Subgroups — #15829568

Order 3328.

988 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123469	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718586	C₂	1	1	yes	maximal, characteristic
3	#13113309	C₂	1	4	yes	maximal, complemented
4	#13113291	C₂	1	4	yes	maximal, complemented
5	#13113231	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#533	—	2	1	no	—
8	C₁₃×#533	—	2	1	no	—
9	C₁₃×#533	—	2	1	no	—
10	C₁₃×#533	—	2	1	no	—
11	C₁₃×#533	C₄	1	2	yes	—
12	C₁₃×#533	C₄	1	2	yes	—
13	C₁₃×#533	C₂²	1	2	yes	—
14	C₁₃×#533	C₂²	1	2	yes	—
15	C₂×C₁₃×C₄⋊Q₈	C₄	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊Q₈	C₄	1	1	yes	characteristic
17	C₂×C₁₃×#125	—	2	1	no	—
18	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₁₃×C₂²⋊Q₈	C₄	1	2	yes	—
20	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
22	C₂×C₁₃×#117	—	2	1	no	—
23	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	#11718868	—	2	1	no	—
25	C₂×C₂²⋊#1055	—	2	1	no	—
26	#11718587	—	2	1	no	—
27	#11718587	C₂²	1	2	yes	—
28	#11718586	—	2	1	no	—
29	#11718586	—	2	1	no	—
30	#11718586	—	2	1	no	—
31	#11718586	C₂²	1	2	yes	—
32	#11718586	C₂²	1	2	yes	—
33	#11718586	C₂²	1	2	yes	—
34	#11718585	C₂²	1	2	yes	—
35	C₂×C₄⋊#1055	—	2	1	no	—
36	C₄×#6099	—	2	1	no	—
37	C₂×C₄×#1055	C₂²	1	2	yes	—
38	Q₈⋊#1055	C₂²	1	16	yes	complemented
39	C₂²×Q₈×C₁₃	—	2	1	no	—
40	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
41	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
44	C₁₃×C₄⋊Q₈	—	2	1	no	—
45	C₁₃×C₄⋊Q₈	—	2	1	no	—
46	C₁₃×C₄⋊Q₈	—	2	1	no	—
47	C₁₃×C₄⋊Q₈	—	2	1	no	—
48	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
49	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
50	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
51	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
52	C₁₃×#125	—	2	2	no	—
53	C₁₃×#125	—	2	2	no	—
54	C₁₃×#125	—	2	2	no	—
55	C₁₃×#125	—	2	2	no	—
56	C₁₃×C₂²⋊Q₈	—	2	2	no	—
57	C₁₃×C₂²⋊Q₈	—	2	2	no	—
58	C₁₃×C₂²⋊Q₈	—	2	2	no	—
59	C₁₃×C₂²⋊Q₈	—	2	2	no	—
60	C₁₃×C₂²⋊Q₈	—	2	2	no	—
61	C₁₃×C₂²⋊Q₈	—	2	2	no	—
62	C₁₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
63	C₁₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
64	C₄×Q₈×C₁₃	—	2	2	no	—
65	C₄×Q₈×C₁₃	—	2	2	no	—
66	C₄×Q₈×C₁₃	—	2	2	no	—
67	C₄×Q₈×C₁₃	—	2	2	no	—
68	C₄×Q₈×C₁₃	—	2	2	no	—
69	C₄×Q₈×C₁₃	—	2	2	no	—
70	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
71	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
72	C₁₃×#117	—	2	2	no	—
73	C₁₃×#117	—	2	2	no	—
74	C₁₃×#117	—	2	2	no	—
75	C₁₃×#117	—	2	2	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
81	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
82	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
83	C₂×C₄²×C₁₃	—	2	2	no	—
84	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
96	C₂×#6099	—	2	2	no	—
97	C₂²×#1055	—	2	2	no	—
98	C₂²⋊#1055	—	2	2	no	—
99	C₂²⋊#1055	—	2	2	no	—
100	C₂²⋊#1055	—	2	2	no	—
101	C₂²⋊#1055	—	2	2	no	—
102	C₄⋊#1055	—	2	2	no	—
103	C₄⋊#1055	—	2	2	no	—
104	C₄⋊#1055	—	2	2	no	—
105	C₄⋊#1055	C₂³	1	4	yes	—
106	#88043	—	2	2	no	—
107	C₄×#1055	—	2	2	no	—
108	C₄×#1055	—	2	2	no	—
109	C₄×#1055	C₂³	1	4	yes	—
110	#17479	—	13	1	no	maximal, Sylow
111	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×Q₈×C₁₃	—	2	2	no	—
113	C₂×Q₈×C₁₃	—	2	2	no	—
114	C₂×Q₈×C₁₃	—	2	2	no	—
115	C₂×Q₈×C₁₃	—	2	8	no	—
116	C₂×Q₈×C₁₃	—	4	4	no	—
117	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₃	—	2	4	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	4	2	no	—
