Subgroups — #15834726

Order 3328.

646 conjugacy classes of subgroups.

The subgroup lattice has 428 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	#13123580	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	C₂×#11718050	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113239	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113235	C₂	1	1	yes	maximal, characteristic
10	#13113125	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3167	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#533	C₂²	1	1	yes	characteristic
13	C₁₃×#532	C₂²	1	1	yes	characteristic
14	C₂×#88202	—	2	1	no	—
15	C₁₃×#498	C₄	1	1	yes	characteristic
16	C₁₃×#492	C₄	1	1	yes	characteristic
17	C₁₃×#487	C₄	1	1	yes	characteristic
18	C₁₃×#486	C₄	1	1	yes	characteristic
19	C₁₃×#465	C₄	1	2	yes	—
20	C₁₃×#465	C₄	1	2	yes	—
21	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
22	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	#11718895	—	2	1	no	—
25	#11718685	—	2	2	no	—
26	#11718685	C₂²	1	2	yes	—
27	Q₈×#1055	C₂²	1	2	yes	—
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	#11718586	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
36	C₄×#6099	C₂²	1	1	yes	characteristic
37	Q₈⋊#1055	C₂²	1	2	yes	—
38	Q₈⋊#1055	C₂²	1	2	yes	—
39	D₄⋊#1055	C₂²	1	2	yes	—
40	D₄⋊#1055	C₂²	1	2	yes	—
41	#11718050	C₂²	1	1	yes	characteristic
42	#11718050	C₂²	1	1	yes	characteristic
43	#11718050	C₂²	1	1	yes	characteristic
44	#11718050	C₂²	1	1	yes	characteristic
45	#11718047	C₂²	1	2	yes	—
46	#11718046	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	—	2	1	no	—
48	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
49	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
50	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
53	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
54	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
55	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
56	C₁₃×#125	—	2	1	no	—
57	C₁₃×#124	—	2	1	no	—
58	C₁₃×C₂²⋊Q₈	—	2	1	no	—
59	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
60	C₁₃×#121	—	2	1	no	—
61	C₁₃×#121	C₂×C₄	1	2	yes	—
62	C₄×Q₈×C₁₃	—	2	1	no	—
63	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
64	C₄×D₄×C₁₃	—	2	1	no	—
65	C₄×D₄×C₁₃	C₂³	1	2	yes	—
66	C₁₃×#117	—	2	1	no	—
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	#88202	—	4	4	no	—
69	C₂×#6099	—	2	2	no	—
70	C₂×#6099	D₄	1	1	yes	characteristic
71	C₂×#6099	D₄	1	1	yes	characteristic
72	C₂²×#1055	—	2	1	no	—
73	C₂²×#1055	—	2	1	no	—
74	C₂²×#1055	—	2	2	no	—
75	C₁₃×#106	C₂×C₄	1	2	yes	—
76	C₁₃×#106	C₂×C₄	1	2	yes	—
77	C₁₃×#103	C₂×C₄	1	2	yes	—
78	C₁₃×#103	C₂×C₄	1	2	yes	—
79	C₁₃×#102	C₂×C₄	1	2	yes	—
80	C₁₃×#102	C₂×C₄	1	2	yes	—
81	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
83	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²⋊#1055	—	2	1	no	—
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	1	no	—
91	C₄⋊#1055	—	2	2	no	—
92	C₄⋊#1055	—	2	2	no	—
93	C₄⋊#1055	C₂³	1	1	yes	characteristic
94	C₄⋊#1055	C₂³	1	1	yes	characteristic
