Subgroups — #15870467

Order 3328.

834 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718685	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11718658	C₂	1	1	yes	maximal, characteristic
3	#13115773	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115555	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115402	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115402	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115016	C₂	1	1	yes	maximal, characteristic
8	#13115016	C₂	1	1	yes	maximal, characteristic
9	#13114820	C₂	1	1	yes	maximal, characteristic
10	#13114711	C₂	1	1	yes	maximal, characteristic, complemented
11	#13114711	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄⋊C₄×#1055	C₂	1	1	yes	maximal, characteristic, complemented
13	#13114620	C₂	1	1	yes	maximal, characteristic
14	#13114620	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#2396	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
18	C₂²×#6099	C₂²	1	1	yes	characteristic
19	C₂³×#1055	C₂²	1	1	yes	characteristic
20	C₁₃×#400	C₄	1	1	yes	characteristic
21	C₁₃×#399	C₄	1	1	yes	characteristic
22	C₁₃×#398	C₄	1	1	yes	characteristic
23	C₁₃×#398	C₄	1	1	yes	characteristic
24	C₁₃×#396	C₄	1	1	yes	characteristic
25	C₁₃×#396	C₄	1	1	yes	characteristic
26	C₁₃×#395	C₄	1	1	yes	characteristic
27	C₁₃×#393	C₄	1	1	yes	characteristic
28	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
35	#11718685	—	2	4	no	—
36	#11718658	—	2	4	no	—
37	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
43	C₂×#88043	C₂²	1	1	yes	characteristic
44	C₂×#88043	C₂²	1	1	yes	characteristic
45	C₂×#88043	C₂²	1	1	yes	characteristic
46	C₂×#88043	C₂²	1	1	yes	characteristic
47	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
48	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
49	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
50	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
51	#11718116	C₂²	1	1	yes	characteristic
52	#11718116	C₂²	1	1	yes	characteristic
53	#11718116	C₂²	1	1	yes	characteristic
54	#11718116	C₂²	1	1	yes	characteristic
55	#11718116	C₂²	1	1	yes	characteristic
56	#11718116	C₂²	1	1	yes	characteristic
57	#11718116	C₂²	1	1	yes	characteristic
58	#11718116	C₂²	1	1	yes	characteristic
59	#11718116	C₂²	1	1	yes	characteristic
60	#11718116	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₄×Q₈×C₁₃	—	2	2	no	—
64	C₄×Q₈×C₁₃	—	2	2	no	—
65	C₁₃×#117	—	2	2	no	—
66	C₁₃×#117	—	2	2	no	—
67	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
90	C₂×#6099	—	2	2	no	—
91	C₂×#6099	—	2	2	no	—
92	C₂×#6099	Q₈	1	4	yes	complemented
93	C₂²×#1055	—	2	2	no	—
94	C₂²×#1055	—	2	2	no	—
95	C₂²×#1055	—	2	2	no	—
96	C₂²×#1055	C₂³	1	1	yes	characteristic
97	C₂²×#1055	C₂³	1	1	yes	characteristic
98	C₂²×#1055	C₂³	1	1	yes	characteristic
99	C₂²×#1055	C₂³	1	1	yes	characteristic
100	C₂²×#1055	C₂³	1	1	yes	characteristic
101	C₂²×#1055	C₂³	1	1	yes	characteristic
102	C₂²×#1055	C₂³	1	1	yes	characteristic
103	C₂²×#1055	C₂³	1	1	yes	characteristic
104	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
105	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
106	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
107	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
108	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
