Subgroups — #1300×D₇₉ #34178459

Order 20224.

786 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#432×D₇₉	C₂	1	1	yes	maximal, characteristic
2	C₄×M₁₆×D₇₉	C₂	1	1	yes	maximal, characteristic
3	#376×D₇₉	C₂	1	1	yes	maximal, characteristic
4	#23761294	C₂	1	1	yes	maximal, characteristic, complemented
5	#23761293	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761292	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1300	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₇₉	—	2	1	no	—
9	C₂×C₄²×D₇₉	—	2	1	no	—
10	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic
11	#19098620	C₂²	1	1	yes	characteristic
12	#19098619	C₄	1	2	yes	complemented
13	#19098618	—	2	1	no	—
14	#19098617	—	2	1	no	—
15	C₄⋊C₈×D₇₉	C₄	1	2	yes	complemented
16	C₂²⋊C₈×D₇₉	—	2	1	no	—
17	C₄×#11929608	C₂²	1	1	yes	characteristic
18	#19098515	C₄	1	2	yes	complemented
19	M₁₆×Dic₇₉	—	2	1	no	—
20	C₄×#11929607	—	2	1	no	—
21	#97×D₇₉	—	2	1	no	—
22	#97×D₇₉	C₄	1	2	yes	complemented
23	C₄×C₈×D₇₉	—	2	1	no	—
24	#19098409	—	2	1	no	—
25	#19098409	C₂²	1	1	yes	characteristic
26	#19098408	—	2	1	no	—
27	#19098408	C₄	1	2	yes	—
28	#95×D₇₉	—	2	1	no	—
29	#95×D₇₉	C₄	1	2	yes	—
30	#432×C₇₉	C₂²	1	1	yes	characteristic
31	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
32	#376×C₇₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₇₉	—	2	2	no	—
34	C₂²×C₄×D₇₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₇₉	D₄	1	1	yes	characteristic
36	C₂²×C₄×D₇₉	D₄	1	1	yes	characteristic
37	C₂×#11929608	—	2	1	no	—
38	C₂×#11929607	—	2	2	no	—
39	M₁₆×D₇₉	—	2	8	no	—
40	C₂×C₈×D₇₉	—	2	2	no	—
41	C₂×C₈×D₇₉	—	2	2	no	—
42	C₂×C₄×Dic₇₉	—	2	1	no	—
43	C₂×C₄×Dic₇₉	—	2	2	no	—
44	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
46	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
47	C₄²×D₇₉	—	2	8	no	—
48	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
49	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
50	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
51	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₇₉	D₄	1	1	yes	characteristic
53	C₄²×D₇₉	D₄	1	1	yes	characteristic
54	C₄²×D₇₉	Q₈	1	1	yes	characteristic
55	C₄²×D₇₉	Q₈	1	1	yes	characteristic
56	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	complemented
57	Dic₇₉⋊C₈	—	2	2	no	—
58	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
59	(C₂×D₇₉)⋊C₈	—	2	2	no	—
60	#14579072	—	2	1	no	—
61	#14579072	C₂×C₄	1	2	yes	complemented
62	#14579071	—	2	2	no	—
63	#14579071	—	2	2	no	—
64	C₄×C₇₉⋊C₈	—	2	1	no	—
65	C₈×Dic₇₉	—	2	2	no	—
66	C₇₉⋊#95	—	2	1	no	—
67	C₇₉⋊#95	—	2	2	no	—
68	C₇₉⋊#95	—	2	2	no	—
