Subgroups — #15881727

Order 3328.

832 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718340	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718492	C₂	1	1	yes	maximal, characteristic
3	C₄×#88141	C₂	1	1	yes	maximal, characteristic
4	#13115558	C₂	1	2	yes	maximal
5	#13115556	C₂	1	2	yes	maximal
6	#13115555	C₂	1	1	yes	maximal, characteristic
7	#13114987	C₂	1	1	yes	maximal, characteristic
8	#13114987	C₂	1	2	yes	maximal
9	#13114688	C₂	1	2	yes	maximal
10	C₄×#88054	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic
12	C₂×#88141	C₄	1	1	yes	characteristic
13	C₂×#88141	C₄	1	1	yes	characteristic
14	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×#88055	C₂²	1	2	yes	—
20	C₂×#88055	C₂²	1	2	yes	—
21	C₂×#88054	C₂²	1	1	yes	characteristic
22	C₂×#88054	C₂²	1	2	yes	—
23	C₂×#88054	C₂²	1	2	yes	—
24	C₂×#88054	C₂²	1	2	yes	—
25	C₂×#88054	C₂²	1	2	yes	—
26	C₂×#88054	C₂²	1	1	yes	characteristic
27	C₄⋊C₄×Dic₁₃	C₄	1	1	yes	characteristic
28	C₄⋊C₄×Dic₁₃	C₄	1	1	yes	characteristic
29	C₄×#6101	C₂²	1	2	yes	—
30	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
31	C₄²×Dic₁₃	C₂²	1	2	yes	—
32	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊#1055	C₂²	1	2	yes	—
34	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
35	#11718492	—	2	4	no	—
36	#11718340	—	2	4	no	—
37	#11718310	C₄	1	2	yes	—
38	#11718310	C₄	1	2	yes	—
39	C₁₃×#336	C₂²	1	2	yes	—
40	#11718142	C₂²	1	1	yes	characteristic
41	#11718142	C₂²	1	1	yes	characteristic
42	#11718116	C₂²	1	2	yes	—
43	C₂²×Dic₂₆	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
50	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
51	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×#6101	C₂×C₄	1	2	yes	—
53	C₂×#6101	C₂×C₄	1	2	yes	—
54	C₂×#6101	C₂×C₄	1	2	yes	—
55	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
56	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
57	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
60	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
62	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
65	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
66	C₂²×#1055	C₂³	1	2	yes	—
67	C₂²×#1055	C₂³	1	1	yes	characteristic
68	C₂²×#1055	C₂³	1	1	yes	characteristic
69	#88141	—	2	4	no	—
70	#88141	—	2	4	no	—
71	C₄×Dic₂₆	D₄	1	4	yes	—
72	C₄×Dic₂₆	Q₈	1	4	yes	—
73	C₁₃×C₄⋊C₈	—	2	2	no	—
74	C₁₃×C₄⋊C₈	—	4	2	no	—
75	C₄×C₈×C₁₃	—	2	2	no	—
76	C₁₃×#95	C₂×C₄	1	2	yes	—
77	#88071	C₂×C₄	1	2	yes	—
78	#88071	C₂×C₄	1	2	yes	—
79	#88055	—	2	4	no	—
80	#88055	—	2	4	no	—
81	#88054	—	2	4	no	—
82	#88054	—	2	4	no	—
83	#88054	—	2	2	no	—
84	#88054	—	2	4	no	—
85	#88054	—	4	2	no	—
86	#88054	Q₈	1	4	yes	complemented
87	C₄⋊#1055	—	2	2	no	—
88	C₄⋊#1055	—	4	2	no	—
89	C₄×#1055	—	2	2	no	—
90	#22722	—	13	1	no	maximal, Sylow
91	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
96	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
98	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
99	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂×Dic₂₆	—	2	2	no	—
103	C₂×Dic₂₆	—	2	2	no	—
104	C₂×Dic₂₆	C₄⋊C₄	1	4	yes	—
105	C₂×C₈×C₁₃	—	2	1	no	—
106	C₂×C₈×C₁₃	—	2	1	no	—
107	C₂×C₈×C₁₃	—	2	1	no	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	1	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
