Subgroups — #15829623

Order 3328.

1026 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718586	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718585	C₂	1	1	yes	maximal, characteristic
3	#13113291	C₂	1	4	yes	maximal, complemented
4	#13113265	C₂	1	4	yes	maximal, complemented
5	#13113239	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	C₂²×#6099	—	2	1	no	—
25	C₂×C₂²⋊#1055	—	2	1	no	—
26	#11718586	—	2	1	no	—
27	#11718586	—	2	1	no	—
28	#11718586	C₂²	1	2	yes	—
29	#11718586	C₂²	1	2	yes	—
30	#11718585	—	2	1	no	—
31	#11718585	—	2	1	no	—
32	#11718585	C₂²	1	2	yes	—
33	#11718585	C₂²	1	2	yes	—
34	C₂×C₄⋊#1055	—	2	1	no	—
35	C₂×C₄⋊#1055	—	2	1	no	—
36	C₂×C₄⋊#1055	C₂²	1	2	yes	—
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	C₂×#6099	—	2	2	no	—
98	C₂×#6099	—	4	4	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	C₄⋊#1055	—	2	2	no	—
104	C₄⋊#1055	—	2	2	no	—
105	C₄⋊#1055	—	2	2	no	—
106	C₄⋊#1055	—	2	2	no	—
107	C₄⋊#1055	—	2	2	no	—
108	C₄⋊#1055	C₂³	1	4	yes	—
109	C₄×#1055	—	2	2	no	—
110	C₄×#1055	C₂³	1	4	yes	—
111	#17486	—	13	1	no	maximal, Sylow
112	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×Q₈×C₁₃	—	2	2	no	—
114	C₂×Q₈×C₁₃	—	2	2	no	—
115	C₂×Q₈×C₁₃	—	2	2	no	—
116	C₂×Q₈×C₁₃	—	4	4	no	—
117	C₂×Q₈×C₁₃	—	4	4	no	—
118	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	4	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	SD₁₆	1	4	yes	—
133	C₂²×C₄×C₁₃	Q₁₆	1	4	yes	—
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	2	no	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	2	4	no	—
150	C₁₃×C₄⋊C₄	—	2	4	no	—
151	C₁₃×C₄⋊C₄	—	2	4	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	4	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	#6099	—	4	4	no	—
177	C₂×#1055	—	2	4	no	—
178	C₂×#1055	—	2	4	no	—
179	C₂×#1055	—	4	4	no	—
180	C₂×#1055	—	4	4	no	—
181	C₂×#533	D₁₃	1	1	yes	characteristic
182	C₂×#431	—	13	1	no	—
183	C₂×#423	—	13	1	no	—
184	#1493	—	13	4	no	—
185	#1487	—	13	4	no	—
186	#1481	—	13	4	no	—
187	C₂³×C₁₃	—	4	1	no	—
188	C₂³×C₁₃	—	4	1	no	—
189	C₂³×C₁₃	#103	1	4	yes	—
190	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	Q₈×C₁₃	—	2	8	no	—
194	Q₈×C₁₃	—	4	4	no	—
195	Q₈×C₁₃	—	4	4	no	—
196	Q₈×C₁₃	—	4	4	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	4	no	—
204	C₂×C₄×C₁₃	—	2	4	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	1	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	#103	1	4	yes	—
214	C₂×C₄×C₁₃	#103	1	4	yes	—
215	C₂×C₄×C₁₃	#103	1	4	yes	—
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	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×SD₁₆	1	2	yes	—
226	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
227	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
228	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
229	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
230	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
231	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
234	#1055	—	4	4	no	—
235	#1055	—	4	4	no	—
236	C₂²×M₁₆	—	26	1	no	—
237	#533	—	2	1	no	—
238	#533	—	2	1	no	—
239	#533	—	2	1	no	—
240	#533	—	2	1	no	—
241	#533	Dic₁₃	1	2	yes	—
242	#533	Dic₁₃	1	2	yes	—
243	#533	C₂×D₁₃	1	2	yes	—
244	#533	C₂×D₁₃	1	2	yes	—
245	C₂×C₄⋊Q₈	Dic₁₃	1	1	yes	characteristic
246	C₂×C₄⋊Q₈	Dic₁₃	1	1	yes	characteristic
247	C₂×#125	—	2	1	no	—
248	C₂×C₂²⋊Q₈	—	2	1	no	—
249	C₂×C₂²⋊Q₈	Dic₁₃	1	2	yes	—
250	C₂×C₄×Q₈	—	2	1	no	—
251	C₂×C₄×Q₈	C₂×D₁₃	1	2	yes	—
252	C₂×#117	—	2	1	no	—
253	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
254	#431	—	13	2	no	—
255	#431	—	13	2	no	—
256	#431	—	26	1	no	—
257	#431	—	26	1	no	—
258	#423	—	13	2	no	—
259	#423	—	13	2	no	—
260	#423	—	26	1	no	—
261	#423	—	26	1	no	—
262	C₂×C₄⋊C₈	—	13	2	no	—
263	C₂×C₄⋊C₈	—	26	1	no	—
264	C₂×C₄⋊C₈	—	26	1	no	—
265	C₂×C₂²⋊C₈	—	26	1	no	—
266	C₂×C₄×C₈	—	13	2	no	—
