Subgroups — #23777888

Order 10112.

910 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19099314	C₂	1	4	yes	maximal, complemented
2	Q₈×Dic₁₅₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#19099292	C₂	1	1	yes	maximal, characteristic, complemented
4	#19099291	C₂	1	2	yes	maximal, complemented
5	#19099286	C₂	1	2	yes	maximal, complemented
6	#19099286	C₂	1	1	yes	maximal, characteristic, complemented
7	#19099284	C₂	1	2	yes	maximal, complemented
8	#19099273	C₂	1	1	yes	maximal, characteristic, complemented
9	#19099247	C₂	1	2	yes	maximal, complemented
10	#19099190	C₂	1	2	yes	maximal, complemented
11	#19099184	C₂	1	2	yes	maximal
12	#19099175	C₂	1	2	yes	maximal, complemented
13	#19099174	C₂	1	2	yes	maximal, complemented
14	#19099172	C₂	1	4	yes	maximal, complemented
15	#19099120	C₂	1	1	yes	maximal, characteristic, complemented
16	#19099097	C₂	1	1	yes	maximal, characteristic
17	#533×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#14579161	C₂²	1	2	yes	—
19	#14579161	C₂²	1	2	yes	—
20	#14579161	C₂²	1	1	yes	characteristic
21	#14579161	C₂²	1	1	yes	characteristic
22	#14579160	C₂²	1	4	yes	—
23	#14579160	C₂²	1	2	yes	—
24	#14579159	C₂²	1	4	yes	—
25	#14579156	C₂²	1	4	yes	—
26	#14579156	C₂²	1	4	yes	—
27	#14579156	C₂²	1	4	yes	—
28	#14579156	C₂²	1	4	yes	—
29	#14579155	C₂²	1	2	yes	—
30	#14579154	C₂²	1	4	yes	—
31	#14579154	C₂²	1	4	yes	—
32	#14579153	C₂²	1	2	yes	—
33	#14579153	C₂²	1	2	yes	—
34	#14579153	C₂²	1	1	yes	characteristic
35	#14579152	C₂²	1	4	yes	—
36	#14579152	C₂²	1	2	yes	—
37	#14579151	C₂²	1	4	yes	—
38	#14579151	C₂²	1	4	yes	—
39	#14579151	C₂²	1	4	yes	—
40	#14579151	C₂²	1	4	yes	—
41	#14579149	C₂²	1	2	yes	—
42	#14579149	C₂²	1	1	yes	characteristic
43	#14579147	C₂²	1	4	yes	—
44	#14579144	C₂²	1	2	yes	—
45	#14579143	C₂²	1	4	yes	—
46	#14579140	C₂²	1	1	yes	characteristic
47	#14579140	C₂²	1	2	yes	—
48	#14579140	C₂²	1	2	yes	—
49	#14579139	C₂²	1	4	yes	—
50	#14579139	C₂²	1	4	yes	—
51	#14579137	C₂²	1	2	yes	—
52	#14579137	C₂²	1	2	yes	—
53	#14579137	C₂²	1	4	yes	—
54	#14579135	C₂²	1	1	yes	characteristic
55	Q₈×Dic₇₉	C₂²	1	2	yes	—
56	Q₈×Dic₇₉	C₂²	1	2	yes	—
57	C₄×Dic₁₅₈	C₂²	1	2	yes	—
58	C₄×Dic₁₅₈	C₂²	1	2	yes	—
59	C₄×Dic₁₅₈	C₂²	1	2	yes	—
60	C₄×Dic₁₅₈	C₂²	1	2	yes	—
61	C₄×Dic₁₅₈	C₂²	1	2	yes	—
62	C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
63	#14579126	C₂²	1	4	yes	—
64	C₄×D₃₁₆	C₂²	1	2	yes	—
65	C₄×D₃₁₆	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊D₇₉	C₂²	1	2	yes	—
67	#14579120	C₂²	1	2	yes	—
68	#14579119	C₂²	1	4	yes	—
69	#14579119	C₂²	1	2	yes	—
70	#14579118	C₂²	1	2	yes	—
71	C₄⋊C₄×D₇₉	C₂²	1	2	yes	—
72	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
73	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
74	#125×C₇₉	C₂²	1	2	yes	—
75	C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
