Subgroups — C₇₉×#7678 #34119367

Order 20224.

630 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	C₇₉×#2854	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#1728	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#336×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#1271	C₂	1	2	yes	maximal, complemented
5	C₇₉×#1270	C₂	1	2	yes	maximal, complemented
6	C₂²×M₁₆×C₇₉	—	2	1	no	—
7	C₂³×C₈×C₇₉	—	2	1	no	—
8	C₂×#123×C₇₉	—	2	1	no	—
9	C₂×#121×C₇₉	C₄	1	1	yes	characteristic
10	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
11	#390×C₇₉	C₄	1	1	yes	characteristic
12	#390×C₇₉	C₂²	1	1	yes	characteristic
13	#389×C₇₉	C₄	1	1	yes	characteristic
14	#389×C₇₉	C₂²	1	1	yes	characteristic
15	#388×C₇₉	—	2	1	no	—
16	#388×C₇₉	—	2	1	no	—
17	#386×C₇₉	—	2	1	no	—
18	#380×C₇₉	C₄	1	1	yes	characteristic
19	#336×C₇₉	—	2	1	no	—
20	#336×C₇₉	—	2	1	no	—
21	#336×C₇₉	C₂²	1	2	yes	—
22	#336×C₇₉	C₂²	1	2	yes	—
23	C₂²×D₄×C₇₉	—	2	1	no	—
24	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
28	C₂×M₁₆×C₇₉	—	2	4	no	—
29	C₂×M₁₆×C₇₉	—	4	2	no	—
30	C₂×M₁₆×C₇₉	—	4	2	no	—
31	C₂²×C₈×C₇₉	—	2	4	no	—
32	C₂²×C₈×C₇₉	—	2	2	no	—
33	C₂²×C₈×C₇₉	—	2	2	no	—
34	C₂²×C₈×C₇₉	—	4	2	no	—
35	C₂²×C₈×C₇₉	—	4	2	no	—
36	#123×C₇₉	—	4	2	no	—
37	#123×C₇₉	—	4	2	no	—
38	#121×C₇₉	—	4	2	no	—
39	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
41	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
46	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
48	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
49	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
50	C₂×C₄²×C₇₉	—	4	2	no	—
51	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
55	#95×C₇₉	—	2	1	no	—
56	#95×C₇₉	—	2	1	no	—
57	#95×C₇₉	—	2	1	no	—
58	C₂⁴×C₇₉	—	2	1	no	—
59	C₂⁴×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×D₄×C₇₉	—	2	2	no	—
61	C₂×D₄×C₇₉	—	4	1	no	—
62	C₂×D₄×C₇₉	—	4	1	no	—
63	C₂×D₄×C₇₉	—	4	2	no	—
64	C₂×D₄×C₇₉	—	4	2	no	—
65	C₂×D₄×C₇₉	—	4	2	no	—
66	C₂²×C₄×C₇₉	—	2	2	no	—
67	C₂²×C₄×C₇₉	—	2	2	no	—
68	C₂²×C₄×C₇₉	—	2	2	no	—
69	C₂²×C₄×C₇₉	—	2	2	no	—
70	C₂²×C₄×C₇₉	—	2	1	no	—
71	C₂²×C₄×C₇₉	—	2	1	no	—
72	C₂²×C₄×C₇₉	—	2	2	no	—
73	C₂²×C₄×C₇₉	—	2	2	no	—
74	C₂²×C₄×C₇₉	—	2	1	no	—
75	C₂²×C₄×C₇₉	—	2	1	no	—
76	C₂²×C₄×C₇₉	—	2	1	no	—
77	C₂²×C₄×C₇₉	—	4	1	no	—
78	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₇₉	D₈	1	2	yes	—
82	C₂²×C₄×C₇₉	SD₁₆	1	2	yes	—
83	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
86	M₁₆×C₇₉	—	4	8	no	—
87	C₂×C₈×C₇₉	—	2	4	no	—
88	C₂×C₈×C₇₉	—	2	4	no	—
89	C₂×C₈×C₇₉	—	4	8	no	—
90	C₂×C₈×C₇₉	—	4	2	no	—
91	C₂×C₈×C₇₉	—	4	2	no	—
92	C₂×C₈×C₇₉	—	4	2	no	—
93	C₂×C₈×C₇₉	—	4	2	no	—
94	C₄⋊C₄×C₇₉	—	2	2	no	—
95	C₄⋊C₄×C₇₉	—	4	1	no	—
96	C₄⋊C₄×C₇₉	—	4	1	no	—
97	C₄⋊C₄×C₇₉	—	4	2	no	—
98	C₄⋊C₄×C₇₉	—	4	1	no	—
99	C₄⋊C₄×C₇₉	—	4	1	no	—
100	C₂²⋊C₄×C₇₉	—	4	2	no	—
101	C₂²⋊C₄×C₇₉	—	4	2	no	—