69	C₇₉⋊#95	C₂×C₄	1	2	yes	—
70	C₂×M₁₆×C₇₉	—	2	1	no	—
71	C₂×C₄²×C₇₉	—	2	1	no	—
72	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
73	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	complemented
74	C₂²⋊C₈×C₇₉	—	2	1	no	—
75	#97×C₇₉	—	2	1	no	—
76	#97×C₇₉	C₂×C₄	1	2	yes	complemented
77	C₄×C₈×C₇₉	—	2	1	no	—
78	#95×C₇₉	—	2	1	no	—
79	#95×C₇₉	C₂×C₄	1	2	yes	—
80	C₂³×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×Dic₇₉	—	2	2	no	—
82	C₂²×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×D₇₉	—	2	4	no	—
86	C₂×C₄×D₇₉	—	2	8	no	—
87	C₂×C₄×D₇₉	—	2	4	no	—
88	C₂×C₄×D₇₉	—	4	2	no	—
89	C₂×C₄×D₇₉	—	4	4	no	—
90	C₂×C₄×D₇₉	—	4	4	no	—
91	C₂×C₄×D₇₉	C₄²	1	1	yes	characteristic
92	C₂×C₄×D₇₉	C₄²	1	1	yes	characteristic
93	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
103	#11929608	—	2	4	no	—
104	#11929607	—	2	8	no	—
105	C₂×C₇₉⋊C₈	—	2	2	no	—
106	C₂×C₇₉⋊C₈	—	2	2	no	—
107	C₈×D₇₉	—	2	8	no	—
108	C₈×D₇₉	—	4	4	no	—
109	C₄×Dic₇₉	—	2	4	no	—
110	C₄×Dic₇₉	—	2	8	no	—
111	C₄×Dic₇₉	C₄²	1	1	yes	characteristic
112	C₄×Dic₇₉	C₄²	1	1	yes	characteristic
113	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
114	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
115	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
116	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
117	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
118	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
119	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
120	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
121	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
122	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₇₉	—	2	2	no	—
124	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
127	M₁₆×C₇₉	—	2	4	no	—
128	C₂×C₈×C₇₉	—	2	2	no	—
129	C₂×C₈×C₇₉	—	2	2	no	—
130	C₄²×C₇₉	—	2	4	no	—
131	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₇₉	C₂×Q₈	1	1	yes	characteristic
135	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×D₇₉	—	2	2	no	—
137	C₂²×D₇₉	—	2	2	no	—
138	C₂²×D₇₉	#95	1	1	yes	characteristic
139	C₂²×D₇₉	#95	1	1	yes	characteristic
140	C₂²×D₇₉	#104	1	4	yes	—
141	C₂×C₄×C₇₉	—	2	2	no	—
142	C₂×C₄×C₇₉	—	2	2	no	—
143	C₂×C₄×C₇₉	—	2	4	no	—
144	C₂×C₄×C₇₉	—	4	1	no	—
145	C₂×C₄×C₇₉	—	4	2	no	—
146	C₂×C₄×C₇₉	—	4	2	no	—
147	C₂×C₄×C₇₉	C₂×C₄²	1	1	yes	characteristic
148	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×Dic₇₉	—	2	2	no	—
154	C₂×Dic₇₉	—	2	2	no	—
155	C₂×Dic₇₉	—	2	4	no	—
156	C₂×Dic₇₉	—	4	1	no	—
157	C₂×Dic₇₉	—	4	2	no	—
158	C₂×Dic₇₉	—	4	2	no	—
159	C₂×Dic₇₉	#95	1	1	yes	characteristic
160	C₂×Dic₇₉	#95	1	1	yes	characteristic
