Subgroups — #15831967

Order 3328.

666 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123953	C₂	1	1	yes	maximal, characteristic
2	C₄×#88202	C₂	1	1	yes	maximal, characteristic
3	#13113604	C₂	1	2	yes	maximal, complemented
4	#13113601	C₂	1	2	yes	maximal, complemented
5	#13113597	C₂	1	2	yes	maximal, complemented
6	#13113594	C₂	1	2	yes	maximal, complemented
7	#13113589	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113586	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113582	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#11718071	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2989	C₂	1	1	yes	maximal, characteristic
12	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂×#88202	C₄	1	1	yes	characteristic
14	C₂×#88202	C₄	1	1	yes	characteristic
15	C₁₃×#446	—	2	1	no	—
16	C₁₃×#436	—	2	1	no	—
17	C₁₃×#435	—	2	2	no	—
18	C₁₃×#432	C₂²	1	2	yes	—
19	C₁₃×#431	C₂²	1	1	yes	characteristic
20	C₁₃×#423	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	#11718685	—	2	1	no	—
23	#11718673	—	2	1	no	—
24	#11718672	—	2	2	no	—
25	#11718658	C₄	1	1	yes	characteristic
26	#11718658	C₄	1	2	yes	—
27	#11718658	C₄	1	2	yes	—
28	#11718658	C₄	1	1	yes	characteristic
29	#11718587	C₂²	1	2	yes	—
30	#11718586	C₂²	1	1	yes	characteristic
31	#11718585	C₂²	1	2	yes	—
32	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
33	C₄×#6099	C₂²	1	2	yes	—
34	C₄×#6099	C₂²	1	1	yes	characteristic
35	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
36	C₂×C₄×#1055	C₂²	1	2	yes	—
37	#11718072	C₂²	1	1	yes	characteristic
38	#11718072	C₂²	1	2	yes	—
39	#11718072	C₂²	1	1	yes	characteristic
40	#11718072	C₂²	1	2	yes	—
41	#11718071	C₂²	1	2	yes	—
42	#11718071	C₂²	1	2	yes	—
43	#11718071	C₂²	1	2	yes	—
44	#11718071	C₂²	1	2	yes	—
45	#11718071	C₂²	1	1	yes	characteristic
46	#11718071	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₃×M₁₆	—	2	2	no	—
49	C₂²×C₈×C₁₃	—	2	1	no	—
50	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
51	C₄×Q₈×C₁₃	Q₈	1	1	yes	characteristic
52	C₄×D₄×C₁₃	D₄	1	2	yes	—
53	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
54	C₄×D₄×C₁₃	Q₈	1	2	yes	—
55	C₄×D₄×C₁₃	Q₈	1	1	yes	characteristic
56	C₁₃×#117	C₂×C₄	1	2	yes	—
57	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
60	#88202	—	2	4	no	—
61	#88202	—	2	4	no	—
62	C₂×#6099	—	2	2	no	—
63	C₂×#6099	C₂×C₄	1	1	yes	characteristic
64	C₂×#6099	C₂×C₄	1	2	yes	—
65	C₂×#6099	C₂×C₄	1	2	yes	—
66	C₂×#6099	C₂×C₄	1	1	yes	characteristic
67	C₂²×#1055	—	2	1	no	—
68	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
69	C₂²×#1055	C₂×C₄	1	2	yes	—
70	C₂²×#1055	C₂×C₄	1	2	yes	—
71	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
72	C₁₃×C₄⋊C₈	—	2	1	no	—
73	C₁₃×C₄⋊C₈	—	2	2	no	—
74	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
75	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
76	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
77	C₁₃×C₂²⋊C₈	—	2	1	no	—
78	C₁₃×C₂²⋊C₈	—	2	2	no	—
79	C₁₃×#97	—	2	2	no	—
80	C₄×C₈×C₁₃	—	2	1	no	—
81	C₂²⋊#1055	—	2	1	no	—
82	C₂²⋊#1055	—	2	2	no	—
83	C₄⋊#1055	—	2	2	no	—
84	C₄⋊#1055	—	2	1	no	—
85	C₄⋊#1055	C₂³	1	2	yes	—
86	C₄⋊#1055	C₂³	1	1	yes	characteristic
87	C₄⋊#1055	C₂³	1	1	yes	characteristic
88	#88043	—	2	2	no	—
89	#88043	C₂×C₄	1	2	yes	—
90	#88043	C₂×C₄	1	2	yes	—
91	#88043	C₂×C₄	1	2	yes	—
92	C₄×#1055	—	2	1	no	—
