Subgroups — #15833881

Order 3328.

672 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123785	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#6099	C₂	1	1	yes	maximal, characteristic
3	#13113739	C₂	1	2	yes	maximal, complemented
4	#13113715	C₂	1	2	yes	maximal, complemented
5	#13113694	C₂	1	2	yes	maximal, complemented
6	SD₁₆⋊#1055	C₂	1	2	yes	maximal, complemented
7	#13113611	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113291	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₄⋊#1055	C₂	1	1	yes	maximal, characteristic
10	#13113126	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3101	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#533	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂²×#6099	—	2	1	no	—
15	C₁₃×#483	C₄	1	2	yes	—
16	C₁₃×#476	C₄	1	1	yes	characteristic
17	C₁₃×#476	C₄	1	1	yes	characteristic
18	C₁₃×#461	C₄	1	1	yes	characteristic
19	C₁₃×#461	C₄	1	1	yes	characteristic
20	C₁₃×#450	C₄	1	2	yes	—
21	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
22	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
23	C₁₃×#431	C₂²	1	1	yes	characteristic
24	#11718868	—	2	1	no	—
25	#11718685	—	2	2	no	—
26	#11718685	C₂²	1	2	yes	complemented
27	Q₈×#1055	C₂²	1	2	yes	complemented
28	#11718673	C₂²	1	2	yes	—
29	#11718672	—	2	2	no	—
30	D₄×#1055	C₂²	1	2	yes	—
31	#11718660	—	2	1	no	—
32	#11718658	—	2	1	no	—
33	#11718585	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
35	C₄×#6099	C₂²	1	1	yes	characteristic
36	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
37	Q₈⋊#1055	C₂²	1	2	yes	complemented
38	Q₈⋊#1055	C₂²	1	2	yes	complemented
39	D₄⋊#1055	C₂²	1	1	yes	characteristic
40	D₄⋊#1055	C₂²	1	1	yes	characteristic
41	D₄⋊#1055	C₂²	1	1	yes	characteristic
42	D₄⋊#1055	C₂²	1	1	yes	characteristic
43	#11718050	C₂²	1	2	yes	complemented
44	#11718050	C₂²	1	2	yes	complemented
45	#11718047	C₂²	1	2	yes	complemented
46	#11718046	C₂²	1	2	yes	complemented
47	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	—	2	1	no	—
49	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
50	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
51	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
52	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
53	C₁₃×#125	—	2	1	no	—
54	C₁₃×C₂²⋊Q₈	—	2	1	no	—
55	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
56	C₄×Q₈×C₁₃	—	2	1	no	—
57	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
58	C₄×D₄×C₁₃	—	2	1	no	—
59	C₄×D₄×C₁₃	—	2	1	no	—
60	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
61	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
62	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₁₃×#117	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×#6099	—	2	1	no	—
69	C₂×#6099	—	2	2	no	—
70	C₂×#6099	—	4	4	no	—
71	C₂×#6099	D₄	1	1	yes	characteristic
72	C₂×#6099	D₄	1	1	yes	characteristic
73	C₂²×#1055	—	2	1	no	—
74	C₂²×#1055	—	2	1	no	—
75	C₂²×#1055	—	2	2	no	—
76	C₁₃×#106	C₂×C₄	1	2	yes	—
77	C₁₃×#106	C₂×C₄	1	2	yes	—
78	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
80	C₁₃×#103	C₂×C₄	1	2	yes	—
81	C₁₃×#103	C₂×C₄	1	2	yes	—
82	C₁₃×#102	C₂×C₄	1	2	yes	—
83	C₁₃×#102	C₂×C₄	1	2	yes	—
84	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
85	C₄×C₈×C₁₃	C₂³	1	2	yes	—
86	C₂²⋊#1055	—	2	2	no	—
87	C₂²⋊#1055	—	2	2	no	—
