Subgroups — #15831468

Order 3328.

952 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	#13123469	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718587	C₂	1	1	yes	maximal, characteristic
3	#13113566	C₂	1	4	yes	maximal, complemented
4	#13113562	C₂	1	2	yes	maximal, complemented
5	#13113553	C₂	1	2	yes	maximal, complemented
6	#13113493	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#533	—	2	1	no	—
9	C₁₃×#533	—	2	1	no	—
10	C₁₃×#533	—	2	1	no	—
11	C₁₃×#533	—	2	1	no	—
12	C₁₃×#533	C₄	1	2	yes	—
13	C₁₃×#533	C₄	1	2	yes	—
14	C₁₃×#533	C₂²	1	2	yes	—
15	C₁₃×#533	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#125	—	2	1	no	—
19	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₁₃×C₂²⋊Q₈	C₄	1	2	yes	—
21	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
22	C₂×C₄×Q₈×C₁₃	C₄	1	2	yes	—
23	C₂×C₁₃×#117	—	2	1	no	—
24	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
25	#11718868	—	2	1	no	—
26	C₂×C₂²⋊#1055	—	2	1	no	—
27	#11718587	—	2	1	no	—
28	#11718587	—	2	1	no	—
29	#11718587	—	2	1	no	—
30	#11718587	C₂²	1	2	yes	—
31	#11718587	C₂²	1	2	yes	—
32	#11718587	C₂²	1	2	yes	—
33	#11718586	—	2	1	no	—
34	#11718586	C₂²	1	2	yes	—
35	#11718585	C₂²	1	2	yes	—
36	C₂×C₄⋊#1055	C₂²	1	2	yes	—
37	C₄×#6099	—	2	1	no	—
38	C₂×#88043	—	2	1	no	—
39	#11718139	C₂²	1	8	yes	complemented
40	#11718138	C₂²	1	8	yes	complemented
41	C₂²×Q₈×C₁₃	—	2	1	no	—
42	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
43	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
46	C₁₃×C₄⋊Q₈	—	2	1	no	—
47	C₁₃×C₄⋊Q₈	—	2	1	no	—
48	C₁₃×C₄⋊Q₈	—	2	1	no	—
49	C₁₃×C₄⋊Q₈	—	2	1	no	—
50	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
51	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
52	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
53	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
54	C₁₃×#125	—	2	2	no	—
55	C₁₃×#125	—	2	2	no	—
56	C₁₃×#125	—	2	2	no	—
57	C₁₃×#125	—	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	—	2	2	no	—
63	C₁₃×C₂²⋊Q₈	—	2	2	no	—
64	C₁₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
65	C₁₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
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	—	2	2	no	—
71	C₄×Q₈×C₁₃	—	2	2	no	—
72	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
73	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
74	C₁₃×#117	—	2	2	no	—
75	C₁₃×#117	—	2	2	no	—
76	C₁₃×#117	—	2	2	no	—
77	C₁₃×#117	—	2	2	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
84	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
85	C₂×C₄²×C₁₃	—	2	2	no	—
86	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	C₂×C₄	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	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×#6099	—	2	2	no	—
99	C₂²×#1055	—	2	2	no	—
100	C₂²⋊#1055	—	2	2	no	—
101	C₂²⋊#1055	—	2	2	no	—
102	C₂²⋊#1055	—	2	2	no	—
103	C₂²⋊#1055	—	2	2	no	—
104	C₄⋊#1055	—	2	2	no	—
105	C₄⋊#1055	—	2	2	no	—
106	C₄⋊#1055	C₂³	1	4	yes	—
107	C₄⋊#1055	C₂³	1	4	yes	—
108	#88043	—	2	2	no	—
109	#88043	—	2	2	no	—
110	#88043	—	2	2	no	—
111	C₄×#1055	—	2	2	no	—
112	#17734	—	13	1	no	maximal, Sylow
113	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₂×Q₈×C₁₃	—	2	2	no	—
115	C₂×Q₈×C₁₃	—	2	2	no	—
116	C₂×Q₈×C₁₃	—	2	2	no	—
117	C₂×Q₈×C₁₃	—	4	4	no	—
118	C₂×Q₈×C₁₃	—	4	4	no	—
119	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
120	C₂²×C₄×C₁₃	—	2	4	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	4	2	no	—
124	C₂²×C₄×C₁₃	—	4	2	no	—
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	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂²×C₄	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	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	4	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	2	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
155	C₁₃×C₂²⋊C₄	—	2	4	no	—
156	C₁₃×C₂²⋊C₄	—	2	4	no	—
157	C₄²×C₁₃	—	2	4	no	—
158	C₄²×C₁₃	—	2	4	no	—
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	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₁₃	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
