Subgroups — #34442536

Order 20224.

718 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098993	C₂	1	2	yes	maximal, complemented
2	#23773828	C₂	1	1	yes	maximal, characteristic, complemented
3	#23765462	C₂	1	2	yes	maximal, complemented
4	#23765455	C₂	1	2	yes	maximal, complemented
5	#23765450	C₂	1	1	yes	maximal, characteristic, complemented
6	#23765445	C₂	1	1	yes	maximal, characteristic, complemented
7	#23765440	C₂	1	1	yes	maximal, characteristic, complemented
8	#23765435	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄⋊(C₇₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
10	#23765105	C₂	1	2	yes	maximal, complemented
11	C₄×#135×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579183	—	2	1	no	—
13	C₂×#14579183	C₂²	1	2	yes	—
14	#19099113	—	2	1	no	—
15	#19098993	—	2	8	no	—
16	C₂×#14579107	C₂²	1	2	yes	—
17	C₂×#14579105	C₂²	1	2	yes	—
18	C₂×#14579104	C₂²	1	2	yes	—
19	C₂×#14579102	C₂²	1	2	yes	—
20	C₂²×C₇₉⋊C₁₆	C₂²	1	2	yes	—
21	#19098947	—	2	1	no	—
22	#19098947	C₂²	1	2	yes	—
23	#19098943	C₂²	1	1	yes	characteristic
24	#19098940	C₂²	1	1	yes	characteristic
25	#19098936	—	2	1	no	—
26	C₄⋊(C₇₉⋊C₁₆)	C₂²	1	1	yes	characteristic
27	C₄⋊(C₇₉⋊C₁₆)	C₂²	1	1	yes	characteristic
28	C₄⋊(C₇₉⋊C₁₆)	C₂²	1	2	yes	—
29	#19098366	C₂²	1	2	yes	—
30	#19098366	C₂²	1	2	yes	—
31	#19098363	C₂²	1	2	yes	—
32	#19098363	C₂²	1	2	yes	—
33	C₂×#135×C₇₉	C₂²	1	1	yes	characteristic
34	C₄×#41×C₇₉	—	2	1	no	—
35	C₄×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
36	C₄×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
37	C₄×SD₁₆×C₇₉	—	2	1	no	—
38	C₄×SD₁₆×C₇₉	—	2	1	no	—
39	C₄×D₈×C₇₉	C₂²	1	1	yes	characteristic
40	C₄×D₈×C₇₉	C₂²	1	1	yes	characteristic
41	#427×C₇₉	C₂²	1	1	yes	characteristic
42	#416×C₇₉	—	2	1	no	—
43	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
44	C₂×#11929624	—	2	2	no	—
45	#14579183	—	2	4	no	—
46	#14579183	—	2	4	no	—
47	#14579183	—	4	4	no	—
48	C₂×Dic₃₁₆	—	2	1	no	—
49	C₂×Dic₃₁₆	C₂³	1	2	yes	—
50	C₂×#11929613	—	2	2	no	—
51	C₂×#11929613	—	2	2	no	—
52	C₂×D₆₃₂	—	2	1	no	—
53	C₂×D₆₃₂	C₂³	1	2	yes	—
54	#14579161	—	2	1	no	—
55	#14579158	—	2	1	no	—
56	#14579149	—	2	2	no	—
57	#14579135	—	4	1	no	—
58	#14579135	—	4	1	no	—
59	C₄×D₃₁₆	—	4	1	no	—
60	C₄×D₃₁₆	—	4	1	no	—
61	#14579107	—	2	4	no	—
62	#14579105	—	2	4	no	—
63	#14579104	—	2	4	no	—
64	#14579102	—	2	4	no	—
65	C₂×C₇₉⋊C₁₆	—	2	4	no	—
66	C₂×C₇₉⋊C₁₆	C₂³	1	2	yes	—
67	C₂×C₇₉⋊C₁₆	C₂³	1	2	yes	—
68	C₂×#41×C₇₉	—	2	1	no	—
69	#135×C₇₉	—	2	2	no	—
70	#135×C₇₉	D₄	1	4	yes	complemented
71	C₂×Q₁₆×C₇₉	C₂³	1	1	yes	characteristic
72	C₂×SD₁₆×C₇₉	—	2	1	no	—
73	C₂×D₈×C₇₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
75	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
76	C₄×Q₈×C₇₉	—	2	1	no	—
77	C₄×Q₈×C₇₉	—	2	1	no	—
78	C₄×D₄×C₇₉	—	2	1	no	—
