Subgroups — C₂×C₁₃×#3175 #15747018

Order 3328.

1970 conjugacy classes of subgroups.

The subgroup lattice has 512 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×#3175	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#489	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#468	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₃×#440	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
15	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#542	—	2	8	no	—
19	C₁₃×#542	C₂²	1	16	yes	complemented
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₁₃×#126	—	2	2	no	—
22	C₂×C₁₃×#124	—	2	2	no	—
23	C₂×C₁₃×#124	C₂²	1	2	yes	—
24	C₂×C₁₃×#123	—	2	2	no	—
25	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₁₃×#121	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
30	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
31	C₁₃×#500	C₂²	1	8	yes	complemented
32	C₁₃×#495	C₂²	1	8	yes	complemented
33	C₁₃×#489	C₂²	1	16	yes	complemented
34	C₁₃×#468	C₂²	1	16	yes	complemented
35	C₁₃×#467	C₂²	1	8	yes	complemented
36	C₁₃×#466	C₂²	1	8	yes	—
37	C₁₃×#440	C₂²	1	16	yes	complemented
38	C₄×C₁₃×Q₁₆	C₂²	1	8	yes	complemented
39	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
40	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#107	C₂²	1	2	yes	—
43	C₂×C₁₃×#103	C₂²	1	2	yes	—
44	C₂×C₁₃×#103	C₂²	1	2	yes	—
45	C₂×C₁₃×#102	C₂²	1	2	yes	—
46	C₂×C₁₃×#102	C₂²	1	2	yes	—
47	C₁₃×#405	C₂²	1	8	yes	complemented
48	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
52	C₂²×Q₈×C₁₃	—	2	2	no	—
53	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
54	C₂²×D₄×C₁₃	—	2	2	no	—
55	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₃	—	2	2	no	—
57	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×Q₁₆	—	2	4	no	—
59	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
60	C₂×C₁₃×SD₁₆	—	2	8	no	—
61	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
62	C₂×C₁₃×D₈	—	2	4	no	—
63	C₂×C₁₃×D₈	C₂³	1	4	yes	—
64	C₂×C₁₃×M₁₆	—	2	4	no	—
65	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
66	C₂²×C₈×C₁₃	—	2	4	no	—
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₁₃×C₄⋊Q₈	—	2	4	no	—
73	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
74	C₁₃×#126	—	2	16	no	—
75	C₁₃×#124	—	2	16	no	—
76	C₁₃×#124	—	2	4	no	—
77	C₁₃×#124	C₂³	1	8	yes	—
78	C₁₃×#123	—	2	16	no	—
79	C₁₃×C₂²⋊Q₈	—	2	4	no	—
80	C₁₃×C₂²⋊Q₈	—	2	16	no	—
81	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
82	C₁₃×#121	—	2	4	no	—
83	C₁₃×#121	C₂³	1	8	yes	—
84	C₄×Q₈×C₁₃	—	2	4	no	—
85	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
86	C₄×D₄×C₁₃	—	2	4	no	—
87	C₄×D₄×C₁₃	C₂³	1	8	yes	—
88	C₁₃×#117	D₄	1	4	yes	—
89	C₁₃×#117	C₂³	1	4	yes	—
90	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
93	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
94	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
100	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
102	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
103	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₁₃	—	2	2	no	—
105	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
107	C₁₃×#107	C₂³	1	4	yes	—
108	C₁₃×#107	C₂³	1	4	yes	—
109	C₁₃×#107	C₂³	1	8	yes	—
110	C₁₃×#103	C₂³	1	8	yes	—
111	C₁₃×#103	C₂³	1	8	yes	—
112	C₁₃×#102	C₂³	1	8	yes	—
113	C₁₃×#102	C₂³	1	8	yes	—
114	C₁₃×#97	C₂³	1	4	yes	—
115	C₁₃×#97	C₂³	1	4	yes	—
116	C₄×C₈×C₁₃	C₂³	1	4	yes	—
