Subgroups — C₂×C₁₃×#2193 #15719875

Order 3328.

1098 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#472	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2193	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₃×#362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#359	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#350	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×2₋¹⁺⁴	—	2	1	no	—
10	C₁₃×#578	—	2	2	no	—
11	C₁₃×#578	—	2	2	no	—
12	C₁₃×#578	—	2	2	no	—
13	C₁₃×#578	C₂²	1	4	yes	complemented
14	C₂×C₁₃×#137	—	2	2	no	—
15	C₂×C₁₃×#137	—	2	1	no	—
16	C₂×C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
17	C₂×C₁₃×#135	—	2	1	no	—
18	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×Q₁₆	—	2	1	no	—
20	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
23	C₁₃×#509	—	2	2	no	—
24	C₁₃×#509	C₂²	1	4	yes	complemented
25	C₂×C₁₃×SD₃₂	—	2	2	no	—
26	C₂×C₁₃×SD₃₂	—	2	2	no	—
27	C₂×C₁₃×SD₃₂	—	2	1	no	—
28	C₂×C₁₃×SD₃₂	C₂²	1	4	yes	complemented
29	C₂×C₁₃×D₁₆	—	2	1	no	—
30	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
31	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
32	C₁₃×#472	—	2	2	no	—
33	C₁₃×#472	C₂²	1	4	yes	complemented
34	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#100	—	2	1	no	—
36	C₁₃×#362	C₂²	1	4	yes	complemented
37	C₁₃×#359	C₂²	1	4	yes	complemented
38	C₁₃×#350	C₂²	1	4	yes	complemented
39	C₁₃×2₋¹⁺⁴	—	2	4	no	—
40	C₁₃×2₋¹⁺⁴	—	2	4	no	—
41	C₁₃×2₋¹⁺⁴	—	4	2	no	—
42	C₁₃×2₋¹⁺⁴	—	4	2	no	—
43	C₂×C₁₃×#41	—	2	2	no	—
44	C₂×C₁₃×#41	—	2	1	no	—
45	C₂×C₁₃×#41	—	4	2	no	—
46	C₂×C₁₃×#41	—	4	1	no	—
47	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
48	C₂²×Q₈×C₁₃	—	2	2	no	—
49	C₂²×Q₈×C₁₃	—	2	1	no	—
50	C₂²×Q₈×C₁₃	—	4	1	no	—
51	C₂²×D₄×C₁₃	—	2	1	no	—
52	C₁₃×#137	—	2	4	no	—
53	C₁₃×#137	—	2	8	no	—
54	C₁₃×#137	—	2	8	no	—
55	C₁₃×#137	—	2	4	no	—
56	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
57	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
58	C₁₃×#135	—	2	4	no	—
59	C₁₃×#135	—	2	4	no	—
60	C₁₃×#135	—	2	1	no	—
61	C₁₃×#135	—	2	1	no	—
62	C₁₃×#135	D₄	1	2	yes	—
63	C₁₃×#135	C₂³	1	2	yes	—
64	C₂×C₁₃×Q₁₆	—	2	2	no	—
65	C₂×C₁₃×Q₁₆	—	2	4	no	—
66	C₂×C₁₃×Q₁₆	—	2	4	no	—
67	C₂×C₁₃×Q₁₆	—	2	1	no	—
68	C₂×C₁₃×Q₁₆	—	2	1	no	—
69	C₂×C₁₃×Q₁₆	—	2	1	no	—
70	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
71	C₂×C₁₃×Q₁₆	D₄	1	2	yes	—
72	C₂×C₁₃×Q₁₆	D₄	1	2	yes	—
73	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
74	C₂×C₁₃×SD₁₆	—	2	2	no	—
75	C₂×C₁₃×SD₁₆	—	2	1	no	—
76	C₂×C₁₃×SD₁₆	—	4	1	no	—
77	C₂×C₁₃×D₈	—	2	1	no	—
78	C₂×C₁₃×D₈	—	2	1	no	—
79	C₂×C₁₃×D₈	—	2	1	no	—
80	C₂×C₁₃×D₈	—	2	1	no	—
81	C₂×C₁₃×D₈	—	2	1	no	—
82	C₂×C₁₃×D₈	—	4	1	no	—
