Subgroups — #23776889

Order 10112.

1648 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11929625	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#19099232	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×C₂²⋊D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#19099225	C₂	1	1	yes	maximal, characteristic, complemented
6	#19099215	C₂	1	3	yes	maximal, complemented
7	#19099209	C₂	1	3	yes	maximal, complemented
8	#19099206	C₂	1	3	yes	maximal, complemented
9	#19099197	C₂	1	3	yes	maximal, complemented
10	#19099112	C₂	1	3	yes	maximal, complemented
11	#19099076	C₂	1	3	yes	maximal, complemented
12	#19099073	C₂	1	3	yes	maximal, complemented
13	C₄×#11929625	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×D₄×D₇₉	C₂	1	3	yes	maximal, complemented
15	#548×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11929625	—	2	8	no	—
17	C₂×#11929625	C₂²	1	1	yes	characteristic
18	C₂×#11929625	C₂²	1	3	yes	complemented
19	C₂×#11929625	C₂²	1	1	yes	characteristic, complemented
20	C₂×#11929625	C₂²	1	3	yes	complemented
21	C₂×#11929624	C₂²	1	3	yes	complemented
22	C₂×#11929623	C₂²	1	3	yes	complemented
23	#41×D₇₉	—	2	8	no	—
24	C₂×Q₈×D₇₉	C₂²	1	1	yes	characteristic, complemented
25	C₂²×D₃₁₆	C₂²	1	3	yes	complemented
26	C₂×D₄×D₇₉	C₂²	1	3	yes	—
27	C₂×D₄×D₇₉	C₂²	1	3	yes	complemented
28	C₂²×C₄×D₇₉	C₂²	1	3	yes	complemented
29	C₂²×C₄×D₇₉	C₂²	1	3	yes	complemented
30	#14579159	C₂²	1	3	yes	complemented
31	#14579157	C₂²	1	3	yes	complemented
32	#14579149	C₂²	1	3	yes	complemented
33	#14579146	C₂²	1	6	yes	complemented
34	#14579143	C₂²	1	6	yes	complemented
35	#14579141	C₂²	1	3	yes	complemented
36	#14579140	C₂²	1	3	yes	complemented
37	#14579137	C₂²	1	3	yes	complemented
38	#14579136	C₂²	1	3	yes	complemented
39	#14579135	C₂²	1	3	yes	complemented
40	#14579134	C₂²	1	6	yes	complemented
41	#14579134	C₂²	1	6	yes	complemented
42	#14579132	C₂²	1	3	yes	complemented
43	#14579131	C₂²	1	6	yes	complemented
44	#14579129	C₂²	1	6	yes	complemented
45	Q₈×Dic₇₉	C₂²	1	1	yes	characteristic, complemented
46	C₄×D₃₁₆	C₂²	1	3	yes	complemented
47	C₄×D₃₁₆	C₂²	1	3	yes	complemented
48	D₄×Dic₇₉	C₂²	1	3	yes	complemented
49	#14579123	C₂²	1	3	yes	complemented
50	#14579123	C₂²	1	3	yes	complemented