93	C₄×#1055	C₂×C₄	1	2	yes	—
94	C₄×#1055	C₂×C₄	1	1	yes	characteristic
95	C₄×#1055	C₂×C₄	1	1	yes	characteristic
96	C₄×#1055	C₂×C₄	1	2	yes	—
97	C₄×#1055	C₂³	1	1	yes	characteristic
98	C₄×#1055	C₂³	1	1	yes	characteristic
99	C₄×#1055	C₂³	1	2	yes	—
100	#17799	—	13	1	no	maximal, Sylow
101	C₁₃×#41	—	2	2	no	—
102	C₁₃×#41	—	2	2	no	—
103	C₂×Q₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
104	C₂×D₄×C₁₃	C₄⋊C₄	1	2	yes	—
105	C₂×D₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
112	C₁₃×M₁₆	—	8	2	no	—
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	8	1	no	—
117	C₁₃×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
118	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
119	C₁₃×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
120	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
121	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
122	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
123	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
124	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
126	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₃	C₂×D₄	1	2	yes	—
128	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
129	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
130	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
131	#6099	—	2	2	no	—
132	#6099	—	2	4	no	—
133	#6099	—	2	4	no	—
134	#6099	—	8	2	no	—
135	#6099	M₁₆	1	4	yes	complemented
136	C₂×#1055	—	2	2	no	—
137	C₂×#1055	—	2	4	no	—
138	C₂×#1055	—	2	4	no	—
139	C₂×#1055	—	2	1	no	—
140	C₂×#1055	—	2	2	no	—
141	C₂×#1055	—	2	1	no	—
142	C₂×#1055	—	8	1	no	—
143	C₂×#1055	M₁₆	1	4	yes	complemented
144	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
145	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
146	C₂×#1055	C₂²×C₄	1	2	yes	—
147	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
148	C₂×#1055	C₂²×C₄	1	2	yes	—
149	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
150	#2989	—	13	1	no	—
151	#2989	D₁₃	1	1	yes	characteristic
152	C₄×#131	—	13	1	no	—
153	#1569	—	13	2	no	—
154	#1569	—	13	2	no	—
155	#1568	—	13	2	no	—
156	#1567	—	13	2	no	—
157	#1565	—	13	1	no	—
158	#1565	—	13	1	no	—
159	#1564	—	13	1	no	—
160	C₂×#335	—	13	1	no	—
161	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
162	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	Q₈×C₁₃	—	2	2	no	—
164	D₄×C₁₃	—	2	4	no	—
165	D₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
176	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
178	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
179	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
181	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
182	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
185	C₈×C₁₃	—	4	2	no	—
186	C₈×C₁₃	—	4	1	no	—
187	C₈×C₁₃	—	4	1	no	—
188	#1055	—	2	1	no	—
189	#1055	—	2	1	no	—
190	#1055	—	2	2	no	—
191	#1055	—	4	2	no	—
192	#1055	—	4	1	no	—
193	#1055	—	4	1	no	—
194	#1055	C₂×M₁₆	1	2	yes	—
195	#1055	C₂×M₁₆	1	4	yes	—
196	#1055	C₂×M₁₆	1	2	yes	—
197	C₂×#131	—	13	1	no	—
198	C₂×#131	—	13	1	no	—
199	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
200	#446	—	2	1	no	—
201	#446	—	26	1	no	—
202	#436	—	2	1	no	—
203	#436	—	26	1	no	—
204	#435	—	2	2	no	—
205	#435	—	26	2	no	—
206	#432	—	13	2	no	—
207	#432	C₂×D₁₃	1	2	yes	—
208	#431	—	13	1	no	—