123	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	2	4	no	—
148	C₁₃×C₄⋊C₄	—	2	4	no	—
149	C₁₃×C₄⋊C₄	—	2	4	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	2	4	no	—
152	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
153	C₁₃×C₂²⋊C₄	—	2	4	no	—
154	C₁₃×C₂²⋊C₄	—	2	4	no	—
155	C₄²×C₁₃	—	2	4	no	—
156	C₄²×C₁₃	—	2	4	no	—
157	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
158	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
159	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
160	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
161	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
162	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
163	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
164	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
165	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
166	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
173	#6099	—	4	4	no	—
174	C₂×#1055	—	2	4	no	—
175	C₂×#1055	—	2	4	no	—
176	C₂×#1055	—	4	4	no	—
177	C₂×#533	D₁₃	1	1	yes	characteristic
178	#2920	—	13	1	no	—
179	C₂×#431	—	13	1	no	—
180	#1497	—	13	4	no	—
181	#1493	—	13	4	no	—
182	#1479	—	13	4	no	—
183	C₂³×C₁₃	—	2	2	no	—
184	C₂³×C₁₃	—	2	2	no	—
185	C₂³×C₁₃	—	4	1	no	—
186	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	Q₈×C₁₃	—	2	8	no	—
190	Q₈×C₁₃	—	4	4	no	—
191	Q₈×C₁₃	—	4	4	no	—
192	Q₈×C₁₃	—	4	4	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	4	no	—
207	C₂×C₄×C₁₃	—	2	4	no	—
208	C₂×C₄×C₁₃	—	4	1	no	—
209	C₂×C₄×C₁₃	—	4	1	no	—
210	C₂×C₄×C₁₃	—	4	1	no	—
211	C₂×C₄×C₁₃	—	4	4	no	—
212	C₂×C₄×C₁₃	—	4	4	no	—
213	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	#131	1	4	yes	—
223	C₂×C₄×C₁₃	#137	1	4	yes	—
224	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	#1055	—	4	4	no	—
228	#1055	—	4	4	no	—
229	#533	—	2	1	no	—
230	#533	—	2	1	no	—
231	#533	—	2	1	no	—
232	#533	—	2	1	no	—
233	#533	Dic₁₃	1	2	yes	—
234	#533	Dic₁₃	1	2	yes	—
235	#533	C₂×D₁₃	1	2	yes	—
236	#533	C₂×D₁₃	1	2	yes	—
237	C₂×C₄⋊Q₈	Dic₁₃	1	1	yes	characteristic
238	C₂×C₄⋊Q₈	Dic₁₃	1	1	yes	characteristic
239	C₂×#125	—	2	1	no	—
240	C₂×C₂²⋊Q₈	—	2	1	no	—
241	C₂×C₂²⋊Q₈	Dic₁₃	1	2	yes	—
242	C₂×C₄×Q₈	—	2	1	no	—
243	C₂×C₄×Q₈	C₂×D₁₃	1	2	yes	—
244	C₂×#117	—	2	1	no	—
245	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
246	#432	—	13	2	no	—
247	#432	—	26	1	no	—
248	#431	—	13	2	no	—
249	#431	—	13	2	no	—
250	#431	—	13	2	no	—
251	#431	—	26	1	no	—
252	#431	—	26	1	no	—
253	#431	—	26	1	no	—
254	#423	—	13	2	no	—
255	C₂×C₄⋊C₈	—	26	1	no	—
256	#407	—	26	1	no	—
257	C₂×C₂²⋊C₈	—	26	1	no	—
258	C₄×M₁₆	—	26	1	no	—
259	C₂×C₄×C₈	—	13	2	no	—
260	Q₈⋊C₈	—	13	16	no	—
261	C₂²×C₁₃	—	2	1	no	—
262	C₂²×C₁₃	—	2	1	no	—
263	C₂²×C₁₃	—	2	1	no	—
264	C₂²×C₁₃	—	2	1	no	—
265	C₂²×C₁₃	—	2	1	no	—
266	C₂²×C₁₃	—	2	1	no	—
267	C₂²×C₁₃	—	2	1	no	—
268	C₂²×C₁₃	—	4	4	no	—
269	C₂²×C₁₃	#408	1	2	yes	—
270	C₂²×C₁₃	#419	1	2	yes	—
271	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
272	C₄×C₁₃	—	2	1	no	—
273	C₄×C₁₃	—	2	1	no	—
274	C₄×C₁₃	—	2	1	no	—
275	C₄×C₁₃	—	2	1	no	—
276	C₄×C₁₃	—	2	1	no	—
277	C₄×C₁₃	—	2	1	no	—
278	C₄×C₁₃	—	2	1	no	—
279	C₄×C₁₃	—	4	4	no	—
280	C₄×C₁₃	—	4	4	no	—
281	C₄×C₁₃	#408	1	2	yes	—
282	C₄×C₁₃	#419	1	2	yes	—
283	C₄×C₁₃	#421	1	2	yes	—
284	C₄×C₁₃	C₂×#131	1	2	yes	—
285	C₄×C₁₃	C₂×#137	1	2	yes	—
286	C₂²×Q₈	—	2	1	no	—
287	C₂²×Q₈	C₂×Dic₁₃	1	2	yes	—
