Subgroups — #15834637

Order 3328.

650 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123968	C₂	1	1	yes	maximal, characteristic, complemented
2	#13123961	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113739	C₂	1	2	yes	maximal, complemented
4	#13113687	C₂	1	2	yes	maximal, complemented
5	#13113666	C₂	1	2	yes	maximal, complemented
6	SD₁₆⋊#1055	C₂	1	2	yes	maximal, complemented
7	#13113595	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113275	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113275	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113125	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#135	C₄	1	1	yes	characteristic
13	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
15	C₄×C₁₃×Q₁₆	C₄	1	1	yes	characteristic
16	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
17	C₄×C₁₃×SD₁₆	C₄	1	1	yes	characteristic
18	C₄×C₁₃×SD₁₆	C₄	1	1	yes	characteristic
19	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
20	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
21	C₄×C₁₃×D₈	C₄	1	1	yes	characteristic
22	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
23	C₁₃×#427	C₄	1	1	yes	characteristic
24	C₁₃×#416	C₄	1	1	yes	characteristic
25	C₁₃×#416	C₄	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	#11718685	C₂²	1	2	yes	—
28	Q₈×#1055	C₂²	1	2	yes	—
29	#11718673	—	2	2	no	—
30	#11718673	C₂²	1	2	yes	—
31	#11718672	—	2	2	no	—
32	D₄×#1055	C₂²	1	2	yes	—
33	#11718587	—	2	1	no	—
34	#11718586	—	2	1	no	—
35	#11718586	C₂²	1	1	yes	characteristic
36	#11718585	—	2	1	no	—
37	#11718585	C₂²	1	1	yes	characteristic
38	#11718585	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊#1055	—	2	1	no	—
40	C₄×#6099	C₂²	1	1	yes	characteristic
41	Q₈⋊#1055	C₂²	1	2	yes	—
42	Q₈⋊#1055	C₂²	1	2	yes	—
43	D₄⋊#1055	C₂²	1	2	yes	—
44	D₄⋊#1055	C₂²	1	2	yes	—
45	#11718050	C₂²	1	2	yes	—
46	#11718050	C₂²	1	2	yes	—
47	#11718047	C₂²	1	2	yes	—
48	#11718046	C₂²	1	2	yes	—
49	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
51	C₁₃×#135	—	2	4	no	—
52	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
53	C₂×C₁₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
58	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
60	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₄×D₄×C₁₃	—	2	1	no	—
63	C₄×D₄×C₁₃	—	2	1	no	—
64	C₄×D₄×C₁₃	—	2	1	no	—
65	C₄×D₄×C₁₃	—	2	1	no	—
66	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
67	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
68	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×#117	—	2	1	no	—
71	C₁₃×#117	—	2	1	no	—
72	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
73	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	—	2	1	no	—
75	C₂×C₄²×C₁₃	—	2	1	no	—
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×#6099	—	2	1	no	—
78	C₂×#6099	—	2	1	no	—
79	C₂×#6099	—	2	1	no	—
80	C₂×#6099	—	2	2	no	—
81	C₂²×#1055	—	2	2	no	—
82	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
83	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
84	C₁₃×#106	C₂×C₄	1	1	yes	characteristic
85	C₁₃×#106	C₂×C₄	1	1	yes	characteristic
86	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
87	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
88	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
89	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
90	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
91	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
92	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
93	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
94	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
95	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
96	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²⋊#1055	—	2	2	no	—