95	C₄⋊#1055	C₂³	1	1	yes	characteristic
96	C₄⋊#1055	C₂³	1	1	yes	characteristic
97	#88043	—	2	2	no	—
98	#88043	D₄	1	2	yes	—
99	C₄×#1055	—	2	2	no	—
100	C₄×#1055	C₂³	1	2	yes	—
101	C₄×#1055	C₂³	1	2	yes	—
102	#18071	—	13	1	no	maximal, Sylow
103	C₁₃×#41	—	4	2	no	—
104	C₁₃×#41	—	4	2	no	—
105	C₂×Q₈×C₁₃	—	2	1	no	—
106	C₂×Q₈×C₁₃	—	2	1	no	—
107	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	—	2	1	no	—
110	C₂×D₄×C₁₃	—	2	1	no	—
111	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
116	C₁₃×SD₁₆	—	2	4	no	—
117	C₁₃×SD₁₆	—	4	2	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	4	1	no	—
120	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₁₃	C₂²×C₄	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	C₁₃×C₄⋊C₄	—	2	1	no	—
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	2	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
131	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
132	C₁₃×C₂²⋊C₄	—	2	2	no	—
133	C₁₃×C₂²⋊C₄	—	2	2	no	—
134	C₁₃×C₂²⋊C₄	—	2	2	no	—
135	C₄²×C₁₃	—	2	2	no	—
136	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₁₃	#41	1	1	yes	characteristic
139	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
140	#6099	—	2	2	no	—
141	#6099	—	2	2	no	—
142	#6099	—	4	4	no	—
143	C₂×#1055	—	2	1	no	—
144	C₂×#1055	—	2	1	no	—
145	C₂×#1055	—	2	1	no	—
146	C₂×#1055	—	2	1	no	—
147	C₂×#1055	—	2	2	no	—
148	C₂×#1055	—	4	4	no	—
149	C₂×#1055	—	4	2	no	—
150	C₂×#1055	—	4	2	no	—
151	C₂×#1055	C₂×D₄	1	2	yes	—
152	C₂×#1055	C₂×D₄	1	2	yes	—
153	#3167	D₁₃	1	1	yes	characteristic
154	#2962	—	13	1	no	—
155	#2935	—	13	1	no	—
156	#1592	—	13	2	no	—
157	#1588	—	13	2	no	—
158	#1585	—	13	2	no	—
159	SD₁₆⋊C₈	—	13	2	no	—
160	C₂×#335	—	13	1	no	—
161	#1481	—	13	1	no	—
162	#1480	—	13	1	no	—
163	#1451	—	13	1	no	—
164	C₂³×C₁₃	—	2	2	no	—
165	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
166	Q₈×C₁₃	—	2	2	no	—
167	Q₈×C₁₃	—	2	2	no	—
168	Q₈×C₁₃	—	4	2	no	—
169	Q₈×C₁₃	—	8	1	no	—
170	D₄×C₁₃	—	2	2	no	—
171	D₄×C₁₃	—	2	2	no	—
172	D₄×C₁₃	—	4	4	no	—
173	D₄×C₁₃	—	4	2	no	—
174	D₄×C₁₃	—	8	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
187	C₂×C₄×C₁₃	#137	1	2	yes	—
188	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
191	C₈×C₁₃	—	2	1	no	—
192	C₈×C₁₃	—	2	1	no	—
193	C₈×C₁₃	—	2	1	no	—
194	C₈×C₁₃	#131	1	2	yes	complemented
195	#1055	—	2	2	no	—
196	#1055	—	2	2	no	—
197	#1055	—	4	2	no	—
198	#1055	—	4	1	no	—
199	#1055	—	4	1	no	—
200	#1055	—	4	1	no	—
201	#1055	—	4	1	no	—
202	C₂×#131	—	26	1	no	—
203	#533	C₂×D₁₃	1	1	yes	characteristic
204	#532	C₂×D₁₃	1	1	yes	characteristic
205	#498	Dic₁₃	1	1	yes	characteristic
206	#492	Dic₁₃	1	1	yes	characteristic
207	#487	Dic₁₃	1	1	yes	characteristic
208	#486	Dic₁₃	1	1	yes	characteristic
209	#465	Dic₁₃	1	2	yes	—
210	#465	Dic₁₃	1	2	yes	—
211	#446	—	13	2	no	—
212	#446	—	26	2	no	—
213	C₈×Q₈	—	13	2	no	—
214	C₄×SD₁₆	C₂×D₁₃	1	2	yes	—
215	C₄×SD₁₆	C₂×D₁₃	1	2	yes	—
216	#436	—	13	2	no	—
217	#435	—	26	2	no	—
218	C₈×D₄	—	13	2	no	—
219	#431	—	13	1	no	—
220	#424	—	26	1	no	—
221	C₂×C₄⋊C₈	—	13	1	no	—
