Subgroups — C₇₃×#32810 #32942214

Order 18688.

866 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2861	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#2858	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2055	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2054	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2025	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2024	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2023	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#2014	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#2012	C₂	1	2	yes	maximal, complemented
10	C₇₃×#2011	C₂	1	1	yes	maximal, characteristic
11	C₇₃×#1831	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
13	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×#124×C₇₃	—	2	1	no	—
18	C₂×#124×C₇₃	—	2	1	no	—
19	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
21	C₂×#103×C₇₃	C₂²	1	2	yes	—
22	C₂×#102×C₇₃	C₂²	1	2	yes	—
23	C₂×#102×C₇₃	C₂²	1	2	yes	—
24	C₂×#102×C₇₃	C₂²	1	2	yes	—
25	#391×C₇₃	C₂²	1	1	yes	characteristic
26	#391×C₇₃	C₂²	1	1	yes	characteristic
27	#390×C₇₃	—	2	1	no	—
28	#390×C₇₃	—	2	1	no	—
29	#390×C₇₃	C₂²	1	1	yes	characteristic
30	#390×C₇₃	C₂²	1	2	yes	—
31	#390×C₇₃	C₂²	1	1	yes	characteristic
32	#390×C₇₃	C₂²	1	2	yes	—
33	#388×C₇₃	—	2	1	no	—
34	#388×C₇₃	—	2	1	no	—
35	#388×C₇₃	—	2	1	no	—
36	#388×C₇₃	—	2	1	no	—
37	C₄³×C₇₃	C₂²	1	1	yes	characteristic
38	#340×C₇₃	C₂²	1	2	yes	—
39	#340×C₇₃	C₂²	1	2	yes	—
40	#336×C₇₃	C₂²	1	1	yes	characteristic
41	#336×C₇₃	C₂²	1	2	yes	—
42	#336×C₇₃	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₇₃	—	2	1	no	—
44	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₇₃	—	2	1	no	—
46	C₂²×D₄×C₇₃	—	2	1	no	—
47	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
49	C₂×SD₁₆×C₇₃	—	4	2	no	—
50	C₂×SD₁₆×C₇₃	—	4	2	no	—
51	C₂×SD₁₆×C₇₃	—	4	2	no	—
52	C₂×D₈×C₇₃	—	4	2	no	—
53	C₂×D₈×C₇₃	—	4	2	no	—
54	C₂×D₈×C₇₃	—	4	2	no	—
55	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₇₃	—	4	2	no	—
58	#127×C₇₃	—	4	2	no	—
59	#125×C₇₃	—	4	2	no	—
60	#124×C₇₃	—	4	2	no	—
61	#124×C₇₃	—	4	4	no	—
62	#124×C₇₃	—	4	4	no	—
63	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
79	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₇₃	—	4	2	no	—
87	#103×C₇₃	—	4	2	no	—
88	#102×C₇₃	—	4	2	no	—
89	#102×C₇₃	—	4	2	no	—
90	#102×C₇₃	—	4	2	no	—
91	#95×C₇₃	—	2	1	no	—
92	#95×C₇₃	—	2	1	no	—
93	#95×C₇₃	—	2	1	no	—
94	#95×C₇₃	—	2	1	no	—
95	C₂⁴×C₇₃	—	2	1	no	—
96	C₂⁴×C₇₃	—	2	2	no	—
97	C₂×Q₈×C₇₃	—	2	2	no	—
98	C₂×Q₈×C₇₃	—	2	2	no	—
99	C₂×Q₈×C₇₃	—	2	1	no	—
100	C₂×Q₈×C₇₃	—	2	1	no	—
101	C₂×Q₈×C₇₃	—	4	2	no	—
102	C₂×Q₈×C₇₃	—	4	2	no	—
103	C₂×Q₈×C₇₃	—	4	2	no	—
104	C₂×D₄×C₇₃	—	2	2	no	—
105	C₂×D₄×C₇₃	—	2	2	no	—
106	C₂×D₄×C₇₃	—	2	2	no	—
107	C₂×D₄×C₇₃	—	2	2	no	—
108	C₂×D₄×C₇₃	—	2	2	no	—
109	C₂×D₄×C₇₃	—	2	2	no	—
110	C₂×D₄×C₇₃	—	2	1	no	—
111	C₂×D₄×C₇₃	—	2	2	no	—
112	C₂×D₄×C₇₃	—	2	1	no	—
