Subgroups — #15834127

Order 3328.

638 conjugacy classes of subgroups.

The subgroup lattice has 454 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	#13123903	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113721	C₂	1	2	yes	maximal, complemented
4	#13113715	C₂	1	2	yes	maximal, complemented
5	#13113701	C₂	1	2	yes	maximal, complemented
6	SD₁₆×#1055	C₂	1	2	yes	maximal, complemented
7	#13113625	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113287	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113218	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113120	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3106	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#532	C₂²	1	1	yes	characteristic
13	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
14	C₁₃×#482	C₄	1	2	yes	—
15	C₁₃×#477	C₄	1	1	yes	characteristic
16	C₁₃×#476	C₄	1	1	yes	characteristic
17	C₁₃×#460	C₄	1	1	yes	characteristic
18	C₁₃×#459	C₄	1	1	yes	characteristic
19	C₁₃×#449	C₄	1	2	yes	—
20	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
21	C₄×C₁₃×D₈	C₂²	1	2	yes	—
22	C₁₃×#431	C₂²	1	1	yes	characteristic
23	#11718895	—	2	2	no	—
24	Q₈×#1055	C₂²	1	2	yes	—
25	#11718673	—	2	1	no	—
26	#11718673	—	2	2	no	—
27	#11718673	C₂²	1	2	yes	—
28	#11718673	C₂²	1	2	yes	—
29	D₄×#1055	—	2	1	no	—
30	D₄×#1055	C₂²	1	2	yes	—
31	#11718586	—	2	1	no	—
32	#11718586	C₂²	1	1	yes	characteristic
33	#11718586	C₂²	1	1	yes	characteristic
34	#11718585	—	2	1	no	—
35	#11718585	C₂²	1	1	yes	characteristic
36	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
37	Q₈⋊#1055	C₂²	1	1	yes	characteristic
38	Q₈⋊#1055	C₂²	1	1	yes	characteristic
39	D₄⋊#1055	C₂²	1	2	yes	—
40	D₄⋊#1055	C₂²	1	1	yes	characteristic
41	D₄⋊#1055	C₂²	1	2	yes	—
42	D₄⋊#1055	C₂²	1	1	yes	characteristic
43	#11718050	C₂²	1	2	yes	—
44	#11718049	C₂²	1	2	yes	—
45	#11718046	C₂²	1	2	yes	—
46	C₈×#1055	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	—	2	1	no	—
48	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
50	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
51	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
52	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
53	C₁₃×#124	—	2	1	no	—
54	C₁₃×#121	—	2	1	no	—
55	C₁₃×#121	C₂×C₄	1	2	yes	—
56	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
57	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₄×D₄×C₁₃	—	2	1	no	—
59	C₄×D₄×C₁₃	—	2	1	no	—
60	C₄×D₄×C₁₃	—	2	1	no	—
61	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
62	C₄×D₄×C₁₃	C₂³	1	2	yes	—
63	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₁₃×#117	—	2	1	no	—
65	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	—	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	—	2	2	no	—
71	C₂²×#1055	—	2	1	no	—
72	C₂²×#1055	—	2	2	no	—
73	C₁₃×#107	C₂×C₄	1	2	yes	—
74	C₁₃×#106	C₂×C₄	1	2	yes	—
75	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
76	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
77	C₁₃×#103	C₂×C₄	1	2	yes	—
78	C₁₃×#102	C₂×C₄	1	2	yes	—
79	C₁₃×#102	C₂×C₄	1	2	yes	—
80	C₁₃×#102	C₂×C₄	1	2	yes	—
81	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