161	C₂×Dic₇₉	#95	1	1	yes	characteristic
162	C₂×Dic₇₉	#95	1	1	yes	characteristic
163	C₂×Dic₇₉	#95	1	1	yes	characteristic
164	C₂×Dic₇₉	#95	1	1	yes	characteristic
165	C₄×D₇₉	—	2	2	no	—
166	C₄×D₇₉	—	2	2	no	—
167	C₄×D₇₉	—	2	2	no	—
168	C₄×D₇₉	—	2	2	no	—
169	C₄×D₇₉	—	2	2	no	—
170	C₄×D₇₉	—	2	2	no	—
171	C₄×D₇₉	—	2	2	no	—
172	C₄×D₇₉	—	2	2	no	—
173	C₄×D₇₉	—	2	2	no	—
174	C₄×D₇₉	—	4	1	no	—
175	C₄×D₇₉	—	4	1	no	—
176	C₄×D₇₉	—	4	16	no	—
177	C₄×D₇₉	#104	1	4	yes	—
178	C₈×C₇₉	—	2	4	no	—
179	C₈×C₇₉	—	4	2	no	—
180	C₇₉⋊C₈	—	2	4	no	—
181	C₇₉⋊C₈	—	4	2	no	—
182	C₂²×C₇₉	—	2	1	no	—
183	C₂²×C₇₉	—	2	1	no	—
184	C₂²×C₇₉	C₂×#95	1	1	yes	characteristic
185	C₂²×C₇₉	C₂×#104	1	2	yes	—
186	C₂×D₇₉	—	2	1	no	—
187	C₂×D₇₉	—	2	1	no	—
188	C₂×D₇₉	—	2	8	no	—
189	C₂×D₇₉	#339	1	2	yes	—
190	C₂×D₇₉	#339	1	2	yes	—
191	C₂×D₇₉	#339	1	2	yes	—
192	C₂×D₇₉	#344	1	2	yes	—
193	C₄×C₇₉	—	2	1	no	—
194	C₄×C₇₉	—	2	1	no	—
195	C₄×C₇₉	—	2	1	no	—
196	C₄×C₇₉	—	2	1	no	—
197	C₄×C₇₉	—	2	1	no	—
198	C₄×C₇₉	—	4	4	no	—
199	C₄×C₇₉	C₂×#104	1	2	yes	—
200	Dic₇₉	—	2	1	no	—
201	Dic₇₉	—	2	1	no	—
202	Dic₇₉	—	2	1	no	—
203	Dic₇₉	—	2	1	no	—
204	Dic₇₉	—	2	1	no	—
205	Dic₇₉	—	4	4	no	—
206	Dic₇₉	#339	1	2	yes	—
207	C₂×#1300	—	79	1	no	maximal, Sylow
208	C₂×C₇₉	—	2	2	no	—
209	C₂×C₇₉	C₂×#339	1	1	yes	characteristic
210	C₂×C₇₉	C₂×#339	1	1	yes	characteristic
211	C₂×C₇₉	C₂×#344	1	1	yes	characteristic
212	D₇₉	—	2	2	no	—
213	D₇₉	#1300	1	4	yes	direct product factor
214	C₂×#432	—	79	1	no	—
215	C₂×C₄×M₁₆	—	79	1	no	—
216	C₂×#376	—	79	1	no	—
217	#1300	—	79	1	no	—
218	#1300	—	79	1	no	—
219	#1300	—	79	1	no	—
220	#1300	D₇₉	1	1	yes	characteristic, direct product factor
221	C₇₉	C₂×#1300	1	1	yes	characteristic, complemented, Sylow
222	C₂²×M₁₆	—	158	1	no	—
223	C₂²×C₄²	—	79	1	no	—
224	C₂²×C₄²	—	158	1	no	—
225	#432	—	79	1	no	—
226	#432	—	79	2	no	—
227	#432	—	158	1	no	—
228	#432	—	158	1	no	—
229	#432	C₂×D₇₉	1	1	yes	characteristic
230	C₂×C₄⋊C₈	—	79	2	no	—
231	C₂×C₂²⋊C₈	—	158	1	no	—
232	C₄×M₁₆	—	79	1	no	—
233	C₄×M₁₆	—	79	2	no	—
234	C₄×M₁₆	—	158	1	no	—
235	C₄×M₁₆	—	158	1	no	—
236	C₄×M₁₆	C₂×D₇₉	1	1	yes	characteristic
237	C₂×#97	—	79	2	no	—
238	C₂×#97	—	158	1	no	—
239	C₂×C₄×C₈	—	158	1	no	—
240	#376	—	79	1	no	—
241	#376	—	79	2	no	—
242	#376	—	158	1	no	—
243	#376	—	158	1	no	—
244	#376	C₂×D₇₉	1	1	yes	characteristic
245	C₂×#95	—	79	2	no	—
246	C₂×#95	—	158	1	no	—
247	C₂³×C₄	—	79	1	no	—
248	C₂³×C₄	—	79	1	no	—
249	C₂³×C₄	—	79	1	no	—
250	C₂³×C₄	—	158	2	no	—
251	C₂×M₁₆	—	2	1	no	—
252	C₂×M₁₆	—	158	2	no	—
253	C₂×M₁₆	—	158	8	no	—
254	C₂×M₁₆	—	158	1	no	—
255	C₂²×C₈	—	158	2	no	—
256	C₂²×C₈	—	158	2	no	—
257	C₂×C₄²	—	2	1	no	—
258	C₂×C₄²	—	79	1	no	—
