Subgroups — C₄×#19098915 #34296247

Order 20224.

878 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098915	C₂	1	1	yes	maximal, characteristic
2	C₄×#14579161	C₂	1	1	yes	maximal, characteristic
3	#23764362	C₂	1	1	yes	maximal, characteristic
4	#23764201	C₂	1	1	yes	maximal, characteristic
5	#23764075	C₂	1	4	yes	maximal
6	#23763527	C₂	1	1	yes	maximal, characteristic
7	C₄×#14579084	C₂	1	4	yes	maximal
8	C₄²×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic
9	C₄×C₄⋊Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic
10	C₂×#14579161	C₂²	1	1	yes	characteristic
11	C₂×C₄×Dic₁₅₈	C₂²	1	2	yes	—
12	#19098915	C₄	1	8	yes	direct product factor
13	C₂×#14579084	C₂²	1	4	yes	—
14	C₂×#14579084	C₂²	1	4	yes	—
15	C₂×C₄×C₇₉⋊C₈	C₂²	1	2	yes	—
16	C₂×C₄×C₇₉⋊C₈	C₂²	1	2	yes	—
17	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
19	#19098469	C₂²	1	2	yes	—
20	#19098461	—	2	1	no	—
21	#19098461	—	2	1	no	—
22	#19098433	C₂²	1	1	yes	characteristic
23	C₄×C₄⋊Dic₇₉	—	2	1	no	—
24	C₄×C₄⋊Dic₇₉	—	2	1	no	—
25	#19098325	C₂²	1	4	yes	—
26	#19098325	C₂²	1	4	yes	—
27	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₇₉	—	2	1	no	—
29	#391×C₇₉	—	2	1	no	—
30	#389×C₇₉	—	2	1	no	—
31	#389×C₇₉	C₂²	1	2	yes	—
32	#384×C₇₉	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₇₉	—	2	1	no	—
34	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
35	C₄³×C₇₉	C₂²	1	1	yes	characteristic
36	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
37	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
38	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
39	#14579161	—	2	2	no	—
40	#14579161	C₂×C₄	1	4	yes	—
41	C₄×Dic₁₅₈	—	2	8	no	—
42	C₂×C₄⋊Dic₇₉	—	2	1	no	—
43	C₂×C₄⋊Dic₇₉	—	2	1	no	—
44	C₂×C₄⋊Dic₇₉	—	2	1	no	—
45	C₂×C₄⋊Dic₇₉	—	2	1	no	—
46	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
47	C₂×Dic₇₉⋊C₄	—	2	2	no	—
48	C₂×C₄×Dic₇₉	—	2	2	no	—
49	#14579084	—	2	8	no	—
50	#14579084	C₂×C₄	1	16	yes	—
51	C₄×C₇₉⋊C₈	—	2	2	no	—
52	C₄×C₇₉⋊C₈	—	2	4	no	—
53	C₄×C₇₉⋊C₈	—	2	4	no	—
54	C₄×C₇₉⋊C₈	C₂×C₄	1	4	yes	—
55	C₇₉⋊#95	—	2	2	no	—
56	C₇₉⋊#95	—	2	2	no	—
57	C₂²×Q₈×C₇₉	—	2	1	no	—
58	C₄⋊Q₈×C₇₉	—	2	2	no	—
59	C₄⋊Q₈×C₇₉	C₂×C₄	1	4	yes	—
60	C₄×Q₈×C₇₉	—	4	4	no	—
61	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
67	C₂×C₄²×C₇₉	—	2	2	no	—
68	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
75	#95×C₇₉	—	2	2	no	—
76	#95×C₇₉	—	2	2	no	—
77	C₂×Dic₁₅₈	—	2	4	no	—
78	C₂×Dic₁₅₈	—	2	4	no	—
79	C₂×Dic₁₅₈	—	2	2	no	—
80	C₂×Dic₁₅₈	C₂²×C₄	1	4	yes	—
81	C₂²×Dic₇₉	—	2	2	no	—
82	C₂²×Dic₇₉	—	2	2	no	—
83	C₂×C₇₉⋊C₈	—	2	2	no	—
84	C₂×C₇₉⋊C₈	—	2	2	no	—
85	C₂×C₇₉⋊C₈	—	2	2	no	—
86	C₂×C₇₉⋊C₈	—	2	2	no	—
87	C₂×C₇₉⋊C₈	C₂²×C₄	1	4	yes	—
88	C₂×C₇₉⋊C₈	#41	1	4	yes	—
89	C₄⋊Dic₇₉	—	2	4	no	—
90	C₄⋊Dic₇₉	—	2	4	no	—
91	C₄⋊Dic₇₉	—	2	4	no	—
92	C₄⋊Dic₇₉	—	4	2	no	—
93	C₄⋊Dic₇₉	—	4	2	no	—
94	Dic₇₉⋊C₄	—	4	4	no	—
95	C₄×Dic₇₉	—	4	4	no	—
96	C₂×Q₈×C₇₉	—	2	4	no	—
97	C₂×Q₈×C₇₉	—	4	2	no	—
98	C₂×Q₈×C₇₉	—	4	2	no	—