222	C₂×C₄⋊C₈	—	13	1	no	—
223	#408	—	26	1	no	—
224	#405	—	26	1	no	—
225	C₄×M₁₆	—	13	1	no	—
226	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
227	#335	—	13	1	no	—
228	#335	—	13	1	no	—
229	#335	—	13	1	no	—
230	#335	—	13	1	no	—
231	Q₈⋊C₈	—	13	2	no	—
232	Q₈⋊C₈	—	13	2	no	—
233	D₄⋊C₈	—	13	2	no	—
234	D₄⋊C₈	—	13	2	no	—
235	#322	—	13	2	no	—
236	#322	—	13	2	no	—
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	—	2	1	no	—
239	C₂²×C₁₃	—	4	2	no	—
240	C₂²×C₁₃	—	4	2	no	—
241	C₂²×C₁₃	—	4	2	no	—
242	C₂²×C₁₃	#440	1	2	yes	—
243	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
244	C₄×C₁₃	—	2	1	no	—
245	C₄×C₁₃	—	2	1	no	—
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	—	4	2	no	—
248	C₄×C₁₃	—	4	2	no	—
249	C₄×C₁₃	—	4	2	no	—
250	C₄×C₁₃	#440	1	2	yes	—
251	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
252	C₄×C₁₃	#568	1	1	yes	characteristic
253	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
254	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
255	C₂×#41	—	2	1	no	—
256	C₂×SD₁₆	C₂×Dic₁₃	1	2	yes	—
257	C₂×SD₁₆	C₂×Dic₁₃	1	2	yes	—
258	#131	—	52	4	no	—
259	C₂×M₁₆	—	13	1	no	—
260	C₂×M₁₆	—	13	1	no	—
261	C₂×M₁₆	—	26	2	no	—
262	C₂²×C₈	—	26	2	no	—
263	C₂²×C₈	—	26	1	no	—
264	C₂²×C₈	—	26	1	no	—
265	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
266	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
267	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
268	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
269	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
270	#127	C₂×Dic₁₃	1	1	yes	characteristic
271	#125	—	2	1	no	—
272	#124	—	2	1	no	—
273	C₂²⋊Q₈	—	2	1	no	—
274	C₂²⋊Q₈	C₂×Dic₁₃	1	2	yes	—
275	#121	—	2	1	no	—
276	#121	C₂×Dic₁₃	1	2	yes	—
277	C₄×Q₈	—	2	1	no	—
278	C₄×Q₈	C₂²×D₁₃	1	2	yes	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	C₂²×D₁₃	1	2	yes	—
281	#117	—	2	1	no	—
282	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
283	#106	C₂×Dic₁₃	1	2	yes	—
284	#106	C₂×Dic₁₃	1	2	yes	—
285	C₄⋊C₈	—	13	1	no	—
286	C₄⋊C₈	—	13	1	no	—
287	C₄⋊C₈	—	13	1	no	—
288	C₄⋊C₈	—	13	1	no	—
289	C₄⋊C₈	—	26	2	no	—
290	C₄⋊C₈	—	26	2	no	—
291	C₄⋊C₈	—	26	1	no	—
292	C₄⋊C₈	—	26	1	no	—
293	C₄⋊C₈	—	26	1	no	—
294	#103	C₂×Dic₁₃	1	2	yes	—
295	#103	C₂×Dic₁₃	1	2	yes	—
296	#102	C₂×Dic₁₃	1	2	yes	—
297	#102	C₂×Dic₁₃	1	2	yes	—
298	C₂²⋊C₈	—	26	2	no	—
299	C₂²⋊C₈	—	26	2	no	—
300	C₂²⋊C₈	—	26	1	no	—
301	#97	—	13	2	no	—
302	#97	—	26	2	no	—
303	C₄×C₈	—	13	2	no	—
304	C₄×C₈	—	13	2	no	—
305	C₄×C₈	—	26	2	no	—
306	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
307	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
308	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
309	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
310	C₂×C₁₃	—	2	2	no	—
311	C₂×C₁₃	—	8	2	no	—
312	C₂×C₁₃	#2935	1	1	yes	characteristic
313	C₂×C₁₃	C₂×#440	1	1	yes	characteristic
314	C₂×C₁₃	#2957	1	1	yes	characteristic
315	#41	—	4	2	no	—
316	#41	—	4	2	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	C₂²×Dic₁₃	1	2	yes	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