109	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
110	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
111	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
112	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
113	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊#1055	—	2	2	no	—
115	C₂²⋊#1055	—	2	2	no	—
116	C₄⋊#1055	—	2	2	no	—
117	C₄⋊#1055	—	2	2	no	—
118	C₄⋊#1055	—	2	2	no	—
119	C₄⋊#1055	—	2	2	no	—
120	C₄⋊#1055	—	2	2	no	—
121	C₄⋊#1055	—	2	2	no	—
122	#88043	—	2	2	no	—
123	#88043	—	2	2	no	—
124	#88043	—	2	2	no	—
125	#88043	D₄	1	4	yes	—
126	C₄×#1055	—	2	2	no	—
127	C₄×#1055	—	2	2	no	—
128	C₄×#1055	—	2	2	no	—
129	C₄×#1055	—	2	2	no	—
130	#21606	—	13	1	no	maximal, Sylow
131	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×Q₈×C₁₃	—	2	2	no	—
133	C₂×Q₈×C₁₃	—	2	2	no	—
134	C₂×Q₈×C₁₃	—	4	1	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
153	C₂²×C₄×C₁₃	#41	1	2	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
155	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	4	1	no	—
164	C₁₃×C₄⋊C₄	—	4	1	no	—
165	C₁₃×C₄⋊C₄	—	4	1	no	—
166	C₁₃×C₂²⋊C₄	—	2	2	no	—
167	C₁₃×C₂²⋊C₄	—	2	2	no	—
168	C₁₃×C₂²⋊C₄	—	2	2	no	—
169	C₁₃×C₂²⋊C₄	—	2	2	no	—
170	C₁₃×C₂²⋊C₄	—	4	1	no	—
171	C₁₃×C₂²⋊C₄	—	4	1	no	—
172	C₄²×C₁₃	—	2	1	no	—
173	C₄²×C₁₃	—	2	1	no	—
174	C₄²×C₁₃	—	2	1	no	—
175	C₄²×C₁₃	—	2	1	no	—
176	C₄²×C₁₃	—	2	1	no	—
177	C₄²×C₁₃	—	2	1	no	—
178	C₄²×C₁₃	—	2	1	no	—
179	C₄²×C₁₃	—	2	1	no	—
180	C₄²×C₁₃	—	2	1	no	—
181	C₄²×C₁₃	—	2	1	no	—
182	C₄²×C₁₃	C₂×D₄	1	2	yes	—
183	C₄²×C₁₃	#41	1	2	yes	—
184	#6099	—	2	8	no	—
185	C₂×#1055	—	2	8	no	—
186	C₂×#1055	—	2	1	no	—
187	C₂×#1055	—	2	1	no	—
188	C₂×#1055	—	2	1	no	—
189	C₂×#1055	—	2	1	no	—
190	C₂×#1055	—	2	1	no	—
191	C₂×#1055	—	2	1	no	—
192	C₂×#1055	—	2	1	no	—
193	C₂×#1055	—	2	1	no	—
194	C₂×#1055	—	2	1	no	—
195	C₂×#1055	—	2	1	no	—
196	C₂×#1055	—	2	1	no	—
197	C₂×#1055	—	2	1	no	—
198	C₂×#1055	—	2	1	no	—
199	C₂×#1055	—	2	1	no	—
200	C₂×#1055	—	2	1	no	—
201	C₂×#1055	—	2	1	no	—
202	C₂×#1055	—	2	1	no	—
203	C₂×#1055	—	2	1	no	—
204	C₂×#1055	C₂×D₄	1	2	yes	—
205	C₂×#1055	C₂×D₄	1	2	yes	—
206	C₂×#1055	C₂×Q₈	1	2	yes	—
207	C₂×#1055	C₂×Q₈	1	2	yes	—
208	C₂×#1055	#41	1	2	yes	—
209	C₂×#1055	#41	1	2	yes	—
210	C₂×#446	—	13	1	no	—
211	C₂×#405	—	13	1	no	—
212	#2396	D₁₃	1	1	yes	characteristic
213	#1984	—	13	1	no	—
214	#1939	—	13	1	no	—
215	#1917	—	13	1	no	—
216	#1917	—	13	1	no	—
217	#1850	—	13	1	no	—
218	#1850	—	13	1	no	—
219	#1798	—	13	1	no	—
220	#1771	—	13	1	no	—
221	#1771	—	13	1	no	—
222	C₈×C₄⋊C₄	—	13	1	no	—
223	#1753	—	13	1	no	—
224	#1753	—	13	1	no	—
225	C₂³×C₁₃	—	2	1	no	—
226	C₂³×C₁₃	—	2	1	no	—
227	C₂³×C₁₃	—	2	1	no	—
228	C₂³×C₁₃	—	2	1	no	—
229	C₂³×C₁₃	—	2	1	no	—
230	C₂³×C₁₃	—	2	1	no	—
231	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
232	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
233	Q₈×C₁₃	—	4	4	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	2	1	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	2	1	no	—
239	C₂×C₄×C₁₃	—	2	1	no	—
240	C₂×C₄×C₁₃	—	2	1	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	2	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	1	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	2	1	no	—
268	C₂×C₄×C₁₃	—	2	1	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	1	no	—
271	C₂×C₄×C₁₃	—	2	1	no	—
272	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