51	C₄×C₂²⋊D₇₉	C₂²	1	3	yes	—
52	C₄×C₂²⋊D₇₉	C₂²	1	3	yes	complemented
53	(C₂²⋊D₇₉)⋊C₄	C₂²	1	1	yes	characteristic
54	(C₂²⋊D₇₉)⋊C₄	C₂²	1	3	yes	complemented
55	(C₂²⋊D₇₉)⋊C₄	C₂²	1	6	yes	complemented
56	#14579119	C₂²	1	3	yes	complemented
57	C₄⋊C₄×D₇₉	C₂²	1	3	yes	complemented
58	C₂²⋊C₄×D₇₉	C₂²	1	3	yes	complemented
59	C₂²⋊C₄×D₇₉	C₂²	1	3	yes	complemented
60	C₄²×D₇₉	C₂²	1	3	yes	complemented
61	C₂×#41×C₇₉	C₂²	1	1	yes	characteristic, complemented
62	C₂²×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
63	#124×C₇₉	C₂²	1	3	yes	complemented
64	C₂²⋊Q₈×C₇₉	C₂²	1	3	yes	complemented
65	#121×C₇₉	C₂²	1	3	yes	complemented
66	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
67	C₄×D₄×C₇₉	C₂²	1	3	yes	complemented
68	C₂³×D₇₉	C₂³	1	3	yes	—
69	C₂³×D₇₉	C₂³	1	3	yes	—
70	#11929625	—	2	12	no	—
71	#11929625	—	2	12	no	—
72	#11929625	—	2	4	no	—
73	#11929625	D₄	1	8	yes	complemented
74	#11929624	—	2	12	no	—
75	#11929623	—	2	12	no	—
76	C₂×Dic₁₅₈	C₂³	1	3	yes	—
77	Q₈×D₇₉	—	2	4	no	—
78	C₂×D₃₁₆	—	2	12	no	—
79	C₂×D₃₁₆	C₂³	1	6	yes	—
80	C₂×D₃₁₆	C₂³	1	3	yes	—
81	C₂×D₃₁₆	C₂³	1	3	yes	—
82	C₂×D₃₁₆	C₂³	1	3	yes	—
83	C₂×C₂²⋊D₇₉	C₂³	1	6	yes	—
84	C₂×C₂²⋊D₇₉	C₂³	1	3	yes	—
85	C₂×C₂²⋊D₇₉	C₂³	1	6	yes	—
86	C₂×C₂²⋊D₇₉	C₂³	1	1	yes	characteristic
87	D₄×D₇₉	—	2	12	no	—
88	D₄×D₇₉	—	2	12	no	—
89	C₂²×Dic₇₉	C₂³	1	3	yes	—
90	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
91	C₂×C₄×D₇₉	—	2	12	no	—
92	C₂×C₄×D₇₉	—	2	12	no	—
93	C₂×C₄×D₇₉	C₂³	1	3	yes	—
94	C₂×C₄×D₇₉	C₂³	1	3	yes	—
95	C₂×C₄×D₇₉	C₂³	1	3	yes	—
96	C₂×C₄×D₇₉	C₂³	1	3	yes	—
97	C₂×C₄×D₇₉	C₂³	1	3	yes	—
98	C₂×C₄×D₇₉	C₂³	1	3	yes	—
99	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₇₉	C₂³	1	3	yes	—
101	C₂×C₄×D₇₉	C₂³	1	3	yes	—
102	C₄⋊Dic₇₉	C₂³	1	3	yes	—
103	C₄⋊Dic₇₉	C₂³	1	3	yes	—
104	Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
105	Dic₇₉⋊C₄	C₂³	1	3	yes	—
106	Dic₇₉⋊C₄	C₂³	1	6	yes	—
107	C₂²⋊Dic₇₉	C₂³	1	3	yes	—
108	C₂²⋊Dic₇₉	C₂³	1	3	yes	—
109	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
110	(C₂×D₇₉)⋊C₄	C₂³	1	3	yes	—
111	(C₂×D₇₉)⋊C₄	C₂³	1	3	yes	—
112	(C₂×D₇₉)⋊C₄	C₂³	1	3	yes	—
113	(C₂×D₇₉)⋊C₄	C₂³	1	6	yes	—
114	(C₂×D₇₉)⋊C₄	C₂³	1	6	yes	—
115	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