113	C₂×D₄×C₇₃	—	2	2	no	—
114	C₂×D₄×C₇₃	—	4	2	no	—
115	C₂×D₄×C₇₃	—	4	2	no	—
116	C₂×D₄×C₇₃	—	4	2	no	—
117	C₂×D₄×C₇₃	—	4	2	no	—
118	C₂×D₄×C₇₃	—	4	2	no	—
119	C₂×D₄×C₇₃	—	4	2	no	—
120	C₂²×C₄×C₇₃	—	2	1	no	—
121	C₂²×C₄×C₇₃	—	2	1	no	—
122	C₂²×C₄×C₇₃	—	2	1	no	—
123	C₂²×C₄×C₇₃	—	2	2	no	—
124	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
131	SD₁₆×C₇₃	—	4	8	no	—
132	D₈×C₇₃	—	4	8	no	—
133	C₂×C₈×C₇₃	—	2	2	no	—
134	C₂×C₈×C₇₃	—	2	2	no	—
135	C₂×C₈×C₇₃	—	2	2	no	—
136	C₂×C₈×C₇₃	—	2	2	no	—
137	C₂×C₈×C₇₃	—	2	2	no	—
138	C₂×C₈×C₇₃	—	2	2	no	—
139	C₄⋊C₄×C₇₃	—	2	2	no	—
140	C₄⋊C₄×C₇₃	—	2	2	no	—
141	C₄⋊C₄×C₇₃	—	2	2	no	—
142	C₄⋊C₄×C₇₃	—	2	2	no	—
143	C₄⋊C₄×C₇₃	—	4	2	no	—
144	C₄⋊C₄×C₇₃	—	4	2	no	—
145	C₄⋊C₄×C₇₃	—	4	2	no	—
146	C₂²⋊C₄×C₇₃	—	4	2	no	—
147	C₂²⋊C₄×C₇₃	—	4	2	no	—
148	C₂²⋊C₄×C₇₃	—	4	2	no	—
149	C₂²⋊C₄×C₇₃	—	4	4	no	—
150	C₂²⋊C₄×C₇₃	—	4	4	no	—
151	C₂²⋊C₄×C₇₃	—	4	4	no	—
152	C₂²⋊C₄×C₇₃	—	4	2	no	—
153	C₂²⋊C₄×C₇₃	—	4	2	no	—
154	C₂²⋊C₄×C₇₃	—	4	2	no	—
155	C₂²⋊C₄×C₇₃	—	4	4	no	—
156	C₄²×C₇₃	—	2	2	no	—
157	C₄²×C₇₃	—	2	2	no	—
158	C₄²×C₇₃	—	2	2	no	—
159	C₄²×C₇₃	—	2	1	no	—
160	C₄²×C₇₃	—	2	2	no	—
161	C₄²×C₇₃	—	2	2	no	—
162	C₄²×C₇₃	—	2	1	no	—
163	C₄²×C₇₃	—	4	1	no	—
164	C₂³×C₇₃	—	4	1	no	—
165	C₂³×C₇₃	—	4	2	no	—
166	C₂³×C₇₃	—	4	2	no	—
167	C₂³×C₇₃	—	4	1	no	—
168	C₂³×C₇₃	—	4	1	no	—
169	C₂³×C₇₃	—	4	2	no	—
170	C₂³×C₇₃	—	4	1	no	—
171	C₂³×C₇₃	—	4	2	no	—
172	C₂³×C₇₃	—	4	2	no	—
173	C₂³×C₇₃	—	4	2	no	—
174	C₂³×C₇₃	—	4	1	no	—
175	C₂³×C₇₃	—	4	1	no	—
176	C₂³×C₇₃	—	4	1	no	—
177	C₂³×C₇₃	—	4	2	no	—
178	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
179	Q₈×C₇₃	—	4	2	no	—
180	Q₈×C₇₃	—	4	2	no	—
181	Q₈×C₇₃	—	8	4	no	—
182	D₄×C₇₃	—	4	2	no	—
183	D₄×C₇₃	—	4	2	no	—
184	D₄×C₇₃	—	4	2	no	—
185	D₄×C₇₃	—	4	2	no	—
186	D₄×C₇₃	—	4	2	no	—
187	D₄×C₇₃	—	4	2	no	—
188	D₄×C₇₃	—	8	4	no	—
189	D₄×C₇₃	—	8	4	no	—
190	C₂×C₄×C₇₃	—	2	1	no	—
191	C₂×C₄×C₇₃	—	2	1	no	—
192	C₂×C₄×C₇₃	—	2	1	no	—
193	C₂×C₄×C₇₃	—	2	1	no	—
194	C₂×C₄×C₇₃	—	2	1	no	—
195	C₂×C₄×C₇₃	—	2	1	no	—
196	C₂×C₄×C₇₃	—	2	1	no	—
197	C₂×C₄×C₇₃	—	2	1	no	—
198	C₂×C₄×C₇₃	—	2	1	no	—
199	C₂×C₄×C₇₃	—	2	1	no	—
200	C₂×C₄×C₇₃	—	2	1	no	—
201	C₂×C₄×C₇₃	—	2	1	no	—
202	C₂×C₄×C₇₃	—	2	1	no	—
203	C₂×C₄×C₇₃	—	2	1	no	—
204	C₂×C₄×C₇₃	—	2	1	no	—
205	C₂×C₄×C₇₃	—	4	1	no	—
206	C₂×C₄×C₇₃	—	4	1	no	—
207	C₂×C₄×C₇₃	—	4	1	no	—
208	C₂×C₄×C₇₃	—	4	2	no	—
209	C₂×C₄×C₇₃	—	4	1	no	—
210	C₂×C₄×C₇₃	—	4	1	no	—
211	C₂×C₄×C₇₃	—	4	1	no	—
212	C₂×C₄×C₇₃	—	4	2	no	—
213	C₂×C₄×C₇₃	—	4	2	no	—
214	C₂×C₄×C₇₃	—	4	1	no	—
215	C₂×C₄×C₇₃	—	4	1	no	—
216	C₂×C₄×C₇₃	—	4	1	no	—
217	C₂×C₄×C₇₃	#135	1	2	yes	—
218	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
219	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
220	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
221	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
222	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
223	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
