Subgroups — #16016415

Order 3328.

490 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123765	C₂	1	1	yes	maximal, characteristic
2	#13116745	C₂	1	1	yes	maximal, characteristic, complemented
3	#13116744	C₂	1	1	yes	maximal, characteristic, complemented
4	#13116743	C₂	1	1	yes	maximal, characteristic, complemented
5	#13116743	C₂	1	1	yes	maximal, characteristic, complemented
6	#13116742	C₂	1	1	yes	maximal, characteristic, complemented
7	#13116742	C₂	1	1	yes	maximal, characteristic, complemented
8	#13116741	C₂	1	1	yes	maximal, characteristic, complemented
9	#13116593	C₂	1	1	yes	maximal, characteristic
10	#13116593	C₂	1	1	yes	maximal, characteristic
11	#13116590	C₂	1	1	yes	maximal, characteristic
12	#13116434	C₂	1	1	yes	maximal, characteristic
13	#13116431	C₂	1	1	yes	maximal, characteristic
14	D₁₃×#346	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#2183	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719283	C₄	1	1	yes	characteristic
17	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	#11718685	C₄	1	1	yes	characteristic
19	C₂×#88038	C₂²	1	1	yes	characteristic
20	C₂×#88038	C₂²	1	1	yes	characteristic
21	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
23	#11718500	C₄	1	1	yes	characteristic
24	#11718500	C₄	1	1	yes	characteristic
25	#11718498	C₄	1	1	yes	characteristic
26	#11718492	C₄	1	1	yes	characteristic
27	#11718489	C₄	1	1	yes	characteristic
28	#11718489	C₄	1	1	yes	characteristic
29	#11718350	C₂²	1	1	yes	characteristic
30	#11718350	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
32	C₈×Dic₂₆	C₂²	1	1	yes	characteristic
33	C₈×Dic₂₆	C₂²	1	1	yes	characteristic
34	C₈×Dic₂₆	C₂²	1	1	yes	characteristic
35	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
37	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
38	C₁₃×#346	C₂²	1	1	yes	characteristic
39	C₁₃×#346	C₂²	1	1	yes	characteristic
40	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
41	#11718094	C₂²	1	1	yes	characteristic
42	#11718094	C₂²	1	1	yes	characteristic
43	#11718094	C₂²	1	1	yes	characteristic
44	#11718094	C₂²	1	1	yes	characteristic
45	#11718093	C₂²	1	1	yes	characteristic
46	#11718093	C₂²	1	1	yes	characteristic
47	#11718093	C₂²	1	1	yes	characteristic
48	#11718093	C₂²	1	1	yes	characteristic
49	#11718093	C₂²	1	1	yes	characteristic
50	#11718093	C₂²	1	1	yes	characteristic
51	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
52	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
53	C₄⋊#6090	C₂²	1	1	yes	characteristic
54	C₄⋊#6090	C₂²	1	1	yes	characteristic
55	C₄⋊#6090	C₂²	1	1	yes	characteristic
56	#11718053	C₂²	1	1	yes	characteristic
57	#11718053	C₂²	1	1	yes	characteristic
58	C₄×#6090	C₂²	1	1	yes	characteristic
59	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
60	#88200	C₈	1	1	yes	characteristic
61	#88198	C₈	1	1	yes	characteristic
62	C₂×#6094	C₂×C₄	1	1	yes	characteristic
63	C₂×#6094	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
66	#88151	C₈	1	1	yes	characteristic
67	#88150	C₈	1	1	yes	characteristic
68	#88150	C₈	1	1	yes	characteristic
69	#88143	C₈	1	1	yes	characteristic
70	#88143	C₈	1	1	yes	characteristic