267	Q₈⋊C₈	—	13	16	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	—	2	1	no	—
273	C₂²×C₁₃	—	2	1	no	—
274	C₂²×C₁₃	—	4	4	no	—
275	C₂²×C₁₃	C₂×#103	1	2	yes	—
276	C₂²×C₁₃	C₂×#103	1	2	yes	—
277	C₂²×C₁₃	C₂×#103	1	2	yes	—
278	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
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	C₂×#103	1	2	yes	—
288	C₄×C₁₃	C₂×#103	1	2	yes	—
289	C₄×C₁₃	C₂×#103	1	2	yes	—
290	C₄×C₁₃	#421	1	2	yes	—
291	C₄×C₁₃	#568	1	2	yes	—
292	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
293	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
294	C₂²×Q₈	—	2	1	no	—
295	C₂²×Q₈	C₂×Dic₁₃	1	2	yes	—
296	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
297	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
298	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
299	C₂×M₁₆	—	26	2	no	—
300	C₂×M₁₆	—	26	2	no	—
301	C₂×M₁₆	—	52	4	no	—
302	C₂²×C₈	—	26	2	no	—
303	C₂²×C₈	—	26	2	no	—
304	C₄⋊Q₈	—	2	1	no	—
305	C₄⋊Q₈	—	2	1	no	—
306	C₄⋊Q₈	—	2	1	no	—
307	C₄⋊Q₈	—	2	1	no	—
308	C₄⋊Q₈	C₂×Dic₁₃	1	2	yes	—
309	C₄⋊Q₈	C₂×Dic₁₃	1	2	yes	—
310	C₄⋊Q₈	C₂×Dic₁₃	1	2	yes	—
311	C₄⋊Q₈	C₂×Dic₁₃	1	2	yes	—
312	#125	—	2	2	no	—
313	#125	—	2	2	no	—
314	#125	—	2	2	no	—
315	#125	—	2	2	no	—
316	C₂²⋊Q₈	—	2	2	no	—
317	C₂²⋊Q₈	—	2	2	no	—
318	C₂²⋊Q₈	—	2	2	no	—
319	C₂²⋊Q₈	—	2	2	no	—
320	C₂²⋊Q₈	—	2	2	no	—
321	C₂²⋊Q₈	—	2	2	no	—
322	C₂²⋊Q₈	C₂×Dic₁₃	1	4	yes	—
323	C₂²⋊Q₈	C₂×Dic₁₃	1	4	yes	—
324	C₄×Q₈	—	2	2	no	—
325	C₄×Q₈	—	2	2	no	—
326	C₄×Q₈	—	2	2	no	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×Q₈	C₂×Dic₁₃	1	4	yes	—
331	C₄×Q₈	C₂²×D₁₃	1	4	yes	—
332	#117	—	2	2	no	—
333	#117	—	2	2	no	—
334	#117	—	2	2	no	—
335	#117	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	2	no	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₄²	—	2	2	no	—
344	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
345	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
346	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
347	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
348	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
349	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
350	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
351	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
352	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
353	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
354	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
355	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
356	C₄⋊C₈	—	13	4	no	—
357	C₄⋊C₈	—	26	2	no	—
358	C₄⋊C₈	—	26	2	no	—
359	C₄⋊C₈	—	26	2	no	—
360	C₄⋊C₈	—	26	2	no	—
361	C₄⋊C₈	—	26	2	no	—
362	C₂²⋊C₈	—	26	2	no	—
363	C₂²⋊C₈	—	26	2	no	—
364	C₄×C₈	—	13	4	no	—
365	C₄×C₈	—	26	2	no	—
366	C₂×C₁₃	—	2	2	no	—
367	C₂×C₁₃	—	2	2	no	—
368	C₂×C₁₃	—	2	2	no	—
369	C₂×C₁₃	#2879	1	1	yes	characteristic
370	C₂×C₁₃	C₂²×#103	1	1	yes	characteristic
371	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
372	C₂⁴	C₂²⋊Dic₁₃	1	1	yes	characteristic
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	4	4	no	—
377	C₂×Q₈	—	4	4	no	—
378	C₂×Q₈	C₂²×Dic₁₃	1	4	yes	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	#6106	1	4	yes	—
384	C₂²×C₄	#6107	1	4	yes	—
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	C₂²⋊Dic₁₃	1	1	yes	characteristic
392	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
396	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
397	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
398	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
399	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
400	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
401	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
402	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
403	M₁₆	—	52	4	no	—
404	M₁₆	—	52	4	no	—