116	C₄×Dic₇₉	C₂³	1	3	yes	—
117	C₄×Dic₇₉	C₂³	1	3	yes	—
118	#41×C₇₉	—	2	4	no	—
119	C₂×Q₈×C₇₉	—	2	4	no	—
120	C₂×Q₈×C₇₉	C₂³	1	3	yes	—
121	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
122	C₂×D₄×C₇₉	C₂³	1	3	yes	—
123	C₂×D₄×C₇₉	C₂³	1	3	yes	—
124	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
125	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
126	C₄⋊C₄×C₇₉	C₂³	1	3	yes	—
127	C₄⋊C₄×C₇₉	C₂³	1	3	yes	—
128	C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
129	C₂²⋊C₄×C₇₉	C₂³	1	3	yes	—
130	C₂²⋊C₄×C₇₉	C₂³	1	6	yes	—
131	C₄²×C₇₉	C₂³	1	3	yes	—
132	C₂³×C₇₉	C₂⁴	1	3	yes	—
133	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
134	C₂²×D₇₉	—	2	6	no	—
135	C₂²×D₇₉	—	2	6	no	—
136	C₂²×D₇₉	—	2	6	no	—
137	C₂²×D₇₉	—	2	6	no	—
138	C₂²×D₇₉	—	4	3	no	—
139	C₂²×D₇₉	—	4	3	no	—
140	C₂²×D₇₉	C₂⁴	1	3	yes	—
141	C₂²×D₇₉	C₂⁴	1	3	yes	—
142	C₂²×D₇₉	C₂⁴	1	1	yes	characteristic
143	Q₈×C₇₉	—	2	6	no	—
144	Q₈×C₇₉	C₂×D₄	1	4	yes	complemented
145	D₄×C₇₉	—	2	6	no	—
146	D₄×C₇₉	—	2	6	no	—
147	C₂×C₄×C₇₉	—	2	6	no	—
148	C₂×C₄×C₇₉	—	2	6	no	—
149	C₂×C₄×C₇₉	C₂⁴	1	3	yes	—
150	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
151	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
152	C₂×C₄×C₇₉	C₂⁴	1	3	yes	—
153	C₂×C₄×C₇₉	C₂⁴	1	3	yes	—
154	C₂²⋊D₇₉	—	2	12	no	—
155	C₂²⋊D₇₉	—	2	6	no	—
156	C₂²⋊D₇₉	—	4	6	no	—
157	C₂²⋊D₇₉	#41	1	4	yes	complemented
158	C₂×Dic₇₉	—	2	2	no	—
159	C₂×Dic₇₉	—	2	6	no	—
160	C₂×Dic₇₉	C₂⁴	1	3	yes	—
161	C₂×Dic₇₉	C₂⁴	1	3	yes	—
162	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
163	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
164	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
165	D₃₁₆	—	2	12	no	—
166	D₃₁₆	—	2	6	no	—
167	D₃₁₆	—	2	6	no	—
168	D₃₁₆	C₂×D₄	1	12	yes	complemented
169	C₄×D₇₉	—	2	6	no	—
170	C₄×D₇₉	—	2	6	no	—
171	C₄×D₇₉	—	2	6	no	—
172	C₄×D₇₉	—	2	6	no	—
173	C₄×D₇₉	—	2	2	no	—
174	C₄×D₇₉	—	2	6	no	—
175	C₄×D₇₉	—	2	6	no	—
176	C₄×D₇₉	—	4	3	no	—
177	C₄×D₇₉	C₂×D₄	1	12	yes	complemented
178	Dic₁₅₈	—	2	6	no	—
179	C₂²×C₇₉	—	2	1	no	—
180	C₂²×C₇₉	—	2	1	no	—
181	C₂²×C₇₉	—	2	3	no	—
182	C₂²×C₇₉	—	2	3	no	—
183	C₂²×C₇₉	—	2	3	no	—
184	C₂²×C₇₉	C₂×#41	1	2	yes	complemented
185	C₂²×C₇₉	C₂⁵	1	1	yes	characteristic
186	C₂×D₇₉	—	2	1	no	—