99	C₂²⋊#1055	—	2	2	no	—
100	C₂²⋊#1055	D₄	1	2	yes	—
101	C₄⋊#1055	—	2	1	no	—
102	C₄⋊#1055	—	2	1	no	—
103	C₄⋊#1055	—	2	2	no	—
104	C₄⋊#1055	—	2	2	no	—
105	C₄⋊#1055	D₄	1	1	yes	characteristic
106	C₄⋊#1055	D₄	1	1	yes	characteristic
107	C₄⋊#1055	C₂³	1	2	yes	—
108	C₄⋊#1055	C₂³	1	2	yes	—
109	#88043	—	2	1	no	—
110	#88043	—	2	2	no	—
111	C₄×#1055	—	2	2	no	—
112	C₄×#1055	C₂³	1	2	yes	—
113	C₄×#1055	C₂³	1	2	yes	—
114	#18061	—	13	1	no	maximal, Sylow
115	C₁₃×#41	—	2	2	no	—
116	C₁₃×#41	—	2	2	no	—
117	C₁₃×#41	—	4	1	no	—
118	C₁₃×#41	—	4	1	no	—
119	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×C₁₃	—	2	1	no	—
123	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
134	C₁₃×Q₁₆	—	2	2	no	—
135	C₁₃×SD₁₆	—	2	2	no	—
136	C₁₃×SD₁₆	M₁₆	1	4	yes	complemented
137	C₁₃×D₈	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	4	1	no	—
140	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
144	C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₁₃×C₄⋊C₄	—	2	1	no	—
146	C₁₃×C₄⋊C₄	—	2	1	no	—
147	C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
149	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
150	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
151	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
152	C₁₃×C₂²⋊C₄	—	2	1	no	—
153	C₁₃×C₂²⋊C₄	—	2	1	no	—
154	C₁₃×C₂²⋊C₄	—	2	1	no	—
155	C₁₃×C₂²⋊C₄	—	2	1	no	—
156	C₁₃×C₂²⋊C₄	—	2	1	no	—
157	C₁₃×C₂²⋊C₄	—	2	1	no	—
158	C₄²×C₁₃	—	2	1	no	—
159	C₄²×C₁₃	—	2	1	no	—
160	C₄²×C₁₃	—	2	1	no	—
161	C₄²×C₁₃	—	2	1	no	—
162	C₄²×C₁₃	—	2	1	no	—
163	C₄²×C₁₃	—	2	1	no	—
164	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
165	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₁₃	#41	1	1	yes	characteristic
167	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
168	#6099	—	4	2	no	—
169	#6099	—	8	2	no	—
170	#6099	—	8	1	no	—
171	#6099	—	8	1	no	—
172	C₂×#1055	—	2	2	no	—
173	C₂×#1055	—	2	2	no	—
174	C₂×#1055	—	2	2	no	—
175	C₂×#1055	—	8	2	no	—
176	C₂×#1055	C₂×D₄	1	2	yes	—
177	C₂×#1055	C₂×D₄	1	2	yes	—
178	#2991	—	13	1	no	—
179	#2990	—	13	1	no	—
180	C₄×#135	D₁₃	1	1	yes	characteristic
181	#1592	—	13	2	no	—
182	#1584	—	13	2	no	—
183	#1581	—	13	2	no	—
184	SD₁₆⋊C₈	—	13	2	no	—
185	#1567	—	13	1	no	—
186	#1489	—	13	1	no	—
187	#1489	—	13	1	no	—
188	#1451	—	13	1	no	—
189	C₂³×C₁₃	—	2	1	no	—
190	C₂³×C₁₃	—	2	1	no	—
191	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
192	Q₈×C₁₃	—	2	1	no	—
193	Q₈×C₁₃	—	2	1	no	—
194	Q₈×C₁₃	—	2	1	no	—
195	Q₈×C₁₃	C₂×M₁₆	1	2	yes	—
196	D₄×C₁₃	—	2	1	no	—
197	D₄×C₁₃	—	2	1	no	—
198	D₄×C₁₃	—	2	1	no	—
199	D₄×C₁₃	—	4	2	no	—
200	D₄×C₁₃	—	4	2	no	—
201	D₄×C₁₃	C₂×M₁₆	1	2	yes	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	1	no	—
204	C₂×C₄×C₁₃	—	2	1	no	—
205	C₂×C₄×C₁₃	—	2	1	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	2	1	no	—
211	C₂×C₄×C₁₃	—	2	1	no	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	1	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
227	C₈×C₁₃	—	2	1	no	—
228	C₈×C₁₃	—	2	1	no	—
229	C₈×C₁₃	—	2	1	no	—
230	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
231	#1055	—	2	2	no	—
232	#1055	—	2	2	no	—
233	#1055	—	4	2	no	—
234	#1055	—	4	2	no	—
235	#1055	—	4	2	no	—
236	C₂×#135	Dic₁₃	1	1	yes	characteristic
237	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
238	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
239	#446	—	13	2	no	—
240	C₈×Q₈	—	13	2	no	—
241	C₄×Q₁₆	Dic₁₃	1	1	yes	characteristic
242	C₄×Q₁₆	C₂×D₁₃	1	1	yes	characteristic
243	C₄×SD₁₆	Dic₁₃	1	1	yes	characteristic
244	C₄×SD₁₆	Dic₁₃	1	1	yes	characteristic
245	C₄×SD₁₆	C₂×D₁₃	1	1	yes	characteristic
246	C₄×SD₁₆	C₂×D₁₃	1	1	yes	characteristic
247	C₄×D₈	Dic₁₃	1	1	yes	characteristic
248	C₄×D₈	C₂×D₁₃	1	1	yes	characteristic