76	C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
77	C₂²⋊Q₈×C₇₉	C₂²	1	2	yes	—
78	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
79	C₄×Q₈×C₇₉	C₂²	1	2	yes	—
80	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
81	#117×C₇₉	C₂²	1	2	yes	—
82	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
83	C₂×Dic₁₅₈	C₂³	1	2	yes	—
84	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
85	C₂×Dic₁₅₈	C₂³	1	4	yes	—
86	C₂×Dic₁₅₈	C₂³	1	2	yes	—
87	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
88	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
89	C₂×C₄×D₇₉	C₂³	1	2	yes	—
90	C₂×C₄×D₇₉	C₂³	1	4	yes	—
91	C₄⋊Dic₇₉	C₂³	1	2	yes	—
92	C₄⋊Dic₇₉	C₂³	1	2	yes	—
93	C₄⋊Dic₇₉	C₂³	1	4	yes	—
94	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
95	C₄⋊Dic₇₉	C₂³	1	2	yes	—
96	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
97	C₄⋊Dic₇₉	C₂³	1	2	yes	—
98	C₄⋊Dic₇₉	C₂³	1	4	yes	—
99	C₄⋊Dic₇₉	C₂³	1	4	yes	—
100	Dic₇₉⋊C₄	C₂³	1	4	yes	—
101	Dic₇₉⋊C₄	C₂³	1	2	yes	—
102	Dic₇₉⋊C₄	C₂³	1	2	yes	—
103	Dic₇₉⋊C₄	C₂³	1	2	yes	—
104	Dic₇₉⋊C₄	C₂³	1	4	yes	—
105	Dic₇₉⋊C₄	C₂³	1	4	yes	—
106	Dic₇₉⋊C₄	C₂³	1	4	yes	—
107	Dic₇₉⋊C₄	C₂³	1	4	yes	—
108	Dic₇₉⋊C₄	C₂³	1	4	yes	—
109	Dic₇₉⋊C₄	C₂³	1	4	yes	—
110	Dic₇₉⋊C₄	C₂³	1	2	yes	—
111	C₂²⋊Dic₇₉	C₂³	1	4	yes	—
112	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
113	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
114	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
115	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
116	(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
117	(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
118	(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
119	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
120	C₄×Dic₇₉	C₂³	1	2	yes	—
121	C₄×Dic₇₉	C₂³	1	4	yes	—
122	C₄×Dic₇₉	C₂³	1	4	yes	—
123	C₄×Dic₇₉	C₂³	1	4	yes	—
124	C₄×Dic₇₉	C₂³	1	4	yes	—
125	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
126	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₇₉	C₂³	1	2	yes	—
128	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
131	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
132	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
133	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
134	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
135	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
136	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
137	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
138	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
139	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
140	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
141	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
142	C₄²×C₇₉	C₂³	1	1	yes	characteristic
143	C₄²×C₇₉	C₂³	1	1	yes	characteristic