79	C₄×D₄×C₇₉	—	2	1	no	—
80	C₄×D₄×C₇₉	—	4	1	no	—
81	C₄×D₄×C₇₉	—	4	1	no	—
82	#117×C₇₉	—	2	1	no	—
83	#117×C₇₉	—	4	1	no	—
84	C₂×C₄²×C₇₉	—	4	1	no	—
85	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
86	#107×C₇₉	C₂³	1	1	yes	characteristic
87	#107×C₇₉	C₂³	1	1	yes	characteristic
88	#106×C₇₉	—	2	1	no	—
89	#103×C₇₉	—	2	1	no	—
90	#103×C₇₉	—	2	1	no	—
91	#102×C₇₉	—	2	1	no	—
92	#102×C₇₉	—	2	1	no	—
93	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
94	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
95	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
97	#11929624	—	4	4	no	—
98	#11929624	—	4	4	no	—
99	C₂×Dic₁₅₈	—	2	2	no	—
100	C₂×D₃₁₆	—	2	2	no	—
101	C₂×D₃₁₆	—	4	1	no	—
102	C₂×D₃₁₆	—	4	1	no	—
103	C₂×C₂²⋊D₇₉	—	4	2	no	—
104	C₂×C₄×D₇₉	—	4	2	no	—
105	Dic₃₁₆	—	2	2	no	—
106	Dic₃₁₆	—	2	2	no	—
107	Dic₃₁₆	—	4	2	no	—
108	#11929613	—	4	4	no	—
109	#11929613	—	4	4	no	—
110	D₆₃₂	—	2	2	no	—
111	D₆₃₂	—	2	2	no	—
112	D₆₃₂	—	4	2	no	—
113	C₄⋊Dic₇₉	—	4	1	no	—
114	C₄⋊Dic₇₉	—	4	1	no	—
115	(C₂×D₇₉)⋊C₄	—	4	2	no	—
116	(C₂×D₇₉)⋊C₄	—	4	2	no	—
117	C₇₉⋊C₁₆	—	2	2	no	—
118	C₇₉⋊C₁₆	—	2	2	no	—
119	#41×C₇₉	—	2	4	no	—
120	#41×C₇₉	—	4	2	no	—
121	C₂×Q₈×C₇₉	—	2	1	no	—
122	C₂×D₄×C₇₉	—	2	1	no	—
123	C₂×D₄×C₇₉	—	4	1	no	—
124	C₂²×C₄×C₇₉	—	4	1	no	—
125	C₂²×C₄×C₇₉	—	4	1	no	—
126	C₂²×C₄×C₇₉	—	4	1	no	—
127	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
128	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
129	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
130	Q₁₆×C₇₉	—	2	1	no	—
131	Q₁₆×C₇₉	C₂×D₄	1	2	yes	—
132	SD₁₆×C₇₉	—	2	4	no	—
133	D₈×C₇₉	—	2	1	no	—
134	D₈×C₇₉	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₇₉	—	2	2	no	—
136	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₇₉	#41	1	2	yes	—
141	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
142	C₄⋊C₄×C₇₉	—	2	1	no	—
143	C₄⋊C₄×C₇₉	—	2	1	no	—
144	C₄⋊C₄×C₇₉	—	4	1	no	—
145	C₄⋊C₄×C₇₉	—	4	1	no	—
146	C₂²⋊C₄×C₇₉	—	4	1	no	—
147	C₂²⋊C₄×C₇₉	—	4	1	no	—
148	C₂²⋊C₄×C₇₉	—	4	1	no	—
149	C₄²×C₇₉	—	4	1	no	—
150	C₄²×C₇₉	—	4	1	no	—
151	C₄²×C₇₉	—	4	1	no	—
152	C₄²×C₇₉	D₈	1	1	yes	characteristic
153	C₄²×C₇₉	D₈	1	1	yes	characteristic
154	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
156	C₂³×C₇₉	—	4	1	no	—
157	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
158	C₂²×D₇₉	—	4	2	no	—
159	Q₈×C₇₉	—	2	2	no	—
160	Q₈×C₇₉	—	4	1	no	—
161	D₄×C₇₉	—	2	2	no	—
162	D₄×C₇₉	—	4	4	no	—
163	D₄×C₇₉	—	4	1	no	—
164	C₂×C₄×C₇₉	—	2	2	no	—
165	C₂×C₄×C₇₉	—	4	1	no	—
166	C₂×C₄×C₇₉	—	4	1	no	—
167	C₂×C₄×C₇₉	—	4	4	no	—
168	C₂×C₄×C₇₉	—	4	1	no	—
169	C₂×C₄×C₇₉	—	4	1	no	—
170	C₂×C₄×C₇₉	—	8	2	no	—
171	C₂×C₄×C₇₉	—	8	2	no	—
172	C₂×C₄×C₇₉	#121	1	2	yes	—
173	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
175	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