82	C₄×C₈×C₁₃	C₂³	1	2	yes	—
83	C₂²⋊#1055	—	2	1	no	—
84	C₂²⋊#1055	—	2	2	no	—
85	C₂²⋊#1055	—	2	2	no	—
86	C₂²⋊#1055	—	2	2	no	—
87	C₂²⋊#1055	D₄	1	2	yes	—
88	C₄⋊#1055	—	2	1	no	—
89	C₄⋊#1055	—	2	2	no	—
90	C₄⋊#1055	D₄	1	1	yes	characteristic
91	C₄⋊#1055	D₄	1	1	yes	characteristic
92	C₄⋊#1055	C₂³	1	1	yes	characteristic
93	C₄⋊#1055	C₂³	1	1	yes	characteristic
94	C₄⋊#1055	C₂³	1	2	yes	—
95	C₄×#1055	—	2	1	no	—
96	C₄×#1055	—	2	1	no	—
97	C₄×#1055	—	2	2	no	—
98	C₄×#1055	C₂³	1	1	yes	characteristic
99	C₄×#1055	C₂³	1	1	yes	characteristic
100	C₄×#1055	C₂³	1	2	yes	—
101	#18018	—	13	1	no	maximal, Sylow
102	C₁₃×#41	—	2	2	no	—
103	C₁₃×#41	—	4	1	no	—
104	C₁₃×#41	—	8	1	no	—
105	C₁₃×#41	—	8	1	no	—
106	C₂×Q₈×C₁₃	—	2	1	no	—
107	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×D₄×C₁₃	—	2	1	no	—
109	C₂×D₄×C₁₃	—	2	2	no	—
110	C₂×D₄×C₁₃	—	2	1	no	—
111	C₂×D₄×C₁₃	—	2	1	no	—
112	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	1	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×D₈	—	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	C₂²×C₄	1	1	yes	characteristic
129	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
130	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
131	C₁₃×C₂²⋊C₄	—	2	1	no	—
132	C₁₃×C₂²⋊C₄	—	2	1	no	—
133	C₁₃×C₂²⋊C₄	—	2	2	no	—
134	C₁₃×C₂²⋊C₄	—	2	1	no	—
135	C₁₃×C₂²⋊C₄	—	2	2	no	—
136	C₄²×C₁₃	—	2	1	no	—
137	C₄²×C₁₃	—	2	1	no	—
138	C₄²×C₁₃	—	2	1	no	—
139	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₁₃	#41	1	1	yes	characteristic
142	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
143	#6099	—	8	2	no	—
144	#6099	—	8	2	no	—
145	#6099	—	8	1	no	—
146	C₂×#1055	—	2	4	no	—
147	C₂×#1055	—	2	1	no	—
148	C₂×#1055	—	2	1	no	—
149	C₂×#1055	—	2	1	no	—
150	C₂×#1055	—	2	1	no	—
151	C₂×#1055	—	2	2	no	—
152	C₂×#1055	—	8	2	no	—
153	C₂×#1055	C₂×D₄	1	2	yes	—
154	C₂×#1055	C₂×D₄	1	2	yes	—
155	#3106	D₁₃	1	1	yes	characteristic
156	#2991	—	13	1	no	—
157	#2979	—	13	1	no	—
158	#1589	—	13	2	no	—
159	#1588	—	13	2	no	—
160	#1586	—	13	2	no	—
161	C₈×SD₁₆	—	13	2	no	—
162	#1574	—	13	1	no	—
163	#1492	—	13	1	no	—
164	#1476	—	13	1	no	—
165	#1450	—	13	1	no	—
166	C₂³×C₁₃	—	2	1	no	—
167	C₂³×C₁₃	—	2	2	no	—
168	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
169	Q₈×C₁₃	—	2	1	no	—
170	Q₈×C₁₃	—	8	1	no	—
171	Q₈×C₁₃	#131	1	2	yes	—
172	D₄×C₁₃	—	2	2	no	—
173	D₄×C₁₃	—	2	1	no	—
174	D₄×C₁₃	—	2	1	no	—
175	D₄×C₁₃	—	2	2	no	—
176	D₄×C₁₃	—	4	2	no	—
177	D₄×C₁₃	—	4	2	no	—
178	D₄×C₁₃	—	8	1	no	—
179	D₄×C₁₃	—	8	2	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
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	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
201	C₈×C₁₃	—	2	2	no	—
202	C₈×C₁₃	—	2	2	no	—
203	#1055	—	2	2	no	—
204	#1055	—	2	2	no	—
205	#1055	—	2	2	no	—
206	#1055	—	2	2	no	—
207	#1055	—	4	1	no	—
208	#1055	—	4	2	no	—
209	#1055	—	4	1	no	—
210	#532	C₂×D₁₃	1	1	yes	characteristic
211	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
212	#482	Dic₁₃	1	2	yes	—
213	#477	Dic₁₃	1	1	yes	characteristic
214	#476	Dic₁₃	1	1	yes	characteristic
215	#460	Dic₁₃	1	1	yes	characteristic
216	#459	Dic₁₃	1	1	yes	characteristic
217	#449	Dic₁₃	1	2	yes	—