102	C₂²⋊C₄×C₇₉	—	4	2	no	—
103	C₂²⋊C₄×C₇₉	—	4	2	no	—
104	C₂²⋊C₄×C₇₉	—	4	1	no	—
105	C₂²⋊C₄×C₇₉	—	4	1	no	—
106	C₂²⋊C₄×C₇₉	—	4	1	no	—
107	C₂²⋊C₄×C₇₉	—	4	1	no	—
108	C₄²×C₇₉	—	4	1	no	—
109	C₄²×C₇₉	—	4	1	no	—
110	C₄²×C₇₉	—	4	1	no	—
111	C₄²×C₇₉	—	4	1	no	—
112	C₂³×C₇₉	—	2	1	no	—
113	C₂³×C₇₉	—	2	1	no	—
114	C₂³×C₇₉	—	2	1	no	—
115	C₂³×C₇₉	—	2	1	no	—
116	C₂³×C₇₉	—	4	1	no	—
117	C₂³×C₇₉	—	4	1	no	—
118	C₂³×C₇₉	—	4	1	no	—
119	C₂³×C₇₉	—	4	1	no	—
120	C₂³×C₇₉	—	4	1	no	—
121	C₂³×C₇₉	—	4	1	no	—
122	C₂³×C₇₉	—	4	1	no	—
123	C₂³×C₇₉	#99	1	2	yes	—
124	C₂³×C₇₉	#102	1	2	yes	—
125	C₂³×C₇₉	#104	1	2	yes	—
126	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	D₄×C₇₉	—	8	2	no	—
128	D₄×C₇₉	—	8	4	no	—
129	C₂×C₄×C₇₉	—	2	4	no	—
130	C₂×C₄×C₇₉	—	2	4	no	—
131	C₂×C₄×C₇₉	—	2	4	no	—
132	C₂×C₄×C₇₉	—	2	4	no	—
133	C₂×C₄×C₇₉	—	2	1	no	—
134	C₂×C₄×C₇₉	—	2	1	no	—
135	C₂×C₄×C₇₉	—	2	1	no	—
136	C₂×C₄×C₇₉	—	2	1	no	—
137	C₂×C₄×C₇₉	—	2	1	no	—
138	C₂×C₄×C₇₉	—	2	1	no	—
139	C₂×C₄×C₇₉	—	2	1	no	—
140	C₂×C₄×C₇₉	—	2	1	no	—
141	C₂×C₄×C₇₉	—	2	1	no	—
142	C₂×C₄×C₇₉	—	2	1	no	—
143	C₂×C₄×C₇₉	—	2	1	no	—
144	C₂×C₄×C₇₉	—	2	1	no	—
145	C₂×C₄×C₇₉	—	2	1	no	—
146	C₂×C₄×C₇₉	—	4	4	no	—
147	C₂×C₄×C₇₉	—	4	1	no	—
148	C₂×C₄×C₇₉	—	4	1	no	—
149	C₂×C₄×C₇₉	—	4	1	no	—
150	C₂×C₄×C₇₉	—	4	1	no	—
151	C₂×C₄×C₇₉	—	4	1	no	—
152	C₂×C₄×C₇₉	—	4	1	no	—
153	C₂×C₄×C₇₉	—	4	1	no	—
154	C₂×C₄×C₇₉	—	4	1	no	—
155	C₂×C₄×C₇₉	—	4	1	no	—
156	C₂×C₄×C₇₉	#102	1	2	yes	—
157	C₂×C₄×C₇₉	#104	1	2	yes	—
158	C₂×C₄×C₇₉	#131	1	2	yes	—
159	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
160	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
161	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
162	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
163	C₈×C₇₉	—	4	4	no	—
164	C₈×C₇₉	—	4	4	no	—
165	C₂²×C₇₉	—	2	2	no	—
166	C₂²×C₇₉	—	2	2	no	—
167	C₂²×C₇₉	—	2	2	no	—
168	C₂²×C₇₉	—	2	2	no	—
169	C₂²×C₇₉	—	2	2	no	—
170	C₂²×C₇₉	—	2	2	no	—
171	C₂²×C₇₉	—	8	1	no	—
172	C₂²×C₇₉	—	8	1	no	—
173	C₂²×C₇₉	—	8	1	no	—
174	C₂²×C₇₉	—	8	1	no	—
175	C₂²×C₇₉	—	8	1	no	—
176	C₂²×C₇₉	—	8	1	no	—
177	C₂²×C₇₉	—	8	1	no	—
178	C₂²×C₇₉	#327	1	4	yes	—
179	C₂²×C₇₉	#408	1	1	yes	characteristic
180	C₂²×C₇₉	C₂×#99	1	1	yes	characteristic
181	C₂²×C₇₉	#413	1	1	yes	characteristic
182	C₂²×C₇₉	C₂×#102	1	1	yes	characteristic
183	C₂²×C₇₉	#417	1	1	yes	characteristic
184	C₂²×C₇₉	C₂×#104	1	1	yes	characteristic
185	C₂²×C₇₉	C₂×#104	1	1	yes	characteristic
186	C₄×C₇₉	—	2	2	no	—
187	C₄×C₇₉	—	2	2	no	—
188	C₄×C₇₉	—	2	1	no	—
189	C₄×C₇₉	—	2	1	no	—
190	C₄×C₇₉	—	2	2	no	—
191	C₄×C₇₉	—	2	1	no	—
192	C₄×C₇₉	—	2	1	no	—
193	C₄×C₇₉	—	4	1	no	—
194	C₄×C₇₉	—	8	1	no	—
195	C₄×C₇₉	—	8	1	no	—
196	C₄×C₇₉	—	8	1	no	—
197	#7678	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂×C₇₉	—	2	4	no	—
199	C₂×C₇₉	—	16	1	no	—
200	C₂×C₇₉	#1468	1	1	yes	characteristic