176	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
177	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
178	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
179	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
180	C₂²⋊D₇₉	—	8	4	no	—
181	C₂×Dic₇₉	—	4	2	no	—
182	D₃₁₆	—	4	2	no	—
183	D₃₁₆	—	4	2	no	—
184	D₃₁₆	—	8	2	no	—
185	D₃₁₆	—	8	2	no	—
186	C₄×D₇₉	—	8	4	no	—
187	Dic₁₅₈	—	4	2	no	—
188	Dic₁₅₈	—	4	2	no	—
189	C₈×C₇₉	—	2	1	no	—
190	C₈×C₇₉	—	2	1	no	—
191	C₈×C₇₉	#121	1	2	yes	—
192	C₈×C₇₉	C₂²×D₄	1	1	yes	characteristic
193	C₈×C₇₉	C₂×#41	1	1	yes	characteristic
194	C₂²×C₇₉	—	2	1	no	—
195	C₂²×C₇₉	—	2	1	no	—
196	C₂²×C₇₉	—	4	2	no	—
197	C₂²×C₇₉	—	8	1	no	—
198	C₂²×C₇₉	—	8	1	no	—
199	C₂²×C₇₉	#459	1	2	yes	—
200	C₂²×C₇₉	C₂²×D₈	1	1	yes	characteristic
201	C₂×D₇₉	—	8	2	no	—
202	C₂×D₇₉	—	8	2	no	—
203	C₂×D₇₉	—	8	2	no	—
204	C₄×C₇₉	—	2	1	no	—
205	C₄×C₇₉	—	2	1	no	—
206	C₄×C₇₉	—	2	1	no	—
207	C₄×C₇₉	—	4	2	no	—
208	C₄×C₇₉	—	8	1	no	—
209	C₄×C₇₉	—	8	1	no	—
210	C₄×C₇₉	#459	1	2	yes	—
211	C₄×C₇₉	#508	1	2	yes	complemented
212	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
213	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
214	Dic₇₉	—	8	2	no	—
215	#33579	—	79	1	no	maximal, Sylow
216	C₂×C₇₉	—	2	2	no	—
217	C₂×C₇₉	—	8	2	no	—
218	C₂×C₇₉	C₂×#459	1	1	yes	characteristic
219	C₂×C₇₉	C₂×#508	1	1	yes	characteristic
220	C₂×C₇₉	#3414	1	1	yes	characteristic
221	D₇₉	—	16	2	no	—
222	C₂×#508	—	79	2	no	—
223	#3147	—	79	1	no	—
224	C₄×#135	D₇₉	1	1	yes	characteristic, complemented
225	#2211	—	79	2	no	—
226	#2210	—	79	2	no	—
227	#2209	—	79	1	no	—
228	#2208	—	79	1	no	—
229	#2207	—	79	1	no	—
230	#2206	—	79	1	no	—
231	C₂×C₄⋊C₁₆	—	79	1	no	—
232	#2138	—	79	2	no	—
233	C₇₉	#33579	1	1	yes	characteristic, complemented, Sylow
234	C₂×#135	—	79	2	no	—
235	C₂×#135	—	158	1	no	—
236	C₂×#135	C₂×D₇₉	1	1	yes	characteristic
237	#532	—	158	1	no	—
238	C₄×#41	—	2	1	no	—
239	#508	—	158	8	no	—
240	C₂×Q₃₂	—	79	2	no	—
241	C₂×SD₃₂	—	79	2	no	—
242	C₂×SD₃₂	—	79	2	no	—
243	C₂×D₁₆	—	79	2	no	—
244	C₂²×C₁₆	—	79	2	no	—
245	#495	—	79	2	no	—
246	#495	—	158	1	no	—
247	#494	—	79	1	no	—
248	#493	—	79	1	no	—
249	#492	—	158	1	no	—
250	C₄×Q₁₆	C₂×D₇₉	1	1	yes	characteristic
251	C₄×Q₁₆	C₂×D₇₉	1	1	yes	characteristic
252	C₄×SD₁₆	—	2	1	no	—
253	C₄×SD₁₆	—	2	1	no	—
254	C₄×D₈	C₂×D₇₉	1	1	yes	characteristic
255	C₄×D₈	C₂×D₇₉	1	1	yes	characteristic
256	#427	C₂×D₇₉	1	1	yes	characteristic
257	#416	—	2	1	no	—
258	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
259	C₄⋊C₁₆	—	79	1	no	—
260	C₄⋊C₁₆	—	79	1	no	—
261	C₄⋊C₁₆	—	79	2	no	—
262	#358	—	79	2	no	—
263	#358	—	79	2	no	—
264	#357	—	79	2	no	—
265	#357	—	79	2	no	—
266	C₂×#41	—	2	1	no	—
267	C₂×#41	—	158	2	no	—
268	#135	—	2	2	no	—
269	#135	—	316	4	no	—
270	#135	—	158	4	no	—