273	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
274	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
275	C₂×C₄×C₁₃	#131	1	2	yes	—
276	C₂×C₄×C₁₃	#131	1	2	yes	—
277	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
279	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
280	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
281	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
282	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
283	#1055	—	2	2	no	—
284	#1055	—	2	2	no	—
285	#1055	—	2	2	no	—
286	#1055	—	4	1	no	—
287	#1055	—	4	1	no	—
288	#1055	—	4	1	no	—
289	#1055	—	4	1	no	—
290	#1055	C₂²⋊Q₈	1	4	yes	—
291	C₂²×M₁₆	—	13	1	no	—
292	C₂³×C₈	—	13	1	no	—
293	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
294	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
295	#446	—	26	4	no	—
296	C₂×C₄⋊C₈	—	13	1	no	—
297	C₂×C₄⋊C₈	—	13	1	no	—
298	C₂×C₄⋊C₈	—	13	1	no	—
299	C₂×C₄⋊C₈	—	13	1	no	—
300	C₂×C₄⋊C₈	—	13	1	no	—
301	C₂×C₄⋊C₈	—	13	1	no	—
302	C₂×C₂²⋊C₈	—	13	1	no	—
303	C₂×C₂²⋊C₈	—	13	1	no	—
304	#405	—	26	4	no	—
305	C₂×#97	—	13	1	no	—
306	C₂×#97	—	13	1	no	—
307	C₂×#97	—	13	1	no	—
308	C₂×#97	—	13	1	no	—
309	C₂×C₄×C₈	—	13	1	no	—
310	C₂×C₄×C₈	—	13	1	no	—
311	C₂×C₄×C₈	—	13	1	no	—
312	C₂×C₄×C₈	—	13	1	no	—
313	#400	Dic₁₃	1	1	yes	characteristic
314	#399	Dic₁₃	1	1	yes	characteristic
315	#398	Dic₁₃	1	1	yes	characteristic
316	#398	Dic₁₃	1	1	yes	characteristic
317	#396	Dic₁₃	1	1	yes	characteristic
318	#396	Dic₁₃	1	1	yes	characteristic
319	#395	Dic₁₃	1	1	yes	characteristic
320	#393	Dic₁₃	1	1	yes	characteristic
321	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
322	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
323	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
324	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
325	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
326	#336	—	13	1	no	—
327	#336	—	13	1	no	—
328	#336	—	13	1	no	—
329	#336	—	13	1	no	—
330	#336	—	13	1	no	—
331	#336	—	13	1	no	—
332	#336	—	13	1	no	—
333	#336	—	13	1	no	—
334	#336	—	13	1	no	—
335	#336	—	13	1	no	—
336	C₂²×C₁₃	—	2	2	no	—
337	C₂²×C₁₃	—	2	2	no	—
338	C₂²×C₁₃	—	2	2	no	—
339	C₂²×C₁₃	—	4	1	no	—
340	C₂²×C₁₃	—	4	1	no	—
341	C₂²×C₁₃	—	4	1	no	—
342	C₂²×C₁₃	—	4	1	no	—
343	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
344	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
345	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
346	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
347	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
348	C₂²×C₁₃	#568	1	1	yes	characteristic
349	C₂²×C₁₃	#568	1	1	yes	characteristic
350	C₄×C₁₃	—	2	2	no	—
351	C₄×C₁₃	—	2	2	no	—
352	C₄×C₁₃	—	2	2	no	—
353	C₄×C₁₃	—	2	2	no	—
354	C₄×C₁₃	—	2	2	no	—
355	C₄×C₁₃	—	4	1	no	—
356	C₄×C₁₃	—	4	1	no	—
357	C₄×C₁₃	—	4	1	no	—
358	C₄×C₁₃	—	4	1	no	—
359	C₄×C₁₃	—	4	1	no	—
360	C₄×C₁₃	—	4	1	no	—
361	C₄×C₁₃	—	4	1	no	—
362	C₄×C₁₃	—	4	1	no	—
363	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
364	C₄×C₁₃	#525	1	1	yes	characteristic
365	C₄×C₁₃	#529	1	1	yes	characteristic
366	C₄×C₁₃	#533	1	1	yes	characteristic
367	C₂²×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
368	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
369	C₂×M₁₆	—	13	4	no	—
370	C₂×M₁₆	—	26	2	no	—
371	C₂×M₁₆	—	26	2	no	—