114	C₁₃×C₄⋊C₄	—	2	2	no	—
115	C₁₃×C₄⋊C₄	M₁₆	1	4	yes	—
116	C₄²×C₁₃	—	2	2	no	—
117	C₄²×C₁₃	—	2	2	no	—
118	C₄²×C₁₃	C₂×D₄	1	2	yes	—
119	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
120	C₄⋊Dic₁₃	C₄⋊C₄	1	4	yes	—
121	#6101	—	2	4	no	—
122	#6101	—	2	4	no	—
123	#6101	C₄⋊C₄	1	8	yes	—
124	C₄×Dic₁₃	—	2	4	no	—
125	C₄×Dic₁₃	—	2	2	no	—
126	C₄×Dic₁₃	—	2	1	no	—
127	C₄×Dic₁₃	—	2	1	no	—
128	C₄×Dic₁₃	—	2	4	no	—
129	C₄×Dic₁₃	—	2	4	no	—
130	C₄×Dic₁₃	—	2	2	no	—
131	C₄×Dic₁₃	—	4	1	no	—
132	C₄×Dic₁₃	—	4	2	no	—
133	C₄×Dic₁₃	M₁₆	1	4	yes	—
134	C₄×Dic₁₃	C₂×D₄	1	4	yes	—
135	C₄×Dic₁₃	C₂×Q₈	1	4	yes	—
136	C₄×Dic₁₃	C₂×Q₈	1	2	yes	—
137	C₄×Dic₁₃	#41	1	2	yes	—
138	C₂×#1055	—	2	1	no	—
139	C₂×#1055	—	2	1	no	—
140	C₂×#1055	—	2	1	no	—
141	C₂×#1055	—	2	2	no	—
142	C₂×#1055	—	2	2	no	—
143	C₂×#1055	—	2	1	no	—
144	C₂×#1055	—	2	1	no	—
145	C₂×#1055	—	2	2	no	—
146	C₂×#1055	C₂×Q₈	1	2	yes	—
147	C₂×#446	—	13	1	no	—
148	C₂×#446	—	13	1	no	—
149	C₄²×Q₈	—	13	1	no	—
150	#1940	—	13	2	no	—
151	#1940	—	13	2	no	—
152	#1939	—	13	1	no	—
153	#1939	D₁₃	1	1	yes	characteristic
154	#1842	—	13	1	no	—
155	#1842	—	13	2	no	—
156	#1767	—	13	2	no	—
157	C₄×C₄⋊C₈	—	13	1	no	—
158	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	1	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
167	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
168	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
169	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
170	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
171	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
177	C₂×Dic₁₃	—	2	1	no	—
178	C₂×Dic₁₃	—	2	1	no	—
179	C₂×Dic₁₃	—	2	2	no	—
180	C₂×Dic₁₃	—	2	2	no	—
181	C₂×Dic₁₃	—	2	2	no	—
182	C₂×Dic₁₃	—	2	1	no	—
183	C₂×Dic₁₃	—	2	2	no	—
184	C₂×Dic₁₃	—	2	1	no	—
185	C₂×Dic₁₃	—	2	1	no	—
186	C₂×Dic₁₃	—	2	1	no	—
187	C₂×Dic₁₃	—	2	1	no	—
188	C₂×Dic₁₃	C₂×C₄⋊C₄	1	4	yes	—
189	C₂×Dic₁₃	C₂×C₄⋊C₄	1	4	yes	—
190	C₂×Dic₁₃	C₄×Q₈	1	2	yes	—
191	C₂×Dic₁₃	C₄×Q₈	1	2	yes	—
192	C₂×Dic₁₃	C₂×M₁₆	1	2	yes	—
193	C₂×Dic₁₃	C₂×M₁₆	1	2	yes	—
194	C₂×Dic₁₃	#131	1	2	yes	—
195	Dic₂₆	—	2	8	no	—
196	C₈×C₁₃	—	2	2	no	—
197	C₈×C₁₃	—	4	1	no	—
198	C₈×C₁₃	—	4	2	no	—
199	#1055	—	2	2	no	—
200	#1055	—	4	1	no	—
201	#1055	—	4	2	no	—
202	C₂×C₄×Q₈	—	13	1	no	—
203	C₂×C₄×Q₈	—	13	1	no	—
204	C₂×C₄×Q₈	—	13	1	no	—
205	#446	—	26	4	no	—
206	#446	—	26	4	no	—
207	C₂×C₄⋊C₈	—	13	1	no	—
208	C₂×C₄⋊C₈	—	13	1	no	—
209	C₂×C₄⋊C₈	—	13	2	no	—
210	C₂×C₄⋊C₈	—	13	2	no	—
211	C₂×C₄⋊C₈	—	13	2	no	—
212	C₂×C₄⋊C₈	—	13	1	no	—
213	C₂×C₄⋊C₈	—	13	2	no	—
214	C₂×C₄⋊C₈	—	13	2	no	—
215	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
216	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	—
217	C₂×#97	—	13	2	no	—
218	C₂×#97	—	13	2	no	—
219	C₂×C₄×C₈	—	13	1	no	—
220	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
221	C₄×C₄⋊C₄	—	13	1	no	—
222	C₄×C₄⋊C₄	—	13	1	no	—
223	C₄×C₄⋊C₄	—	13	2	no	—
224	C₄×C₄⋊C₄	—	13	2	no	—
225	C₄×C₄⋊C₄	—	13	2	no	—
226	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
227	C₄³	—	13	1	no	—
228	C₄³	—	13	2	no	—
229	#336	—	13	1	no	—
230	#336	—	13	1	no	—
231	#336	—	13	2	no	—
232	#336	C₂×D₁₃	1	2	yes	—
233	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