209	#431	C₂×D₁₃	1	1	yes	characteristic
210	#423	—	13	2	no	—
211	#423	C₂×D₁₃	1	2	yes	—
212	C₂×C₄⋊C₈	—	13	1	no	—
213	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
214	#405	—	13	1	no	—
215	#405	—	13	2	no	—
216	#405	—	13	2	no	—
217	#405	—	13	1	no	—
218	C₄×M₁₆	—	13	1	no	—
219	C₄×M₁₆	—	13	2	no	—
220	C₂×C₄×C₈	—	13	1	no	—
221	C₂×C₄×C₈	—	13	2	no	—
222	#335	—	13	2	no	—
223	#335	—	13	2	no	—
224	#335	—	13	1	no	—
225	#335	—	13	1	no	—
226	#335	—	13	2	no	—
227	#335	—	13	2	no	—
228	#334	—	13	1	no	—
229	#334	—	13	1	no	—
230	#334	—	13	2	no	—
231	#334	—	13	2	no	—
232	C₂²×C₁₃	—	2	1	no	—
233	C₂²×C₁₃	—	2	1	no	—
234	C₂²×C₁₃	—	2	2	no	—
235	C₂²×C₁₃	—	2	2	no	—
236	C₂²×C₁₃	—	2	2	no	—
237	C₂²×C₁₃	#423	1	2	yes	—
238	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
239	C₄×C₁₃	—	2	2	no	—
240	C₄×C₁₃	—	2	1	no	—
241	C₄×C₁₃	—	2	2	no	—
242	C₄×C₁₃	—	2	1	no	—
243	C₄×C₁₃	—	2	1	no	—
244	C₄×C₁₃	—	2	2	no	—
245	C₄×C₁₃	#423	1	2	yes	—
246	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
247	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
248	C₄×C₁₃	#576	1	1	yes	characteristic
249	C₄×C₁₃	#578	1	1	yes	characteristic
250	C₂×#41	C₄×D₁₃	1	1	yes	characteristic
251	#131	—	26	4	no	—
252	#131	—	26	4	no	—
253	C₂×M₁₆	—	2	2	no	—
254	C₂×M₁₆	—	13	1	no	—
255	C₂×M₁₆	—	13	2	no	—
256	C₂×M₁₆	—	13	2	no	—
257	C₂×M₁₆	—	13	1	no	—
258	C₂×M₁₆	—	26	2	no	—
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	—	13	1	no	—
261	C₂²×C₈	—	13	2	no	—
262	C₂²×C₈	—	13	2	no	—
263	C₂²×C₈	—	13	1	no	—
264	C₂²×C₈	—	26	1	no	—
265	C₄×Q₈	Dic₂₆	1	1	yes	characteristic
266	C₄×Q₈	C₂²⋊D₁₃	1	1	yes	characteristic
267	C₄×D₄	Dic₂₆	1	2	yes	—
268	C₄×D₄	Dic₂₆	1	1	yes	characteristic
269	C₄×D₄	C₂²⋊D₁₃	1	2	yes	—
270	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
271	#117	C₄×D₁₃	1	2	yes	—
272	#117	C₄×D₁₃	1	1	yes	characteristic
273	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
274	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	2	no	—
277	C₄⋊C₈	—	13	1	no	—
278	C₄⋊C₈	—	13	2	no	—
279	C₄⋊C₈	—	13	1	no	—
280	C₄⋊C₈	—	26	1	no	—
281	C₄⋊C₈	—	26	2	no	—
282	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
283	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
284	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
285	C₂²⋊C₈	—	2	1	no	—
286	C₂²⋊C₈	—	2	2	no	—
287	C₂²⋊C₈	—	26	1	no	—
288	C₂²⋊C₈	—	26	2	no	—
289	#97	—	2	2	no	—
290	#97	—	13	2	no	—
291	#97	—	13	2	no	—
292	#97	—	13	2	no	—
293	#97	—	26	2	no	—
294	C₄×C₈	—	2	1	no	—
295	C₄×C₈	—	13	2	no	—
296	C₄×C₈	—	13	1	no	—
297	C₄×C₈	—	13	1	no	—
298	C₄×C₈	—	13	2	no	—
299	C₄×C₈	—	13	1	no	—
300	C₄×C₈	—	13	2	no	—
301	C₄×C₈	—	13	1	no	—
302	C₄×C₈	—	26	1	no	—
303	C₂×C₁₃	—	2	2	no	—
304	C₂×C₁₃	—	4	2	no	—
305	C₂×C₁₃	C₂×#423	1	1	yes	characteristic
306	C₂×C₁₃	#2913	1	1	yes	characteristic
307	C₂×C₁₃	#2916	1	1	yes	characteristic
308	#41	—	2	2	no	—
309	#41	—	2	2	no	—
310	C₂×Q₈	#6101	1	1	yes	characteristic
311	C₂×D₄	#6101	1	2	yes	—
312	C₂×D₄	#6101	1	1	yes	characteristic
313	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
314	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
316	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
317	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
318	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
319	M₁₆	—	8	2	no	—
320	M₁₆	—	13	4	no	—
321	M₁₆	—	26	4	no	—