88	C₄⋊#1055	—	2	1	no	—
89	C₄⋊#1055	—	2	1	no	—
90	C₄⋊#1055	—	2	2	no	—
91	C₄⋊#1055	—	2	2	no	—
92	C₄⋊#1055	C₂³	1	2	yes	—
93	C₄⋊#1055	C₂³	1	1	yes	characteristic
94	C₄⋊#1055	C₂³	1	1	yes	characteristic
95	#88043	—	2	2	no	—
96	#88043	D₄	1	2	yes	—
97	C₄×#1055	—	2	1	no	—
98	C₄×#1055	—	2	2	no	—
99	C₄×#1055	C₂³	1	1	yes	characteristic
100	C₄×#1055	C₂³	1	1	yes	characteristic
101	C₄×#1055	C₂³	1	2	yes	—
102	#18000	—	13	1	no	maximal, Sylow
103	C₂⁴×C₁₃	—	2	1	no	—
104	C₂×Q₈×C₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
106	C₂×D₄×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	—	2	1	no	—
108	C₂×D₄×C₁₃	—	4	1	no	—
109	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	4	2	no	—
117	C₂²×C₄×C₁₃	—	4	2	no	—
118	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
121	C₁₃×SD₁₆	—	2	4	no	—
122	C₁₃×SD₁₆	—	4	2	no	—
123	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
125	C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
132	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
133	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
134	C₁₃×C₂²⋊C₄	—	2	2	no	—
135	C₁₃×C₂²⋊C₄	—	2	1	no	—
136	C₁₃×C₂²⋊C₄	—	2	1	no	—
137	C₁₃×C₂²⋊C₄	—	2	1	no	—
138	C₁₃×C₂²⋊C₄	—	2	1	no	—
139	C₄²×C₁₃	—	2	2	no	—
140	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₁₃	#41	1	1	yes	characteristic
143	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
144	#6099	—	2	2	no	—
145	#6099	—	2	2	no	—
146	#6099	—	4	4	no	—
147	#6099	—	4	2	no	—
148	C₂×#1055	—	2	1	no	—
149	C₂×#1055	—	2	2	no	—
150	C₂×#1055	—	2	1	no	—
151	C₂×#1055	—	2	1	no	—
152	C₂×#1055	—	2	1	no	—
153	C₂×#1055	—	4	2	no	—
154	C₂×#1055	—	4	4	no	—
155	C₂×#1055	—	4	2	no	—
156	C₂×#1055	C₂×D₄	1	2	yes	—
157	C₂×#1055	C₂×D₄	1	2	yes	—
158	#3101	D₁₃	1	1	yes	characteristic
159	#2962	—	13	1	no	—
160	D₄×M₁₆	—	13	1	no	—
161	#1592	—	13	2	no	—
162	#1588	—	13	2	no	—
163	#1585	—	13	2	no	—
164	SD₁₆⋊C₈	—	13	2	no	—
165	#1571	—	13	1	no	—
166	#1493	—	13	1	no	—
167	C₂×D₄⋊C₈	—	13	1	no	—
168	#1451	—	13	1	no	—
169	C₂³×C₁₃	—	2	1	no	—
170	C₂³×C₁₃	—	2	1	no	—
171	C₂³×C₁₃	—	4	2	no	—
172	C₂³×C₁₃	—	4	2	no	—
173	C₂³×C₁₃	—	8	1	no	—
174	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
175	Q₈×C₁₃	—	2	2	no	—
176	Q₈×C₁₃	—	2	2	no	—
177	Q₈×C₁₃	—	8	1	no	—
178	D₄×C₁₃	—	2	1	no	—
179	D₄×C₁₃	—	2	1	no	—
180	D₄×C₁₃	—	2	1	no	—
181	D₄×C₁₃	—	4	2	no	—
182	D₄×C₁₃	#131	1	2	yes	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
201	C₂×C₄×C₁₃	#137	1	2	yes	—
202	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
205	C₈×C₁₃	—	2	2	no	—
206	C₈×C₁₃	—	2	2	no	—
207	#1055	—	2	2	no	—
208	#1055	—	2	2	no	—
209	#1055	—	2	2	no	—
210	#1055	—	4	1	no	—
211	#1055	—	4	1	no	—
212	#1055	—	4	1	no	—
213	#1055	—	4	2	no	—
214	C₂²×M₁₆	—	26	1	no	—
215	#533	C₂×D₁₃	1	1	yes	characteristic
216	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
217	#483	Dic₁₃	1	2	yes	—
218	#476	Dic₁₃	1	1	yes	characteristic
219	#476	Dic₁₃	1	1	yes	characteristic
220	#461	Dic₁₃	1	1	yes	characteristic
221	#461	Dic₁₃	1	1	yes	characteristic
222	#450	Dic₁₃	1	2	yes	—
223	#446	—	13	2	no	—
224	#446	—	26	2	no	—
225	C₈×Q₈	—	13	2	no	—
226	C₄×SD₁₆	C₂×D₁₃	1	2	yes	—
227	C₄×SD₁₆	C₂×D₁₃	1	2	yes	—
228	#436	—	13	2	no	—
229	#435	—	26	2	no	—
230	C₈×D₄	—	13	2	no	—
231	#431	C₂×D₁₃	1	1	yes	characteristic
232	#424	—	26	1	no	—
233	#423	—	13	1	no	—