71	#88142	C₈	1	1	yes	characteristic
72	#88126	C₂×C₄	1	1	yes	characteristic
73	#88126	C₂×C₄	1	1	yes	characteristic
74	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
75	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
76	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
77	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
78	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
82	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
83	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
84	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
85	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	#88055	C₂×C₄	1	1	yes	characteristic
89	#88055	C₂×C₄	1	1	yes	characteristic
90	#88054	C₂×C₄	1	1	yes	characteristic
91	#88054	C₂×C₄	1	1	yes	characteristic
92	#88054	C₂×C₄	1	1	yes	characteristic
93	#88054	C₂×C₄	1	1	yes	characteristic
94	#88054	C₂×C₄	1	1	yes	characteristic
95	#88054	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
98	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
99	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
100	C₂×#6090	C₂³	1	1	yes	characteristic
101	C₂×#6090	C₂³	1	1	yes	characteristic
102	C₂×#6090	C₂³	1	1	yes	characteristic
103	C₂×#6090	C₂³	1	1	yes	characteristic
104	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
105	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
106	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
107	#88043	C₂×C₄	1	1	yes	characteristic
108	#88043	C₂×C₄	1	1	yes	characteristic
109	C₄×#1055	C₂×C₄	1	1	yes	characteristic
110	#88038	—	2	2	no	—
111	#88038	—	2	2	no	—
112	C₁₆×D₁₃	—	2	2	no	—
113	C₁₆×D₁₃	Q₈	1	4	yes	complemented
114	#33475	—	13	1	no	maximal, Sylow
115	C₂×Q₈×C₁₃	C₂×C₈	1	1	yes	characteristic
116	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
117	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
118	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×Dic₂₆	C₂×C₈	1	1	yes	characteristic
120	C₂×Dic₂₆	C₂×C₈	1	1	yes	characteristic
121	C₂×Dic₂₆	C₂×C₈	1	1	yes	characteristic
122	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
126	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
127	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
128	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
129	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	#6103	C₂×C₈	1	1	yes	characteristic
133	#6103	C₂×C₈	1	1	yes	characteristic
134	#6103	C₂×C₈	1	1	yes	characteristic
135	#6103	C₂×C₈	1	1	yes	characteristic
136	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
137	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
138	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
139	#6101	C₂×C₈	1	1	yes	characteristic
140	#6101	C₂×C₈	1	1	yes	characteristic
141	#6101	C₂×C₈	1	1	yes	characteristic
142	#6101	C₂×C₈	1	1	yes	characteristic
143	#6101	C₂×C₈	1	1	yes	characteristic
144	#6101	C₂×C₈	1	1	yes	characteristic
145	#6101	C₂×C₈	1	1	yes	characteristic
146	#6101	C₂×C₈	1	1	yes	characteristic
147	#6101	C₂×C₈	1	1	yes	characteristic
148	#6101	C₂×C₈	1	1	yes	characteristic