175	#6099	—	4	4	no	—
176	C₂×#1055	—	2	4	no	—
177	C₂×#1055	—	2	4	no	—
178	C₂×#1055	—	4	4	no	—
179	C₂×#533	D₁₃	1	1	yes	characteristic
180	#2920	—	13	1	no	—
181	C₂×#432	—	13	1	no	—
182	#1559	—	13	4	no	—
183	#1558	—	13	2	no	—
184	#1556	—	13	2	no	—
185	#1542	—	13	4	no	—
186	C₂³×C₁₃	—	2	2	no	—
187	C₂³×C₁₃	—	2	2	no	—
188	C₂³×C₁₃	—	4	1	no	—
189	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	Q₈×C₁₃	—	4	4	no	—
193	Q₈×C₁₃	—	4	4	no	—
194	Q₈×C₁₃	—	4	4	no	—
195	Q₈×C₁₃	—	4	4	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	1	no	—
212	C₂×C₄×C₁₃	—	4	1	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	4	no	—
216	C₂×C₄×C₁₃	—	4	4	no	—
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	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	#137	1	4	yes	—
227	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
230	#1055	—	4	4	no	—
231	#1055	—	4	4	no	—
232	#533	—	2	1	no	—
233	#533	—	2	1	no	—
234	#533	—	2	1	no	—
235	#533	—	2	1	no	—
236	#533	Dic₁₃	1	2	yes	—
237	#533	Dic₁₃	1	2	yes	—
238	#533	C₂×D₁₃	1	2	yes	—
239	#533	C₂×D₁₃	1	2	yes	—
240	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
241	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
242	C₂×#125	—	2	1	no	—
243	C₂×C₂²⋊Q₈	—	2	1	no	—
244	C₂×C₂²⋊Q₈	Dic₁₃	1	2	yes	—
245	C₂×C₄×Q₈	—	2	1	no	—
246	C₂×C₄×Q₈	Dic₁₃	1	2	yes	—
247	C₂×#117	—	2	1	no	—
248	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
249	#432	—	13	2	no	—
250	#432	—	13	2	no	—
251	#432	—	13	2	no	—
252	#432	—	26	1	no	—
253	#432	—	26	1	no	—
254	#432	—	26	1	no	—
255	#431	—	13	2	no	—
256	#431	—	26	1	no	—
257	#423	—	13	2	no	—
258	C₂×C₄⋊C₈	—	13	2	no	—
259	#407	—	26	1	no	—
260	C₂×C₂²⋊C₈	—	26	1	no	—
261	C₄×M₁₆	—	26	1	no	—
262	C₂×#97	—	26	1	no	—
263	#333	—	13	8	no	—
264	#332	—	13	8	no	—
265	C₂²×C₁₃	—	2	1	no	—
266	C₂²×C₁₃	—	2	1	no	—
267	C₂²×C₁₃	—	2	1	no	—
268	C₂²×C₁₃	—	2	1	no	—
269	C₂²×C₁₃	—	2	1	no	—
270	C₂²×C₁₃	—	2	1	no	—
271	C₂²×C₁₃	—	2	1	no	—
272	C₂²×C₁₃	—	4	4	no	—
273	C₂²×C₁₃	#413	1	2	yes	—
274	C₂²×C₁₃	#419	1	2	yes	—
275	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
276	C₄×C₁₃	—	2	1	no	—
277	C₄×C₁₃	—	2	1	no	—
278	C₄×C₁₃	—	2	1	no	—
279	C₄×C₁₃	—	2	1	no	—
280	C₄×C₁₃	—	2	1	no	—
281	C₄×C₁₃	—	2	1	no	—
282	C₄×C₁₃	—	2	1	no	—
283	C₄×C₁₃	—	2	1	no	—
284	C₄×C₁₃	—	2	1	no	—
285	C₄×C₁₃	—	4	4	no	—
286	C₄×C₁₃	—	4	4	no	—
287	C₄×C₁₃	#419	1	2	yes	—
288	C₄×C₁₃	C₂×#137	1	2	yes	—
289	C₄×C₁₃	#575	1	2	yes	—
290	C₂²×Q₈	—	2	1	no	—
291	C₂²×Q₈	C₂×Dic₁₃	1	2	yes	—
292	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
293	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
294	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
295	C₂×M₁₆	—	26	2	no	—
296	C₂²×C₈	—	26	2	no	—
297	C₄⋊Q₈	—	2	1	no	—
298	C₄⋊Q₈	—	2	1	no	—
299	C₄⋊Q₈	—	2	1	no	—
300	C₄⋊Q₈	—	2	1	no	—
301	C₄⋊Q₈	C₂×Dic₁₃	1	2	yes	—
302	C₄⋊Q₈	C₂×Dic₁₃	1	2	yes	—
303	C₄⋊Q₈	C₂²×D₁₃	1	2	yes	—
304	C₄⋊Q₈	C₂²×D₁₃	1	2	yes	—
305	#125	—	2	2	no	—
306	#125	—	2	2	no	—
307	#125	—	2	2	no	—
308	#125	—	2	2	no	—
309	C₂²⋊Q₈	—	2	2	no	—
310	C₂²⋊Q₈	—	2	2	no	—
311	C₂²⋊Q₈	—	2	2	no	—
312	C₂²⋊Q₈	—	2	2	no	—
313	C₂²⋊Q₈	—	2	2	no	—
314	C₂²⋊Q₈	—	2	2	no	—
315	C₂²⋊Q₈	C₂×Dic₁₃	1	4	yes	—
316	C₂²⋊Q₈	C₂×Dic₁₃	1	4	yes	—
317	C₄×Q₈	—	2	2	no	—
318	C₄×Q₈	—	2	2	no	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×Q₈	—	2	2	no	—
321	C₄×Q₈	—	2	2	no	—
322	C₄×Q₈	—	2	2	no	—
323	C₄×Q₈	C₂×Dic₁₃	1	4	yes	—
324	C₄×Q₈	C₂×Dic₁₃	1	4	yes	—
325	#117	—	2	2	no	—
326	#117	—	2	2	no	—
327	#117	—	2	2	no	—
328	#117	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₄²	—	2	2	no	—
337	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
338	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
339	C₂×C₄²	C₂×Dic₁₃	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	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
346	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
347	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
348	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
349	C₄⋊C₈	—	13	4	no	—
350	C₄⋊C₈	—	13	4	no	—
351	C₄⋊C₈	—	26	2	no	—
