Subgroups — #15829366

Order 3328.

1214 conjugacy classes of subgroups.

The subgroup lattice has 534 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	#13123469	C₂	1	1	yes	maximal, characteristic
3	#13113283	C₂	1	4	yes	maximal, complemented
4	#13113265	C₂	1	4	yes	maximal, complemented
5	#13113231	C₂	1	4	yes	maximal, complemented
6	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
7	C₂³×Q₈×C₁₃	C₄	1	1	yes	characteristic
8	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
9	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
10	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
11	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
12	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
13	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
14	C₂×C₄×Q₈×C₁₃	C₄	1	2	yes	—
15	C₂×C₄×Q₈×C₁₃	C₄	1	2	yes	—
16	C₂×C₄×Q₈×C₁₃	C₄	1	2	yes	—
17	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
20	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
21	C₂²×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
22	C₂²×C₄²×C₁₃	—	2	1	no	—
23	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	#11718868	—	2	1	no	—
25	#11718868	—	2	1	no	—
26	#11718587	—	2	1	no	—
27	#11718587	—	2	1	no	—
28	#11718587	—	2	1	no	—
29	#11718587	C₂²	1	2	yes	—
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	—	2	1	no	—
35	#11718585	C₂²	1	2	yes	—
36	C₄×#6099	—	2	1	no	—
37	C₄×#6099	C₂²	1	2	yes	—
38	Q₈⋊#1055	C₂²	1	16	yes	complemented
39	C₂²×Q₈×C₁₃	—	2	8	no	—
40	C₂²×Q₈×C₁₃	—	2	1	no	—
41	C₂²×Q₈×C₁₃	—	2	1	no	—
42	C₂²×Q₈×C₁₃	—	2	1	no	—
43	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
44	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
45	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂³×C₄×C₁₃	—	2	1	no	—
48	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
51	C₄×Q₈×C₁₃	—	2	2	no	—
52	C₄×Q₈×C₁₃	—	2	2	no	—
53	C₄×Q₈×C₁₃	—	2	2	no	—
54	C₄×Q₈×C₁₃	—	2	2	no	—
55	C₄×Q₈×C₁₃	—	2	2	no	—
56	C₄×Q₈×C₁₃	—	2	2	no	—
57	C₄×Q₈×C₁₃	—	2	2	no	—
58	C₄×Q₈×C₁₃	—	2	2	no	—
59	C₄×Q₈×C₁₃	—	2	2	no	—
60	C₄×Q₈×C₁₃	—	2	2	no	—
61	C₄×Q₈×C₁₃	—	2	2	no	—
62	C₄×Q₈×C₁₃	—	2	2	no	—
63	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
64	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
65	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
66	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
67	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
78	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
79	C₂×C₄²×C₁₃	—	2	2	no	—
80	C₂×C₄²×C₁₃	—	2	2	no	—
81	C₂×C₄²×C₁₃	—	2	2	no	—
82	C₂×C₄²×C₁₃	—	2	2	no	—
83	C₂×C₄²×C₁₃	—	2	2	no	—
84	C₂×C₄²×C₁₃	—	2	2	no	—
85	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	C₂×C₄	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	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×#6099	—	2	2	no	—
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	C₄⋊#1055	—	2	2	no	—
104	C₄⋊#1055	—	2	2	no	—
105	C₄⋊#1055	—	2	2	no	—
106	C₄⋊#1055	C₂³	1	4	yes	—
107	#88043	—	2	2	no	—
108	#88043	—	2	2	no	—
109	C₄×#1055	—	2	2	no	—
110	C₄×#1055	C₂³	1	4	yes	—
111	#17449	—	13	1	no	maximal, Sylow
112	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×Q₈×C₁₃	—	2	8	no	—
114	C₂×Q₈×C₁₃	—	2	8	no	—
115	C₂×Q₈×C₁₃	—	2	8	no	—
116	C₂×Q₈×C₁₃	—	2	8	no	—
117	C₂×Q₈×C₁₃	—	2	8	no	—
118	C₂×Q₈×C₁₃	—	2	2	no	—
119	C₂×Q₈×C₁₃	—	2	2	no	—
120	C₂×Q₈×C₁₃	—	2	2	no	—
121	C₂×Q₈×C₁₃	—	2	4	no	—
122	C₂×Q₈×C₁₃	M₁₆	1	8	yes	complemented
123	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