249	#436	—	13	2	no	—
250	#436	—	26	2	no	—
251	#435	—	26	2	no	—
252	C₈×D₄	—	13	2	no	—
253	#432	—	26	1	no	—
254	#431	—	13	1	no	—
255	#431	—	26	1	no	—
256	#427	Dic₁₃	1	1	yes	characteristic
257	#423	—	13	1	no	—
258	#423	—	13	1	no	—
259	#423	—	26	1	no	—
260	C₂×C₄⋊C₈	—	26	1	no	—
261	#416	Dic₁₃	1	1	yes	characteristic
262	#416	Dic₁₃	1	1	yes	characteristic
263	C₄×M₁₆	—	13	1	no	—
264	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
265	#335	—	13	2	no	—
266	#335	—	13	2	no	—
267	Q₈⋊C₈	—	13	2	no	—
268	Q₈⋊C₈	—	13	2	no	—
269	D₄⋊C₈	—	13	2	no	—
270	D₄⋊C₈	—	13	2	no	—
271	#322	—	13	2	no	—
272	#322	—	13	2	no	—
273	C₂²×C₁₃	—	2	1	no	—
274	C₂²×C₁₃	—	2	2	no	—
275	C₂²×C₁₃	—	2	1	no	—
276	C₂²×C₁₃	—	2	1	no	—
277	C₂²×C₁₃	—	4	1	no	—
278	C₂²×C₁₃	—	4	1	no	—
279	C₂²×C₁₃	—	4	1	no	—
280	C₂²×C₁₃	—	4	1	no	—
281	C₂²×C₁₃	—	4	1	no	—
282	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
283	C₄×C₁₃	—	2	1	no	—
284	C₄×C₁₃	—	2	2	no	—
285	C₄×C₁₃	—	2	1	no	—
286	C₄×C₁₃	—	2	1	no	—
287	C₄×C₁₃	—	4	1	no	—
288	C₄×C₁₃	—	4	1	no	—
289	C₄×C₁₃	—	4	1	no	—
290	C₄×C₁₃	—	4	1	no	—
291	C₄×C₁₃	—	4	1	no	—
292	C₄×C₁₃	#444	1	2	yes	—
293	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
294	C₄×C₁₃	#568	1	1	yes	characteristic
295	C₄×C₁₃	#576	1	1	yes	characteristic
296	C₄×C₁₃	#578	1	1	yes	characteristic
297	C₂×#41	C₂×Dic₁₃	1	1	yes	characteristic
298	C₂×#41	C₂×Dic₁₃	1	1	yes	characteristic
299	#135	—	2	4	no	—
300	C₂×Q₁₆	C₂×Dic₁₃	1	1	yes	characteristic
301	C₂×SD₁₆	C₂×Dic₁₃	1	1	yes	characteristic
302	C₂×SD₁₆	C₂×Dic₁₃	1	1	yes	characteristic
303	C₂×D₈	C₂×Dic₁₃	1	1	yes	characteristic
304	C₂×M₁₆	—	26	2	no	—
305	C₂×M₁₆	—	26	1	no	—
306	C₂×M₁₆	—	26	1	no	—
307	C₂×M₁₆	—	26	1	no	—
308	C₂²×C₈	—	26	2	no	—
309	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
310	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
311	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
312	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
313	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
314	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	—	2	1	no	—
319	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
320	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
321	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
322	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
323	#117	—	2	1	no	—
324	#117	—	2	1	no	—
325	#117	C₂×Dic₁₃	1	1	yes	characteristic
326	#117	C₂×Dic₁₃	1	1	yes	characteristic
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
330	#107	C₂×Dic₁₃	1	1	yes	characteristic
331	#107	C₂×Dic₁₃	1	1	yes	characteristic
332	#106	C₂×Dic₁₃	1	1	yes	characteristic
333	#106	C₂×Dic₁₃	1	1	yes	characteristic
334	C₄⋊C₈	—	13	1	no	—
335	C₄⋊C₈	—	13	1	no	—
336	C₄⋊C₈	—	13	2	no	—
337	C₄⋊C₈	—	13	2	no	—
338	C₄⋊C₈	—	26	2	no	—
339	C₄⋊C₈	—	26	2	no	—
340	C₄⋊C₈	—	26	1	no	—
341	C₄⋊C₈	—	26	1	no	—
342	#103	C₂×Dic₁₃	1	1	yes	characteristic
343	#103	C₂×Dic₁₃	1	1	yes	characteristic
344	#103	C₂×Dic₁₃	1	1	yes	characteristic
345	#103	C₂×Dic₁₃	1	1	yes	characteristic
346	#102	C₂×Dic₁₃	1	1	yes	characteristic
347	#102	C₂×Dic₁₃	1	1	yes	characteristic
348	#102	C₂×Dic₁₃	1	1	yes	characteristic
349	#102	C₂×Dic₁₃	1	1	yes	characteristic
350	C₂²⋊C₈	—	13	2	no	—
351	C₂²⋊C₈	—	26	2	no	—
352	C₂²⋊C₈	—	26	2	no	—
353	#97	—	26	2	no	—
354	#97	—	26	1	no	—
355	C₄×C₈	—	13	2	no	—
356	C₄×C₈	—	13	2	no	—
357	C₄×C₈	—	26	2	no	—
358	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
359	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
360	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
361	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
362	C₂×C₁₃	—	4	1	no	—
363	C₂×C₁₃	—	4	2	no	—
364	C₂×C₁₃	—	8	1	no	—
365	C₂×C₁₃	D₄×M₁₆	1	1	yes	characteristic
366	C₂×C₁₃	#2951	1	1	yes	characteristic