144	C₄²×C₇₉	C₂³	1	1	yes	characteristic
145	C₄²×C₇₉	C₂³	1	1	yes	characteristic
146	C₄²×C₇₉	C₂³	1	2	yes	—
147	C₄²×C₇₉	C₂³	1	2	yes	—
148	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
149	C₂²×D₇₉	C₂⁴	1	2	yes	—
150	Q₈×C₇₉	—	2	2	no	—
151	Q₈×C₇₉	—	2	2	no	—
152	Q₈×C₇₉	—	4	2	no	—
153	C₂×C₄×C₇₉	—	2	2	no	—
154	C₂×C₄×C₇₉	—	2	2	no	—
155	C₂×C₄×C₇₉	—	4	1	no	—
156	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
157	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
158	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
159	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
160	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
161	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
162	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
163	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
164	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
166	C₂²⋊D₇₉	—	4	2	no	—
167	C₂×Dic₇₉	C₂⁴	1	2	yes	—
168	C₂×Dic₇₉	C₂⁴	1	4	yes	—
169	C₂×Dic₇₉	C₂⁴	1	2	yes	—
170	C₂×Dic₇₉	C₂⁴	1	2	yes	—
171	C₂×Dic₇₉	C₂⁴	1	4	yes	—
172	D₃₁₆	—	2	2	no	—
173	C₄×D₇₉	—	2	4	no	—
174	C₄×D₇₉	—	4	4	no	—
175	Dic₁₅₈	—	2	4	no	—
176	Dic₁₅₈	—	2	2	no	—
177	Dic₁₅₈	—	4	4	no	—
178	Dic₁₅₈	—	4	2	no	—
179	C₂²×C₇₉	—	2	1	no	—
180	C₂²×C₇₉	—	2	1	no	—
181	C₂²×C₇₉	—	2	1	no	—
182	C₂²×C₇₉	C₂⁵	1	1	yes	characteristic
183	C₂×D₇₉	—	2	2	no	—
184	C₂×D₇₉	—	2	2	no	—
185	C₂×D₇₉	—	2	2	no	—
186	C₄×C₇₉	—	2	1	no	—
187	C₄×C₇₉	—	2	1	no	—
188	C₄×C₇₉	—	2	2	no	—
189	C₄×C₇₉	—	2	2	no	—
190	C₄×C₇₉	—	2	1	no	—
191	C₄×C₇₉	—	2	1	no	—
192	C₄×C₇₉	—	2	2	no	—
193	C₄×C₇₉	—	2	2	no	—
194	C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
195	C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
196	Dic₇₉	—	2	2	no	—
197	Dic₇₉	—	2	4	no	—
198	Dic₇₉	—	2	2	no	—
199	Dic₇₉	—	2	2	no	—
200	Dic₇₉	—	2	4	no	—
201	C₂×C₇₉	—	4	1	no	—
202	C₂×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
203	C₂×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
204	C₂×C₇₉	#585	1	1	yes	characteristic
205	D₇₉	—	4	2	no	—
206	#3555	—	79	1	no	maximal, Sylow
207	C₇₉	#3555	1	1	yes	characteristic, complemented, Sylow
208	#563	—	79	4	no	—
209	Q₈²	—	79	1	no	—
210	#557	—	79	2	no	—
211	#557	—	79	1	no	—
212	#556	—	79	2	no	—
213	#556	—	79	2	no	—
214	#556	—	79	1	no	—
215	#554	—	79	1	no	—
216	#552	—	79	2	no	—
217	#544	—	79	2	no	—
218	#542	—	79	2	no	—
219	#541	—	79	2	no	—
220	#541	—	79	4	no	—
221	#541	—	79	2	no	—
222	#533	—	79	1	no	—
223	#533	D₇₉	1	1	yes	characteristic, complemented
224	#529	—	79	1	no	—
225	C₄⋊Q₈	—	79	4	no	—
226	C₄⋊Q₈	—	79	4	no	—
227	C₄⋊Q₈	—	79	2	no	—
228	C₄⋊Q₈	—	79	1	no	—
229	C₄⋊Q₈	—	79	1	no	—
230	C₄⋊Q₈	—	79	2	no	—
231	C₄⋊Q₈	—	79	2	no	—
232	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
233	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
234	#126	—	79	4	no	—
235	#126	—	79	4	no	—