187	C₂×D₇₉	—	2	3	no	—
188	C₂×D₇₉	—	2	1	no	—
189	C₂×D₇₉	—	2	3	no	—
190	C₂×D₇₉	—	2	3	no	—
191	C₂×D₇₉	—	2	3	no	—
192	C₂×D₇₉	—	2	3	no	—
193	C₂×D₇₉	—	4	12	no	—
194	C₂×D₇₉	—	4	12	no	—
195	C₂×D₇₉	C₂²×D₄	1	6	yes	—
196	C₂×D₇₉	C₂×#41	1	2	yes	complemented
197	C₄×C₇₉	—	2	1	no	—
198	C₄×C₇₉	—	2	3	no	—
199	C₄×C₇₉	—	2	3	no	—
200	C₄×C₇₉	—	2	1	no	—
201	C₄×C₇₉	C₂²×D₄	1	6	yes	—
202	Dic₇₉	—	2	3	no	—
203	Dic₇₉	—	2	1	no	—
204	Dic₇₉	—	2	3	no	—
205	Dic₇₉	C₂²×D₄	1	2	yes	—
206	Dic₇₉	C₂×#41	1	2	yes	complemented
207	C₂×C₇₉	—	2	2	no	—
208	C₂×C₇₉	—	4	3	no	—
209	C₂×C₇₉	C₂³×D₄	1	1	yes	characteristic
210	C₂×C₇₉	C₂²×#41	1	1	yes	characteristic
211	C₂×C₇₉	#585	1	1	yes	characteristic
212	D₇₉	—	2	2	no	—
213	D₇₉	—	2	6	no	—
214	D₇₉	—	4	3	no	—
215	D₄×#41	—	79	1	no	maximal, Sylow
216	C₇₉	D₄×#41	1	1	yes	characteristic, complemented, Sylow
217	C₂²×#41	—	79	1	no	—
218	C₂²×#41	—	79	1	no	—
219	#550	—	79	1	no	—
220	D₄×Q₈	—	79	1	no	—
221	#548	—	79	1	no	—
222	#548	D₇₉	1	1	yes	characteristic, complemented
223	#547	—	79	3	no	—
224	#546	—	79	3	no	—
225	#546	—	79	3	no	—
226	D₄²	—	79	3	no	—
227	#532	—	79	3	no	—
228	#525	—	79	3	no	—
229	#525	—	79	3	no	—
230	C₄×#41	—	79	1	no	—
231	C₂×C₄×D₄	—	79	3	no	—
232	C₂×#41	—	79	1	no	—
233	C₂×#41	—	79	3	no	—
234	C₂×#41	—	79	3	no	—
235	C₂×#41	—	79	1	no	—
236	C₂×#41	—	79	3	no	—
237	C₂×#41	—	79	3	no	—
238	C₂×#41	—	158	8	no	—
239	C₂×#41	—	158	8	no	—
240	C₂×#41	C₂×D₇₉	1	1	yes	characteristic, complemented
241	C₂²×Q₈	—	79	1	no	—
242	C₂²×Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
243	C₂²×D₄	—	79	3	no	—
244	C₂²×D₄	—	79	3	no	—
245	C₂²×D₄	—	79	3	no	—
246	C₂³×C₄	—	79	3	no	—
247	C₂³×C₄	—	79	3	no	—
248	C₄⋊Q₈	—	79	3	no	—
249	#127	—	79	3	no	—
250	#124	—	79	3	no	—
251	#124	C₂×D₇₉	1	3	yes	complemented
252	#123	—	79	6	no	—
253	#123	—	79	6	no	—
254	C₂²⋊Q₈	—	79	3	no	—
255	C₂²⋊Q₈	—	79	3	no	—
256	C₂²⋊Q₈	—	79	3	no	—
257	C₂²⋊Q₈	C₂×D₇₉	1	3	yes	complemented
258	#121	—	79	3	no	—
259	#121	—	79	3	no	—
260	#121	—	79	3	no	—
261	#121	—	79	6	no	—
262	#121	—	79	6	no	—
263	#121	C₂×D₇₉	1	3	yes	complemented
264	#120	—	79	6	no	—
265	#120	—	79	6	no	—
266	C₄×Q₈	—	79	1	no	—
267	C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
268	C₄×D₄	—	79	3	no	—
269	C₄×D₄	—	79	3	no	—