271	#135	—	158	4	no	—
272	#135	D₃₁₆	1	4	yes	complemented
273	C₂×Q₁₆	—	79	2	no	—
274	C₂×Q₁₆	—	158	1	no	—
275	C₂×Q₁₆	C₂²×D₇₉	1	1	yes	characteristic
276	C₂×SD₁₆	—	2	1	no	—
277	C₂×SD₁₆	—	158	2	no	—
278	C₂×SD₁₆	—	158	2	no	—
279	C₂×D₈	—	79	2	no	—
280	C₂×D₈	—	158	1	no	—
281	C₂×D₈	C₂²×D₇₉	1	1	yes	characteristic
282	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
283	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
284	C₄⋊Q₈	—	158	1	no	—
285	#127	—	158	1	no	—
286	#124	—	158	2	no	—
287	#121	—	316	1	no	—
288	#121	—	316	1	no	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	—	4	1	no	—
294	C₄×D₄	—	4	1	no	—
295	C₄×D₄	—	316	1	no	—
296	C₄×D₄	—	316	1	no	—
297	#117	—	2	1	no	—
298	#117	—	4	1	no	—
299	C₂×C₄²	—	4	1	no	—
300	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
301	Q₃₂	—	158	4	no	—
302	SD₃₂	—	158	4	no	—
303	SD₃₂	—	158	4	no	—
304	D₁₆	—	158	4	no	—
305	C₂×C₁₆	—	79	2	no	—
306	C₂×C₁₆	—	79	2	no	—
307	C₂×C₁₆	—	158	4	no	—
308	#107	C₂²×D₇₉	1	1	yes	characteristic
309	#107	C₂²×D₇₉	1	1	yes	characteristic
310	#106	—	2	1	no	—
311	#103	—	2	1	no	—
312	#103	—	2	1	no	—
313	#102	—	2	1	no	—
314	#102	—	2	1	no	—
315	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
316	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
317	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
318	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
319	#41	—	2	4	no	—
320	#41	—	4	2	no	—
321	#41	—	316	4	no	—
322	#41	—	316	4	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	158	2	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	316	2	no	—
328	C₂×D₄	—	316	1	no	—
329	C₂×D₄	—	316	1	no	—
330	C₂×D₄	—	158	2	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	—	4	1	no	—
334	C₂²×C₄	—	316	2	no	—
335	C₂²×C₄	#11929609	1	1	yes	characteristic
336	C₂²×C₄	#11929609	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
338	Q₁₆	—	2	1	no	—
339	Q₁₆	—	316	2	no	—
340	Q₁₆	—	158	2	no	—
341	Q₁₆	—	158	2	no	—
342	Q₁₆	C₂×D₃₁₆	1	2	yes	—
343	SD₁₆	—	2	4	no	—
344	SD₁₆	—	316	4	no	—
345	SD₁₆	—	316	4	no	—
346	D₈	—	2	1	no	—
347	D₈	—	316	2	no	—
348	D₈	—	158	2	no	—
349	D₈	—	158	2	no	—
350	D₈	C₂×D₃₁₆	1	2	yes	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
353	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
354	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
355	C₂×C₈	C₂×D₃₁₆	1	2	yes	—
356	C₂×C₈	#11929624	1	2	yes	—
357	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₄⋊C₄	—	316	1	no	—
363	C₄⋊C₄	—	316	1	no	—
364	C₂²⋊C₄	—	4	1	no	—
365	C₂²⋊C₄	—	4	1	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₂²⋊C₄	—	316	2	no	—
368	C₂²⋊C₄	—	316	2	no	—
369	C₄²	—	4	1	no	—
370	C₄²	—	4	1	no	—
371	C₄²	—	4	1	no	—
372	C₄²	#11929609	1	1	yes	characteristic
373	C₄²	#11929609	1	1	yes	characteristic