99	C₂²×C₄×C₇₉	—	2	2	no	—
100	C₂²×C₄×C₇₉	—	2	2	no	—
101	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
108	C₄⋊C₄×C₇₉	—	2	4	no	—
109	C₄⋊C₄×C₇₉	—	2	2	no	—
110	C₄⋊C₄×C₇₉	—	2	4	no	—
111	C₄⋊C₄×C₇₉	—	4	4	no	—
112	C₄⋊C₄×C₇₉	—	4	2	no	—
113	C₄⋊C₄×C₇₉	—	4	2	no	—
114	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
115	C₄²×C₇₉	—	2	2	no	—
116	C₄²×C₇₉	—	2	2	no	—
117	C₄²×C₇₉	—	2	2	no	—
118	C₄²×C₇₉	—	4	4	no	—
119	C₄²×C₇₉	SD₁₆	1	4	yes	—
120	C₄²×C₇₉	Q₁₆	1	4	yes	—
121	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
122	C₄²×C₇₉	#41	1	2	yes	—
123	C₄²×C₇₉	#41	1	4	yes	—
124	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
125	Q₈×C₇₉	—	4	8	no	—
126	C₂×C₄×C₇₉	—	2	1	no	—
127	C₂×C₄×C₇₉	—	2	1	no	—
128	C₂×C₄×C₇₉	—	2	1	no	—
129	C₂×C₄×C₇₉	—	2	1	no	—
130	C₂×C₄×C₇₉	—	2	1	no	—
131	C₂×C₄×C₇₉	—	2	1	no	—
132	C₂×C₄×C₇₉	—	2	4	no	—
133	C₂×C₄×C₇₉	—	4	2	no	—
134	C₂×C₄×C₇₉	—	4	2	no	—
135	C₂×C₄×C₇₉	—	4	2	no	—
136	C₂×C₄×C₇₉	—	4	2	no	—
137	C₂×C₄×C₇₉	—	4	2	no	—
138	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
139	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
140	C₂×C₄×C₇₉	#124	1	2	yes	—
141	C₂×C₄×C₇₉	#124	1	2	yes	—
142	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
143	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
144	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
145	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
146	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
147	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
148	C₂×C₄×C₇₉	#135	1	2	yes	—
149	C₂×C₄×C₇₉	#135	1	2	yes	—
150	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
152	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
154	C₂×Dic₇₉	—	2	4	no	—
155	C₂×Dic₇₉	—	4	2	no	—
156	C₂×Dic₇₉	—	4	2	no	—
157	C₂×Dic₇₉	—	4	2	no	—
158	C₂×Dic₇₉	—	4	2	no	—
159	C₂×Dic₇₉	—	4	2	no	—
160	Dic₁₅₈	—	2	8	no	—
161	Dic₁₅₈	—	4	4	no	—
162	C₇₉⋊C₈	—	2	4	no	—
163	C₇₉⋊C₈	—	2	4	no	—
164	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
165	C₂²×C₇₉	C₂×#124	1	1	yes	characteristic
166	C₂²×C₇₉	#532	1	1	yes	characteristic
167	C₂²×C₇₉	C₂²×SD₁₆	1	1	yes	characteristic
168	C₂²×C₇₉	C₂²×Q₁₆	1	1	yes	characteristic
169	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
170	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
171	C₄×C₇₉	—	2	2	no	—
172	C₄×C₇₉	—	2	2	no	—
173	C₄×C₇₉	—	2	2	no	—
174	C₄×C₇₉	—	4	4	no	—
175	C₄×C₇₉	—	8	2	no	—
176	C₄×C₇₉	C₄×SD₁₆	1	4	yes	—
177	C₄×C₇₉	C₄×Q₁₆	1	4	yes	—
178	C₄×C₇₉	#487	1	4	yes	complemented
179	C₄×C₇₉	C₄×#41	1	2	yes	—
180	C₄×C₇₉	#529	1	2	yes	—
181	Dic₇₉	—	4	4	no	—
182	Dic₇₉	—	8	2	no	—
183	C₄×#487	—	79	1	no	maximal, Sylow
184	C₂×C₇₉	C₄×#124	1	1	yes	characteristic
185	C₂×C₇₉	C₂×C₄×SD₁₆	1	1	yes	characteristic
186	C₂×C₇₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
187	C₂×C₇₉	C₂×#487	1	1	yes	characteristic
188	C₂×C₇₉	#3131	1	1	yes	characteristic
189	C₂×C₇₉	#3167	1	1	yes	characteristic