270	C₄×D₄	—	79	3	no	—
271	C₄×D₄	—	79	3	no	—
272	C₄×D₄	—	79	3	no	—
273	C₄×D₄	—	79	1	no	—
274	C₄×D₄	—	79	3	no	—
275	C₄×D₄	—	79	6	no	—
276	C₄×D₄	—	79	3	no	—
277	C₄×D₄	—	79	3	no	—
278	C₄×D₄	C₂×D₇₉	1	3	yes	complemented
279	#117	—	79	3	no	—
280	C₂×C₄⋊C₄	—	79	3	no	—
281	C₂×C₂²⋊C₄	—	79	3	no	—
282	C₂×C₂²⋊C₄	—	79	3	no	—
283	C₂×C₄²	—	79	3	no	—
284	C₂⁴	—	79	3	no	—
285	C₂⁴	—	79	3	no	—
286	#41	—	2	4	no	—
287	#41	—	79	8	no	—
288	#41	—	158	12	no	—
289	#41	—	158	12	no	—
290	#41	—	158	12	no	—
291	#41	—	158	12	no	—
292	#41	—	158	4	no	—
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	—	79	3	no	—
295	C₂×Q₈	—	158	4	no	—
296	C₂×Q₈	C₂²×D₇₉	1	3	yes	—
297	C₂×Q₈	C₂²×D₇₉	1	1	yes	characteristic
298	C₂×D₄	—	79	6	no	—
299	C₂×D₄	—	79	1	no	—
300	C₂×D₄	—	79	3	no	—
301	C₂×D₄	—	79	6	no	—
302	C₂×D₄	—	79	3	no	—
303	C₂×D₄	—	79	3	no	—
304	C₂×D₄	—	79	6	no	—
305	C₂×D₄	—	79	3	no	—
306	C₂×D₄	—	158	12	no	—
307	C₂×D₄	—	158	12	no	—
308	C₂×D₄	—	158	12	no	—
309	C₂×D₄	C₂²×D₇₉	1	3	yes	—
310	C₂×D₄	C₂²×D₇₉	1	3	yes	—
311	C₂²×C₄	—	79	3	no	—
312	C₂²×C₄	—	79	3	no	—
313	C₂²×C₄	—	79	1	no	—
314	C₂²×C₄	—	79	3	no	—
315	C₂²×C₄	—	79	3	no	—
316	C₂²×C₄	—	79	3	no	—
317	C₂²×C₄	—	79	3	no	—
318	C₂²×C₄	—	79	1	no	—
319	C₂²×C₄	—	79	3	no	—
320	C₂²×C₄	—	79	3	no	—
321	C₂²×C₄	—	79	3	no	—
322	C₂²×C₄	—	158	12	no	—
323	C₂²×C₄	—	158	12	no	—
324	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
325	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
326	C₄⋊C₄	—	79	1	no	—
327	C₄⋊C₄	—	79	3	no	—
328	C₄⋊C₄	—	79	6	no	—
329	C₄⋊C₄	—	79	3	no	—
330	C₄⋊C₄	—	79	3	no	—
331	C₄⋊C₄	C₂²×D₇₉	1	3	yes	—
332	C₄⋊C₄	C₂²×D₇₉	1	3	yes	—
333	C₂²⋊C₄	—	79	3	no	—
334	C₂²⋊C₄	—	79	3	no	—
335	C₂²⋊C₄	—	79	1	no	—
336	C₂²⋊C₄	—	79	3	no	—
337	C₂²⋊C₄	—	79	3	no	—
338	C₂²⋊C₄	—	79	3	no	—
339	C₂²⋊C₄	—	79	6	no	—
340	C₂²⋊C₄	—	79	6	no	—
341	C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
342	C₂²⋊C₄	C₂²×D₇₉	1	3	yes	—
343	C₂²⋊C₄	C₂²×D₇₉	1	6	yes	—
344	C₄²	—	79	1	no	—
345	C₄²	—	79	3	no	—
346	C₄²	—	79	3	no	—
347	C₄²	C₂²×D₇₉	1	3	yes	—
348	C₂³	—	316	3	no	—
349	C₂³	—	316	3	no	—
350	C₂³	—	79	1	no	—
351	C₂³	—	79	3	no	—
352	C₂³	—	79	3	no	—
353	C₂³	—	158	6	no	—
354	C₂³	—	158	6	no	—
355	C₂³	—	158	6	no	—
356	C₂³	—	158	6	no	—
357	C₂³	C₂³×D₇₉	1	3	yes	—