218	C₈×Q₈	—	13	2	no	—
219	C₄×SD₁₆	C₂×D₁₃	1	2	yes	—
220	C₄×D₈	C₂×D₁₃	1	2	yes	—
221	#436	—	13	2	no	—
222	#436	—	13	2	no	—
223	#436	—	26	2	no	—
224	#436	—	26	1	no	—
225	C₈×D₄	—	13	2	no	—
226	C₈×D₄	—	26	1	no	—
227	#431	—	13	1	no	—
228	#431	—	13	1	no	—
229	#431	—	26	1	no	—
230	#431	C₂×D₁₃	1	1	yes	characteristic
231	#423	—	13	1	no	—
232	#423	—	26	1	no	—
233	#408	—	26	2	no	—
234	C₂×C₄×C₈	—	13	1	no	—
235	#335	—	13	2	no	—
236	#334	—	13	2	no	—
237	Q₈⋊C₈	—	13	1	no	—
238	Q₈⋊C₈	—	13	1	no	—
239	D₄⋊C₈	—	13	2	no	—
240	D₄⋊C₈	—	13	1	no	—
241	D₄⋊C₈	—	13	2	no	—
242	D₄⋊C₈	—	13	1	no	—
243	#322	—	13	2	no	—
244	C₈²	—	13	2	no	—
245	C₂²×C₁₃	—	2	1	no	—
246	C₂²×C₁₃	—	2	1	no	—
247	C₂²×C₁₃	—	2	1	no	—
248	C₂²×C₁₃	—	4	1	no	—
249	C₂²×C₁₃	—	4	2	no	—
250	C₂²×C₁₃	—	4	2	no	—
251	C₂²×C₁₃	—	4	1	no	—
252	C₂²×C₁₃	—	4	1	no	—
253	C₂²×C₁₃	—	4	2	no	—
254	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
255	C₄×C₁₃	—	2	1	no	—
256	C₄×C₁₃	—	2	2	no	—
257	C₄×C₁₃	—	2	1	no	—
258	C₄×C₁₃	—	2	1	no	—
259	C₄×C₁₃	—	4	1	no	—
260	C₄×C₁₃	—	4	2	no	—
261	C₄×C₁₃	—	4	1	no	—
262	C₄×C₁₃	#443	1	2	yes	—
263	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
264	C₄×C₁₃	#568	1	1	yes	characteristic
265	C₄×C₁₃	#576	1	1	yes	characteristic
266	C₄×C₁₃	#577	1	1	yes	characteristic
267	C₂×#41	—	2	1	no	—
268	C₂×#41	C₂×Dic₁₃	1	1	yes	characteristic
269	C₂×SD₁₆	C₂×Dic₁₃	1	2	yes	—
270	C₂×D₈	C₂×Dic₁₃	1	2	yes	—
271	C₂×M₁₆	—	26	2	no	—
272	C₂×M₁₆	—	26	2	no	—
273	C₂×M₁₆	—	26	1	no	—
274	C₂²×C₈	—	26	2	no	—
275	C₂²×C₈	—	26	1	no	—
276	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
277	#127	C₂×Dic₁₃	1	1	yes	characteristic
278	#124	—	2	1	no	—
279	#121	—	2	1	no	—
280	#121	C₂×Dic₁₃	1	2	yes	—
281	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
282	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
283	C₄×D₄	—	2	1	no	—
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
287	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
288	C₄×D₄	C₂²×D₁₃	1	2	yes	—
289	#117	—	2	1	no	—
290	#117	C₂×Dic₁₃	1	1	yes	characteristic
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
293	#107	C₂×Dic₁₃	1	2	yes	—
294	#106	C₂×Dic₁₃	1	2	yes	—
295	C₄⋊C₈	—	13	1	no	—
296	C₄⋊C₈	—	13	1	no	—
297	C₄⋊C₈	—	13	2	no	—
298	C₄⋊C₈	—	13	1	no	—
299	C₄⋊C₈	—	13	1	no	—
300	C₄⋊C₈	—	26	2	no	—
301	C₄⋊C₈	—	26	1	no	—
302	C₄⋊C₈	C₂×Dic₁₃	1	1	yes	characteristic
303	C₄⋊C₈	C₂×Dic₁₃	1	1	yes	characteristic
304	#103	C₂×Dic₁₃	1	2	yes	—
305	#102	C₂×Dic₁₃	1	2	yes	—
306	#102	C₂×Dic₁₃	1	2	yes	—
307	#102	C₂×Dic₁₃	1	2	yes	—
308	C₂²⋊C₈	—	13	2	no	—
309	C₂²⋊C₈	—	26	2	no	—
310	C₂²⋊C₈	—	26	2	no	—
311	C₂²⋊C₈	—	26	2	no	—
312	C₂²⋊C₈	—	26	1	no	—
313	C₂²⋊C₈	C₂×Dic₁₃	1	2	yes	—
314	C₄×C₈	—	13	2	no	—
315	C₄×C₈	—	13	1	no	—
316	C₄×C₈	—	13	1	no	—
317	C₄×C₈	—	26	2	no	—
318	C₄×C₈	—	26	1	no	—
319	C₄×C₈	—	26	1	no	—
320	C₄×C₈	C₂²×D₁₃	1	2	yes	—
321	C₂×C₁₃	—	4	1	no	—
322	C₂×C₁₃	—	8	1	no	—
323	C₂×C₁₃	—	8	2	no	—
324	C₂×C₁₃	#2933	1	1	yes	characteristic
325	C₂×C₁₃	#2946	1	1	yes	characteristic
326	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
327	#41	—	2	2	no	—
328	#41	—	4	1	no	—
329	#41	—	8	1	no	—
330	#41	—	8	1	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