149	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
150	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
151	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
154	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
155	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
156	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
157	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
158	#6094	—	2	2	no	—
159	#6094	—	2	2	no	—
160	C₈×D₁₃	—	2	2	no	—
161	C₈×D₁₃	C₂×Q₈	1	2	yes	—
162	C₈×D₁₃	#41	1	2	yes	—
163	C₁₃×C₁₆	—	2	1	no	—
164	C₁₃×C₁₆	—	2	1	no	—
165	C₁₃×C₁₆	—	2	1	no	—
166	C₁₃×C₁₆	C₂×Q₈	1	2	yes	—
167	#6090	—	2	1	no	—
168	#6090	—	2	1	no	—
169	#6090	—	2	1	no	—
170	#6090	C₂×Q₈	1	2	yes	—
171	#2960	—	13	1	no	—
172	#2183	—	13	1	no	—
173	#2183	—	13	1	no	—
174	#2183	—	13	1	no	—
175	#2183	—	13	1	no	—
176	#2183	—	13	1	no	—
177	#2183	—	13	1	no	—
178	#2183	—	13	1	no	—
179	#2183	D₁₃	1	1	yes	characteristic, complemented
180	#2151	—	13	1	no	—
181	#2151	—	13	1	no	—
182	#2150	—	13	1	no	—
183	#2108	—	13	1	no	—
184	#2108	—	13	1	no	—
185	C₂×#346	—	13	1	no	—
186	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
187	Q₈×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
195	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
196	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
197	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
198	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
199	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
200	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
201	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
202	C₄×D₁₃	—	4	1	no	—
203	C₄×D₁₃	—	4	1	no	—
204	C₄×D₁₃	C₄×Q₈	1	2	yes	—
205	C₄×D₁₃	#131	1	2	yes	—
206	Dic₂₆	—	4	1	no	—
207	Dic₂₆	—	4	1	no	—
208	Dic₂₆	—	4	1	no	—
209	C₈×C₁₃	—	2	1	no	—
210	C₈×C₁₃	—	2	1	no	—
211	C₈×C₁₃	—	2	1	no	—
212	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
213	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
214	#1055	—	2	1	no	—
215	#1055	—	2	1	no	—
216	#1055	—	2	1	no	—
217	#1055	C₄×Q₈	1	2	yes	—
218	#533	—	13	1	no	—
219	C₂×M₃₂	—	13	1	no	—
220	C₂×M₃₂	—	13	1	no	—
221	C₂²×C₁₆	—	13	1	no	—
222	C₂²×C₁₆	—	13	1	no	—
223	#446	—	13	1	no	—
224	#446	—	13	1	no	—
225	#446	—	13	1	no	—
226	#446	—	13	1	no	—
227	C₈×Q₈	—	13	1	no	—
228	C₈×Q₈	—	13	1	no	—
229	C₈×Q₈	—	13	1	no	—
230	C₈×Q₈	C₂×D₁₃	1	1	yes	characteristic
231	#424	—	13	1	no	—
232	#424	—	13	1	no	—
233	#423	—	13	1	no	—
234	#405	—	13	1	no	—
235	#405	—	13	1	no	—
236	C₂×C₄×C₈	—	13	1	no	—
237	C₄⋊C₁₆	—	13	1	no	—
238	C₄⋊C₁₆	—	13	1	no	—
239	C₄⋊C₁₆	—	13	1	no	—
240	C₄⋊C₁₆	—	13	1	no	—
241	C₄⋊C₁₆	—	13	1	no	—
242	C₄⋊C₁₆	—	13	1	no	—
243	C₄⋊C₁₆	—	13	1	no	—
244	C₄⋊C₁₆	—	13	1	no	—
245	C₄⋊C₁₆	—	13	1	no	—
246	C₄⋊C₁₆	C₂×D₁₃	1	1	yes	characteristic
247	C₄⋊C₁₆	C₂×D₁₃	1	1	yes	characteristic
248	C₄⋊C₁₆	C₂×D₁₃	1	1	yes	characteristic
249	#346	—	13	1	no	—
250	#346	—	13	1	no	—
251	#346	—	13	1	no	—
252	#346	—	13	1	no	—
253	#346	—	13	1	no	—
254	#346	—	13	1	no	—
255	#346	C₂×D₁₃	1	1	yes	characteristic
256	#346	C₂×D₁₃	1	1	yes	characteristic
257	C₄×C₁₆	—	13	1	no	—
258	C₄×C₁₆	—	13	1	no	—
259	C₄×C₁₆	—	13	1	no	—