358	C₂³	C₂³×D₇₉	1	1	yes	characteristic
359	Q₈	—	2	6	no	—
360	Q₈	—	158	6	no	—
361	Q₈	D₄×D₇₉	1	4	yes	complemented
362	D₄	—	2	6	no	—
363	D₄	—	2	6	no	—
364	D₄	—	316	6	no	—
365	D₄	—	79	4	no	—
366	D₄	—	79	12	no	—
367	D₄	—	158	12	no	—
368	D₄	—	158	6	no	—
369	D₄	—	158	6	no	—
370	D₄	—	158	12	no	—
371	D₄	—	158	6	no	—
372	C₂×C₄	—	2	6	no	—
373	C₂×C₄	—	2	6	no	—
374	C₂×C₄	—	316	3	no	—
375	C₂×C₄	—	79	1	no	—
376	C₂×C₄	—	79	1	no	—
377	C₂×C₄	—	79	12	no	—
378	C₂×C₄	—	79	3	no	—
379	C₂×C₄	—	79	1	no	—
380	C₂×C₄	—	79	3	no	—
381	C₂×C₄	—	158	2	no	—
382	C₂×C₄	—	158	6	no	—
383	C₂×C₄	—	158	6	no	—
384	C₂×C₄	—	158	6	no	—
385	C₂×C₄	—	158	6	no	—
386	C₂×C₄	—	158	2	no	—
387	C₂×C₄	—	158	6	no	—
388	C₂×C₄	—	158	6	no	—
389	C₂×C₄	—	158	6	no	—
390	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
391	C₂×C₄	C₂³×D₇₉	1	3	yes	—
392	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
393	C₂×C₄	C₂³×D₇₉	1	3	yes	—
394	C₂×C₄	C₂³×D₇₉	1	3	yes	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	3	no	—
398	C₂²	—	2	3	no	—
399	C₂²	—	2	3	no	—
400	C₂²	—	316	12	no	—
401	C₂²	—	316	12	no	—
402	C₂²	—	79	6	no	—
403	C₂²	—	79	2	no	—
404	C₂²	—	158	3	no	—
405	C₂²	—	158	3	no	—
406	C₂²	—	158	3	no	—
407	C₂²	—	158	3	no	—
408	C₂²	—	158	1	no	—
409	C₂²	—	158	1	no	—
410	C₂²	—	158	3	no	—
411	C₂²	#41×D₇₉	1	2	yes	complemented
412	C₂²	C₂⁴×D₇₉	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	3	no	—
416	C₄	—	2	3	no	—
417	C₄	—	79	2	no	—
418	C₄	—	79	2	no	—
419	C₄	—	158	3	no	—
420	C₄	—	158	1	no	—
421	C₄	—	158	3	no	—
422	C₄	C₂×D₄×D₇₉	1	6	yes	—
423	C₂	—	2	2	no	—
424	C₂	—	4	3	no	—
425	C₂	—	316	3	no	—
426	C₂	—	158	2	no	—
427	C₂	—	158	6	no	—
428	C₂	C₂²×D₄×D₇₉	1	1	yes	characteristic
429	C₂	C₂×#41×D₇₉	1	1	yes	characteristic
430	C₂	#19099400	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁵
Fitting	#548×C₇₉	C₂
hypercenter	#548	D₇₉
hypocenter	C₇₉	D₄×#41
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #548

Complements

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

N	H ≅ G/N	type
1. C₂²×#11929625	C₂	semidirect
2. C₂×#41×D₇₉	C₂	semidirect
3. #19099232	C₂	semidirect
4. Q₈×C₂²⋊D₇₉	C₂	semidirect
5. #19099225	C₂	semidirect
6. #19099215	C₂	semidirect
7. #19099209	C₂	semidirect