338	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
344	C₂²×C₄	#6129	1	1	yes	characteristic
345	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
346	SD₁₆	—	2	4	no	—
347	D₈	—	4	2	no	—
348	M₁₆	—	104	2	no	—
349	M₁₆	—	104	2	no	—
350	M₁₆	—	104	1	no	—
351	C₂×C₈	—	13	2	no	—
352	C₂×C₈	—	13	2	no	—
353	C₂×C₈	—	26	4	no	—
354	C₂×C₈	—	26	1	no	—
355	C₂×C₈	—	26	1	no	—
356	C₂×C₈	—	26	1	no	—
357	C₂×C₈	—	26	1	no	—
358	C₂×C₈	—	26	2	no	—
359	C₂×C₈	—	104	2	no	—
360	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
361	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
366	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
367	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	1	no	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	D₄×D₁₃	1	1	yes	characteristic
377	C₄²	#6129	1	1	yes	characteristic
378	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
379	C₄²	C₂³×D₁₃	1	1	yes	characteristic
380	C₁₃	#18018	1	1	yes	characteristic, complemented, Sylow
381	C₂³	—	2	1	no	—
382	C₂³	—	2	2	no	—
383	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	8	1	no	—
386	Q₈	#88202	1	2	yes	—
387	D₄	—	2	2	no	—
388	D₄	—	2	1	no	—
389	D₄	—	2	1	no	—
390	D₄	—	2	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	8	1	no	—
394	D₄	—	8	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
411	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
412	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
413	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
414	C₂×C₄	C₂×#6129	1	1	yes	characteristic
415	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	26	2	no	—
419	C₈	—	26	2	no	—
420	C₈	—	26	2	no	—
421	C₈	—	26	2	no	—
422	C₈	—	52	1	no	—
423	C₈	—	52	2	no	—
424	C₈	—	52	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	2	no	—
434	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	2	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	1	no	—
442	C₄	#11718857	1	2	yes	—
443	C₄	#11719479	1	1	yes	characteristic
444	C₄	#11719480	1	1	yes	characteristic
445	C₄	C₂×#88202	1	1	yes	characteristic
446	C₄	#11719524	1	1	yes	characteristic
447	C₂	—	4	1	no	—
448	C₂	—	8	2	no	—
449	C₂	—	8	1	no	—
450	C₂	#13123563	1	1	yes	characteristic
451	C₂	#13123669	1	1	yes	characteristic
452	C₂	C₂×#11718857	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting, prime radical	C₁₃×#3106	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#3106	D₁₃
hypocenter	C₁₃	#18018
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3106

Complements

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

N	H ≅ G/N	type
1. #13123968	C₂	semidirect
2. #13123903	C₂	semidirect
3. #13113721	C₂	semidirect
4. #13113715	C₂	semidirect
5. #13113701	C₂	semidirect
6. SD₁₆×#1055	C₂	semidirect
7. #13113625	C₂	semidirect
8. #13113287	C₂	semidirect
9. #13113218	C₂	semidirect
10. #13113120	C₂	semidirect
380. C₁₃	#18018	semidirect

Maximal subgroups

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

subgroup	index
#13123968	2
#13123903	2
#13113721	2
#13113715	2
#13113701	2
SD₁₆×#1055	2
#13113625	2
#13113287	2
#13113218	2
#13113120	2
C₁₃×#3106	2
#18018	13