367	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
368	#41	—	2	2	no	—
369	#41	—	2	2	no	—
370	#41	—	4	1	no	—
371	#41	—	4	1	no	—
372	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
373	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
377	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
385	C₂²×C₄	#6129	1	1	yes	characteristic
386	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
387	Q₁₆	—	2	2	no	—
388	SD₁₆	—	2	2	no	—
389	SD₁₆	#6099	1	4	yes	complemented
390	D₈	—	2	2	no	—
391	M₁₆	—	52	2	no	—
392	M₁₆	—	104	2	no	—
393	M₁₆	—	104	1	no	—
394	M₁₆	—	104	1	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	4	1	no	—
397	C₂×C₈	—	13	2	no	—
398	C₂×C₈	—	13	2	no	—
399	C₂×C₈	—	26	2	no	—
400	C₂×C₈	—	26	2	no	—
401	C₂×C₈	—	26	2	no	—
402	C₂×C₈	—	104	2	no	—
403	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
404	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
405	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
406	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
412	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
413	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
414	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	1	no	—
427	C₄²	D₄×D₁₃	1	1	yes	characteristic
428	C₄²	#6129	1	1	yes	characteristic
429	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
430	C₄²	C₂³×D₁₃	1	1	yes	characteristic
431	C₁₃	#18061	1	1	yes	characteristic, complemented, Sylow
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
435	Q₈	—	2	1	no	—
436	Q₈	—	2	1	no	—
437	Q₈	—	2	1	no	—
438	Q₈	C₂×#6099	1	2	yes	—
439	D₄	—	2	1	no	—
440	D₄	—	2	1	no	—
441	D₄	—	2	1	no	—
442	D₄	—	4	2	no	—
443	D₄	—	4	2	no	—
444	D₄	C₂×#6099	1	2	yes	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	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	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
465	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
466	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
467	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
468	C₂×C₄	C₂×#6129	1	1	yes	characteristic
469	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
470	C₈	—	2	1	no	—
471	C₈	—	2	1	no	—
472	C₈	—	2	1	no	—
473	C₈	—	26	2	no	—
474	C₈	—	26	2	no	—
475	C₈	—	52	2	no	—
476	C₈	—	52	2	no	—
477	C₈	—	52	2	no	—
478	C₈	C₂×#6099	1	2	yes	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	1	no	—
488	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	2	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	1	no	—
498	C₄	#11718858	1	2	yes	—
499	C₄	#11719474	1	1	yes	characteristic
500	C₄	#11719476	1	1	yes	characteristic
501	C₄	C₂²×#6099	1	1	yes	characteristic
502	C₄	#11719524	1	1	yes	characteristic
503	C₂	—	4	1	no	—
504	C₂	—	4	2	no	—
505	C₂	—	8	1	no	—
506	C₂	D₄×#6099	1	1	yes	characteristic
507	C₂	#13123712	1	1	yes	characteristic
508	C₂	C₂×#11718858	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₄×C₁₃×#135	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×C₁₃×#135	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₄×#135	D₁₃
hypocenter	C₁₃	#18061
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #13123968	C₂	semidirect
2. #13123961	C₂	semidirect
3. #13113739	C₂	semidirect
4. #13113687	C₂	semidirect
5. #13113666	C₂	semidirect
6. SD₁₆⋊#1055	C₂	semidirect
7. #13113595	C₂	semidirect
8. #13113275	C₂	semidirect
9. #13113275	C₂	semidirect
10. #13113125	C₂	semidirect
136. C₁₃×SD₁₆	M₁₆	semidirect
389. SD₁₆	#6099	semidirect
431. C₁₃	#18061	semidirect

Maximal subgroups

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

subgroup	index
#13123968	2
#13123961	2
#13113739	2
#13113687	2
#13113666	2
SD₁₆⋊#1055	2
#13113595	2
#13113275	2
#13113125	2
C₄×C₁₃×#135	2
#18061	13