234	C₂×C₄⋊C₈	—	13	1	no	—
235	#407	—	26	1	no	—
236	#405	—	26	1	no	—
237	C₄×M₁₆	—	13	1	no	—
238	C₂×C₄×C₈	—	13	1	no	—
239	#335	—	13	2	no	—
240	#335	—	13	2	no	—
241	Q₈⋊C₈	—	13	2	no	—
242	Q₈⋊C₈	—	13	2	no	—
243	D₄⋊C₈	—	13	1	no	—
244	D₄⋊C₈	—	13	1	no	—
245	D₄⋊C₈	—	13	1	no	—
246	D₄⋊C₈	—	13	1	no	—
247	#322	—	13	2	no	—
248	#322	—	13	2	no	—
249	C₂²×C₁₃	—	2	1	no	—
250	C₂²×C₁₃	—	2	1	no	—
251	C₂²×C₁₃	—	2	2	no	—
252	C₂²×C₁₃	—	4	1	no	—
253	C₂²×C₁₃	—	4	1	no	—
254	C₂²×C₁₃	—	4	1	no	—
255	C₂²×C₁₃	—	4	1	no	—
256	C₂²×C₁₃	—	4	1	no	—
257	C₂²×C₁₃	—	8	4	no	—
258	C₂²×C₁₃	#440	1	2	yes	—
259	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
260	C₄×C₁₃	—	2	1	no	—
261	C₄×C₁₃	—	2	1	no	—
262	C₄×C₁₃	—	2	1	no	—
263	C₄×C₁₃	—	4	2	no	—
264	C₄×C₁₃	—	4	1	no	—
265	C₄×C₁₃	—	4	1	no	—
266	C₄×C₁₃	—	4	2	no	—
267	C₄×C₁₃	#440	1	2	yes	—
268	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
269	C₄×C₁₃	#568	1	1	yes	characteristic
270	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
271	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
272	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
273	C₂³×C₄	—	2	1	no	—
274	C₂×SD₁₆	C₂×Dic₁₃	1	2	yes	—
275	C₂×SD₁₆	C₂×Dic₁₃	1	2	yes	—
276	C₂×M₁₆	—	13	1	no	—
277	C₂×M₁₆	—	13	1	no	—
278	C₂×M₁₆	—	26	2	no	—
279	C₂×M₁₆	—	26	1	no	—
280	C₂×M₁₆	—	52	4	no	—
281	C₂²×C₈	—	26	2	no	—
282	C₂²×C₈	—	26	1	no	—
283	C₂²×C₈	—	26	1	no	—
284	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
285	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
286	#125	—	2	1	no	—
287	C₂²⋊Q₈	—	2	1	no	—
288	C₂²⋊Q₈	C₂×Dic₁₃	1	2	yes	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×Q₈	C₂²×D₁₃	1	2	yes	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
294	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
295	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
296	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
297	#117	—	2	1	no	—
298	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
301	#106	C₂×Dic₁₃	1	2	yes	—
302	#106	C₂×Dic₁₃	1	2	yes	—
303	C₄⋊C₈	—	13	1	no	—
304	C₄⋊C₈	—	13	1	no	—
305	C₄⋊C₈	—	13	2	no	—
306	C₄⋊C₈	—	26	2	no	—
307	C₄⋊C₈	—	26	2	no	—
308	C₄⋊C₈	—	26	1	no	—
309	C₄⋊C₈	—	26	1	no	—
310	C₄⋊C₈	C₂×Dic₁₃	1	1	yes	characteristic
311	C₄⋊C₈	C₂×Dic₁₃	1	1	yes	characteristic
312	#103	C₂×Dic₁₃	1	2	yes	—
313	#103	C₂×Dic₁₃	1	2	yes	—
314	#102	C₂×Dic₁₃	1	2	yes	—
315	#102	C₂×Dic₁₃	1	2	yes	—
316	C₂²⋊C₈	—	26	2	no	—
317	C₂²⋊C₈	—	26	2	no	—
318	C₂²⋊C₈	C₂×Dic₁₃	1	2	yes	—
319	#97	—	13	2	no	—
320	#97	—	26	2	no	—
321	C₄×C₈	—	13	2	no	—
322	C₄×C₈	—	13	1	no	—
323	C₄×C₈	—	13	1	no	—
324	C₄×C₈	—	26	2	no	—
325	C₄×C₈	—	26	1	no	—
326	C₄×C₈	C₂²×D₁₃	1	2	yes	—
327	C₂×C₁₃	—	2	2	no	—
328	C₂×C₁₃	—	4	2	no	—
329	C₂×C₁₃	—	8	1	no	—
330	C₂×C₁₃	#2933	1	1	yes	characteristic
331	C₂×C₁₃	C₂×#440	1	1	yes	characteristic
332	C₂×C₁₃	#2956	1	1	yes	characteristic
333	C₂⁴	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	C₂²×Dic₁₃	1	2	yes	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
340	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
349	C₂²×C₄	#6129	1	1	yes	characteristic
350	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
351	SD₁₆	—	2	4	no	—
352	SD₁₆	—	4	2	no	—
353	M₁₆	—	26	2	no	—
354	M₁₆	—	26	2	no	—
355	M₁₆	—	52	4	no	—
356	M₁₆	—	52	2	no	—
357	C₂×C₈	—	13	2	no	—
358	C₂×C₈	—	13	2	no	—
359	C₂×C₈	—	26	1	no	—
