Subgroups — C₂×C₁₃×#2031 #15709810

Order 3328.

1234 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#421	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₃×#104	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#410	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2031	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₃×#344	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₁₃×#533	—	2	2	no	—
13	C₁₃×#533	—	2	2	no	—
14	C₁₃×#533	—	2	2	no	—
15	C₁₃×#533	C₂²	1	4	yes	complemented
16	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
17	C₂×C₁₃×#125	—	2	1	no	—
18	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
19	C₂×C₄×Q₈×C₁₃	—	2	2	no	—
20	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#421	—	2	2	no	—
25	C₁₃×#421	C₂²	1	4	yes	—
26	C₂×C₁₃×#104	—	2	1	no	—
27	C₂×C₁₃×#104	—	2	1	no	—
28	C₂×C₁₃×#104	—	2	2	no	—
29	C₂×C₁₃×#104	—	2	2	no	—
30	C₂×C₁₃×#104	C₂²	1	4	yes	—
31	C₁₃×#410	—	2	2	no	—
32	C₁₃×#410	C₂²	1	4	yes	—
33	C₂×C₁₃×#99	—	2	2	no	—
34	C₁₃×#344	C₂²	1	4	yes	complemented
35	C₁₃×#339	C₂²	1	4	yes	complemented
36	C₁₃×H(3,ℤ/4)	C₂²	1	4	yes	complemented
37	C₂×C₁₃×#41	—	2	1	no	—
38	C₂×C₁₃×#41	—	2	1	no	—
39	C₂×C₁₃×#41	—	2	1	no	—
40	C₂×C₁₃×#41	—	2	1	no	—
41	C₂×C₁₃×#41	—	2	1	no	—
42	C₂×C₁₃×#41	—	2	1	no	—
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂×C₁₃×#41	—	2	1	no	—
45	C₂×C₁₃×#41	—	2	1	no	—
46	C₂×C₁₃×#41	—	2	1	no	—
47	C₂×C₁₃×#41	Q₈	1	2	yes	complemented
48	C₂×C₁₃×#41	C₂³	1	2	yes	—
49	C₂²×Q₈×C₁₃	—	2	2	no	—
50	C₂²×Q₈×C₁₃	Q₈	1	1	yes	characteristic, complemented
51	C₂²×D₄×C₁₃	—	2	1	no	—
52	C₂²×D₄×C₁₃	Q₈	1	1	yes	characteristic, complemented
53	C₂³×C₄×C₁₃	—	2	1	no	—
54	C₂³×C₄×C₁₃	—	2	1	no	—
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×M₁₆	—	2	1	no	—
57	C₂×C₁₃×M₁₆	—	2	1	no	—
58	C₂×C₁₃×M₁₆	—	2	1	no	—
59	C₂×C₁₃×M₁₆	—	2	1	no	—
60	C₂×C₁₃×M₁₆	—	2	1	no	—
61	C₂×C₁₃×M₁₆	—	2	1	no	—
62	C₂×C₁₃×M₁₆	—	2	1	no	—
63	C₂×C₁₃×M₁₆	—	2	1	no	—
64	C₂×C₁₃×M₁₆	—	2	1	no	—
65	C₂×C₁₃×M₁₆	—	2	1	no	—
66	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
67	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
68	C₂²×C₈×C₁₃	—	2	1	no	—
69	C₂²×C₈×C₁₃	—	2	1	no	—
70	C₁₃×C₄⋊Q₈	—	2	4	no	—
71	C₁₃×C₄⋊Q₈	—	2	4	no	—
72	C₁₃×#125	—	2	4	no	—
73	C₁₃×#125	—	2	4	no	—
74	C₁₃×C₂²⋊Q₈	—	2	8	no	—
75	C₁₃×C₂²⋊Q₈	—	2	8	no	—
76	C₄×Q₈×C₁₃	—	2	8	no	—
77	C₄×Q₈×C₁₃	—	2	8	no	—
78	C₁₃×#117	—	2	1	no	—
79	C₁₃×#117	—	2	1	no	—
80	C₁₃×#117	—	2	1	no	—
81	C₁₃×#117	—	2	1	no	—
82	C₁₃×#117	—	2	1	no	—
83	C₁₃×#117	—	2	1	no	—
84	C₁₃×#117	—	2	1	no	—
85	C₁₃×#117	D₄	1	2	yes	—
86	C₁₃×#117	D₄	1	2	yes	—
87	C₁₃×#117	C₂³	1	2	yes	—
88	C₁₃×#117	C₂³	1	2	yes	—
89	C₁₃×#117	C₂³	1	2	yes	—
90	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
98	C₂×C₄²×C₁₃	—	2	1	no	—
99	C₂×C₄²×C₁₃	—	2	1	no	—
100	C₂×C₄²×C₁₃	—	2	1	no	—
101	C₂×C₄²×C₁₃	—	2	1	no	—
102	C₂×C₄²×C₁₃	—	2	1	no	—
103	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₁₃	D₄	1	2	yes	—
106	C₂×C₄²×C₁₃	D₄	1	2	yes	—