372	C₂²×C₈	—	13	1	no	—
373	C₂²×C₈	—	13	1	no	—
374	C₂²×C₈	—	13	1	no	—
375	C₂²×C₈	—	13	1	no	—
376	C₂²×C₈	—	13	1	no	—
377	C₂²×C₈	—	13	1	no	—
378	C₂²×C₈	—	13	1	no	—
379	C₂²×C₈	—	13	1	no	—
380	C₂²×C₈	—	26	2	no	—
381	C₂²×C₈	—	26	2	no	—
382	C₂²×C₈	—	26	2	no	—
383	C₄×Q₈	—	2	2	no	—
384	C₄×Q₈	—	2	2	no	—
385	#117	—	2	2	no	—
386	#117	—	2	2	no	—
387	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
398	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
399	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
400	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
401	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
403	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
404	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
405	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
406	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
407	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
408	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
409	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
410	C₄⋊C₈	—	26	2	no	—
411	C₄⋊C₈	—	26	2	no	—
412	C₄⋊C₈	—	26	2	no	—
413	C₄⋊C₈	—	26	2	no	—
414	C₄⋊C₈	—	26	2	no	—
415	C₄⋊C₈	—	26	2	no	—
416	C₂²⋊C₈	—	26	2	no	—
417	C₂²⋊C₈	—	26	2	no	—
418	#97	—	13	4	no	—
419	#97	—	26	2	no	—
420	#97	—	26	2	no	—
421	#97	—	26	2	no	—
422	C₄×C₈	—	26	2	no	—
423	C₄×C₈	—	26	2	no	—
424	C₄×C₈	—	26	2	no	—
425	C₄×C₈	—	26	2	no	—
426	#95	C₂×Dic₁₃	1	1	yes	characteristic
427	#95	C₂×Dic₁₃	1	1	yes	characteristic
428	#95	C₂×Dic₁₃	1	1	yes	characteristic
429	#95	C₂×Dic₁₃	1	1	yes	characteristic
430	#95	C₂×Dic₁₃	1	1	yes	characteristic
431	#95	C₂×Dic₁₃	1	1	yes	characteristic
432	#95	C₂×Dic₁₃	1	1	yes	characteristic
433	#95	C₂×Dic₁₃	1	1	yes	characteristic
434	#95	C₂×Dic₁₃	1	1	yes	characteristic
435	#95	C₂×Dic₁₃	1	1	yes	characteristic
436	C₂×C₁₃	—	4	2	no	—
437	C₂×C₁₃	C₄×C₂²⋊Q₈	1	1	yes	characteristic
438	C₂×C₁₃	#2933	1	1	yes	characteristic
439	C₂×C₁₃	#2935	1	1	yes	characteristic
440	C₂×C₁₃	#2962	1	1	yes	characteristic
441	C₂×C₁₃	#2962	1	1	yes	characteristic
442	C₂×C₁₃	#2966	1	1	yes	characteristic
443	C₂×C₁₃	#2967	1	1	yes	characteristic
444	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
445	C₂×Q₈	—	2	2	no	—
446	C₂×Q₈	—	2	2	no	—
447	C₂×Q₈	—	4	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	Q₈×D₁₃	1	2	yes	—
453	C₂²×C₄	#6131	1	2	yes	—
454	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
455	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
456	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
457	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
458	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
459	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
460	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
461	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
462	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
463	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
464	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
466	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
467	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
468	M₁₆	—	26	8	no	—
469	C₂×C₈	—	13	2	no	—
470	C₂×C₈	—	13	2	no	—
471	C₂×C₈	—	13	2	no	—
472	C₂×C₈	—	13	2	no	—
473	C₂×C₈	—	13	2	no	—
474	C₂×C₈	—	13	2	no	—
475	C₂×C₈	—	26	8	no	—