234	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
235	C₂²×C₁₃	#520	1	1	yes	characteristic
236	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
237	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
238	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
239	C₂²×C₁₃	#568	1	1	yes	characteristic
240	C₄×C₁₃	—	2	2	no	—
241	C₄×C₁₃	—	2	4	no	—
242	C₄×C₁₃	—	4	2	no	—
243	C₄×C₁₃	#423	1	4	yes	—
244	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
245	C₄×C₁₃	#550	1	1	yes	characteristic
246	C₄×C₁₃	#557	1	1	yes	characteristic
247	C₄×C₁₃	Q₈²	1	1	yes	characteristic
248	Dic₁₃	—	2	4	no	—
249	Dic₁₃	—	2	4	no	—
250	Dic₁₃	—	2	2	no	—
251	Dic₁₃	—	2	2	no	—
252	Dic₁₃	—	4	1	no	—
253	Dic₁₃	#446	1	4	yes	complemented
254	C₂²×Q₈	—	13	1	no	—
255	C₂²×C₈	—	13	1	no	—
256	C₂²×C₈	—	13	1	no	—
257	C₂²×C₈	—	13	2	no	—
258	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
259	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
260	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
261	C₄×Q₈	—	13	4	no	—
262	C₄×Q₈	—	13	4	no	—
263	C₄×Q₈	—	26	4	no	—
264	C₄×Q₈	—	26	4	no	—
265	C₂×C₄⋊C₄	—	13	2	no	—
266	C₂×C₄⋊C₄	—	13	1	no	—
267	C₂×C₄⋊C₄	—	13	2	no	—
268	C₂×C₄⋊C₄	—	13	2	no	—
269	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
271	C₂×C₄²	—	13	1	no	—
272	C₂×C₄²	—	13	2	no	—
273	C₂×C₄²	—	13	1	no	—
274	C₂×C₄²	—	13	2	no	—
275	C₂×C₄²	—	13	2	no	—
276	C₂×C₄²	—	13	1	no	—
277	C₂×C₄²	—	13	2	no	—
278	C₂×C₄²	—	13	1	no	—
279	C₂×C₄²	—	13	1	no	—
280	C₂×C₄²	—	13	2	no	—
281	C₂×C₄²	—	13	1	no	—
282	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
283	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
284	C₄⋊C₈	—	2	2	no	—
285	C₄⋊C₈	—	4	2	no	—
286	C₄⋊C₈	—	13	4	no	—
287	C₄⋊C₈	—	26	4	no	—
288	C₄⋊C₈	—	26	4	no	—
289	C₄⋊C₈	—	26	2	no	—
290	C₄⋊C₈	—	26	4	no	—
291	C₄⋊C₈	—	26	2	no	—
292	C₄⋊C₈	—	52	2	no	—
293	C₄⋊C₈	—	52	2	no	—
294	#97	—	26	4	no	—
295	#97	—	26	4	no	—
296	C₄×C₈	—	2	2	no	—
297	C₄×C₈	—	26	2	no	—
298	#95	—	13	2	no	—
299	#95	—	13	2	no	—
300	#95	C₄×D₁₃	1	2	yes	—
301	C₂×C₁₃	Q₈×C₄⋊C₄	1	1	yes	characteristic
302	C₂×C₁₃	C₂×#423	1	1	yes	characteristic
303	C₂×C₁₃	#2906	1	1	yes	characteristic
304	C₂×C₁₃	C₂×#446	1	1	yes	characteristic
305	C₂×C₁₃	Q₈×M₁₆	1	1	yes	characteristic
306	C₂×C₁₃	#2989	1	1	yes	characteristic
307	C₂×C₁₃	#2990	1	1	yes	characteristic
308	C₂×Q₈	—	13	4	no	—
309	C₂×Q₈	—	26	2	no	—
310	C₂×Q₈	—	26	2	no	—
311	C₂²×C₄	—	13	1	no	—
312	C₂²×C₄	—	13	1	no	—
313	C₂²×C₄	—	13	2	no	—
314	C₂²×C₄	—	13	1	no	—
315	C₂²×C₄	—	13	2	no	—
316	C₂²×C₄	—	13	1	no	—
317	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
318	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
319	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
320	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
321	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	13	2	no	—
331	C₂×C₈	—	26	1	no	—
332	C₂×C₈	—	26	1	no	—
333	C₂×C₈	—	26	1	no	—
334	C₂×C₈	—	26	2	no	—
335	C₂×C₈	—	26	1	no	—
336	C₂×C₈	—	26	2	no	—
337	C₂×C₈	—	26	1	no	—
338	C₂×C₈	—	26	2	no	—
339	C₂×C₈	Q₈×D₁₃	1	2	yes	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	13	8	no	—
342	C₄⋊C₄	—	13	4	no	—
343	C₄⋊C₄	—	26	4	no	—
344	C₄⋊C₄	—	26	4	no	—