107	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
108	C₁₃×#104	—	2	4	no	—
109	C₁₃×#104	—	2	4	no	—
110	C₁₃×#104	—	2	8	no	—
111	C₁₃×#99	—	2	8	no	—
112	C₂×#2031	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂⁴×C₁₃	—	2	1	no	—
114	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₁₃×#41	—	2	2	no	—
116	C₁₃×#41	—	2	2	no	—
117	C₁₃×#41	—	2	2	no	—
118	C₁₃×#41	—	2	2	no	—
119	C₁₃×#41	—	2	2	no	—
120	C₁₃×#41	—	2	2	no	—
121	C₁₃×#41	—	2	2	no	—
122	C₁₃×#41	—	2	2	no	—
123	C₁₃×#41	—	4	1	no	—
124	C₁₃×#41	—	4	1	no	—
125	C₁₃×#41	—	4	1	no	—
126	C₁₃×#41	—	4	1	no	—
127	C₁₃×#41	—	4	1	no	—
128	C₁₃×#41	—	4	1	no	—
129	C₁₃×#41	—	4	1	no	—
130	C₁₃×#41	—	4	1	no	—
131	C₂×Q₈×C₁₃	—	2	8	no	—
132	C₂×Q₈×C₁₃	—	2	1	no	—
133	C₂×Q₈×C₁₃	—	2	1	no	—
134	C₂×Q₈×C₁₃	—	2	1	no	—
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	—	2	1	no	—
137	C₂×Q₈×C₁₃	—	4	8	no	—
138	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	complemented
139	C₂×D₄×C₁₃	—	2	2	no	—
140	C₂×D₄×C₁₃	—	2	2	no	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	4	1	no	—
147	C₂×D₄×C₁₃	—	4	1	no	—
148	C₂×D₄×C₁₃	—	4	1	no	—
149	C₂×D₄×C₁₃	—	4	1	no	—
150	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	complemented
151	C₂²×C₄×C₁₃	—	2	1	no	—
152	C₂²×C₄×C₁₃	—	2	1	no	—
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	2	2	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	2	no	—
159	C₂²×C₄×C₁₃	—	2	2	no	—
160	C₂²×C₄×C₁₃	—	4	4	no	—
161	C₂²×C₄×C₁₃	—	4	1	no	—
162	C₂²×C₄×C₁₃	—	4	1	no	—
163	C₂²×C₄×C₁₃	—	4	1	no	—
164	C₂²×C₄×C₁₃	—	4	1	no	—
165	C₂²×C₄×C₁₃	—	4	1	no	—
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
176	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
178	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
179	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₁₃×M₁₆	—	2	2	no	—
181	C₁₃×M₁₆	—	2	2	no	—
182	C₁₃×M₁₆	—	2	2	no	—
183	C₁₃×M₁₆	—	2	2	no	—
184	C₁₃×M₁₆	—	4	1	no	—
185	C₁₃×M₁₆	—	4	1	no	—
186	C₁₃×M₁₆	—	4	1	no	—
187	C₁₃×M₁₆	—	4	1	no	—
188	C₂×C₈×C₁₃	—	2	2	no	—
189	C₂×C₈×C₁₃	—	2	2	no	—
190	C₂×C₈×C₁₃	—	4	1	no	—
191	C₂×C₈×C₁₃	—	4	1	no	—
192	C₂×C₈×C₁₃	—	4	1	no	—
193	C₂×C₈×C₁₃	—	4	1	no	—
194	C₁₃×C₄⋊C₄	—	2	16	no	—
195	C₁₃×C₄⋊C₄	—	2	8	no	—
196	C₁₃×C₄⋊C₄	—	2	2	no	—
197	C₁₃×C₄⋊C₄	—	2	2	no	—
198	C₁₃×C₄⋊C₄	—	2	2	no	—
199	C₁₃×C₄⋊C₄	—	2	2	no	—
200	C₁₃×C₄⋊C₄	—	2	2	no	—
201	C₁₃×C₄⋊C₄	—	4	1	no	—
202	C₁₃×C₂²⋊C₄	—	2	2	no	—
203	C₁₃×C₂²⋊C₄	—	2	2	no	—
204	C₁₃×C₂²⋊C₄	—	2	2	no	—
205	C₁₃×C₂²⋊C₄	—	2	2	no	—
206	C₁₃×C₂²⋊C₄	—	4	1	no	—
207	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
208	C₄²×C₁₃	—	2	2	no	—
209	C₄²×C₁₃	—	2	1	no	—
210	C₄²×C₁₃	—	2	1	no	—
211	C₄²×C₁₃	—	2	2	no	—
212	C₄²×C₁₃	—	2	2	no	—
213	C₄²×C₁₃	—	2	2	no	—
214	C₄²×C₁₃	—	2	2	no	—
215	C₄²×C₁₃	—	2	2	no	—
216	C₄²×C₁₃	—	4	1	no	—
217	C₄²×C₁₃	C₂×D₄	1	2	yes	—
218	C₄²×C₁₃	C₂×D₄	1	2	yes	—
219	C₄²×C₁₃	C₂×D₄	1	4	yes	—
220	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
221	C₂×#421	C₂×C₁₃	1	1	yes	characteristic
222	C₂²×#104	C₂×C₁₃	1	1	yes	characteristic