117	C₄×C₈×C₁₃	C₂³	1	4	yes	—
118	C₂×#3175	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂⁴×C₁₃	—	2	2	no	—
120	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂×Q₈×C₁₃	—	2	2	no	—
122	C₂×Q₈×C₁₃	—	2	8	no	—
123	C₂×Q₈×C₁₃	—	2	4	no	—
124	C₂×Q₈×C₁₃	—	2	4	no	—
125	C₂×Q₈×C₁₃	—	8	4	no	—
126	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
127	C₂×D₄×C₁₃	—	2	8	no	—
128	C₂×D₄×C₁₃	—	2	2	no	—
129	C₂×D₄×C₁₃	—	2	4	no	—
130	C₂×D₄×C₁₃	—	2	4	no	—
131	C₂×D₄×C₁₃	—	8	4	no	—
132	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
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	2	no	—
138	C₂²×C₄×C₁₃	—	2	8	no	—
139	C₂²×C₄×C₁₃	—	8	4	no	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₁₃×Q₁₆	—	2	8	no	—
149	C₁₃×SD₁₆	—	2	16	no	—
150	C₁₃×D₈	—	2	8	no	—
151	C₁₃×M₁₆	—	2	8	no	—
152	C₂×C₈×C₁₃	—	2	2	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₂×C₈×C₁₃	—	2	8	no	—
155	C₂×C₈×C₁₃	#41	1	4	yes	—
156	C₂×C₈×C₁₃	#41	1	4	yes	—
157	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
158	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
159	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
160	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
161	C₁₃×C₄⋊C₄	—	2	8	no	—
162	C₁₃×C₄⋊C₄	—	2	8	no	—
163	C₁₃×C₄⋊C₄	—	2	8	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
167	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
168	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
169	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
170	C₁₃×C₂²⋊C₄	—	2	8	no	—
171	C₁₃×C₂²⋊C₄	—	2	8	no	—
172	C₁₃×C₂²⋊C₄	—	2	8	no	—
173	C₁₃×C₂²⋊C₄	—	2	8	no	—
174	C₁₃×C₂²⋊C₄	—	2	8	no	—
175	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
176	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
177	C₄²×C₁₃	—	2	8	no	—
178	C₄²×C₁₃	C₂×D₄	1	2	yes	—
179	C₄²×C₁₃	C₂×D₄	1	2	yes	—
180	C₄²×C₁₃	C₂⁴	1	2	yes	—
181	C₄²×C₁₃	C₂⁴	1	2	yes	—
182	C₂×#542	C₂×C₁₃	1	2	yes	complemented
183	#3175	C₂×C₁₃	1	16	yes	direct product factor
184	C₂×#500	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂×#495	C₂×C₁₃	1	1	yes	characteristic, complemented
186	C₂×#489	C₂×C₁₃	1	2	yes	complemented
187	C₂×#468	C₂×C₁₃	1	2	yes	complemented
188	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
189	C₂×#466	C₂×C₁₃	1	1	yes	characteristic
190	C₂×#440	C₂×C₁₃	1	2	yes	complemented
191	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
192	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
193	C₂×#405	C₂×C₁₃	1	1	yes	characteristic, complemented
194	C₂³×C₁₃	—	2	2	no	—
195	C₂³×C₁₃	—	2	2	no	—
196	C₂³×C₁₃	—	2	2	no	—
197	C₂³×C₁₃	—	2	4	no	—
198	C₂³×C₁₃	—	4	4	no	—
199	C₂³×C₁₃	—	4	4	no	—
200	C₂³×C₁₃	—	4	4	no	—
201	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
202	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
203	Q₈×C₁₃	—	2	4	no	—
204	Q₈×C₁₃	—	2	4	no	—
205	Q₈×C₁₃	—	4	4	no	—
206	Q₈×C₁₃	—	8	8	no	—
207	D₄×C₁₃	—	2	4	no	—
208	D₄×C₁₃	—	2	4	no	—
209	D₄×C₁₃	—	4	4	no	—
210	D₄×C₁₃	—	8	8	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	4	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	4	no	—
220	C₂×C₄×C₁₃	—	2	4	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	4	4	no	—
223	C₂×C₄×C₁₃	—	4	4	no	—
224	C₂×C₄×C₁₃	—	4	4	no	—
225	C₂×C₄×C₁₃	—	8	8	no	—
226	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
227	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