360	C₂×C₈	—	26	1	no	—
361	C₂×C₈	—	26	1	no	—
362	C₂×C₈	—	26	2	no	—
363	C₂×C₈	—	26	1	no	—
364	C₂×C₈	—	52	4	no	—
365	C₂×C₈	—	52	2	no	—
366	C₂×C₈	—	52	2	no	—
367	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
368	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
376	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
377	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
378	C₂²⋊C₄	—	2	2	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	C₄²	—	2	2	no	—
384	C₄²	D₄×D₁₃	1	1	yes	characteristic
385	C₄²	#6129	1	1	yes	characteristic
386	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
387	C₄²	C₂³×D₁₃	1	1	yes	characteristic
388	C₁₃	#18000	1	1	yes	characteristic, complemented, Sylow
389	C₂³	—	2	1	no	—
390	C₂³	—	2	1	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	8	1	no	—
394	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
395	Q₈	—	2	2	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	8	1	no	—
398	D₄	—	2	1	no	—
399	D₄	—	2	1	no	—
400	D₄	—	2	1	no	—
401	D₄	—	4	2	no	—
402	D₄	#88202	1	2	yes	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	#88168	1	2	yes	—
418	C₂×C₄	#88169	1	2	yes	—
419	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
420	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
421	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
422	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
423	C₂×C₄	C₂×#6129	1	1	yes	characteristic
424	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	2	2	no	—
427	C₈	—	26	2	no	—
428	C₈	—	26	2	no	—
429	C₈	—	26	2	no	—
430	C₈	—	52	1	no	—
431	C₈	—	52	1	no	—
432	C₈	—	52	1	no	—
433	C₈	—	52	2	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	8	4	no	—
443	C₂²	#11718825	1	2	yes	—
444	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	4	1	no	—
449	C₄	—	4	1	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	#11718825	1	2	yes	—
453	C₄	C₂×#88168	1	1	yes	characteristic
454	C₄	C₂×#88169	1	1	yes	characteristic
455	C₄	C₂×#88202	1	1	yes	characteristic
456	C₄	#11719524	1	1	yes	characteristic
457	C₂	—	2	2	no	—
458	C₂	—	4	2	no	—
459	C₂	—	8	1	no	—
460	C₂	#13123563	1	1	yes	characteristic
461	C₂	C₂×#11718825	1	1	yes	characteristic
462	C₂	#13123746	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#3101	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂²×D₄×C₁₃	C₂×C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#3101	D₁₃
hypocenter	C₁₃	#18000
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3101

Complements

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

N	H ≅ G/N	type
1. #13123785	C₂	semidirect
3. #13113739	C₂	semidirect
4. #13113715	C₂	semidirect
5. #13113694	C₂	semidirect
6. SD₁₆⋊#1055	C₂	semidirect
7. #13113611	C₂	semidirect
8. #13113291	C₂	semidirect
10. #13113126	C₂	semidirect
26. #11718685	C₂²	semidirect
27. Q₈×#1055	C₂²	semidirect
37. Q₈⋊#1055	C₂²	semidirect
38. Q₈⋊#1055	C₂²	semidirect
43. #11718050	C₂²	semidirect
44. #11718050	C₂²	semidirect
45. #11718047	C₂²	semidirect
46. #11718046	C₂²	semidirect
388. C₁₃	#18000	semidirect

Maximal subgroups

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

subgroup	index
#13123785	2
D₄×#6099	2
#13113739	2
#13113715	2
#13113694	2
SD₁₆⋊#1055	2
#13113611	2
#13113291	2
C₂×D₄⋊#1055	2
#13113126	2
C₁₃×#3101	2
#18000	13