223	C₂×#410	C₂×C₁₃	1	1	yes	characteristic
224	#2031	C₂×C₁₃	1	8	yes	direct product factor
225	C₂×#344	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₂×#339	C₂×C₁₃	1	1	yes	characteristic, complemented
227	C₂×H(3,ℤ/4)	C₂×C₁₃	1	1	yes	characteristic, complemented
228	C₂³×C₁₃	—	2	2	no	—
229	C₂³×C₁₃	—	4	2	no	—
230	C₂³×C₁₃	—	4	1	no	—
231	C₂³×C₁₃	—	4	1	no	—
232	C₂³×C₁₃	—	8	2	no	—
233	C₂³×C₁₃	#120	1	1	yes	characteristic
234	C₂³×C₁₃	#120	1	1	yes	characteristic
235	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
236	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
237	C₂³×C₁₃	#124	1	1	yes	characteristic
238	C₂³×C₁₃	#124	1	1	yes	characteristic
239	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
240	Q₈×C₁₃	—	2	2	no	—
241	Q₈×C₁₃	—	2	2	no	—
242	Q₈×C₁₃	—	4	16	no	—
243	Q₈×C₁₃	—	4	1	no	—
244	Q₈×C₁₃	—	4	1	no	—
245	D₄×C₁₃	—	2	2	no	—
246	D₄×C₁₃	—	2	2	no	—
247	D₄×C₁₃	—	4	2	no	—
248	D₄×C₁₃	—	4	2	no	—
249	D₄×C₁₃	—	4	2	no	—
250	D₄×C₁₃	—	4	2	no	—
251	D₄×C₁₃	—	4	1	no	—
252	D₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	4	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	4	4	no	—
260	C₂×C₄×C₁₃	—	4	4	no	—
261	C₂×C₄×C₁₃	—	4	2	no	—
262	C₂×C₄×C₁₃	—	4	4	no	—
263	C₂×C₄×C₁₃	—	4	4	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	2	no	—
267	C₂×C₄×C₁₃	—	4	2	no	—
268	C₂×C₄×C₁₃	—	4	2	no	—
269	C₂×C₄×C₁₃	—	4	2	no	—
270	C₂×C₄×C₁₃	—	4	2	no	—
271	C₂×C₄×C₁₃	—	8	2	no	—
272	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
273	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
277	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
278	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
279	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
280	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
281	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
282	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
283	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
284	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
285	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
286	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
287	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
288	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
289	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
290	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
291	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
292	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
293	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
294	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
297	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
299	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
300	C₈×C₁₃	—	4	2	no	—
301	C₈×C₁₃	—	4	2	no	—
302	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
303	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
304	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