230	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
231	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
233	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
234	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
235	C₈×C₁₃	—	2	2	no	—
236	C₈×C₁₃	—	2	2	no	—
237	C₈×C₁₃	C₂×#41	1	4	yes	—
238	C₈×C₁₃	C₂×#41	1	4	yes	—
239	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
240	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
241	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
242	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
243	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
244	#542	—	2	8	no	—
245	#542	C₂²×C₁₃	1	16	yes	complemented
246	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
247	C₂×#126	—	2	2	no	—
248	C₂×#124	—	2	2	no	—
249	C₂×#124	C₂²×C₁₃	1	2	yes	—
250	C₂×#123	—	2	2	no	—
251	C₂×C₂²⋊Q₈	—	2	2	no	—
252	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
253	C₂×#121	C₂²×C₁₃	1	2	yes	—
254	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
255	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
256	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
257	#500	C₂²×C₁₃	1	8	yes	complemented
258	#495	C₂²×C₁₃	1	8	yes	complemented
259	#489	C₂²×C₁₃	1	16	yes	complemented
260	#468	C₂²×C₁₃	1	16	yes	complemented
261	#467	C₂²×C₁₃	1	8	yes	complemented
262	#466	C₂²×C₁₃	1	8	yes	—
263	#440	C₂²×C₁₃	1	16	yes	complemented
264	C₄×Q₁₆	C₂²×C₁₃	1	8	yes	complemented
265	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
266	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×#107	C₂²×C₁₃	1	2	yes	—
269	C₂×#103	C₂²×C₁₃	1	2	yes	—
270	C₂×#103	C₂²×C₁₃	1	2	yes	—
271	C₂×#102	C₂²×C₁₃	1	2	yes	—
272	C₂×#102	C₂²×C₁₃	1	2	yes	—
273	#405	C₂²×C₁₃	1	8	yes	complemented
274	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
278	C₂²×C₁₃	—	2	2	no	—
279	C₂²×C₁₃	—	2	2	no	—
280	C₂²×C₁₃	—	2	2	no	—
281	C₂²×C₁₃	—	4	4	no	—
282	C₂²×C₁₃	—	4	4	no	—
283	C₂²×C₁₃	—	4	4	no	—
284	C₂²×C₁₃	—	4	4	no	—
285	C₂²×C₁₃	—	8	8	no	—
286	C₂²×C₁₃	#532	1	2	yes	—
287	C₂²×C₁₃	#576	1	2	yes	—
288	C₂²×C₁₃	#578	1	2	yes	—
289	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
290	C₄×C₁₃	—	2	2	no	—
291	C₄×C₁₃	—	2	2	no	—
292	C₄×C₁₃	—	2	2	no	—
293	C₄×C₁₃	—	2	2	no	—
294	C₄×C₁₃	—	2	2	no	—
295	C₄×C₁₃	—	4	4	no	—
296	C₄×C₁₃	—	4	4	no	—
297	C₄×C₁₃	—	4	4	no	—
298	C₄×C₁₃	#532	1	2	yes	—
299	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
300	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
301	C₂²×Q₈	—	2	2	no	—
302	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
303	C₂²×D₄	—	2	2	no	—
304	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
305	C₂³×C₄	—	2	2	no	—
306	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
307	C₂×Q₁₆	—	2	4	no	—
308	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
309	C₂×SD₁₆	—	2	8	no	—
310	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
311	C₂×D₈	—	2	4	no	—
312	C₂×D₈	C₂³×C₁₃	1	4	yes	—
313	C₂×M₁₆	—	2	4	no	—
314	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
315	C₂²×C₈	—	2	4	no	—
316	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
318	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
319	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
320	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
321	C₄⋊Q₈	—	2	4	no	—
322	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