224	C₈×C₇₃	—	4	2	no	—
225	C₈×C₇₃	—	4	2	no	—
226	C₂²×C₇₃	—	8	1	no	—
227	C₂²×C₇₃	—	8	2	no	—
228	C₂²×C₇₃	—	8	1	no	—
229	C₂²×C₇₃	—	8	2	no	—
230	C₂²×C₇₃	—	8	2	no	—
231	C₂²×C₇₃	—	8	1	no	—
232	C₂²×C₇₃	—	8	1	no	—
233	C₂²×C₇₃	—	8	2	no	—
234	C₂²×C₇₃	—	8	2	no	—
235	C₂²×C₇₃	—	8	1	no	—
236	C₂²×C₇₃	—	8	1	no	—
237	C₂²×C₇₃	—	8	2	no	—
238	C₂²×C₇₃	—	8	2	no	—
239	C₂²×C₇₃	—	8	1	no	—
240	C₂²×C₇₃	#535	1	1	yes	characteristic
241	C₂²×C₇₃	#535	1	1	yes	characteristic
242	C₂²×C₇₃	#537	1	1	yes	characteristic
243	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
244	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
245	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
246	C₂²×C₇₃	#575	1	1	yes	characteristic
247	C₄×C₇₃	—	2	2	no	—
248	C₄×C₇₃	—	2	2	no	—
249	C₄×C₇₃	—	2	2	no	—
250	C₄×C₇₃	—	4	1	no	—
251	C₄×C₇₃	—	4	1	no	—
252	C₄×C₇₃	—	4	1	no	—
253	C₄×C₇₃	—	8	1	no	—
254	C₄×C₇₃	—	8	1	no	—
255	C₄×C₇₃	—	8	1	no	—
256	C₄×C₇₃	—	8	2	no	—
257	C₄×C₇₃	H(3,𝔽₄)	1	2	yes	—
258	C₄×C₇₃	#562	1	2	yes	—
259	#32810	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
260	C₂×C₇₃	—	16	2	no	—
261	C₂×C₇₃	—	16	1	no	—
262	C₂×C₇₃	#2819	1	1	yes	characteristic
263	C₂×C₇₃	#3207	1	1	yes	characteristic
264	C₂×C₇₃	#3211	1	1	yes	characteristic
265	C₂×C₇₃	#3214	1	1	yes	characteristic
266	C₂×C₇₃	#3217	1	1	yes	characteristic
267	C₂×C₇₃	#3247	1	1	yes	characteristic
268	C₂×C₇₃	#3251	1	1	yes	characteristic
269	#2861	C₂×C₇₃	1	1	yes	characteristic, complemented
270	#2858	C₂×C₇₃	1	1	yes	characteristic, complemented
271	#2055	C₂×C₇₃	1	2	yes	complemented
272	#2054	C₂×C₇₃	1	2	yes	complemented
273	#2025	C₂×C₇₃	1	2	yes	complemented
274	#2024	C₂×C₇₃	1	1	yes	characteristic, complemented
275	#2023	C₂×C₇₃	1	1	yes	characteristic, complemented
276	#2014	C₂×C₇₃	1	1	yes	characteristic, complemented
277	#2012	C₂×C₇₃	1	2	yes	complemented
278	#2011	C₂×C₇₃	1	1	yes	characteristic
279	#1831	C₂×C₇₃	1	1	yes	characteristic, complemented
280	C₇₃	#32810	1	1	yes	characteristic, direct product factor, Sylow
281	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
282	C₂²×D₈	C₂²×C₇₃	1	2	yes	—
283	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
284	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
285	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
286	C₂×#124	—	2	1	no	—
287	C₂×#124	—	2	1	no	—
288	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
289	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	—
290	C₂×#103	C₂²×C₇₃	1	2	yes	—
291	C₂×#102	C₂²×C₇₃	1	2	yes	—
292	C₂×#102	C₂²×C₇₃	1	2	yes	—
293	C₂×#102	C₂²×C₇₃	1	2	yes	—
294	#391	C₂²×C₇₃	1	1	yes	characteristic
295	#391	C₂²×C₇₃	1	1	yes	characteristic
296	#390	—	2	1	no	—
297	#390	—	2	1	no	—
298	#390	C₂²×C₇₃	1	1	yes	characteristic
299	#390	C₂²×C₇₃	1	2	yes	—
300	#390	C₂²×C₇₃	1	2	yes	—
301	#390	C₂²×C₇₃	1	1	yes	characteristic
302	#388	—	2	1	no	—
303	#388	—	2	1	no	—