305	#533	—	2	2	no	—
306	#533	—	2	2	no	—
307	#533	—	2	2	no	—
308	#533	C₂²×C₁₃	1	4	yes	complemented
309	C₂×C₄⋊Q₈	—	2	1	no	—
310	C₂×#125	—	2	1	no	—
311	C₂×C₂²⋊Q₈	—	2	2	no	—
312	C₂×C₄×Q₈	—	2	2	no	—
313	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
314	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
315	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
316	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
317	#421	—	2	2	no	—
318	#421	C₂²×C₁₃	1	4	yes	—
319	C₂×#104	—	2	1	no	—
320	C₂×#104	—	2	1	no	—
321	C₂×#104	—	2	2	no	—
322	C₂×#104	—	2	2	no	—
323	C₂×#104	C₂²×C₁₃	1	4	yes	—
324	#410	—	2	2	no	—
325	#410	C₂²×C₁₃	1	4	yes	—
326	C₂×#99	—	2	2	no	—
327	#344	C₂²×C₁₃	1	4	yes	complemented
328	#339	C₂²×C₁₃	1	4	yes	complemented
329	H(3,ℤ/4)	C₂²×C₁₃	1	4	yes	complemented
330	C₂²×C₁₃	—	2	2	no	—
331	C₂²×C₁₃	—	2	2	no	—
332	C₂²×C₁₃	—	2	2	no	—
333	C₂²×C₁₃	—	4	1	no	—
334	C₂²×C₁₃	—	4	1	no	—
335	C₂²×C₁₃	—	4	1	no	—
336	C₂²×C₁₃	—	4	1	no	—
337	C₂²×C₁₃	—	4	2	no	—
338	C₂²×C₁₃	—	8	2	no	—
339	C₂²×C₁₃	—	8	2	no	—
340	C₂²×C₁₃	—	8	2	no	—
341	C₂²×C₁₃	#393	1	1	yes	characteristic
342	C₂²×C₁₃	#393	1	1	yes	characteristic
343	C₂²×C₁₃	#393	1	1	yes	characteristic
344	C₂²×C₁₃	#393	1	1	yes	characteristic
345	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
346	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
347	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
348	C₄×C₁₃	—	2	4	no	—
349	C₄×C₁₃	—	4	2	no	—
350	C₄×C₁₃	—	4	4	no	—
351	C₄×C₁₃	—	4	4	no	—
352	C₄×C₁₃	—	4	2	no	—
353	C₄×C₁₃	—	8	2	no	—
354	C₄×C₁₃	#393	1	1	yes	characteristic
355	C₄×C₁₃	#393	1	1	yes	characteristic
356	C₄×C₁₃	#393	1	1	yes	characteristic
357	C₄×C₁₃	#393	1	1	yes	characteristic
358	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
359	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
360	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
361	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
362	C₂×#41	—	2	1	no	—
363	C₂×#41	—	2	1	no	—
364	C₂×#41	—	2	1	no	—
365	C₂×#41	—	2	1	no	—
366	C₂×#41	—	2	1	no	—
367	C₂×#41	—	2	1	no	—
368	C₂×#41	—	2	1	no	—
369	C₂×#41	—	2	1	no	—
370	C₂×#41	—	2	1	no	—
371	C₂×#41	—	2	1	no	—
372	C₂×#41	Q₈×C₁₃	1	2	yes	complemented
373	C₂×#41	C₂³×C₁₃	1	2	yes	—
374	C₂²×Q₈	—	2	2	no	—
375	C₂²×Q₈	Q₈×C₁₃	1	1	yes	characteristic, complemented
376	C₂²×D₄	—	2	1	no	—
377	C₂²×D₄	Q₈×C₁₃	1	1	yes	characteristic, complemented
378	C₂³×C₄	—	2	1	no	—
379	C₂³×C₄	—	2	1	no	—
380	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	—	2	1	no	—
384	C₂×M₁₆	—	2	1	no	—
385	C₂×M₁₆	—	2	1	no	—
386	C₂×M₁₆	—	2	1	no	—
387	C₂×M₁₆	—	2	1	no	—
388	C₂×M₁₆	—	2	1	no	—
389	C₂×M₁₆	—	2	1	no	—
390	C₂×M₁₆	—	2	1	no	—
391	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
392	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
393	C₂²×C₈	—	2	1	no	—
394	C₂²×C₈	—	2	1	no	—
395	C₄⋊Q₈	—	2	4	no	—
396	C₄⋊Q₈	—	2	4	no	—
397	#125	—	2	4	no	—
398	#125	—	2	4	no	—
399	C₂²⋊Q₈	—	2	8	no	—
400	C₂²⋊Q₈	—	2	8	no	—