352	C₄⋊C₈	—	26	2	no	—
353	C₂²⋊C₈	—	26	2	no	—
354	C₂²⋊C₈	—	26	2	no	—
355	C₂²⋊C₈	—	26	2	no	—
356	C₂²⋊C₈	—	26	2	no	—
357	#97	—	26	2	no	—
358	#97	—	26	2	no	—
359	#97	—	26	2	no	—
360	C₄×C₈	—	26	2	no	—
361	C₂×C₁₃	—	2	2	no	—
362	C₂×C₁₃	—	2	2	no	—
363	C₂×C₁₃	—	4	1	no	—
364	C₂×C₁₃	C₂×#413	1	1	yes	characteristic
365	C₂×C₁₃	C₂×#419	1	1	yes	characteristic
366	C₂×C₁₃	#2896	1	1	yes	characteristic
367	C₂⁴	C₂²⋊Dic₁₃	1	1	yes	characteristic
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	4	4	no	—
372	C₂×Q₈	—	4	4	no	—
373	C₂×Q₈	C₂²×Dic₁₃	1	4	yes	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
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	C₂²⋊Dic₁₃	1	1	yes	characteristic
388	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
389	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
390	C₂²×C₄	C₂²×Dic₁₃	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	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
396	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
397	M₁₆	—	52	4	no	—
398	C₂×C₈	—	26	4	no	—
399	C₂×C₈	—	26	4	no	—
400	C₂×C₈	—	52	4	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	C₂²×Dic₁₃	1	4	yes	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₄²	—	2	4	no	—
416	C₄²	—	2	4	no	—
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	C₂²⋊Dic₁₃	1	1	yes	characteristic
423	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
424	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
425	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
426	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
427	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
428	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
429	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
430	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
431	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
432	C₄²	C₂³×D₁₃	1	1	yes	characteristic
433	C₁₃	#17734	1	1	yes	characteristic, complemented, Sylow
434	C₂³	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	4	1	no	—
437	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
438	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
439	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
440	Q₈	—	4	4	no	—
441	Q₈	—	4	4	no	—
442	Q₈	—	4	4	no	—
443	Q₈	—	4	4	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	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	#88196	1	4	yes	—
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	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
472	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
473	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
474	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
475	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
476	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
477	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
478	C₈	—	52	4	no	—
479	C₈	—	52	4	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	4	4	no	—
488	C₂²	#11718886	1	2	yes	—
489	C₂²	#11718898	1	2	yes	—
490	C₂²	C₂²×C₂²⋊Dic₁₃	1	1	yes	characteristic
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	2	1	no	—
498	C₄	—	2	1	no	—
499	C₄	—	2	1	no	—
500	C₄	—	4	4	no	—
501	C₄	—	4	4	no	—
502	C₄	#11718886	1	2	yes	—
503	C₄	C₂×#88196	1	2	yes	—
504	C₄	#11719527	1	2	yes	—
505	C₂	—	2	2	no	—
506	C₂	—	2	2	no	—
507	C₂	—	4	1	no	—
508	C₂	C₂×#11718898	1	1	yes	characteristic
509	C₂	C₂×#11718886	1	1	yes	characteristic
510	C₂	#13123355	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₁₃
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	#17734
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×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. #13113566	C₂	semidirect
4. #13113562	C₂	semidirect
5. #13113553	C₂	semidirect
6. #13113493	C₂	semidirect
39. #11718139	C₂²	semidirect
40. #11718138	C₂²	semidirect
433. C₁₃	#17734	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×#11718587	2
#13113566	2
#13113562	2
#13113553	2
#13113493	2
C₂×C₁₃×#533	2
#17734	13