201	C₂×C₇₉	#1483	1	1	yes	characteristic
202	C₂×C₇₉	#1492	1	1	yes	characteristic
203	C₂×C₇₉	C₂×#327	1	1	yes	characteristic
204	C₂×C₇₉	#1504	1	1	yes	characteristic
205	C₂×C₇₉	#1524	1	1	yes	characteristic
206	C₂×C₇₉	#1547	1	1	yes	characteristic
207	#2854	C₂×C₇₉	1	1	yes	characteristic
208	#1728	C₂×C₇₉	1	1	yes	characteristic, complemented
209	C₂×#336	C₂×C₇₉	1	1	yes	characteristic, complemented
210	#1271	C₂×C₇₉	1	2	yes	complemented
211	#1270	C₂×C₇₉	1	2	yes	complemented
212	C₇₉	#7678	1	1	yes	characteristic, direct product factor, Sylow
213	C₂²×M₁₆	—	2	1	no	—
214	C₂³×C₈	—	2	1	no	—
215	C₂×#123	—	2	1	no	—
216	C₂×#121	C₄×C₇₉	1	1	yes	characteristic
217	C₂²×C₄²	C₂²×C₇₉	1	1	yes	characteristic
218	#390	C₄×C₇₉	1	1	yes	characteristic
219	#390	C₂²×C₇₉	1	1	yes	characteristic
220	#389	C₄×C₇₉	1	1	yes	characteristic
221	#389	C₂²×C₇₉	1	1	yes	characteristic
222	#388	—	2	1	no	—
223	#388	—	2	1	no	—
224	#386	—	2	1	no	—
225	#380	C₄×C₇₉	1	1	yes	characteristic
226	#336	—	2	1	no	—
227	#336	—	2	1	no	—
228	#336	C₂²×C₇₉	1	2	yes	—
229	#336	C₂²×C₇₉	1	2	yes	—
230	C₂²×D₄	—	2	1	no	—
231	C₂²×D₄	C₂×C₄×C₇₉	1	1	yes	characteristic
232	C₂³×C₄	C₂×C₄×C₇₉	1	1	yes	characteristic
233	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
234	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
235	C₂×M₁₆	—	2	4	no	—
236	C₂×M₁₆	—	4	2	no	—
237	C₂×M₁₆	—	4	2	no	—
238	C₂²×C₈	—	2	4	no	—
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	—	2	2	no	—
241	C₂²×C₈	—	4	2	no	—
242	C₂²×C₈	—	4	2	no	—
243	#123	—	4	2	no	—
244	#123	—	4	2	no	—
245	#121	—	4	2	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	C₂×C₄×C₇₉	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂×C₄×C₇₉	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂×C₄×C₇₉	1	1	yes	characteristic
251	C₂×C₂²⋊C₄	—	2	1	no	—
252	C₂×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₂²⋊C₄	—	2	1	no	—
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₂²⋊C₄	—	2	1	no	—
256	C₂×C₂²⋊C₄	—	2	1	no	—
257	C₂×C₄²	—	4	2	no	—
258	C₂×C₄²	C₂×C₄×C₇₉	1	1	yes	characteristic
259	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
260	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
262	#95	—	2	1	no	—
263	#95	—	2	1	no	—
264	#95	—	2	1	no	—
265	C₂⁴	—	2	1	no	—
266	C₂⁴	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	4	1	no	—
269	C₂×D₄	—	4	1	no	—
270	C₂×D₄	—	4	2	no	—
271	C₂×D₄	—	4	2	no	—
272	C₂×D₄	—	4	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
286	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
287	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
288	C₂²×C₄	D₈×C₇₉	1	2	yes	—
289	C₂²×C₄	SD₁₆×C₇₉	1	2	yes	—
290	C₂²×C₄	C₂²×C₄×C₇₉	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
293	M₁₆	—	4	8	no	—
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	4	8	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	—	4	2	no	—