401	C₄×Q₈	—	2	8	no	—
402	C₄×Q₈	—	2	8	no	—
403	#117	—	2	1	no	—
404	#117	—	2	1	no	—
405	#117	—	2	1	no	—
406	#117	—	2	1	no	—
407	#117	—	2	1	no	—
408	#117	—	2	1	no	—
409	#117	—	2	1	no	—
410	#117	D₄×C₁₃	1	2	yes	—
411	#117	D₄×C₁₃	1	2	yes	—
412	#117	C₂³×C₁₃	1	2	yes	—
413	#117	C₂³×C₁₃	1	2	yes	—
414	#117	C₂³×C₁₃	1	2	yes	—
415	C₂×C₄⋊C₄	—	2	4	no	—
416	C₂×C₄⋊C₄	—	2	2	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
423	C₂×C₄²	—	2	1	no	—
424	C₂×C₄²	—	2	1	no	—
425	C₂×C₄²	—	2	1	no	—
426	C₂×C₄²	—	2	1	no	—
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	D₄×C₁₃	1	2	yes	—
429	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
430	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
431	C₂×C₄²	D₄×C₁₃	1	2	yes	—
432	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
433	#104	—	2	4	no	—
434	#104	—	2	4	no	—
435	#104	—	2	8	no	—
436	#99	—	2	8	no	—
437	C₂×C₁₃	—	2	1	no	—
438	C₂×C₁₃	—	2	1	no	—
439	C₂×C₁₃	—	2	1	no	—
440	C₂×C₁₃	—	2	1	no	—
441	C₂×C₁₃	—	2	1	no	—
442	C₂×C₁₃	—	2	1	no	—
443	C₂×C₁₃	—	8	2	no	—
444	C₂×C₁₃	#2031	1	2	yes	direct product factor
445	C₂×C₁₃	C₂×#393	1	1	yes	characteristic
446	C₂⁴	—	2	1	no	—
447	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
448	#41	—	2	2	no	—
449	#41	—	2	2	no	—
450	#41	—	2	2	no	—
451	#41	—	2	2	no	—
452	#41	—	2	2	no	—
453	#41	—	2	2	no	—
454	#41	—	2	2	no	—
455	#41	—	2	2	no	—
456	#41	—	4	1	no	—
457	#41	—	4	1	no	—
458	#41	—	4	1	no	—
459	#41	—	4	1	no	—
460	#41	—	4	1	no	—
461	#41	—	4	1	no	—
462	#41	—	4	1	no	—
463	#41	—	4	1	no	—
464	C₂×Q₈	—	2	8	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	4	8	no	—
471	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	complemented
472	C₂×D₄	—	2	2	no	—
473	C₂×D₄	—	2	2	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	4	1	no	—
480	C₂×D₄	—	4	1	no	—
481	C₂×D₄	—	4	1	no	—
482	C₂×D₄	—	4	1	no	—
483	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	complemented
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	4	4	no	—
494	C₂²×C₄	—	4	1	no	—
495	C₂²×C₄	—	4	1	no	—
496	C₂²×C₄	—	4	1	no	—
497	C₂²×C₄	—	4	1	no	—
498	C₂²×C₄	—	4	1	no	—
499	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
503	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
504	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
505	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
506	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
507	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
508	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
509	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
510	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
511	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
512	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
513	M₁₆	—	2	2	no	—
514	M₁₆	—	2	2	no	—
515	M₁₆	—	2	2	no	—
516	M₁₆	—	2	2	no	—
517	M₁₆	—	4	1	no	—
518	M₁₆	—	4	1	no	—
519	M₁₆	—	4	1	no	—
520	M₁₆	—	4	1	no	—
521	C₂×C₈	—	2	2	no	—
522	C₂×C₈	—	2	2	no	—
523	C₂×C₈	—	4	1	no	—