83	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
84	C₂×C₁₃×D₈	C₂³	1	2	yes	—
85	C₁₃×#131	—	2	1	no	—
86	C₁₃×#131	—	2	1	no	—
87	C₁₃×#131	D₄	1	2	yes	—
88	C₁₃×#131	C₂³	1	2	yes	—
89	C₂×C₁₃×M₁₆	—	2	1	no	—
90	C₂×C₁₃×M₁₆	—	2	1	no	—
91	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
92	C₂²×C₈×C₁₃	—	2	1	no	—
93	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₁₃×SD₃₂	—	2	8	no	—
95	C₁₃×SD₃₂	—	2	4	no	—
96	C₁₃×D₁₆	—	2	4	no	—
97	C₁₃×M₃₂	—	2	1	no	—
98	C₁₃×M₃₂	C₂³	1	2	yes	—
99	C₂×C₁₃×C₁₆	—	2	1	no	—
100	C₂×C₁₃×C₁₆	—	2	1	no	—
101	C₂×C₁₃×C₁₆	—	2	1	no	—
102	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
103	C₁₃×#108	—	2	1	no	—
104	C₁₃×#108	C₂³	1	2	yes	—
105	C₁₃×#100	—	2	4	no	—
106	C₂×#2193	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₂⁴×C₁₃	—	4	1	no	—
108	C₁₃×#41	—	2	1	no	—
109	C₁₃×#41	—	2	1	no	—
110	C₁₃×#41	—	2	8	no	—
111	C₁₃×#41	—	2	2	no	—
112	C₁₃×#41	—	2	2	no	—
113	C₁₃×#41	—	4	4	no	—
114	C₁₃×#41	—	4	8	no	—
115	C₁₃×#41	—	4	8	no	—
116	C₁₃×#41	—	4	4	no	—
117	C₁₃×#41	—	4	4	no	—
118	C₁₃×#41	—	4	1	no	—
119	C₁₃×#41	—	4	1	no	—
120	C₁₃×#41	D₈	1	2	yes	—
121	C₁₃×#41	C₂×D₄	1	2	yes	—
122	C₂×Q₈×C₁₃	—	2	8	no	—
123	C₂×Q₈×C₁₃	—	2	2	no	—
124	C₂×Q₈×C₁₃	—	2	1	no	—
125	C₂×Q₈×C₁₃	—	2	2	no	—
126	C₂×Q₈×C₁₃	—	2	2	no	—
127	C₂×Q₈×C₁₃	—	4	2	no	—
128	C₂×Q₈×C₁₃	—	4	4	no	—
129	C₂×Q₈×C₁₃	—	4	4	no	—
130	C₂×Q₈×C₁₃	—	4	4	no	—
131	C₂×Q₈×C₁₃	—	4	1	no	—
132	C₂×Q₈×C₁₃	—	4	1	no	—
133	C₂×Q₈×C₁₃	—	4	1	no	—
134	C₂×Q₈×C₁₃	D₈	1	1	yes	characteristic
135	C₂×D₄×C₁₃	—	2	1	no	—
136	C₂×D₄×C₁₃	—	2	1	no	—
137	C₂×D₄×C₁₃	—	2	2	no	—
138	C₂×D₄×C₁₃	—	4	2	no	—
139	C₂×D₄×C₁₃	—	4	1	no	—
140	C₂×D₄×C₁₃	—	4	1	no	—
141	C₂×D₄×C₁₃	—	4	1	no	—
142	C₂×D₄×C₁₃	—	4	1	no	—
143	C₂×D₄×C₁₃	—	4	1	no	—
144	C₂×D₄×C₁₃	—	4	1	no	—
145	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	4	2	no	—
148	C₂²×C₄×C₁₃	—	4	2	no	—
149	C₂²×C₄×C₁₃	—	4	1	no	—
150	C₂²×C₄×C₁₃	—	4	1	no	—
151	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₁₃×Q₁₆	—	2	8	no	—
153	C₁₃×Q₁₆	—	2	1	no	—
154	C₁₃×Q₁₆	—	2	2	no	—
155	C₁₃×Q₁₆	—	2	2	no	—
156	C₁₃×Q₁₆	—	2	2	no	—
157	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
158	C₁₃×Q₁₆	C₂×D₄	1	4	yes	—
159	C₁₃×SD₁₆	—	2	8	no	—
160	C₁₃×SD₁₆	—	2	2	no	—
161	C₁₃×SD₁₆	—	2	2	no	—
162	C₁₃×SD₁₆	—	4	4	no	—
163	C₁₃×D₈	—	2	1	no	—
164	C₁₃×D₈	—	2	2	no	—
165	C₁₃×D₈	—	2	2	no	—
166	C₁₃×D₈	—	4	4	no	—
167	C₁₃×D₈	—	4	1	no	—
168	C₁₃×D₈	—	4	1	no	—
169	C₁₃×D₈	C₂×D₄	1	2	yes	—
170	C₁₃×M₁₆	—	2	1	no	—
171	C₁₃×M₁₆	—	2	2	no	—
172	C₁₃×M₁₆	—	2	2	no	—
173	C₁₃×M₁₆	—	2	2	no	—
174	C₁₃×M₁₆	—	4	1	no	—
175	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	2	no	—
178	C₂×C₈×C₁₃	—	2	2	no	—
179	C₂×C₈×C₁₃	—	4	1	no	—
180	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