288	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
289	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
290	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
291	C₂×M₁₆	—	26	2	no	—
292	C₂²×C₈	—	26	2	no	—
293	C₄⋊Q₈	—	2	1	no	—
294	C₄⋊Q₈	—	2	1	no	—
295	C₄⋊Q₈	—	2	1	no	—
296	C₄⋊Q₈	—	2	1	no	—
297	C₄⋊Q₈	C₂×Dic₁₃	1	2	yes	—
298	C₄⋊Q₈	C₂×Dic₁₃	1	2	yes	—
299	C₄⋊Q₈	C₂×Dic₁₃	1	2	yes	—
300	C₄⋊Q₈	C₂×Dic₁₃	1	2	yes	—
301	#125	—	2	2	no	—
302	#125	—	2	2	no	—
303	#125	—	2	2	no	—
304	#125	—	2	2	no	—
305	C₂²⋊Q₈	—	2	2	no	—
306	C₂²⋊Q₈	—	2	2	no	—
307	C₂²⋊Q₈	—	2	2	no	—
308	C₂²⋊Q₈	—	2	2	no	—
309	C₂²⋊Q₈	—	2	2	no	—
310	C₂²⋊Q₈	—	2	2	no	—
311	C₂²⋊Q₈	C₂×Dic₁₃	1	4	yes	—
312	C₂²⋊Q₈	C₂×Dic₁₃	1	4	yes	—
313	C₄×Q₈	—	2	2	no	—
314	C₄×Q₈	—	2	2	no	—
315	C₄×Q₈	—	2	2	no	—
316	C₄×Q₈	—	2	2	no	—
317	C₄×Q₈	—	2	2	no	—
318	C₄×Q₈	—	2	2	no	—
319	C₄×Q₈	C₂×Dic₁₃	1	4	yes	—
320	C₄×Q₈	C₂²×D₁₃	1	4	yes	—
321	#117	—	2	2	no	—
322	#117	—	2	2	no	—
323	#117	—	2	2	no	—
324	#117	—	2	2	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₄²	—	2	2	no	—
333	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
334	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
335	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
336	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
337	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
338	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
339	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
340	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
341	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
342	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
343	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
344	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
345	C₄⋊C₈	—	13	4	no	—
346	C₄⋊C₈	—	26	2	no	—
347	C₄⋊C₈	—	26	2	no	—
348	C₄⋊C₈	—	26	2	no	—
349	C₂²⋊C₈	—	26	2	no	—
350	C₂²⋊C₈	—	26	2	no	—
351	C₂²⋊C₈	—	26	2	no	—
352	C₂²⋊C₈	—	26	2	no	—
353	#97	—	26	2	no	—
354	C₄×C₈	—	13	4	no	—
355	C₄×C₈	—	26	2	no	—
356	C₄×C₈	—	26	2	no	—
357	C₂×C₁₃	—	2	2	no	—
358	C₂×C₁₃	—	2	2	no	—
359	C₂×C₁₃	—	4	1	no	—
360	C₂×C₁₃	C₂×#408	1	1	yes	characteristic
361	C₂×C₁₃	C₂×#419	1	1	yes	characteristic
362	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
363	C₂⁴	C₂²⋊Dic₁₃	1	1	yes	characteristic
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	8	no	—
368	C₂×Q₈	—	4	4	no	—
369	C₂×Q₈	C₂²×Dic₁₃	1	4	yes	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
376	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
377	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
378	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
379	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
380	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
381	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
383	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
384	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
385	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
386	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
387	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
388	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
390	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
391	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
392	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
393	M₁₆	—	52	4	no	—
394	C₂×C₈	—	26	4	no	—
395	C₂×C₈	—	26	4	no	—