299	C₂×C₈	—	4	2	no	—
300	C₂×C₈	—	4	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₂²⋊C₄	—	4	2	no	—
308	C₂²⋊C₄	—	4	2	no	—
309	C₂²⋊C₄	—	4	2	no	—
310	C₂²⋊C₄	—	4	2	no	—
311	C₂²⋊C₄	—	4	1	no	—
312	C₂²⋊C₄	—	4	1	no	—
313	C₂²⋊C₄	—	4	1	no	—
314	C₂²⋊C₄	—	4	1	no	—
315	C₄²	—	4	1	no	—
316	C₄²	—	4	1	no	—
317	C₄²	—	4	1	no	—
318	C₄²	—	4	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	2	1	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	4	1	no	—
324	C₂³	—	4	1	no	—
325	C₂³	—	4	1	no	—
326	C₂³	—	4	1	no	—
327	C₂³	—	4	1	no	—
328	C₂³	—	4	1	no	—
329	C₂³	—	4	1	no	—
330	C₂³	#99×C₇₉	1	2	yes	—
331	C₂³	#102×C₇₉	1	2	yes	—
332	C₂³	#104×C₇₉	1	2	yes	—
333	C₂³	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
334	D₄	—	8	2	no	—
335	D₄	—	8	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	#102×C₇₉	1	2	yes	—
364	C₂×C₄	#104×C₇₉	1	2	yes	—
365	C₂×C₄	#131×C₇₉	1	2	yes	—
366	C₂×C₄	C₂×D₈×C₇₉	1	1	yes	characteristic
367	C₂×C₄	C₂×SD₁₆×C₇₉	1	1	yes	characteristic
368	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
369	C₂×C₄	#137×C₇₉	1	1	yes	characteristic
370	C₈	—	4	4	no	—
371	C₈	—	4	4	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	8	1	no	—
379	C₂²	—	8	1	no	—
380	C₂²	—	8	1	no	—
381	C₂²	—	8	1	no	—
382	C₂²	—	8	1	no	—
383	C₂²	—	8	1	no	—
384	C₂²	—	8	1	no	—
385	C₂²	#327×C₇₉	1	4	yes	—
386	C₂²	#408×C₇₉	1	1	yes	characteristic
387	C₂²	C₂×#99×C₇₉	1	1	yes	characteristic
388	C₂²	#413×C₇₉	1	1	yes	characteristic
389	C₂²	C₂×#102×C₇₉	1	1	yes	characteristic
390	C₂²	#417×C₇₉	1	1	yes	characteristic
391	C₂²	C₂×#104×C₇₉	1	1	yes	characteristic
392	C₂²	C₂×#104×C₇₉	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	2	no	—
400	C₄	—	4	1	no	—
401	C₄	—	8	1	no	—
402	C₄	—	8	1	no	—
403	C₄	—	8	1	no	—
404	C₂	—	2	4	no	—
405	C₂	—	16	1	no	—
406	C₂	C₇₉×#1468	1	1	yes	characteristic
407	C₂	C₇₉×#1483	1	1	yes	characteristic
408	C₂	C₇₉×#1492	1	1	yes	characteristic
409	C₂	C₂×#327×C₇₉	1	1	yes	characteristic
410	C₂	C₇₉×#1504	1	1	yes	characteristic
411	C₂	C₇₉×#1524	1	1	yes	characteristic
412	C₂	C₇₉×#1547	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₇₉
Frattini, cosocle	C₂×C₄²	C₂³×C₇₉
prime radical	C₂×#121×C₇₉	C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂²×C₄²×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₉×#1728	C₂	semidirect
3. C₂×#336×C₇₉	C₂	semidirect
4. C₇₉×#1271	C₂	semidirect
5. C₇₉×#1270	C₂	semidirect
197. #7678	C₇₉	direct (N × H)
208. #1728	C₂×C₇₉	semidirect
209. C₂×#336	C₂×C₇₉	semidirect
210. #1271	C₂×C₇₉	semidirect
211. #1270	C₂×C₇₉	semidirect
212. C₇₉	#7678	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₉×#2854	2
C₇₉×#1728	2
C₂×#336×C₇₉	2
C₇₉×#1271	2
C₇₉×#1270	2
#7678	79

Subgroups — C79×#7678 #34119367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#7678 #34119367