374	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
375	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
376	C₁₆	—	158	2	no	—
377	C₁₆	—	158	2	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	316	2	no	—
380	C₂³	C₂×#11929609	1	1	yes	characteristic
381	Q₈	—	2	2	no	—
382	Q₈	—	4	1	no	—
383	Q₈	—	316	2	no	—
384	Q₈	—	316	2	no	—
385	D₄	—	2	2	no	—
386	D₄	—	4	4	no	—
387	D₄	—	4	1	no	—
388	D₄	—	316	2	no	—
389	D₄	—	316	2	no	—
390	D₄	—	632	2	no	—
391	D₄	—	632	4	no	—
392	D₄	—	632	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	8	2	no	—
400	C₂×C₄	—	8	2	no	—
401	C₂×C₄	—	316	2	no	—
402	C₂×C₄	—	632	4	no	—
403	C₂×C₄	#14579135	1	2	yes	—
404	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
405	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
406	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
407	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
408	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
409	C₂×C₄	#14579186	1	2	yes	—
410	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	#14579135	1	2	yes	—
414	C₈	C₂²×D₃₁₆	1	1	yes	characteristic
415	C₈	C₂×#11929624	1	1	yes	characteristic
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	632	2	no	—
422	C₂²	—	632	2	no	—
423	C₂²	—	632	2	no	—
424	C₂²	#19098758	1	2	yes	—
425	C₂²	C₂²×#11929609	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	4	2	no	—
430	C₄	—	8	1	no	—
431	C₄	—	8	1	no	—
432	C₄	—	632	2	no	—
433	C₄	#19098758	1	2	yes	—
434	C₄	#19098993	1	2	yes	complemented
435	C₄	C₂×#14579135	1	1	yes	characteristic
436	C₄	C₂×#14579186	1	1	yes	characteristic
437	C₂	—	2	2	no	—
438	C₂	—	8	2	no	—
439	C₂	—	1264	2	no	—
440	C₂	C₂×#19098758	1	1	yes	characteristic
441	C₂	C₂×#19098993	1	1	yes	characteristic
442	C₂	#23776534	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#11929609
commutator, cosocle	C₂×C₈×C₇₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₉
Fitting	C₄×#135×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₈
hypercenter	C₄×#135	D₇₉
hypocenter	C₇₉	#33579
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#19098993	C₂	semidirect
2. #23773828	C₂	semidirect
3. #23765462	C₂	semidirect
4. #23765455	C₂	semidirect
5. #23765450	C₂	semidirect
6. #23765445	C₂	semidirect
7. #23765440	C₂	semidirect
8. #23765435	C₂	semidirect
9. C₂×C₄⋊(C₇₉⋊C₁₆)	C₂	semidirect
10. #23765105	C₂	semidirect
11. C₄×#135×C₇₉	C₂	semidirect
70. #135×C₇₉	D₄	semidirect
211. C₄×C₇₉	#508	semidirect
224. C₄×#135	D₇₉	semidirect
233. C₇₉	#33579	semidirect
272. #135	D₃₁₆	semidirect
434. C₄	#19098993	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098993	2
#23773828	2
#23765462	2
#23765455	2
#23765450	2
#23765445	2
#23765440	2
#23765435	2
C₂×C₄⋊(C₇₉⋊C₁₆)	2
#23765105	2
C₄×#135×C₇₉	2
#33579	79