304	#388	—	2	1	no	—
305	#388	—	2	1	no	—
306	C₄³	C₂²×C₇₃	1	1	yes	characteristic
307	#340	C₂²×C₇₃	1	2	yes	—
308	#340	C₂²×C₇₃	1	2	yes	—
309	#336	C₂²×C₇₃	1	1	yes	characteristic
310	#336	C₂²×C₇₃	1	2	yes	—
311	#336	C₂²×C₇₃	1	1	yes	characteristic
312	C₂²×Q₈	—	2	1	no	—
313	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
314	C₂²×D₄	—	2	1	no	—
315	C₂²×D₄	—	2	1	no	—
316	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
317	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
318	C₂×SD₁₆	—	4	2	no	—
319	C₂×SD₁₆	—	4	2	no	—
320	C₂×SD₁₆	—	4	2	no	—
321	C₂×D₈	—	4	2	no	—
322	C₂×D₈	—	4	2	no	—
323	C₂×D₈	—	4	2	no	—
324	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
325	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
326	C₄⋊Q₈	—	4	2	no	—
327	#127	—	4	2	no	—
328	#125	—	4	2	no	—
329	#124	—	4	2	no	—
330	#124	—	4	4	no	—
331	#124	—	4	4	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	—	2	2	no	—
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₂²⋊C₄	—	2	1	no	—
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₂²⋊C₄	—	2	1	no	—
347	C₂×C₂²⋊C₄	—	2	1	no	—
348	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
349	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
350	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
351	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
352	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
354	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
355	C₄⋊C₈	—	4	2	no	—
356	#103	—	4	2	no	—
357	#102	—	4	2	no	—
358	#102	—	4	2	no	—
359	#102	—	4	2	no	—
360	#95	—	2	1	no	—
361	#95	—	2	1	no	—
362	#95	—	2	1	no	—
363	#95	—	2	1	no	—
364	C₂⁴	—	2	1	no	—
365	C₂⁴	—	2	2	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	4	2	no	—
371	C₂×Q₈	—	4	2	no	—
372	C₂×Q₈	—	4	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	—	4	2	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂×D₄	—	4	2	no	—
388	C₂×D₄	—	4	2	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
399	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
400	SD₁₆	—	4	8	no	—
401	D₈	—	4	8	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	4	2	no	—
413	C₄⋊C₄	—	4	2	no	—
414	C₄⋊C₄	—	4	2	no	—
415	C₂²⋊C₄	—	4	2	no	—
416	C₂²⋊C₄	—	4	2	no	—
417	C₂²⋊C₄	—	4	2	no	—
418	C₂²⋊C₄	—	4	4	no	—
419	C₂²⋊C₄	—	4	4	no	—
420	C₂²⋊C₄	—	4	4	no	—
421	C₂²⋊C₄	—	4	2	no	—
422	C₂²⋊C₄	—	4	2	no	—
423	C₂²⋊C₄	—	4	2	no	—
424	C₂²⋊C₄	—	4	4	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	1	no	—
432	C₄²	—	4	1	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	4	1	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	1	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	2	no	—
443	C₂³	—	4	1	no	—
444	C₂³	—	4	1	no	—
445	C₂³	—	4	1	no	—
446	C₂³	—	4	2	no	—
447	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
448	Q₈	—	4	2	no	—
449	Q₈	—	4	2	no	—
450	Q₈	—	8	4	no	—
451	D₄	—	4	2	no	—