186	C₁₃×C₁₆	—	2	2	no	—
187	C₁₃×C₁₆	—	2	2	no	—
188	C₂×#578	C₂×C₁₃	1	1	yes	characteristic, complemented
189	C₂×#509	C₂×C₁₃	1	1	yes	characteristic, complemented
190	C₂²×SD₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
191	C₂×#472	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#2193	C₂×C₁₃	1	8	yes	direct product factor
193	C₂×#362	C₂×C₁₃	1	1	yes	characteristic, complemented
194	C₂×#359	C₂×C₁₃	1	1	yes	characteristic, complemented
195	C₂×#350	C₂×C₁₃	1	1	yes	characteristic, complemented
196	C₂³×C₁₃	—	2	1	no	—
197	C₂³×C₁₃	—	4	1	no	—
198	C₂³×C₁₃	—	4	2	no	—
199	C₂³×C₁₃	—	8	1	no	—
200	C₂³×C₁₃	—	8	1	no	—
201	C₂³×C₁₃	—	16	2	no	—
202	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
203	Q₈×C₁₃	—	2	1	no	—
204	Q₈×C₁₃	—	2	4	no	—
205	Q₈×C₁₃	—	2	2	no	—
206	Q₈×C₁₃	—	4	8	no	—
207	Q₈×C₁₃	—	4	2	no	—
208	Q₈×C₁₃	—	4	1	no	—
209	Q₈×C₁₃	—	4	2	no	—
210	Q₈×C₁₃	—	4	2	no	—
211	Q₈×C₁₃	C₂×D₈	1	2	yes	—
212	D₄×C₁₃	—	2	2	no	—
213	D₄×C₁₃	—	2	2	no	—
214	D₄×C₁₃	—	2	2	no	—
215	D₄×C₁₃	—	2	1	no	—
216	D₄×C₁₃	—	4	8	no	—
217	D₄×C₁₃	—	4	2	no	—
218	D₄×C₁₃	—	4	2	no	—
219	D₄×C₁₃	—	4	2	no	—
220	D₄×C₁₃	—	4	2	no	—
221	D₄×C₁₃	—	4	1	no	—
222	D₄×C₁₃	—	8	1	no	—
223	D₄×C₁₃	—	8	1	no	—
224	D₄×C₁₃	C₂×D₈	1	2	yes	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	4	8	no	—
229	C₂×C₄×C₁₃	—	4	8	no	—
230	C₂×C₄×C₁₃	—	4	2	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	—	4	2	no	—
233	C₂×C₄×C₁₃	—	4	1	no	—
234	C₂×C₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	—	4	2	no	—
236	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
237	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
240	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
242	C₈×C₁₃	—	2	2	no	—
243	C₈×C₁₃	—	4	2	no	—
244	C₈×C₁₃	#120	1	1	yes	characteristic
245	C₈×C₁₃	#120	1	1	yes	characteristic
246	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
247	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
248	C₂×2₋¹⁺⁴	—	2	1	no	—
249	#578	—	2	2	no	—
250	#578	—	2	2	no	—
251	#578	—	2	2	no	—
252	#578	C₂²×C₁₃	1	4	yes	complemented
253	C₂×#137	—	2	2	no	—
254	C₂×#137	—	2	1	no	—
255	C₂×AGL(1,ℤ/8)	—	2	1	no	—
256	C₂×#135	—	2	1	no	—
257	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
258	C₂²×Q₁₆	—	2	1	no	—
259	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
260	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
262	#509	—	2	2	no	—
263	#509	C₂²×C₁₃	1	4	yes	complemented
264	C₂×SD₃₂	—	2	2	no	—
265	C₂×SD₃₂	—	2	2	no	—
266	C₂×SD₃₂	—	2	1	no	—
267	C₂×SD₃₂	C₂²×C₁₃	1	4	yes	complemented
268	C₂×D₁₆	—	2	1	no	—
269	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
270	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