524	C₂×C₈	—	4	1	no	—
525	C₂×C₈	—	4	1	no	—
526	C₂×C₈	—	4	1	no	—
527	C₄⋊C₄	—	2	16	no	—
528	C₄⋊C₄	—	2	8	no	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	2	2	no	—
533	C₄⋊C₄	—	2	2	no	—
534	C₄⋊C₄	—	4	1	no	—
535	C₂²⋊C₄	—	2	2	no	—
536	C₂²⋊C₄	—	2	2	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	4	1	no	—
540	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
541	C₄²	—	2	2	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	2	2	no	—
545	C₄²	—	2	2	no	—
546	C₄²	—	2	2	no	—
547	C₄²	—	2	2	no	—
548	C₄²	—	2	2	no	—
549	C₄²	—	4	1	no	—
550	C₄²	C₂×D₄×C₁₃	1	2	yes	—
551	C₄²	C₂×D₄×C₁₃	1	2	yes	—
552	C₄²	C₂×D₄×C₁₃	1	4	yes	—
553	C₁₃	C₂×#2031	1	1	yes	characteristic, direct product factor, Sylow
554	C₂³	—	2	2	no	—
555	C₂³	—	4	2	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	8	2	no	—
559	C₂³	C₁₃×#120	1	1	yes	characteristic
560	C₂³	C₁₃×#120	1	1	yes	characteristic
561	C₂³	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
562	C₂³	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
563	C₂³	C₁₃×#124	1	1	yes	characteristic
564	C₂³	C₁₃×#124	1	1	yes	characteristic
565	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
566	Q₈	—	2	2	no	—
567	Q₈	—	2	2	no	—
568	Q₈	—	4	16	no	—
569	Q₈	—	4	1	no	—
570	Q₈	—	4	1	no	—
571	D₄	—	2	2	no	—
572	D₄	—	2	2	no	—
573	D₄	—	4	2	no	—
574	D₄	—	4	2	no	—
575	D₄	—	4	2	no	—
576	D₄	—	4	2	no	—
577	D₄	—	4	1	no	—
578	D₄	—	4	1	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	4	4	no	—
586	C₂×C₄	—	4	4	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	4	no	—
589	C₂×C₄	—	4	4	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	4	2	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	8	2	no	—
598	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
599	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
600	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
601	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
602	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
603	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
604	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
605	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
606	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
607	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
608	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
609	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
610	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
611	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
612	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
613	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
614	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
615	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
616	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
617	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
618	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