236	#126	—	79	4	no	—
237	#126	—	79	4	no	—
238	#126	—	79	4	no	—
239	#126	—	79	4	no	—
240	#126	—	79	2	no	—
241	#125	—	79	4	no	—
242	#125	—	79	4	no	—
243	#125	—	79	4	no	—
244	#125	—	79	4	no	—
245	#125	—	79	4	no	—
246	#125	—	79	2	no	—
247	#125	—	79	1	no	—
248	#125	—	79	2	no	—
249	#125	—	79	2	no	—
250	#125	C₂×D₇₉	1	2	yes	—
251	#124	—	79	4	no	—
252	#124	—	79	1	no	—
253	#124	—	79	2	no	—
254	#123	—	79	2	no	—
255	#123	—	79	4	no	—
256	C₂²⋊Q₈	—	79	2	no	—
257	C₂²⋊Q₈	—	79	2	no	—
258	C₂²⋊Q₈	—	79	4	no	—
259	C₂²⋊Q₈	—	79	1	no	—
260	C₂²⋊Q₈	—	79	2	no	—
261	C₂²⋊Q₈	—	79	2	no	—
262	C₂²⋊Q₈	—	79	4	no	—
263	C₂²⋊Q₈	—	79	4	no	—
264	C₂²⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
265	C₂²⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
266	C₂²⋊Q₈	C₂×D₇₉	1	2	yes	—
267	#121	—	79	1	no	—
268	C₄×Q₈	—	79	2	no	—
269	C₄×Q₈	—	79	2	no	—
270	C₄×Q₈	—	79	4	no	—
271	C₄×Q₈	—	79	1	no	—
272	C₄×Q₈	—	79	2	no	—
273	C₄×Q₈	—	79	2	no	—
274	C₄×Q₈	—	79	2	no	—
275	C₄×Q₈	—	79	2	no	—
276	C₄×Q₈	—	79	2	no	—
277	C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
278	C₄×Q₈	C₂×D₇₉	1	2	yes	—
279	C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
280	C₄×D₄	—	79	2	no	—
281	C₄×D₄	—	79	1	no	—
282	C₄×D₄	—	79	2	no	—
283	#117	—	79	2	no	—
284	#117	—	79	4	no	—
285	#117	—	79	2	no	—
286	#117	—	79	2	no	—
287	#117	C₂×D₇₉	1	2	yes	—
288	C₂×C₄⋊C₄	—	79	2	no	—
289	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
290	C₂×Q₈	—	79	2	no	—
291	C₂×Q₈	—	79	4	no	—
292	C₂×Q₈	—	79	1	no	—
293	C₂×Q₈	—	79	2	no	—
294	C₂×Q₈	C₂²×D₇₉	1	1	yes	characteristic
295	C₂×Q₈	C₂²×D₇₉	1	1	yes	characteristic
296	C₂×Q₈	C₂²×D₇₉	1	2	yes	—
297	C₂×D₄	—	79	2	no	—
298	C₂×D₄	—	79	1	no	—
299	C₂²×C₄	—	79	4	no	—
300	C₂²×C₄	—	79	2	no	—
301	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
302	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
303	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
304	C₄⋊C₄	—	79	4	no	—
305	C₄⋊C₄	—	79	2	no	—
306	C₄⋊C₄	—	79	2	no	—
307	C₄⋊C₄	—	79	2	no	—
308	C₄⋊C₄	—	79	4	no	—
309	C₄⋊C₄	—	79	4	no	—
310	C₄⋊C₄	—	79	4	no	—
311	C₄⋊C₄	—	79	4	no	—
312	C₄⋊C₄	—	79	4	no	—
313	C₄⋊C₄	—	79	4	no	—
314	C₄⋊C₄	—	79	2	no	—
315	C₄⋊C₄	—	79	2	no	—
316	C₄⋊C₄	—	79	2	no	—
317	C₄⋊C₄	—	79	4	no	—
318	C₄⋊C₄	—	79	1	no	—
319	C₄⋊C₄	—	79	2	no	—
320	C₄⋊C₄	—	79	1	no	—
321	C₄⋊C₄	—	79	2	no	—
322	C₄⋊C₄	—	79	4	no	—
323	C₄⋊C₄	—	79	4	no	—
324	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
325	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
326	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
327	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
328	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
329	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
330	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
331	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