396	C₂×C₈	—	52	4	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	C₂²×Dic₁₃	1	4	yes	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₄²	—	2	4	no	—
412	C₄²	—	2	4	no	—
413	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
414	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
415	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
416	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
417	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
418	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
419	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
420	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
421	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
422	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
423	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
424	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
425	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
426	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
427	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
428	C₄²	C₂³×D₁₃	1	1	yes	characteristic
429	C₁₃	#17479	1	1	yes	characteristic, complemented, Sylow
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	4	1	no	—
433	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
434	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
435	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
436	Q₈	—	2	8	no	—
437	Q₈	—	4	4	no	—
438	Q₈	—	4	4	no	—
439	Q₈	—	4	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	#88196	1	4	yes	—
461	C₂×C₄	#88202	1	4	yes	—
462	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
463	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
464	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
465	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
466	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
467	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
468	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
469	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
470	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
471	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
472	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
473	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
474	C₈	—	52	4	no	—
475	C₈	—	52	4	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	4	4	no	—
484	C₂²	#11718886	1	2	yes	—
485	C₂²	#11718895	1	2	yes	—
486	C₂²	C₂²×C₂²⋊Dic₁₃	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	4	4	no	—
495	C₄	—	4	4	no	—
496	C₄	#11718886	1	2	yes	—
497	C₄	#11718895	1	2	yes	—
498	C₄	#11718897	1	2	yes	—
499	C₄	C₂×#88196	1	2	yes	—
500	C₄	C₂×#88202	1	2	yes	—
501	C₂	—	2	2	no	—
502	C₂	—	2	2	no	—
503	C₂	—	4	1	no	—
504	C₂	C₂×#11718895	1	1	yes	characteristic
505	C₂	C₂×#11718886	1	1	yes	characteristic
506	C₂	C₂×#11718897	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₂×C₁₃×#533	C₂
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₁₃	C₂²⋊C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₂×#533	D₁₃
hypocenter	C₁₃	#17479
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
3. #13113309	C₂	semidirect
4. #13113291	C₂	semidirect
5. #13113231	C₂	semidirect
38. Q₈⋊#1055	C₂²	semidirect
429. C₁₃	#17479	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#13123469	2
C₂×#11718586	2
#13113309	2
#13113291	2
#13113231	2
C₂×C₁₃×#533	2
#17479	13