190	C₂×C₇₉	#3170	1	1	yes	characteristic
191	C₂×#487	—	79	1	no	—
192	C₄×C₄⋊Q₈	—	79	1	no	—
193	C₄×C₄⋊Q₈	D₇₉	1	1	yes	characteristic
194	#1990	—	79	1	no	—
195	#1956	—	79	1	no	—
196	#1933	—	79	4	no	—
197	#1834	—	79	1	no	—
198	C₄×#103	—	79	4	no	—
199	C₄²×C₈	—	79	1	no	—
200	C₇₉	C₄×#487	1	1	yes	characteristic, complemented, Sylow
201	C₂×C₄⋊Q₈	—	79	1	no	—
202	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
203	C₂×C₄×Q₈	—	2	1	no	—
204	C₂×C₄×Q₈	—	79	2	no	—
205	#487	—	79	8	no	—
206	C₂×#103	—	79	4	no	—
207	C₂×#103	—	79	4	no	—
208	C₂×C₄×C₈	—	79	1	no	—
209	C₂×C₄×C₈	—	79	2	no	—
210	C₂×C₄×C₈	—	79	1	no	—
211	C₂×C₄×C₈	—	79	2	no	—
212	#391	—	2	1	no	—
213	#391	—	79	2	no	—
214	#389	—	2	1	no	—
215	#389	—	158	1	no	—
216	#389	—	158	1	no	—
217	#389	C₂×D₇₉	1	2	yes	—
218	#384	—	79	1	no	—
219	#384	C₂×D₇₉	1	1	yes	characteristic
220	C₄×C₄⋊C₄	—	2	1	no	—
221	C₄×C₄⋊C₄	—	158	1	no	—
222	C₄×C₄⋊C₄	—	158	1	no	—
223	C₄×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
224	C₄³	C₂×D₇₉	1	1	yes	characteristic
225	#340	—	79	4	no	—
226	#340	—	79	4	no	—
227	C₂²×Q₈	—	2	1	no	—
228	C₂²×Q₈	—	79	2	no	—
229	C₂²×C₈	—	79	2	no	—
230	C₂²×C₈	—	79	2	no	—
231	C₄⋊Q₈	—	2	2	no	—
232	C₄⋊Q₈	—	79	4	no	—
233	C₄⋊Q₈	—	158	2	no	—
234	C₄⋊Q₈	C₄×D₇₉	1	4	yes	—
235	C₄×Q₈	—	4	4	no	—
236	C₄×Q₈	—	158	8	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	79	2	no	—
242	C₂×C₄⋊C₄	—	158	2	no	—
243	C₂×C₄⋊C₄	—	158	1	no	—
244	C₂×C₄⋊C₄	—	158	1	no	—
245	C₂×C₄⋊C₄	—	158	1	no	—
246	C₂×C₄⋊C₄	—	158	1	no	—
247	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
248	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
249	C₂×C₄²	—	2	2	no	—
250	C₂×C₄²	—	158	2	no	—
251	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
252	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
253	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
254	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
255	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
256	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
257	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
258	#103	—	79	16	no	—
259	#103	—	158	8	no	—
260	C₄×C₈	—	79	4	no	—
261	C₄×C₈	—	158	4	no	—
262	C₄×C₈	—	158	2	no	—
263	C₄×C₈	—	158	4	no	—
264	#95	—	2	2	no	—
265	#95	—	2	2	no	—
266	#95	—	158	2	no	—
267	#95	—	158	2	no	—
268	C₂×Q₈	—	2	4	no	—
269	C₂×Q₈	—	4	2	no	—
270	C₂×Q₈	—	4	2	no	—
271	C₂×Q₈	—	79	4	no	—
272	C₂×Q₈	—	158	4	no	—
273	C₂×Q₈	—	158	4	no	—
274	C₂×Q₈	—	158	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	158	2	no	—
278	C₂²×C₄	—	158	2	no	—
279	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
280	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
285	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
286	C₂×C₈	—	79	4	no	—
287	C₂×C₈	—	79	4	no	—
288	C₂×C₈	—	158	2	no	—
289	C₂×C₈	—	158	2	no	—
290	C₂×C₈	—	158	2	no	—
291	C₂×C₈	—	158	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	4	4	no	—
296	C₄⋊C₄	—	4	2	no	—