260	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
261	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
262	C₂×D₁₃	—	2	1	no	—
263	C₂×D₁₃	—	2	1	no	—
264	C₂×D₁₃	C₈×Q₈	1	2	yes	—
265	C₄×C₁₃	—	2	1	no	—
266	C₄×C₁₃	—	2	1	no	—
267	C₄×C₁₃	—	2	1	no	—
268	C₄×C₁₃	—	2	1	no	—
269	C₄×C₁₃	—	2	1	no	—
270	C₄×C₁₃	—	2	1	no	—
271	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
272	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
273	Dic₁₃	—	2	1	no	—
274	Dic₁₃	—	2	1	no	—
275	Dic₁₃	—	2	1	no	—
276	Dic₁₃	—	2	1	no	—
277	Dic₁₃	—	2	1	no	—
278	Dic₁₃	—	2	1	no	—
279	Dic₁₃	C₈×Q₈	1	2	yes	—
280	C₂×M₁₆	—	13	1	no	—
281	C₂×M₁₆	—	13	1	no	—
282	C₂²×C₈	—	13	1	no	—
283	C₂²×C₈	—	13	1	no	—
284	C₄⋊Q₈	—	13	1	no	—
285	C₄⋊Q₈	—	13	1	no	—
286	#125	—	13	1	no	—
287	#125	—	13	1	no	—
288	C₂²⋊Q₈	—	13	1	no	—
289	C₂²⋊Q₈	—	13	1	no	—
290	C₂²⋊Q₈	—	13	1	no	—
291	C₂²⋊Q₈	—	13	1	no	—
292	C₄×Q₈	—	13	1	no	—
293	C₄×Q₈	—	13	1	no	—
294	C₄×Q₈	—	13	1	no	—
295	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
296	#117	—	13	1	no	—
297	#117	—	13	1	no	—
298	C₂×C₄²	—	13	1	no	—
299	M₃₂	—	26	2	no	—
300	M₃₂	—	26	2	no	—
301	C₂×C₁₆	—	13	1	no	—
302	C₂×C₁₆	—	13	4	no	—
303	C₂×C₁₆	—	13	1	no	—
304	C₂×C₁₆	—	13	1	no	—
305	C₂×C₁₆	—	13	1	no	—
306	C₂×C₁₆	—	26	2	no	—
307	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
308	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
309	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
310	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
311	C₄⋊C₈	—	13	1	no	—
312	C₄⋊C₈	—	13	1	no	—
313	C₄⋊C₈	—	13	1	no	—
314	C₄⋊C₈	—	13	1	no	—
315	C₄⋊C₈	—	13	1	no	—
316	C₄⋊C₈	—	13	1	no	—
317	C₄⋊C₈	—	13	1	no	—
318	C₄⋊C₈	—	13	1	no	—
319	C₄⋊C₈	—	13	1	no	—
320	C₄⋊C₈	C₄×D₁₃	1	1	yes	characteristic
321	C₄⋊C₈	C₄×D₁₃	1	1	yes	characteristic
322	C₄⋊C₈	C₄×D₁₃	1	1	yes	characteristic
323	#97	—	13	1	no	—
324	#97	—	13	1	no	—
325	#97	—	13	1	no	—
326	#97	—	13	1	no	—
327	C₄×C₈	—	13	1	no	—
328	C₄×C₈	—	13	1	no	—
329	C₄×C₈	—	13	1	no	—
330	C₄×C₈	—	13	1	no	—
331	C₄×C₈	—	13	1	no	—
332	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
333	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
334	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
335	C₂×C₁₃	C₂×C₈×Q₈	1	1	yes	characteristic
336	C₂×C₁₃	#3407	1	1	yes	characteristic
337	C₂×C₁₃	#3407	1	1	yes	characteristic
338	D₁₃	—	2	2	no	—
339	C₂×Q₈	—	13	1	no	—
340	C₂×Q₈	—	13	1	no	—
341	C₂×Q₈	—	13	1	no	—
342	C₂×Q₈	C₈×D₁₃	1	1	yes	characteristic
343	C₂²×C₄	—	13	1	no	—
344	C₂²×C₄	—	13	1	no	—
345	C₂²×C₄	—	13	1	no	—
346	M₁₆	—	26	2	no	—
347	M₁₆	—	26	2	no	—
348	C₂×C₈	—	13	1	no	—
349	C₂×C₈	—	13	2	no	—
350	C₂×C₈	—	13	2	no	—
351	C₂×C₈	—	13	1	no	—
352	C₂×C₈	—	13	1	no	—
353	C₂×C₈	—	13	1	no	—
354	C₂×C₈	—	26	2	no	—
355	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
356	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
357	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
358	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
359	C₄⋊C₄	—	13	1	no	—
360	C₄⋊C₄	—	13	1	no	—
361	C₄⋊C₄	—	13	1	no	—
362	C₄⋊C₄	—	13	1	no	—
363	C₄⋊C₄	—	13	1	no	—
364	C₄⋊C₄	—	13	1	no	—
365	C₄⋊C₄	—	13	1	no	—