323	#126	—	2	16	no	—
324	#124	—	2	16	no	—
325	#124	—	2	4	no	—
326	#124	C₂³×C₁₃	1	8	yes	—
327	#123	—	2	16	no	—
328	C₂²⋊Q₈	—	2	4	no	—
329	C₂²⋊Q₈	—	2	16	no	—
330	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
331	#121	—	2	4	no	—
332	#121	C₂³×C₁₃	1	8	yes	—
333	C₄×Q₈	—	2	4	no	—
334	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
335	C₄×D₄	—	2	4	no	—
336	C₄×D₄	C₂³×C₁₃	1	8	yes	—
337	#117	D₄×C₁₃	1	4	yes	—
338	#117	C₂³×C₁₃	1	4	yes	—
339	C₂×C₄⋊C₄	—	2	2	no	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	—	2	2	no	—
342	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
343	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
352	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
353	C₂×C₄²	—	2	2	no	—
354	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
355	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
356	#107	C₂³×C₁₃	1	4	yes	—
357	#107	C₂³×C₁₃	1	4	yes	—
358	#107	C₂³×C₁₃	1	8	yes	—
359	#103	C₂³×C₁₃	1	8	yes	—
360	#103	C₂³×C₁₃	1	8	yes	—
361	#102	C₂³×C₁₃	1	8	yes	—
362	#102	C₂³×C₁₃	1	8	yes	—
363	#97	C₂³×C₁₃	1	4	yes	—
364	#97	C₂³×C₁₃	1	4	yes	—
365	C₄×C₈	C₂³×C₁₃	1	4	yes	—
366	C₄×C₈	C₂³×C₁₃	1	4	yes	—
367	C₂×C₁₃	—	4	2	no	—
368	C₂×C₁₃	—	8	4	no	—
369	C₂×C₁₃	#3175	1	4	yes	direct product factor
370	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
371	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
372	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
373	C₂⁴	—	2	2	no	—
374	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	8	no	—
377	C₂×Q₈	—	2	4	no	—
378	C₂×Q₈	—	2	4	no	—
379	C₂×Q₈	—	8	4	no	—
380	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
381	C₂×D₄	—	2	8	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	8	4	no	—
386	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	8	no	—
393	C₂²×C₄	—	8	4	no	—
394	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
400	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
401	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
402	Q₁₆	—	2	8	no	—
403	SD₁₆	—	2	16	no	—
404	D₈	—	2	8	no	—
405	M₁₆	—	2	8	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	8	no	—
409	C₂×C₈	C₁₃×#41	1	4	yes	—
410	C₂×C₈	C₁₃×#41	1	4	yes	—
411	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
412	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
413	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
414	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
415	C₄⋊C₄	—	2	8	no	—
416	C₄⋊C₄	—	2	8	no	—
417	C₄⋊C₄	—	2	8	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
421	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
422	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
423	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
424	C₂²⋊C₄	—	2	8	no	—
425	C₂²⋊C₄	—	2	8	no	—
426	C₂²⋊C₄	—	2	8	no	—
427	C₂²⋊C₄	—	2	8	no	—
428	C₂²⋊C₄	—	2	8	no	—
429	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
430	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
431	C₄²	—	2	8	no	—
432	C₄²	C₂×D₄×C₁₃	1	2	yes	—
433	C₄²	C₂×D₄×C₁₃	1	2	yes	—
434	C₄²	C₂⁴×C₁₃	1	2	yes	—
435	C₄²	C₂⁴×C₁₃	1	2	yes	—
436	C₁₃	C₂×#3175	1	1	yes	characteristic, direct product factor, Sylow
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	4	4	no	—
442	C₂³	—	4	4	no	—
443	C₂³	—	4	4	no	—
444	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
445	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