124	C₂²×C₄×C₁₃	—	2	8	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	4	2	no	—
134	C₂²×C₄×C₁₃	—	4	4	no	—
135	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₁₃×C₄⋊C₄	—	2	4	no	—
154	C₁₃×C₄⋊C₄	—	2	4	no	—
155	C₁₃×C₄⋊C₄	—	2	4	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	4	no	—
160	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
161	C₄²×C₁₃	—	2	4	no	—
162	C₄²×C₁₃	—	2	4	no	—
163	C₄²×C₁₃	—	2	4	no	—
164	C₄²×C₁₃	—	2	4	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
169	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
170	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
171	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
181	#6099	—	4	4	no	—
182	#6099	—	4	4	no	—
183	C₂×#1055	—	2	4	no	—
184	C₂×#1055	—	2	4	no	—
185	C₂²×C₄×Q₈	D₁₃	1	1	yes	characteristic
186	#2920	—	13	1	no	—
187	#2920	—	13	1	no	—
188	#1491	—	13	4	no	—
189	#1487	—	13	4	no	—
190	#1479	—	13	4	no	—
191	C₂³×C₁₃	—	2	2	no	—
192	C₂³×C₁₃	—	2	2	no	—
193	C₂³×C₁₃	—	2	2	no	—
194	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	Q₈×C₁₃	—	2	8	no	—
198	Q₈×C₁₃	—	2	8	no	—
199	Q₈×C₁₃	—	2	4	no	—
200	Q₈×C₁₃	—	2	8	no	—
201	Q₈×C₁₃	C₂×M₁₆	1	8	yes	—
202	C₂×C₄×C₁₃	—	2	8	no	—
203	C₂×C₄×C₁₃	—	2	8	no	—
204	C₂×C₄×C₁₃	—	2	4	no	—
205	C₂×C₄×C₁₃	—	2	8	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	4	no	—
219	C₂×C₄×C₁₃	—	4	1	no	—
220	C₂×C₄×C₁₃	—	4	1	no	—
221	C₂×C₄×C₁₃	—	4	1	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	—	4	4	no	—
224	C₂×C₄×C₁₃	—	4	4	no	—
225	C₂×C₄×C₁₃	—	4	4	no	—
226	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
236	C₂×C₄×C₁₃	#137	1	4	yes	—
237	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
240	#1055	—	4	4	no	—
241	#1055	—	4	4	no	—
242	C₂³×Q₈	Dic₁₃	1	1	yes	characteristic
243	C₂×C₄×Q₈	—	2	1	no	—
244	C₂×C₄×Q₈	—	2	1	no	—
245	C₂×C₄×Q₈	—	2	1	no	—
246	C₂×C₄×Q₈	—	2	1	no	—
247	C₂×C₄×Q₈	—	2	1	no	—
248	C₂×C₄×Q₈	—	2	1	no	—
249	C₂×C₄×Q₈	Dic₁₃	1	2	yes	—
250	C₂×C₄×Q₈	Dic₁₃	1	2	yes	—
251	C₂×C₄×Q₈	Dic₁₃	1	2	yes	—
252	C₂×C₄×Q₈	C₂×D₁₃	1	2	yes	—
253	C₂×C₄×Q₈	C₂×D₁₃	1	2	yes	—
254	C₂×C₄×Q₈	C₂×D₁₃	1	2	yes	—
255	C₂²×C₄⋊C₄	—	2	1	no	—
256	C₂²×C₄⋊C₄	Dic₁₃	1	1	yes	characteristic
257	C₂²×C₄²	—	2	1	no	—
258	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
259	#432	—	13	2	no	—
260	#432	—	26	1	no	—
261	#432	—	26	1	no	—
262	#432	—	26	1	no	—
263	#431	—	13	2	no	—
264	#431	—	13	2	no	—
265	#431	—	13	2	no	—
266	#431	—	26	1	no	—
267	#423	—	13	2	no	—
268	#423	—	26	1	no	—
269	#407	—	26	1	no	—
270	#407	—	26	1	no	—
271	C₄×M₁₆	—	13	2	no	—
272	C₄×M₁₆	—	26	1	no	—
273	Q₈⋊C₈	—	13	16	no	—
274	C₂²×C₁₃	—	2	8	no	—
275	C₂²×C₁₃	—	2	1	no	—
276	C₂²×C₁₃	—	2	1	no	—
277	C₂²×C₁₃	—	2	1	no	—
278	C₂²×C₁₃	—	2	1	no	—
279	C₂²×C₁₃	—	2	1	no	—
280	C₂²×C₁₃	—	2	1	no	—
281	C₂²×C₁₃	#407	1	2	yes	—
282	C₂²×C₁₃	#419	1	2	yes	—
283	C₂²×C₁₃	#421	1	2	yes	—
284	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
285	C₄×C₁₃	—	2	8	no	—
286	C₄×C₁₃	—	2	1	no	—
287	C₄×C₁₃	—	2	1	no	—
288	C₄×C₁₃	—	2	1	no	—
289	C₄×C₁₃	—	2	1	no	—
290	C₄×C₁₃	—	2	1	no	—
291	C₄×C₁₃	—	2	1	no	—
292	C₄×C₁₃	—	2	1	no	—
293	C₄×C₁₃	—	2	1	no	—
294	C₄×C₁₃	—	4	4	no	—
295	C₄×C₁₃	#407	1	2	yes	—
296	C₄×C₁₃	#419	1	2	yes	—
297	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
298	C₄×C₁₃	C₂×#137	1	2	yes	—
299	C₂²×Q₈	—	2	8	no	—
300	C₂²×Q₈	—	2	1	no	—
301	C₂²×Q₈	—	2	1	no	—
302	C₂²×Q₈	—	2	1	no	—
303	C₂²×Q₈	C₂×Dic₁₃	1	2	yes	—
304	C₂²×Q₈	C₂×Dic₁₃	1	2	yes	—
305	C₂²×Q₈	C₂×Dic₁₃	1	2	yes	—
306	C₂³×C₄	—	2	1	no	—
307	C₂³×C₄	—	2	1	no	—