366	C₄⋊C₄	—	13	1	no	—
367	C₄⋊C₄	—	13	1	no	—
368	C₄⋊C₄	—	13	1	no	—
369	C₄⋊C₄	—	13	1	no	—
370	C₄⋊C₄	—	13	1	no	—
371	C₄⋊C₄	—	13	1	no	—
372	C₄⋊C₄	C₈×D₁₃	1	1	yes	characteristic
373	C₄⋊C₄	C₈×D₁₃	1	1	yes	characteristic
374	C₄⋊C₄	C₈×D₁₃	1	1	yes	characteristic
375	C₂²⋊C₄	—	13	1	no	—
376	C₂²⋊C₄	—	13	1	no	—
377	C₂²⋊C₄	—	13	1	no	—
378	C₂²⋊C₄	—	13	1	no	—
379	C₄²	—	13	1	no	—
380	C₄²	—	13	1	no	—
381	C₄²	—	13	1	no	—
382	C₄²	—	13	1	no	—
383	C₄²	—	13	1	no	—
384	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
385	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
386	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
387	C₁₆	—	2	1	no	—
388	C₁₆	—	2	1	no	—
389	C₁₆	—	2	1	no	—
390	C₁₆	—	13	2	no	—
391	C₁₆	—	26	1	no	—
392	C₁₆	—	26	1	no	—
393	C₁₆	—	26	1	no	—
394	C₁₆	Q₈×D₁₃	1	2	yes	—
395	C₁₃	#33475	1	1	yes	characteristic, complemented, Sylow
396	C₂³	—	13	1	no	—
397	Q₈	—	4	1	no	—
398	Q₈	—	52	1	no	—
399	Q₈	—	52	1	no	—
400	Q₈	—	52	1	no	—
401	C₂×C₄	—	13	1	no	—
402	C₂×C₄	—	13	2	no	—
403	C₂×C₄	—	13	2	no	—
404	C₂×C₄	—	13	1	no	—
405	C₂×C₄	—	13	1	no	—
406	C₂×C₄	—	13	1	no	—
407	C₂×C₄	—	13	1	no	—
408	C₂×C₄	—	13	1	no	—
409	C₂×C₄	—	13	1	no	—
410	C₂×C₄	—	52	1	no	—
411	C₂×C₄	—	52	1	no	—
412	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
413	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
414	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
415	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
416	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
417	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
418	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	2	1	no	—
422	C₈	—	13	2	no	—
423	C₈	—	26	1	no	—
424	C₈	—	26	1	no	—
425	C₈	—	26	1	no	—
426	C₈	C₂×Q₈×D₁₃	1	1	yes	characteristic
427	C₈	#41×D₁₃	1	1	yes	characteristic
428	C₂²	—	13	2	no	—
429	C₂²	—	26	1	no	—
430	C₂²	—	26	1	no	—
431	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	13	2	no	—
439	C₄	—	26	1	no	—
440	C₄	—	26	1	no	—
441	C₄	—	26	1	no	—
442	C₄	—	26	1	no	—
443	C₄	—	26	1	no	—
444	C₄	—	26	1	no	—
445	C₄	C₄×Q₈×D₁₃	1	1	yes	characteristic
446	C₄	D₁₃×#131	1	1	yes	characteristic
447	C₂	—	26	2	no	—
448	C₂	C₈×Q₈×D₁₃	1	1	yes	characteristic
449	C₂	#13127937	1	1	yes	characteristic
450	C₂	#13127938	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting	C₁₃×#2183	C₂
prime radical	C₂²×D₁₃	C₂²×C₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	#2183	D₁₃
hypocenter	C₁₃	#33475
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ #2183

Complements

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

N	H ≅ G/N	type
2. #13116745	C₂	semidirect
3. #13116744	C₂	semidirect
4. #13116743	C₂	semidirect
5. #13116743	C₂	semidirect
6. #13116742	C₂	semidirect
7. #13116742	C₂	semidirect
8. #13116741	C₂	semidirect
15. C₁₃×#2183	C₂	semidirect
113. C₁₆×D₁₃	Q₈	semidirect
179. #2183	D₁₃	semidirect
395. C₁₃	#33475	semidirect

Maximal subgroups

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

subgroup	index
#13123765	2
#13116745	2
#13116744	2
#13116743	2
#13116742	2
#13116741	2
#13116593	2
#13116590	2
#13116434	2
#13116431	2
D₁₃×#346	2
C₁₃×#2183	2
#33475	13