452	D₄	—	4	2	no	—
453	D₄	—	4	2	no	—
454	D₄	—	4	2	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	2	no	—
457	D₄	—	8	4	no	—
458	D₄	—	8	4	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	#135×C₇₃	1	2	yes	—
487	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
488	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
489	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
490	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
491	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
492	C₂×C₄	2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
493	C₈	—	4	2	no	—
494	C₈	—	4	2	no	—
495	C₂²	—	8	1	no	—
496	C₂²	—	8	2	no	—
497	C₂²	—	8	2	no	—
498	C₂²	—	8	1	no	—
499	C₂²	—	8	1	no	—
500	C₂²	—	8	2	no	—
501	C₂²	—	8	2	no	—
502	C₂²	—	8	1	no	—
503	C₂²	—	8	1	no	—
504	C₂²	—	8	2	no	—
505	C₂²	—	8	2	no	—
506	C₂²	—	8	1	no	—
507	C₂²	—	8	1	no	—
508	C₂²	—	8	2	no	—
509	C₂²	#535×C₇₃	1	1	yes	characteristic
510	C₂²	#535×C₇₃	1	1	yes	characteristic
511	C₂²	#537×C₇₃	1	1	yes	characteristic
512	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
513	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
514	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
515	C₂²	#575×C₇₃	1	1	yes	characteristic
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	2	2	no	—
519	C₄	—	4	1	no	—
520	C₄	—	4	1	no	—
521	C₄	—	4	1	no	—
522	C₄	—	8	1	no	—
523	C₄	—	8	1	no	—
524	C₄	—	8	2	no	—
525	C₄	—	8	1	no	—
526	C₄	H(3,𝔽₄)×C₇₃	1	2	yes	—
527	C₄	#562×C₇₃	1	2	yes	—
528	C₂	—	16	2	no	—
529	C₂	—	16	1	no	—
530	C₂	C₇₃×#2819	1	1	yes	characteristic
531	C₂	C₇₃×#3207	1	1	yes	characteristic
532	C₂	C₇₃×#3211	1	1	yes	characteristic
533	C₂	C₇₃×#3214	1	1	yes	characteristic
534	C₂	C₇₃×#3217	1	1	yes	characteristic
535	C₂	C₇₃×#3247	1	1	yes	characteristic
536	C₂	C₇₃×#3251	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₇₃×#2011	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₄³×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#2861	C₂	semidirect
2. C₇₃×#2858	C₂	semidirect
3. C₇₃×#2055	C₂	semidirect
4. C₇₃×#2054	C₂	semidirect
5. C₇₃×#2025	C₂	semidirect
6. C₇₃×#2024	C₂	semidirect
7. C₇₃×#2023	C₂	semidirect
8. C₇₃×#2014	C₂	semidirect
9. C₇₃×#2012	C₂	semidirect
11. C₇₃×#1831	C₂	semidirect
259. #32810	C₇₃	direct (N × H)
269. #2861	C₂×C₇₃	semidirect
270. #2858	C₂×C₇₃	semidirect
271. #2055	C₂×C₇₃	semidirect
272. #2054	C₂×C₇₃	semidirect
273. #2025	C₂×C₇₃	semidirect
274. #2024	C₂×C₇₃	semidirect
275. #2023	C₂×C₇₃	semidirect
276. #2014	C₂×C₇₃	semidirect
277. #2012	C₂×C₇₃	semidirect
279. #1831	C₂×C₇₃	semidirect
280. C₇₃	#32810	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₃×#2861	2
C₇₃×#2858	2
C₇₃×#2055	2
C₇₃×#2054	2
C₇₃×#2025	2
C₇₃×#2024	2
C₇₃×#2023	2
C₇₃×#2014	2
C₇₃×#2012	2
C₇₃×#2011	2
C₇₃×#1831	2
#32810	73

Subgroups — C73×#32810 #32942214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#32810 #32942214