405	C₂×C₈	—	26	4	no	—
406	C₂×C₈	—	26	4	no	—
407	C₂×C₈	—	52	4	no	—
408	C₂×C₈	—	52	4	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	C₂²×Dic₁₃	1	4	yes	—
421	C₂²⋊C₄	—	2	4	no	—
422	C₂²⋊C₄	—	2	4	no	—
423	C₄²	—	2	4	no	—
424	C₄²	—	2	4	no	—
425	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
426	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
427	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
428	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
429	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
430	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
431	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
432	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
433	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
434	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
435	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
436	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
437	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
438	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
439	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
440	C₄²	C₂³×D₁₃	1	1	yes	characteristic
441	C₁₃	#17486	1	1	yes	characteristic, complemented, Sylow
442	C₂³	—	4	1	no	—
443	C₂³	—	4	1	no	—
444	C₂³	#88075	1	4	yes	—
445	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
446	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
447	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
448	Q₈	—	2	8	no	—
449	Q₈	—	4	4	no	—
450	Q₈	—	4	4	no	—
451	Q₈	—	4	4	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	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	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	4	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	#88075	1	4	yes	—
469	C₂×C₄	#88075	1	4	yes	—
470	C₂×C₄	#88075	1	4	yes	—
471	C₂×C₄	C₂×#6106	1	2	yes	—
472	C₂×C₄	C₂×#6106	1	2	yes	—
473	C₂×C₄	C₂×#6106	1	2	yes	—
474	C₂×C₄	C₂×#6107	1	2	yes	—
475	C₂×C₄	C₂×#6107	1	2	yes	—
476	C₂×C₄	C₂×#6107	1	2	yes	—
477	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
478	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
479	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
480	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
481	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
482	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
483	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
484	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
485	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
486	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
487	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
488	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
489	C₈	—	52	4	no	—
490	C₈	—	52	4	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	4	4	no	—
498	C₂²	C₂×#88075	1	2	yes	—
499	C₂²	C₂×#88075	1	2	yes	—
500	C₂²	C₂×#88075	1	2	yes	—
501	C₂²	C₂²×C₂²⋊Dic₁₃	1	1	yes	characteristic
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	4	4	no	—
509	C₄	—	4	4	no	—
510	C₄	C₂×#88075	1	2	yes	—
511	C₄	C₂×#88075	1	2	yes	—
512	C₄	C₂×#88075	1	2	yes	—
513	C₄	#11718897	1	2	yes	—
514	C₄	C₂²×#6106	1	1	yes	characteristic
515	C₄	C₂²×#6107	1	1	yes	characteristic
516	C₄	#11719524	1	2	yes	—
517	C₂	—	2	2	no	—
518	C₂	—	2	2	no	—
519	C₂	—	2	2	no	—
520	C₂	#13123281	1	1	yes	characteristic
521	C₂	C₂²×#88075	1	1	yes	characteristic
522	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	#17486
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. #13113291	C₂	semidirect
4. #13113265	C₂	semidirect
5. #13113239	C₂	semidirect
38. Q₈⋊#1055	C₂²	semidirect
441. C₁₃	#17486	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718586	2
C₂×#11718585	2
#13113291	2
#13113265	2
#13113239	2
C₂×C₁₃×#533	2
#17486	13