308	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
309	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
310	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
311	C₂×M₁₆	—	26	2	no	—
312	C₂×M₁₆	—	26	2	no	—
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	—	2	2	no	—
320	C₄×Q₈	—	2	2	no	—
321	C₄×Q₈	—	2	2	no	—
322	C₄×Q₈	—	2	2	no	—
323	C₄×Q₈	—	2	2	no	—
324	C₄×Q₈	—	2	2	no	—
325	C₄×Q₈	C₂×Dic₁₃	1	4	yes	—
326	C₄×Q₈	C₂×Dic₁₃	1	4	yes	—
327	C₄×Q₈	C₂×Dic₁₃	1	4	yes	—
328	C₄×Q₈	C₂²×D₁₃	1	4	yes	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
339	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
340	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
341	C₂×C₄²	—	2	2	no	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	—	2	2	no	—
344	C₂×C₄²	—	2	2	no	—
345	C₂×C₄²	—	2	2	no	—
346	C₂×C₄²	—	2	2	no	—
347	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
348	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
349	C₂×C₄²	C₂×Dic₁₃	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	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
357	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
358	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
359	C₄⋊C₈	—	13	4	no	—
360	C₄⋊C₈	—	26	2	no	—
361	C₄⋊C₈	—	26	2	no	—
362	C₄⋊C₈	—	26	2	no	—
363	C₂²⋊C₈	—	26	2	no	—
364	C₂²⋊C₈	—	26	2	no	—
365	C₂²⋊C₈	—	26	2	no	—
366	C₂²⋊C₈	—	26	2	no	—
367	#97	—	26	2	no	—
368	#97	—	26	2	no	—
369	C₄×C₈	—	13	4	no	—
370	C₄×C₈	—	26	2	no	—
371	C₂×C₁₃	—	2	2	no	—
372	C₂×C₁₃	—	2	2	no	—
373	C₂×C₁₃	—	2	2	no	—
374	C₂×C₁₃	C₂×#407	1	1	yes	characteristic
375	C₂×C₁₃	C₂×#419	1	1	yes	characteristic
376	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
377	C₂⁴	C₂²⋊Dic₁₃	1	1	yes	characteristic
378	C₂×Q₈	—	2	8	no	—
379	C₂×Q₈	—	2	8	no	—
380	C₂×Q₈	—	2	8	no	—
381	C₂×Q₈	—	2	8	no	—
382	C₂×Q₈	—	2	8	no	—
383	C₂×Q₈	—	2	4	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	#6099	1	8	yes	complemented
388	C₂×Q₈	C₂²×Dic₁₃	1	4	yes	—
389	C₂²×C₄	—	2	8	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	4	no	—
400	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
401	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
402	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
403	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
404	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
405	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
406	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
407	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
408	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
409	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
410	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
411	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
412	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
413	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
414	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
415	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
416	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
417	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
418	M₁₆	—	52	4	no	—
419	M₁₆	—	52	4	no	—
420	C₂×C₈	—	26	4	no	—
421	C₂×C₈	—	26	4	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	C₂²×Dic₁₃	1	4	yes	—
430	C₄²	—	2	4	no	—
431	C₄²	—	2	4	no	—
432	C₄²	—	2	4	no	—
433	C₄²	—	2	4	no	—
434	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
435	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
436	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