322	M₁₆	—	26	4	no	—
323	M₁₆	—	26	2	no	—
324	M₁₆	—	104	2	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	8	1	no	—
329	C₂×C₈	—	13	4	no	—
330	C₂×C₈	—	13	1	no	—
331	C₂×C₈	—	13	1	no	—
332	C₂×C₈	—	13	2	no	—
333	C₂×C₈	—	13	1	no	—
334	C₂×C₈	—	13	2	no	—
335	C₂×C₈	—	13	1	no	—
336	C₂×C₈	—	26	4	no	—
337	C₂×C₈	—	26	4	no	—
338	C₂×C₈	—	26	2	no	—
339	C₂×C₈	—	26	1	no	—
340	C₂×C₈	—	26	1	no	—
341	C₂×C₈	—	26	2	no	—
342	C₂×C₈	—	104	1	no	—
343	C₄⋊C₄	#6101	1	2	yes	—
344	C₄⋊C₄	#6101	1	1	yes	characteristic
345	C₄⋊C₄	#6101	1	2	yes	—
346	C₄⋊C₄	#6101	1	1	yes	characteristic
347	C₂²⋊C₄	#6101	1	2	yes	—
348	C₂²⋊C₄	#6101	1	2	yes	—
349	C₂²⋊C₄	#6101	1	2	yes	—
350	C₄²	C₂×Dic₂₆	1	2	yes	—
351	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
352	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
353	C₄²	C₂×C₄×D₁₃	1	2	yes	—
354	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
355	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
356	C₄²	C₂³×D₁₃	1	1	yes	characteristic
357	C₁₃	#17799	1	1	yes	characteristic, complemented, Sylow
358	C₂³	C₂×#6101	1	2	yes	—
359	C₂³	C₂×#6101	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	D₄	—	2	4	no	—
362	D₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
372	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
373	C₂×C₄	C₂×#6101	1	1	yes	characteristic
374	C₂×C₄	C₂×#6101	1	2	yes	—
375	C₂×C₄	C₂×#6101	1	2	yes	—
376	C₂×C₄	C₂×#6101	1	1	yes	characteristic
377	C₂×C₄	C₂×#6101	1	2	yes	—
378	C₂×C₄	C₂×#6101	1	1	yes	characteristic
379	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
381	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
382	C₈	—	4	2	no	—
383	C₈	—	4	1	no	—
384	C₈	—	4	1	no	—
385	C₈	—	13	2	no	—
386	C₈	—	13	2	no	—
387	C₈	—	13	4	no	—
388	C₈	—	26	1	no	—
389	C₈	—	26	2	no	—
390	C₈	—	26	1	no	—
391	C₈	—	52	2	no	—
392	C₈	—	52	1	no	—
393	C₈	—	52	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	#11718779	1	2	yes	—
400	C₂²	C₂²×#6101	1	1	yes	characteristic
401	C₄	—	2	2	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	2	no	—
407	C₄	#11718779	1	2	yes	—
408	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
409	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
410	C₄	#11719540	1	1	yes	characteristic
411	C₄	#11719543	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	4	2	no	—
414	C₂	C₂×#11718779	1	1	yes	characteristic
415	C₂	#13123434	1	1	yes	characteristic
416	C₂	#13123445	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#2989	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂×C₁₃×#41	C₂×C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2989	D₁₃
hypocenter	C₁₃	#17799
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2989

Complements

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

N	H ≅ G/N	type
3. #13113604	C₂	semidirect
4. #13113601	C₂	semidirect
5. #13113597	C₂	semidirect
6. #13113594	C₂	semidirect
7. #13113589	C₂	semidirect
8. #13113586	C₂	semidirect
9. #13113582	C₂	semidirect
10. C₂×#11718071	C₂	semidirect
135. #6099	M₁₆	semidirect
143. C₂×#1055	M₁₆	semidirect
357. C₁₃	#17799	semidirect

Maximal subgroups

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

subgroup	index
#13123953	2
C₄×#88202	2
#13113604	2
#13113601	2
#13113597	2
#13113594	2
#13113589	2
#13113586	2
#13113582	2
C₂×#11718071	2
C₁₃×#2989	2
#17799	13