332	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
333	C₂²⋊C₄	—	79	4	no	—
334	C₂²⋊C₄	—	79	2	no	—
335	C₂²⋊C₄	—	79	2	no	—
336	C₂²⋊C₄	—	79	2	no	—
337	C₂²⋊C₄	—	79	2	no	—
338	C₂²⋊C₄	—	79	4	no	—
339	C₂²⋊C₄	—	79	4	no	—
340	C₂²⋊C₄	—	79	2	no	—
341	C₂²⋊C₄	—	79	4	no	—
342	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
343	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
344	C₄²	—	79	4	no	—
345	C₄²	—	79	2	no	—
346	C₄²	—	79	4	no	—
347	C₄²	—	79	4	no	—
348	C₄²	—	79	4	no	—
349	C₄²	C₂²×D₇₉	1	1	yes	characteristic
350	C₄²	C₂²×D₇₉	1	1	yes	characteristic
351	C₄²	C₂²×D₇₉	1	1	yes	characteristic
352	C₄²	C₂²×D₇₉	1	1	yes	characteristic
353	C₄²	C₂²×D₇₉	1	2	yes	—
354	C₄²	C₂²×D₇₉	1	2	yes	—
355	C₂³	—	79	2	no	—
356	C₂³	C₂³×D₇₉	1	1	yes	characteristic
357	Q₈	—	2	2	no	—
358	Q₈	—	2	2	no	—
359	Q₈	—	4	2	no	—
360	Q₈	—	316	2	no	—
361	Q₈	—	316	4	no	—
362	Q₈	—	158	2	no	—
363	Q₈	—	158	4	no	—
364	D₄	—	316	2	no	—
365	D₄	—	158	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	316	4	no	—
370	C₂×C₄	—	79	4	no	—
371	C₂×C₄	—	79	2	no	—
372	C₂×C₄	—	79	2	no	—
373	C₂×C₄	—	79	2	no	—
374	C₂×C₄	—	79	4	no	—
375	C₂×C₄	—	158	4	no	—
376	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
377	C₂×C₄	C₂³×D₇₉	1	2	yes	—
378	C₂×C₄	C₂³×D₇₉	1	2	yes	—
379	C₂×C₄	C₂³×D₇₉	1	2	yes	—
380	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
381	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
382	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
383	C₂×C₄	C₂³×D₇₉	1	2	yes	—
384	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
385	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	158	2	no	—
390	C₂²	—	158	2	no	—
391	C₂²	—	158	2	no	—
392	C₂²	C₂⁴×D₇₉	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	158	2	no	—
402	C₄	—	158	4	no	—
403	C₄	—	158	2	no	—
404	C₄	—	158	4	no	—
405	C₄	—	158	2	no	—
406	C₄	#14579208	1	2	yes	—
407	C₄	#14579209	1	2	yes	—
408	C₂	—	4	1	no	—
409	C₂	—	316	2	no	—
410	C₂	C₂×#14579208	1	1	yes	characteristic
411	C₂	C₂×#14579209	1	1	yes	characteristic
412	C₂	#19099399	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁵
Fitting	#533×C₇₉	C₂
prime radical	#14579135	C₂²
hypercenter	#533	D₇₉
hypocenter	C₇₉	#3555
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #533

Complements

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

N	H ≅ G/N	type
1. #19099314	C₂	semidirect
2. Q₈×Dic₁₅₈	C₂	semidirect
3. #19099292	C₂	semidirect
4. #19099291	C₂	semidirect
5. #19099286	C₂	semidirect
6. #19099286	C₂	semidirect
7. #19099284	C₂	semidirect
8. #19099273	C₂	semidirect
9. #19099247	C₂	semidirect
10. #19099190	C₂	semidirect
12. #19099175	C₂	semidirect
13. #19099174	C₂	semidirect
14. #19099172	C₂	semidirect
15. #19099120	C₂	semidirect
17. #533×C₇₉	C₂	semidirect
207. C₇₉	#3555	semidirect
223. #533	D₇₉	semidirect