271	#472	—	2	2	no	—
272	#472	C₂²×C₁₃	1	4	yes	complemented
273	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
274	C₂×#100	—	2	1	no	—
275	#362	C₂²×C₁₃	1	4	yes	complemented
276	#359	C₂²×C₁₃	1	4	yes	complemented
277	#350	C₂²×C₁₃	1	4	yes	complemented
278	C₂²×C₁₃	—	2	2	no	—
279	C₂²×C₁₃	—	2	2	no	—
280	C₂²×C₁₃	—	4	2	no	—
281	C₂²×C₁₃	—	4	2	no	—
282	C₂²×C₁₃	—	8	2	no	—
283	C₂²×C₁₃	—	8	2	no	—
284	C₂²×C₁₃	—	16	2	no	—
285	C₂²×C₁₃	—	16	2	no	—
286	C₂²×C₁₃	—	16	2	no	—
287	C₂²×C₁₃	#447	1	1	yes	characteristic
288	C₂²×C₁₃	#447	1	1	yes	characteristic
289	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
290	C₄×C₁₃	—	2	2	no	—
291	C₄×C₁₃	—	4	4	no	—
292	C₄×C₁₃	—	4	2	no	—
293	C₄×C₁₃	#447	1	1	yes	characteristic
294	C₄×C₁₃	#447	1	1	yes	characteristic
295	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
296	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
297	2₋¹⁺⁴	—	2	4	no	—
298	2₋¹⁺⁴	—	2	4	no	—
299	2₋¹⁺⁴	—	4	2	no	—
300	2₋¹⁺⁴	—	4	2	no	—
301	C₂×#41	—	2	2	no	—
302	C₂×#41	—	2	1	no	—
303	C₂×#41	—	4	2	no	—
304	C₂×#41	—	4	1	no	—
305	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
306	C₂²×Q₈	—	2	2	no	—
307	C₂²×Q₈	—	2	1	no	—
308	C₂²×Q₈	—	4	1	no	—
309	C₂²×D₄	—	2	1	no	—
310	#137	—	2	4	no	—
311	#137	—	2	8	no	—
312	#137	—	2	8	no	—
313	#137	—	2	4	no	—
314	AGL(1,ℤ/8)	—	2	4	no	—
315	AGL(1,ℤ/8)	—	4	2	no	—
316	#135	—	2	4	no	—
317	#135	—	2	4	no	—
318	#135	—	2	1	no	—
319	#135	—	2	1	no	—
320	#135	D₄×C₁₃	1	2	yes	—
321	#135	C₂³×C₁₃	1	2	yes	—
322	C₂×Q₁₆	—	2	2	no	—
323	C₂×Q₁₆	—	2	4	no	—
324	C₂×Q₁₆	—	2	4	no	—
325	C₂×Q₁₆	—	2	1	no	—
326	C₂×Q₁₆	—	2	1	no	—
327	C₂×Q₁₆	—	2	1	no	—
328	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
329	C₂×Q₁₆	D₄×C₁₃	1	2	yes	—
330	C₂×Q₁₆	D₄×C₁₃	1	2	yes	—
331	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
332	C₂×SD₁₆	—	2	2	no	—
333	C₂×SD₁₆	—	2	1	no	—
334	C₂×SD₁₆	—	4	1	no	—
335	C₂×D₈	—	2	1	no	—
336	C₂×D₈	—	2	1	no	—
337	C₂×D₈	—	2	1	no	—
338	C₂×D₈	—	2	1	no	—
339	C₂×D₈	—	2	1	no	—
340	C₂×D₈	—	4	1	no	—
341	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
342	C₂×D₈	C₂³×C₁₃	1	2	yes	—
343	#131	—	2	1	no	—
344	#131	—	2	1	no	—
345	#131	D₄×C₁₃	1	2	yes	—
346	#131	C₂³×C₁₃	1	2	yes	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
350	C₂²×C₈	—	2	1	no	—
351	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
352	SD₃₂	—	2	8	no	—
353	SD₃₂	—	2	4	no	—
354	D₁₆	—	2	4	no	—
355	M₃₂	—	2	1	no	—
356	M₃₂	C₂³×C₁₃	1	2	yes	—
357	C₂×C₁₆	—	2	1	no	—
358	C₂×C₁₆	—	2	1	no	—
359	C₂×C₁₆	—	2	1	no	—
360	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
361	#108	—	2	1	no	—
362	#108	C₂³×C₁₃	1	2	yes	—
363	#100	—	2	4	no	—
364	C₂×C₁₃	—	2	1	no	—
365	C₂×C₁₃	—	2	1	no	—