437	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
438	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
439	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
440	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
441	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
442	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
443	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
444	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
445	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
446	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
447	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
448	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
449	C₄²	C₂³×D₁₃	1	1	yes	characteristic
450	C₁₃	#17449	1	1	yes	characteristic, complemented, Sylow
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
455	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
456	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
457	Q₈	—	2	8	no	—
458	Q₈	—	2	8	no	—
459	Q₈	—	2	4	no	—
460	Q₈	—	2	8	no	—
461	Q₈	C₂×#6099	1	8	yes	—
462	C₂×C₄	—	2	8	no	—
463	C₂×C₄	—	2	8	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	8	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	4	4	no	—
486	C₂×C₄	C₂×#6099	1	4	yes	—
487	C₂×C₄	#88196	1	4	yes	—
488	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
489	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
490	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
491	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
492	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
493	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
494	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
495	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
496	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
497	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
498	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
499	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
500	C₈	—	52	4	no	—
501	C₈	—	52	4	no	—
502	C₂²	—	2	8	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	2	1	no	—
509	C₂²	#11718868	1	2	yes	—
510	C₂²	#11718886	1	2	yes	—
511	C₂²	#11718897	1	2	yes	—
512	C₂²	C₂²×C₂²⋊Dic₁₃	1	1	yes	characteristic
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	2	1	no	—
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	2	8	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	1	no	—
522	C₄	—	4	4	no	—
523	C₄	#11718868	1	2	yes	—
524	C₄	#11718886	1	2	yes	—
525	C₄	C₂²×#6099	1	2	yes	—
526	C₄	C₂×#88196	1	2	yes	—
527	C₂	—	2	2	no	—
528	C₂	—	2	2	no	—
529	C₂	—	2	2	no	—
530	C₂	C₂×#11718868	1	1	yes	characteristic
531	C₂	C₂×#11718886	1	1	yes	characteristic
532	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	C₂²×C₄×Q₈×C₁₃	C₂
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₁₃	C₂²⋊C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₂²×C₄×Q₈	D₁₃
hypocenter	C₁₃	#17449
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄×Q₈

Complements

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

N	H ≅ G/N	type
3. #13113283	C₂	semidirect
4. #13113265	C₂	semidirect
5. #13113231	C₂	semidirect
38. Q₈⋊#1055	C₂²	semidirect
122. C₂×Q₈×C₁₃	M₁₆	semidirect
387. C₂×Q₈	#6099	semidirect
450. C₁₃	#17449	semidirect

Maximal subgroups

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

subgroup	index
#13123469	2
#13113283	2
#13113265	2
#13113231	2
C₂²×C₄×Q₈×C₁₃	2
#17449	13