297	C₄⋊C₄	—	4	2	no	—
298	C₄⋊C₄	—	316	4	no	—
299	C₄⋊C₄	—	316	2	no	—
300	C₄⋊C₄	—	316	2	no	—
301	C₄⋊C₄	—	158	4	no	—
302	C₄⋊C₄	—	158	4	no	—
303	C₄⋊C₄	—	158	4	no	—
304	C₄⋊C₄	C₂×C₄×D₇₉	1	4	yes	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	4	4	no	—
309	C₄²	—	316	4	no	—
310	C₄²	#11929612	1	4	yes	—
311	C₄²	#11929614	1	4	yes	—
312	C₄²	C₂×C₄×D₇₉	1	2	yes	—
313	C₄²	#11929624	1	2	yes	—
314	C₄²	#11929625	1	4	yes	—
315	C₂³	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
316	Q₈	—	4	8	no	—
317	Q₈	—	316	4	no	—
318	Q₈	—	158	8	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	316	2	no	—
332	C₂×C₄	—	316	2	no	—
333	C₂×C₄	—	316	2	no	—
334	C₂×C₄	—	316	2	no	—
335	C₂×C₄	—	316	2	no	—
336	C₂×C₄	—	158	4	no	—
337	C₂×C₄	C₄×C₂²⋊D₇₉	1	2	yes	—
338	C₂×C₄	C₄×C₂²⋊D₇₉	1	2	yes	—
339	C₂×C₄	#14579150	1	2	yes	—
340	C₂×C₄	#14579150	1	2	yes	—
341	C₂×C₄	C₂×#11929612	1	2	yes	—
342	C₂×C₄	C₂×#11929612	1	2	yes	—
343	C₂×C₄	C₂×#11929612	1	2	yes	—
344	C₂×C₄	C₂×#11929614	1	2	yes	—
345	C₂×C₄	C₂×#11929614	1	2	yes	—
346	C₂×C₄	C₂×#11929614	1	2	yes	—
347	C₂×C₄	#14579181	1	2	yes	—
348	C₂×C₄	#14579181	1	2	yes	—
349	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
350	C₂×C₄	#41×D₇₉	1	2	yes	—
351	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
352	C₂×C₄	C₂×#11929625	1	2	yes	—
353	C₈	—	158	4	no	—
354	C₈	—	158	4	no	—
355	C₂²	C₂×C₄×C₂²⋊D₇₉	1	1	yes	characteristic
356	C₂²	C₂×#14579150	1	1	yes	characteristic
357	C₂²	#19099109	1	1	yes	characteristic
358	C₂²	C₂²×#11929612	1	1	yes	characteristic
359	C₂²	C₂²×#11929614	1	1	yes	characteristic
360	C₂²	C₂×#14579181	1	1	yes	characteristic
361	C₂²	C₂×#14579181	1	1	yes	characteristic
362	C₄	—	2	2	no	—
363	C₄	—	2	2	no	—
364	C₄	—	2	2	no	—
365	C₄	—	4	4	no	—
366	C₄	—	8	2	no	—
367	C₄	—	316	4	no	—
368	C₄	—	632	2	no	—
369	C₄	C₄×#11929612	1	4	yes	—
370	C₄	C₄×#11929614	1	4	yes	—
371	C₄	#19098915	1	4	yes	direct product factor
372	C₄	C₄×#11929625	1	2	yes	—
373	C₄	#19099100	1	2	yes	—
374	C₂	C₄×#14579150	1	1	yes	characteristic
375	C₂	C₂×C₄×#11929612	1	1	yes	characteristic
376	C₂	C₂×C₄×#11929614	1	1	yes	characteristic
377	C₂	C₂×#19098915	1	1	yes	characteristic
378	C₂	#23773725	1	1	yes	characteristic
379	C₂	#23773955	1	1	yes	characteristic
380	C₂	#23773982	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₄×C₄⋊Q₈×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂²×D₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₄×C₄⋊Q₈	D₇₉
hypocenter	C₇₉	C₄×#487
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
12. #19098915	C₄	direct (N × H)
178. C₄×C₇₉	#487	semidirect
200. C₇₉	C₄×#487	semidirect
371. C₄	#19098915	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#19098915	2
C₄×#14579161	2
#23764362	2
#23764201	2
#23764075	2
#23763527	2
C₄×#14579084	2
C₄²×C₇₉⋊C₈	2
C₄×C₄⋊Q₈×C₇₉	2
C₄×#487	79

Subgroups — C4×#19098915 #34296247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#19098915 #34296247