366	C₂×C₁₃	—	4	2	no	—
367	C₂×C₁₃	—	8	2	no	—
368	C₂×C₁₃	—	16	2	no	—
369	C₂×C₁₃	#2193	1	2	yes	direct product factor
370	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
371	C₂⁴	—	4	1	no	—
372	#41	—	2	1	no	—
373	#41	—	2	1	no	—
374	#41	—	2	8	no	—
375	#41	—	2	2	no	—
376	#41	—	2	2	no	—
377	#41	—	4	4	no	—
378	#41	—	4	8	no	—
379	#41	—	4	8	no	—
380	#41	—	4	4	no	—
381	#41	—	4	4	no	—
382	#41	—	4	1	no	—
383	#41	—	4	1	no	—
384	#41	C₁₃×D₈	1	2	yes	—
385	#41	C₂×D₄×C₁₃	1	2	yes	—
386	C₂×Q₈	—	2	8	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	4	2	no	—
392	C₂×Q₈	—	4	4	no	—
393	C₂×Q₈	—	4	4	no	—
394	C₂×Q₈	—	4	4	no	—
395	C₂×Q₈	—	4	1	no	—
396	C₂×Q₈	—	4	1	no	—
397	C₂×Q₈	—	4	1	no	—
398	C₂×Q₈	C₁₃×D₈	1	1	yes	characteristic
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂×D₄	—	4	1	no	—
404	C₂×D₄	—	4	1	no	—
405	C₂×D₄	—	4	1	no	—
406	C₂×D₄	—	4	1	no	—
407	C₂×D₄	—	4	1	no	—
408	C₂×D₄	—	4	1	no	—
409	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	4	2	no	—
412	C₂²×C₄	—	4	2	no	—
413	C₂²×C₄	—	4	1	no	—
414	C₂²×C₄	—	4	1	no	—
415	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
416	Q₁₆	—	2	8	no	—
417	Q₁₆	—	2	1	no	—
418	Q₁₆	—	2	2	no	—
419	Q₁₆	—	2	2	no	—
420	Q₁₆	—	2	2	no	—
421	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
422	Q₁₆	C₂×D₄×C₁₃	1	4	yes	—
423	SD₁₆	—	2	8	no	—
424	SD₁₆	—	2	2	no	—
425	SD₁₆	—	2	2	no	—
426	SD₁₆	—	4	4	no	—
427	D₈	—	2	1	no	—
428	D₈	—	2	2	no	—
429	D₈	—	2	2	no	—
430	D₈	—	4	4	no	—
431	D₈	—	4	1	no	—
432	D₈	—	4	1	no	—
433	D₈	C₂×D₄×C₁₃	1	2	yes	—
434	M₁₆	—	2	1	no	—
435	M₁₆	—	2	2	no	—
436	M₁₆	—	2	2	no	—
437	M₁₆	—	2	2	no	—
438	M₁₆	—	4	1	no	—
439	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	4	1	no	—
444	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
445	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
446	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
448	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
449	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
450	C₁₆	—	2	2	no	—
451	C₁₆	—	2	2	no	—
452	C₁₃	C₂×#2193	1	1	yes	characteristic, direct product factor, Sylow
453	C₂³	—	2	1	no	—
454	C₂³	—	4	1	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	8	1	no	—
457	C₂³	—	8	1	no	—
458	C₂³	—	16	2	no	—
459	C₂³	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
460	Q₈	—	2	1	no	—
461	Q₈	—	2	4	no	—
462	Q₈	—	2	2	no	—
463	Q₈	—	4	8	no	—
464	Q₈	—	4	1	no	—
465	Q₈	—	4	2	no	—
466	Q₈	—	4	2	no	—
467	Q₈	—	4	2	no	—
468	Q₈	C₂×C₁₃×D₈	1	2	yes	—
469	D₄	—	2	2	no	—
470	D₄	—	2	2	no	—
471	D₄	—	2	1	no	—
472	D₄	—	2	2	no	—
473	D₄	—	4	8	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	1	no	—
477	D₄	—	4	2	no	—
478	D₄	—	4	2	no	—
479	D₄	—	8	1	no	—