619	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
620	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
621	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
622	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
623	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
624	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
625	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
626	C₈	—	4	2	no	—
627	C₈	—	4	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	8	2	no	—
637	C₂²	—	8	2	no	—
638	C₂²	—	8	2	no	—
639	C₂²	C₁₃×#393	1	1	yes	characteristic
640	C₂²	C₁₃×#393	1	1	yes	characteristic
641	C₂²	C₁₃×#393	1	1	yes	characteristic
642	C₂²	C₁₃×#393	1	1	yes	characteristic
643	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
644	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
645	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
646	C₄	—	2	4	no	—
647	C₄	—	4	2	no	—
648	C₄	—	4	4	no	—
649	C₄	—	4	4	no	—
650	C₄	—	4	2	no	—
651	C₄	—	8	2	no	—
652	C₄	C₁₃×#393	1	1	yes	characteristic
653	C₄	C₁₃×#393	1	1	yes	characteristic
654	C₄	C₁₃×#393	1	1	yes	characteristic
655	C₄	C₁₃×#393	1	1	yes	characteristic
656	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
657	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
658	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
659	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
660	C₂	—	2	1	no	—
661	C₂	—	2	1	no	—
662	C₂	—	2	1	no	—
663	C₂	—	2	1	no	—
664	C₂	—	2	1	no	—
665	C₂	—	2	1	no	—
666	C₂	—	8	2	no	—
667	C₂	C₁₃×#2031	1	2	yes	direct product factor
668	C₂	C₂×C₁₃×#393	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	#393
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#533	C₂	semidirect
5. C₁₃×#2031	C₂	direct (N × H)
6. C₂×C₁₃×#344	C₂	semidirect
7. C₂×C₁₃×#339	C₂	semidirect
8. C₂×C₁₃×H(3,ℤ/4)	C₂	semidirect
15. C₁₃×#533	C₂²	semidirect
34. C₁₃×#344	C₂²	semidirect
35. C₁₃×#339	C₂²	semidirect
36. C₁₃×H(3,ℤ/4)	C₂²	semidirect
47. C₂×C₁₃×#41	Q₈	semidirect
50. C₂²×Q₈×C₁₃	Q₈	semidirect
52. C₂²×D₄×C₁₃	Q₈	semidirect
112. C₂×#2031	C₁₃	direct (N × H)
138. C₂×Q₈×C₁₃	C₂×Q₈	semidirect
150. C₂×D₄×C₁₃	C₂×Q₈	semidirect
220. C₂×#533	C₂×C₁₃	semidirect
224. #2031	C₂×C₁₃	direct (N × H)
225. C₂×#344	C₂×C₁₃	semidirect
226. C₂×#339	C₂×C₁₃	semidirect
227. C₂×H(3,ℤ/4)	C₂×C₁₃	semidirect
308. #533	C₂²×C₁₃	semidirect
327. #344	C₂²×C₁₃	semidirect
328. #339	C₂²×C₁₃	semidirect
329. H(3,ℤ/4)	C₂²×C₁₃	semidirect
372. C₂×#41	Q₈×C₁₃	semidirect
375. C₂²×Q₈	Q₈×C₁₃	semidirect
377. C₂²×D₄	Q₈×C₁₃	semidirect
444. C₂×C₁₃	#2031	direct (N × H)
471. C₂×Q₈	C₂×Q₈×C₁₃	semidirect
483. C₂×D₄	C₂×Q₈×C₁₃	semidirect
553. C₁₃	C₂×#2031	direct (N × H)
667. C₂	C₁₃×#2031	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×#533	2
C₂×C₁₃×#421	2
C₂²×C₁₃×#104	2
C₂×C₁₃×#410	2
C₁₃×#2031	2
C₂×C₁₃×#344	2
C₂×C₁₃×#339	2
C₂×C₁₃×H(3,ℤ/4)	2
C₂×#2031	13

Subgroups — C2×C13×#2031 #15709810

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2031 #15709810