345	C₄⋊C₄	#6094	1	4	yes	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	13	4	no	—
349	C₄²	—	13	4	no	—
350	C₄²	—	13	2	no	—
351	C₄²	—	13	4	no	—
352	C₄²	—	13	2	no	—
353	C₄²	—	26	4	no	—
354	C₄²	—	26	4	no	—
355	C₄²	—	26	2	no	—
356	C₄²	—	26	4	no	—
357	C₄²	—	26	2	no	—
358	C₄²	—	26	1	no	—
359	C₄²	—	26	1	no	—
360	C₄²	—	52	1	no	—
361	C₄²	—	52	2	no	—
362	C₄²	D₄×D₁₃	1	2	yes	—
363	C₄²	Q₈×D₁₃	1	2	yes	—
364	C₁₃	#22722	1	1	yes	characteristic, complemented, Sylow
365	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
366	Q₈	—	26	8	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	13	2	no	—
375	C₂×C₄	—	13	2	no	—
376	C₂×C₄	—	13	2	no	—
377	C₂×C₄	—	13	2	no	—
378	C₂×C₄	—	13	4	no	—
379	C₂×C₄	—	13	4	no	—
380	C₂×C₄	—	13	2	no	—
381	C₂×C₄	—	26	1	no	—
382	C₂×C₄	—	26	2	no	—
383	C₂×C₄	—	26	2	no	—
384	C₂×C₄	—	26	2	no	—
385	C₂×C₄	—	26	1	no	—
386	C₂×C₄	—	26	2	no	—
387	C₂×C₄	—	26	1	no	—
388	C₂×C₄	—	26	1	no	—
389	C₂×C₄	—	26	1	no	—
390	C₂×C₄	—	26	1	no	—
391	C₂×C₄	—	26	1	no	—
392	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
393	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
394	C₂×C₄	C₂×#6094	1	4	yes	—
395	C₂×C₄	C₂×#6094	1	2	yes	—
396	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
397	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
398	C₂×C₄	#88251	1	1	yes	characteristic
399	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
400	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
401	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
402	C₂×C₄	#88257	1	1	yes	characteristic
403	C₈	—	2	2	no	—
404	C₈	—	4	1	no	—
405	C₈	—	4	2	no	—
406	C₈	—	26	2	no	—
407	C₈	—	52	1	no	—
408	C₈	—	52	2	no	—
409	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
410	C₂²	#11719251	1	1	yes	characteristic
411	C₂²	C₄×Q₈×D₁₃	1	1	yes	characteristic
412	C₂²	C₂²×#6094	1	1	yes	characteristic
413	C₂²	C₂×M₁₆×D₁₃	1	1	yes	characteristic
414	C₂²	D₁₃×#131	1	1	yes	characteristic
415	C₂²	#11719455	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	4	no	—
418	C₄	—	4	2	no	—
419	C₄	—	13	4	no	—
420	C₄	—	26	4	no	—
421	C₄	—	26	4	no	—
422	C₄	—	26	2	no	—
423	C₄	—	26	2	no	—
424	C₄	—	52	1	no	—
425	C₄	#11718498	1	4	yes	—
426	C₄	#11719304	1	1	yes	characteristic
427	C₄	#11719337	1	1	yes	characteristic
428	C₄	#11719390	1	1	yes	characteristic
429	C₄	#11719427	1	1	yes	characteristic
430	C₂	#13117750	1	1	yes	characteristic
431	C₂	C₂×#11718498	1	1	yes	characteristic
432	C₂	#13123403	1	1	yes	characteristic
433	C₂	D₁₃×#446	1	1	yes	characteristic
434	C₂	Q₈×#6094	1	1	yes	characteristic
435	C₂	#13123951	1	1	yes	characteristic
436	C₂	#13123959	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle, prime radical	C₂³×C₁₃	C₂³×C₄
Fitting	C₁₃×#1939	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1939	D₁₃
hypocenter	C₁₃	#22722
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1939

Complements

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

N	H ≅ G/N	type
86. #88054	Q₈	semidirect
253. Dic₁₃	#446	semidirect
364. C₁₃	#22722	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718340	2
C₂×#11718492	2
C₄×#88141	2
#13115558	2
#13115556	2
#13115555	2
#13114987	2
#13114688	2
C₄×#88054	2
C₁₃×#1939	2
#22722	13