259	C₂×C₄²	—	79	1	no	—
260	C₂×C₄²	—	79	1	no	—
261	C₂×C₄²	—	79	1	no	—
262	C₂×C₄²	—	79	1	no	—
263	C₂×C₄²	—	79	1	no	—
264	C₂×C₄²	—	79	1	no	—
265	C₂×C₄²	—	79	1	no	—
266	C₂×C₄²	—	79	1	no	—
267	C₂×C₄²	—	79	1	no	—
268	C₂×C₄²	—	79	1	no	—
269	C₂×C₄²	—	158	8	no	—
270	C₂×C₄²	—	158	2	no	—
271	C₂×C₄²	—	158	1	no	—
272	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
273	C₄⋊C₈	—	79	2	no	—
274	C₄⋊C₈	—	158	2	no	—
275	C₄⋊C₈	C₄×D₇₉	1	2	yes	complemented
276	C₂²⋊C₈	—	2	1	no	—
277	C₂²⋊C₈	—	158	2	no	—
278	C₂²⋊C₈	—	158	1	no	—
279	#97	—	2	1	no	—
280	#97	—	79	2	no	—
281	#97	—	158	2	no	—
282	#97	—	158	2	no	—
283	#97	—	158	1	no	—
284	#97	C₄×D₇₉	1	2	yes	complemented
285	C₄×C₈	—	2	1	no	—
286	C₄×C₈	—	158	2	no	—
287	C₄×C₈	—	158	1	no	—
288	#95	—	2	1	no	—
289	#95	—	79	2	no	—
290	#95	—	158	2	no	—
291	#95	—	158	2	no	—
292	#95	—	158	1	no	—
293	#95	C₄×D₇₉	1	2	yes	—
294	C₂⁴	—	79	1	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	316	4	no	—
297	C₂²×C₄	—	316	4	no	—
298	C₂²×C₄	—	316	2	no	—
299	C₂²×C₄	—	79	1	no	—
300	C₂²×C₄	—	79	1	no	—
301	C₂²×C₄	—	79	1	no	—
302	C₂²×C₄	—	79	1	no	—
303	C₂²×C₄	—	79	1	no	—
304	C₂²×C₄	—	79	1	no	—
305	C₂²×C₄	—	79	1	no	—
306	C₂²×C₄	—	79	1	no	—
307	C₂²×C₄	—	79	1	no	—
308	C₂²×C₄	—	79	1	no	—
309	C₂²×C₄	—	79	1	no	—
310	C₂²×C₄	—	79	1	no	—
311	C₂²×C₄	—	79	1	no	—
312	C₂²×C₄	—	79	1	no	—
313	C₂²×C₄	—	79	1	no	—
314	C₂²×C₄	—	158	8	no	—
315	C₂²×C₄	—	158	4	no	—
316	C₂²×C₄	—	158	4	no	—
317	C₂²×C₄	—	158	2	no	—
318	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
319	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
320	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
321	M₁₆	—	2	4	no	—
322	M₁₆	—	158	8	no	—
323	M₁₆	—	158	4	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	316	4	no	—
327	C₂×C₈	—	158	8	no	—
328	C₂×C₈	—	158	2	no	—
329	C₂×C₈	—	158	2	no	—
330	C₄²	—	2	4	no	—
331	C₄²	—	79	1	no	—
332	C₄²	—	79	1	no	—
333	C₄²	—	79	1	no	—
334	C₄²	—	79	1	no	—
335	C₄²	—	79	1	no	—
336	C₄²	—	79	1	no	—
337	C₄²	—	79	1	no	—
338	C₄²	—	79	1	no	—
339	C₄²	—	79	1	no	—
340	C₄²	—	79	1	no	—
341	C₄²	—	79	1	no	—
342	C₄²	—	79	1	no	—
343	C₄²	—	158	4	no	—
344	C₄²	—	158	8	no	—
345	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
346	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
347	C₄²	D₄×D₇₉	1	1	yes	characteristic
348	C₄²	Q₈×D₇₉	1	1	yes	characteristic
349	C₂³	—	79	1	no	—
350	C₂³	—	79	1	no	—
351	C₂³	—	79	4	no	—
352	C₂³	—	158	2	no	—
353	C₂³	—	158	2	no	—
354	C₂³	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	316	1	no	—
362	C₂×C₄	—	316	1	no	—
363	C₂×C₄	—	316	16	no	—
364	C₂×C₄	—	316	2	no	—
365	C₂×C₄	—	316	2	no	—
