₁₃	1	4	yes	—
390	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
391	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
392	#103	C₂³×C₁₃	1	8	yes	—
393	#103	C₂³×C₁₃	1	4	yes	—
394	#102	C₂³×C₁₃	1	8	yes	—
395	#102	C₂³×C₁₃	1	4	yes	—
396	C₄×C₈	C₂³×C₁₃	1	4	yes	—
397	C₄×C₈	C₂³×C₁₃	1	8	yes	—
398	C₂×C₁₃	—	8	2	no	—
399	C₂×C₁₃	—	8	4	no	—
400	C₂×C₁₃	#3394	1	4	yes	direct product factor
401	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
402	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
403	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
404	C₂⁴	—	2	1	no	—
405	C₂⁴	—	2	2	no	—
406	C₂×Q₈	—	2	4	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	4	no	—
411	C₂×Q₈	—	2	4	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
414	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
415	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	4	4	no	—
425	C₂×D₄	—	8	2	no	—
426	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
427	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	8	no	—
434	C₂²×C₄	—	4	4	no	—
435	C₂²×C₄	—	8	4	no	—
436	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
437	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
438	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
440	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
441	Q₁₆	—	4	8	no	—
442	SD₁₆	—	2	16	no	—
443	SD₁₆	—	2	8	no	—
444	SD₁₆	—	4	8	no	—
445	D₈	—	4	8	no	—
446	C₂×C₈	—	2	4	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	C₁₃×#41	1	4	yes	—
449	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
450	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
451	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
452	C₄⋊C₄	—	2	4	no	—
453	C₄⋊C₄	—	2	8	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
459	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
460	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
461	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
462	C₂²⋊C₄	—	2	8	no	—
463	C₂²⋊C₄	—	2	8	no	—
464	C₂²⋊C₄	—	2	8	no	—
465	C₂²⋊C₄	—	2	4	no	—
466	C₂²⋊C₄	—	2	8	no	—
467	C₂²⋊C₄	—	2	8	no	—
468	C₄²	—	2	8	no	—
469	C₄²	—	2	4	no	—
470	C₄²	C₂×D₄×C₁₃	1	4	yes	—
471	C₄²	C₂×D₄×C₁₃	1	2	yes	—
472	C₄²	C₂⁴×C₁₃	1	4	yes	—
473	C₄²	C₂⁴×C₁₃	1	2	yes	—
474	C₁₃	C₂×#3394	1	1	yes	characteristic, direct product factor, Sylow
475	C₂³	—	2	2	no	—
476	C₂³	—	2	4	no	—
477	C₂³	—	4	2	no	—
478	C₂³	—	4	4	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	4	no	—
481	C₂³	—	4	4	no	—
482	C₂³	—	4	2	no	—
483	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
484	Q₈	—	2	8	no	—
485	Q₈	—	2	2	no	—
486	Q₈	—	2	4	no	—
487	Q₈	—	2	4	no	—
488	Q₈	—	2	2	no	—
489	Q₈	—	4	2	no	—
490	Q₈	—	4	4	no	—
491	D₄	—	2	2	no	—
492	D₄	—	2	4	no	—
493	D₄	—	2	2	no	—
494	D₄	—	2	4	no	—
495	D₄	—	4	2	no	—
496	D₄	—	4	4	no	—
497	D₄	—	4	8	no	—
498	D₄	—	8	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	4	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	8	no	—
511	C₂×C₄	—	8	8	no	—
512	C₂×C₄	C₁₃×#135	1	4	yes	—
513	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
514	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
515	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
516	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
518	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
519	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
520	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
521	C₈	—	2	4	no	—
522	C₈	—	2	2	no	—
523	C₈	C₂×C₁₃×#41	1	4	yes	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	4	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	4	no	—
530	C₂²	—	8	4	no	—
531	C₂²	—	8	8	no	—
532	C₂²	C₁₃×#550	1	2	yes	—
533	C₂²	C₂×C₁₃×#135	1	2	yes	—
534	C₂²	C₁₃×#577	1	2	yes	—
535	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
536	C₄	—	2	4	no	—
537	C₄	—	2	4	no	—
538	C₄	—	2	2	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	2	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	4	no	—
543	C₄	C₁₃×#550	1	2	yes	—
544	C₄	C₂×C₁₃×#135	1	4	yes	—
545	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
546	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
547	C₂	—	8	2	no	—
548	C₂	—	8	4	no	—
549	C₂	C₁₃×#3394	1	4	yes	direct product factor
550	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
551	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
552	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×#459	C₂
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
1. C₂×C₁₃×#559	C₂	semidirect
2. C₂×C₁₃×#556	C₂	semidirect
3. C₁₃×#3394	C₂	direct (N × H)
4. C₂×C₁₃×#495	C₂	semidirect
5. C₂×C₁₃×#492	C₂	semidirect
6. C₂×C₁₃×#464	C₂	semidirect
7. C₂×C₁₃×#462	C₂	semidirect
8. C₂×C₁₃×#463	C₂	semidirect
10. C₂×C₈×Q₈×C₁₃	C₂	semidirect
11. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
12. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
19. C₁₃×#559	C₂²	semidirect
21. C₁₃×#556	C₂²	semidirect
37. C₁₃×#495	C₂²	semidirect
38. C₁₃×#492	C₂²	semidirect
39. C₁₃×#464	C₂²	semidirect
40. C₁₃×#463	C₂²	semidirect
41. C₁₃×#462	C₂²	semidirect
43. C₈×Q₈×C₁₃	C₂²	semidirect
44. C₄×C₁₃×SD₁₆	C₂²	semidirect
45. C₄×C₁₃×SD₁₆	C₂²	semidirect
128. C₂×#3394	C₁₃	direct (N × H)
199. C₂×#559	C₂×C₁₃	semidirect
200. C₂×#556	C₂×C₁₃	semidirect
201. #3394	C₂×C₁₃	direct (N × H)
202. C₂×#495	C₂×C₁₃	semidirect
203. C₂×#492	C₂×C₁₃	semidirect
204. C₂×#464	C₂×C₁₃	semidirect
205. C₂×#462	C₂×C₁₃	semidirect
206. C₂×#463	C₂×C₁₃	semidirect
208. C₂×C₈×Q₈	C₂×C₁₃	semidirect
209. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
210. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
266. #559	C₂²×C₁₃	semidirect
268. #556	C₂²×C₁₃	semidirect
284. #495	C₂²×C₁₃	semidirect
285. #492	C₂²×C₁₃	semidirect
286. #464	C₂²×C₁₃	semidirect
287. #463	C₂²×C₁₃	semidirect
288. #462	C₂²×C₁₃	semidirect
290. C₈×Q₈	C₂²×C₁₃	semidirect
291. C₄×SD₁₆	C₂²×C₁₃	semidirect
292. C₄×SD₁₆	C₂²×C₁₃	semidirect
400. C₂×C₁₃	#3394	direct (N × H)
474. C₁₃	C₂×#3394	direct (N × H)
549. C₂	C₁₃×#3394	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×#556	2
C₁₃×#3394	2
C₂×C₁₃×#495	2
C₂×C₁₃×#492	2
C₂×C₁₃×#464	2
C₂×C₁₃×#462	2
C₂×C₁₃×#463	2
C₂×C₁₃×#459	2
C₂×C₈×Q₈×C₁₃	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×#3394	13

Subgroups — C2×C13×#3394 #15747729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3394 #15747729