8. #19099206	C₂	semidirect
9. #19099197	C₂	semidirect
10. #19099112	C₂	semidirect
11. #19099076	C₂	semidirect
12. #19099073	C₂	semidirect
13. C₄×#11929625	C₂	semidirect
14. C₄×D₄×D₇₉	C₂	semidirect
15. #548×C₇₉	C₂	semidirect
18. C₂×#11929625	C₂²	semidirect
19. C₂×#11929625	C₂²	semidirect
20. C₂×#11929625	C₂²	semidirect
21. C₂×#11929624	C₂²	semidirect
22. C₂×#11929623	C₂²	semidirect
24. C₂×Q₈×D₇₉	C₂²	semidirect
25. C₂²×D₃₁₆	C₂²	semidirect
27. C₂×D₄×D₇₉	C₂²	semidirect
28. C₂²×C₄×D₇₉	C₂²	semidirect
29. C₂²×C₄×D₇₉	C₂²	semidirect
30. #14579159	C₂²	semidirect
31. #14579157	C₂²	semidirect
32. #14579149	C₂²	semidirect
33. #14579146	C₂²	semidirect
34. #14579143	C₂²	semidirect
35. #14579141	C₂²	semidirect
36. #14579140	C₂²	semidirect
37. #14579137	C₂²	semidirect
38. #14579136	C₂²	semidirect
39. #14579135	C₂²	semidirect
40. #14579134	C₂²	semidirect
41. #14579134	C₂²	semidirect
42. #14579132	C₂²	semidirect
43. #14579131	C₂²	semidirect
44. #14579129	C₂²	semidirect
45. Q₈×Dic₇₉	C₂²	semidirect
46. C₄×D₃₁₆	C₂²	semidirect
47. C₄×D₃₁₆	C₂²	semidirect
48. D₄×Dic₇₉	C₂²	semidirect
49. #14579123	C₂²	semidirect
50. #14579123	C₂²	semidirect
52. C₄×C₂²⋊D₇₉	C₂²	semidirect
54. (C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
55. (C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
56. #14579119	C₂²	semidirect
57. C₄⋊C₄×D₇₉	C₂²	semidirect
58. C₂²⋊C₄×D₇₉	C₂²	semidirect
59. C₂²⋊C₄×D₇₉	C₂²	semidirect
60. C₄²×D₇₉	C₂²	semidirect
61. C₂×#41×C₇₉	C₂²	semidirect
62. C₂²×Q₈×C₇₉	C₂²	semidirect
63. #124×C₇₉	C₂²	semidirect
64. C₂²⋊Q₈×C₇₉	C₂²	semidirect
65. #121×C₇₉	C₂²	semidirect
66. C₄×Q₈×C₇₉	C₂²	semidirect
67. C₄×D₄×C₇₉	C₂²	semidirect
73. #11929625	D₄	semidirect
144. Q₈×C₇₉	C₂×D₄	semidirect
157. C₂²⋊D₇₉	#41	semidirect
168. D₃₁₆	C₂×D₄	semidirect
177. C₄×D₇₉	C₂×D₄	semidirect
184. C₂²×C₇₉	C₂×#41	semidirect
196. C₂×D₇₉	C₂×#41	semidirect
206. Dic₇₉	C₂×#41	semidirect
216. C₇₉	D₄×#41	semidirect
222. #548	D₇₉	semidirect
240. C₂×#41	C₂×D₇₉	semidirect
242. C₂²×Q₈	C₂×D₇₉	semidirect
251. #124	C₂×D₇₉	semidirect
257. C₂²⋊Q₈	C₂×D₇₉	semidirect
263. #121	C₂×D₇₉	semidirect
267. C₄×Q₈	C₂×D₇₉	semidirect
278. C₄×D₄	C₂×D₇₉	semidirect
361. Q₈	D₄×D₇₉	semidirect
411. C₂²	#41×D₇₉	semidirect