480	D₄	—	8	1	no	—
481	D₄	C₂×C₁₃×D₈	1	2	yes	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	4	8	no	—
486	C₂×C₄	—	4	8	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
494	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
495	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
496	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
497	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
498	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
499	C₈	—	2	2	no	—
500	C₈	—	4	2	no	—
501	C₈	C₁₃×#120	1	1	yes	characteristic
502	C₈	C₁₃×#120	1	1	yes	characteristic
503	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
504	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	2	no	—
511	C₂²	—	16	2	no	—
512	C₂²	—	16	2	no	—
513	C₂²	—	16	2	no	—
514	C₂²	C₁₃×#447	1	1	yes	characteristic
515	C₂²	C₁₃×#447	1	1	yes	characteristic
516	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	4	4	no	—
519	C₄	—	4	2	no	—
520	C₄	C₁₃×#447	1	1	yes	characteristic
521	C₄	C₁₃×#447	1	1	yes	characteristic
522	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
523	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
524	C₂	—	2	1	no	—
525	C₂	—	2	1	no	—
526	C₂	—	4	2	no	—
527	C₂	—	8	2	no	—
528	C₂	—	16	2	no	—
529	C₂	C₁₃×#2193	1	2	yes	direct product factor
530	C₂	C₂×C₁₃×#447	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#578	C₂	semidirect
2. C₂×C₁₃×#509	C₂	semidirect
3. C₂²×C₁₃×SD₃₂	C₂	semidirect
4. C₂×C₁₃×#472	C₂	semidirect
5. C₁₃×#2193	C₂	direct (N × H)
6. C₂×C₁₃×#362	C₂	semidirect
7. C₂×C₁₃×#359	C₂	semidirect
8. C₂×C₁₃×#350	C₂	semidirect
13. C₁₃×#578	C₂²	semidirect
24. C₁₃×#509	C₂²	semidirect
28. C₂×C₁₃×SD₃₂	C₂²	semidirect
33. C₁₃×#472	C₂²	semidirect
36. C₁₃×#362	C₂²	semidirect
37. C₁₃×#359	C₂²	semidirect
38. C₁₃×#350	C₂²	semidirect
106. C₂×#2193	C₁₃	direct (N × H)
188. C₂×#578	C₂×C₁₃	semidirect
189. C₂×#509	C₂×C₁₃	semidirect
190. C₂²×SD₃₂	C₂×C₁₃	semidirect
191. C₂×#472	C₂×C₁₃	semidirect
192. #2193	C₂×C₁₃	direct (N × H)
193. C₂×#362	C₂×C₁₃	semidirect
194. C₂×#359	C₂×C₁₃	semidirect
195. C₂×#350	C₂×C₁₃	semidirect
252. #578	C₂²×C₁₃	semidirect
263. #509	C₂²×C₁₃	semidirect
267. C₂×SD₃₂	C₂²×C₁₃	semidirect
272. #472	C₂²×C₁₃	semidirect
275. #362	C₂²×C₁₃	semidirect
276. #359	C₂²×C₁₃	semidirect
277. #350	C₂²×C₁₃	semidirect
369. C₂×C₁₃	#2193	direct (N × H)
452. C₁₃	C₂×#2193	direct (N × H)
529. C₂	C₁₃×#2193	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×#578	2
C₂×C₁₃×#509	2
C₂²×C₁₃×SD₃₂	2
C₂×C₁₃×#472	2
C₁₃×#2193	2
C₂×C₁₃×#362	2
C₂×C₁₃×#359	2
C₂×C₁₃×#350	2
C₂×#2193	13

Subgroups — C2×C13×#2193 #15719875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2193 #15719875