326	C₂²×C₄	#6129	1	1	yes	characteristic
327	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
328	SD₁₆	—	2	4	no	—
329	SD₁₆	—	4	2	no	—
330	M₁₆	—	26	2	no	—
331	M₁₆	—	26	2	no	—
332	M₁₆	—	52	4	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	13	2	no	—
336	C₂×C₈	—	13	2	no	—
337	C₂×C₈	—	26	1	no	—
338	C₂×C₈	—	26	1	no	—
339	C₂×C₈	—	26	1	no	—
340	C₂×C₈	—	26	1	no	—
341	C₂×C₈	—	26	2	no	—
342	C₂×C₈	—	52	4	no	—
343	C₂×C₈	—	52	2	no	—
344	C₂×C₈	—	52	2	no	—
345	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
346	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
347	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
348	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
356	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	D₄×D₁₃	1	1	yes	characteristic
362	C₄²	#6129	1	1	yes	characteristic
363	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
364	C₄²	C₂³×D₁₃	1	1	yes	characteristic
365	C₁₃	#18071	1	1	yes	characteristic, complemented, Sylow
366	C₂³	—	2	2	no	—
367	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	8	1	no	—
372	D₄	—	2	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	4	4	no	—
375	D₄	—	4	2	no	—
376	D₄	—	8	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	#88168	1	2	yes	—
386	C₂×C₄	#88169	1	2	yes	—
387	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
388	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
389	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
390	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
391	C₂×C₄	C₂×#6129	1	1	yes	characteristic
392	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	26	2	no	—
397	C₈	—	26	2	no	—
398	C₈	—	52	2	no	—
399	C₈	—	52	1	no	—
400	C₈	—	52	1	no	—
401	C₈	—	52	1	no	—
402	C₈	—	52	1	no	—
403	C₈	#88202	1	2	yes	complemented
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	#11718825	1	2	yes	—
410	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	#11718825	1	2	yes	—
418	C₄	C₂×#88168	1	1	yes	characteristic
419	C₄	C₂×#88169	1	1	yes	characteristic
420	C₄	C₂×#88202	1	1	yes	characteristic
421	C₄	#11719524	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	8	2	no	—
424	C₂	#13123580	1	1	yes	characteristic
425	C₂	C₂×#11718825	1	1	yes	characteristic
426	C₂	#13123753	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×#3167	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₁₃×#532	C₂²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#3167	D₁₃
hypocenter	C₁₃	#18071
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3167

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. C₂×#11718050	C₂	semidirect
8. #13113239	C₂	semidirect
10. #13113125	C₂	semidirect
194. C₈×C₁₃	#131	semidirect
365. C₁₃	#18071	semidirect
403. C₈	#88202	semidirect

Maximal subgroups

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

subgroup	index
#13123785	2
#13123580	2
#13113739	2
#13113715	2
#13113694	2
SD₁₆⋊#1055	2
C₂×#11718050	2
#13113239	2
#13113235	2
#13113125	2
C₁₃×#3167	2
#18071	13