366	C₂×C₄	—	316	1	no	—
367	C₂×C₄	—	79	1	no	—
368	C₂×C₄	—	79	4	no	—
369	C₂×C₄	—	79	1	no	—
370	C₂×C₄	—	79	1	no	—
371	C₂×C₄	—	79	1	no	—
372	C₂×C₄	—	79	1	no	—
373	C₂×C₄	—	79	1	no	—
374	C₂×C₄	—	158	2	no	—
375	C₂×C₄	—	158	2	no	—
376	C₂×C₄	—	158	2	no	—
377	C₂×C₄	—	158	2	no	—
378	C₂×C₄	—	158	2	no	—
379	C₂×C₄	—	158	2	no	—
380	C₂×C₄	—	158	2	no	—
381	C₂×C₄	—	158	2	no	—
382	C₂×C₄	—	158	4	no	—
383	C₂×C₄	—	158	2	no	—
384	C₂×C₄	—	158	2	no	—
385	C₂×C₄	—	158	2	no	—
386	C₂×C₄	C₄²×D₇₉	1	1	yes	characteristic
387	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
388	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
389	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
390	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
391	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
392	C₈	—	2	4	no	—
393	C₈	—	4	2	no	—
394	C₈	—	316	2	no	—
395	C₈	—	158	4	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	79	2	no	—
399	C₂²	—	79	2	no	—
400	C₂²	—	79	2	no	—
401	C₂²	—	79	2	no	—
402	C₂²	—	158	8	no	—
403	C₂²	—	158	1	no	—
404	C₂²	—	158	1	no	—
405	C₂²	#95×D₇₉	1	1	yes	characteristic
406	C₂²	#104×D₇₉	1	2	yes	—
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	4	4	no	—
413	C₄	—	316	4	no	—
414	C₄	—	79	2	no	—
415	C₄	—	158	1	no	—
416	C₄	—	158	1	no	—
417	C₄	—	158	1	no	—
418	C₄	—	158	1	no	—
419	C₄	—	158	1	no	—
420	C₄	#104×D₇₉	1	2	yes	—
421	C₂	—	2	2	no	—
422	C₂	—	79	4	no	—
423	C₂	—	158	2	no	—
424	C₂	#339×D₇₉	1	1	yes	characteristic
425	C₂	#339×D₇₉	1	1	yes	characteristic
426	C₂	#344×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1300	C₂
socle	C₂²×C₇₉	C₂×#95
prime radical	C₂³×D₇₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1300	D₇₉
hypocenter	C₇₉	C₂×#1300
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1300

Complements

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

N	H ≅ G/N	type
4. #23761294	C₂	semidirect
5. #23761293	C₂	semidirect
6. #23761292	C₂	semidirect
7. C₇₉×#1300	C₂	semidirect
12. #19098619	C₄	semidirect
15. C₄⋊C₈×D₇₉	C₄	semidirect
18. #19098515	C₄	semidirect
22. #97×D₇₉	C₄	semidirect
56. C₄⋊(C₇₉⋊C₈)	C₂×C₄	semidirect
61. #14579072	C₂×C₄	semidirect
73. C₄⋊C₈×C₇₉	C₂×C₄	semidirect
76. #97×C₇₉	C₂×C₄	semidirect
213. D₇₉	#1300	direct (N × H)
220. #1300	D₇₉	direct (N × H)
221. C₇₉	C₂×#1300	semidirect
275. C₄⋊C₈	C₄×D₇₉	semidirect
284. #97	C₄×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#432×D₇₉	2
C₄×M₁₆×D₇₉	2
#376×D₇₉	2
#23761294	2
#23761293	2
#23761292	2
C₇₉×#1300	2
C₂×#1300	79

Subgroups — #1300×D79 #34178459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1300×D₇₉ #34178459