446	Q₈	—	2	4	no	—
447	Q₈	—	2	4	no	—
448	Q₈	—	4	4	no	—
449	Q₈	—	8	8	no	—
450	D₄	—	2	4	no	—
451	D₄	—	2	4	no	—
452	D₄	—	4	4	no	—
453	D₄	—	8	8	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	4	4	no	—
466	C₂×C₄	—	4	4	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	8	8	no	—
469	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
470	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
471	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
472	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
473	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
474	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
475	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
476	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
477	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
478	C₈	—	2	2	no	—
479	C₈	—	2	2	no	—
480	C₈	C₂×C₁₃×#41	1	4	yes	—
481	C₈	C₂×C₁₃×#41	1	4	yes	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	8	8	no	—
490	C₂²	C₁₃×#532	1	2	yes	—
491	C₂²	C₁₃×#576	1	2	yes	—
492	C₂²	C₁₃×#578	1	2	yes	—
493	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	2	2	no	—
498	C₄	—	2	2	no	—
499	C₄	—	4	4	no	—
500	C₄	—	4	4	no	—
501	C₄	—	4	4	no	—
502	C₄	C₁₃×#532	1	2	yes	—
503	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
504	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
505	C₂	—	4	2	no	—
506	C₂	—	8	4	no	—
507	C₂	C₁₃×#3175	1	4	yes	direct product factor
508	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
509	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
510	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×#3175	C₂	direct (N × H)
3. C₂×C₁₃×#500	C₂	semidirect
4. C₂×C₁₃×#495	C₂	semidirect
5. C₂×C₁₃×#489	C₂	semidirect
6. C₂×C₁₃×#468	C₂	semidirect
7. C₂×C₁₃×#467	C₂	semidirect
9. C₂×C₁₃×#440	C₂	semidirect
10. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
11. C₂×C₄×C₁₃×D₈	C₂	semidirect
12. C₂×C₁₃×#405	C₂	semidirect
19. C₁₃×#542	C₂²	semidirect
31. C₁₃×#500	C₂²	semidirect
32. C₁₃×#495	C₂²	semidirect
33. C₁₃×#489	C₂²	semidirect
34. C₁₃×#468	C₂²	semidirect
35. C₁₃×#467	C₂²	semidirect
37. C₁₃×#440	C₂²	semidirect
38. C₄×C₁₃×Q₁₆	C₂²	semidirect
39. C₄×C₁₃×D₈	C₂²	semidirect
47. C₁₃×#405	C₂²	semidirect
118. C₂×#3175	C₁₃	direct (N × H)
182. C₂×#542	C₂×C₁₃	semidirect
183. #3175	C₂×C₁₃	direct (N × H)
184. C₂×#500	C₂×C₁₃	semidirect
185. C₂×#495	C₂×C₁₃	semidirect
186. C₂×#489	C₂×C₁₃	semidirect
187. C₂×#468	C₂×C₁₃	semidirect
188. C₂×#467	C₂×C₁₃	semidirect
190. C₂×#440	C₂×C₁₃	semidirect
191. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
192. C₂×C₄×D₈	C₂×C₁₃	semidirect
193. C₂×#405	C₂×C₁₃	semidirect
245. #542	C₂²×C₁₃	semidirect
257. #500	C₂²×C₁₃	semidirect
258. #495	C₂²×C₁₃	semidirect
259. #489	C₂²×C₁₃	semidirect
260. #468	C₂²×C₁₃	semidirect
261. #467	C₂²×C₁₃	semidirect
263. #440	C₂²×C₁₃	semidirect
264. C₄×Q₁₆	C₂²×C₁₃	semidirect
265. C₄×D₈	C₂²×C₁₃	semidirect
273. #405	C₂²×C₁₃	semidirect
369. C₂×C₁₃	#3175	direct (N × H)
436. C₁₃	C₂×#3175	direct (N × H)
507. C₂	C₁₃×#3175	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×#3175	2
C₂×C₁₃×#500	2
C₂×C₁₃×#495	2
C₂×C₁₃×#489	2
C₂×C₁₃×#468	2
C₂×C₁₃×#467	2
C₂×C₁₃×#466	2
C₂×C₁₃×#440	2
C₂×C₄×C₁₃×Q₁₆	2
C₂×C₄×C₁₃×D₈	2
C₂×C₁₃×#405	2
C₂×#3175	13

Subgroups — C2×C13×#3175 #15747018

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3175 #15747018