476	C₂×C₈	—	26	1	no	—
477	C₂×C₈	—	26	1	no	—
478	C₂×C₈	—	26	1	no	—
479	C₂×C₈	—	26	1	no	—
480	C₂×C₈	—	26	1	no	—
481	C₂×C₈	—	26	1	no	—
482	C₂×C₈	—	26	1	no	—
483	C₂×C₈	—	26	1	no	—
484	C₂×C₈	—	26	1	no	—
485	C₂×C₈	—	26	1	no	—
486	C₂×C₈	—	26	1	no	—
487	C₂×C₈	—	26	1	no	—
488	C₂×C₈	—	26	1	no	—
489	C₂×C₈	—	26	1	no	—
490	C₂×C₈	—	26	1	no	—
491	C₂×C₈	—	26	1	no	—
492	C₂×C₈	—	26	1	no	—
493	C₂×C₈	—	26	1	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	4	1	no	—
503	C₄⋊C₄	—	4	1	no	—
504	C₄⋊C₄	—	4	1	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₂²⋊C₄	—	4	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	D₄×D₁₃	1	2	yes	—
522	C₄²	#6129	1	2	yes	—
523	C₁₃	#21606	1	1	yes	characteristic, complemented, Sylow
524	C₂³	—	2	1	no	—
525	C₂³	—	2	1	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	Q₈×Dic₁₃	1	2	yes	—
531	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
532	Q₈	—	4	4	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
572	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
573	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
574	C₂×C₄	#88202	1	2	yes	—
575	C₂×C₄	#88202	1	2	yes	—
576	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
577	C₂×C₄	C₂×#6129	1	1	yes	characteristic
578	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
579	C₂×C₄	C₂×#6131	1	1	yes	characteristic
580	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
581	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
582	C₈	—	13	4	no	—
583	C₈	—	26	2	no	—
584	C₈	—	26	2	no	—
585	C₈	—	26	2	no	—
586	C₈	—	52	1	no	—
587	C₈	—	52	1	no	—
588	C₈	—	52	1	no	—
589	C₈	—	52	1	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	2	2	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
598	C₂²	C₂×Q₈×Dic₁₃	1	1	yes	characteristic
599	C₂²	C₂×#88202	1	1	yes	characteristic
600	C₂²	C₂×#88202	1	1	yes	characteristic
601	C₂²	#11719524	1	1	yes	characteristic
602	C₂²	#11719524	1	1	yes	characteristic
603	C₂²	#41×Dic₁₃	1	1	yes	characteristic
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	2	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	1	no	—
617	C₄	#11719327	1	1	yes	characteristic
618	C₄	#11719329	1	1	yes	characteristic
619	C₄	D₁₃×C₂²⋊Q₈	1	1	yes	characteristic
620	C₄	#11719332	1	1	yes	characteristic
621	C₂	—	4	2	no	—
622	C₂	C₂²⋊Q₈×Dic₁₃	1	1	yes	characteristic
623	C₂	#13123563	1	1	yes	characteristic
624	C₂	#13123580	1	1	yes	characteristic
625	C₂	#13123785	1	1	yes	characteristic
626	C₂	#13123785	1	1	yes	characteristic
627	C₂	#13123812	1	1	yes	characteristic
628	C₂	#13123823	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₁₃×#2396	C₂
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#2396	D₁₃
hypocenter	C₁₃	#21606
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #2396

Complements

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

N	H ≅ G/N	type
1. C₂×#11718685	C₂	semidirect
3. #13115773	C₂	semidirect
4. #13115555	C₂	semidirect
5. #13115402	C₂	semidirect
6. #13115402	C₂	semidirect
10. #13114711	C₂	semidirect
11. #13114711	C₂	semidirect
12. C₄⋊C₄×#1055	C₂	semidirect
92. C₂×#6099	Q₈	semidirect
523. C₁₃	#21606	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718685	2
C₂×#11718658	2
#13115773	2
#13115555	2
#13115402	2
#13115016	2
#13114820	2
#13114711	2
C₄⋊C₄×#1055	2
#13114620	2
C₁₃×#2396	2
#21606	13