Subgroups — C₇₃×#59935 #32969339

Order 18688.

1688 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2809	C₂	1	2	yes	maximal, complemented
2	C₇₃×#2784	C₂	1	2	yes	maximal
3	C₇₃×#2612	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2574	C₂	1	4	yes	maximal, complemented
5	C₇₃×#2568	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2567	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2497	C₂	1	4	yes	maximal, complemented
8	C₇₃×#2492	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2429	C₂	1	2	yes	maximal, complemented
10	C₇₃×#2417	C₂	1	2	yes	maximal
11	C₇₃×#2372	C₂	1	2	yes	maximal
12	C₇₃×#2360	C₂	1	2	yes	maximal, complemented
13	C₇₃×#2345	C₂	1	2	yes	maximal, complemented
14	C₄×#124×C₇₃	C₂	1	1	yes	maximal, characteristic
15	C₇₃×#2295	C₂	1	2	yes	maximal, complemented
16	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
20	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
25	#400×C₇₃	C₂²	1	4	yes	—
26	#400×C₇₃	C₂²	1	2	yes	—
27	#400×C₇₃	C₂²	1	2	yes	—
28	#398×C₇₃	C₂²	1	4	yes	—
29	#398×C₇₃	C₂²	1	4	yes	—
30	#396×C₇₃	C₂²	1	4	yes	—
31	#396×C₇₃	C₂²	1	4	yes	—
32	#395×C₇₃	C₂²	1	2	yes	—
33	#395×C₇₃	C₂²	1	2	yes	—
34	#393×C₇₃	C₂²	1	4	yes	—
35	#391×C₇₃	C₂²	1	2	yes	—
36	#391×C₇₃	C₂²	1	2	yes	—
37	#391×C₇₃	C₂²	1	4	yes	—
38	#391×C₇₃	C₂²	1	2	yes	—
39	#391×C₇₃	C₂²	1	1	yes	characteristic
40	#391×C₇₃	C₂²	1	2	yes	—
41	#391×C₇₃	C₂²	1	2	yes	—
42	#390×C₇₃	C₂²	1	1	yes	characteristic
43	#389×C₇₃	C₂²	1	4	yes	—
44	#389×C₇₃	C₂²	1	4	yes	—
45	#389×C₇₃	C₂²	1	2	yes	—
46	#389×C₇₃	C₂²	1	2	yes	—
47	#389×C₇₃	C₂²	1	2	yes	—
48	#388×C₇₃	C₂²	1	4	yes	—
49	#388×C₇₃	C₂²	1	2	yes	—
50	#388×C₇₃	C₂²	1	2	yes	—
51	#388×C₇₃	C₂²	1	4	yes	—
52	#387×C₇₃	C₂²	1	4	yes	—
53	#387×C₇₃	C₂²	1	4	yes	—
54	#387×C₇₃	C₂²	1	4	yes	—
55	#387×C₇₃	C₂²	1	4	yes	—
56	#387×C₇₃	C₂²	1	4	yes	—
57	#386×C₇₃	C₂²	1	4	yes	—
58	#385×C₇₃	C₂²	1	4	yes	—
59	#384×C₇₃	C₂²	1	2	yes	—
60	#382×C₇₃	C₂²	1	1	yes	characteristic
61	#382×C₇₃	C₂²	1	2	yes	—
62	#380×C₇₃	C₂²	1	2	yes	—
63	#380×C₇₃	C₂²	1	4	yes	—
64	#380×C₇₃	C₂²	1	4	yes	—
65	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
66	C₄×C₄⋊C₄×C₇₃	C₂²	1	4	yes	—
67	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
68	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
70	C₄×C₂²⋊C₄×C₇₃	C₂²	1	4	yes	—
71	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
72	C₄×C₂²⋊C₄×C₇₃	C₂²	1	4	yes	—
73	#376×C₇₃	C₂²	1	4	yes	—
74	C₄³×C₇₃	C₂²	1	1	yes	characteristic
75	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
76	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
77	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
80	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
81	C₄⋊Q₈×C₇₃	—	4	2	no	—
82	C₄⋊Q₈×C₇₃	—	4	2	no	—
83	#124×C₇₃	Q₈	1	8	yes	complemented
84	C₂²⋊Q₈×C₇₃	—	2	8	no	—
85	C₂²⋊Q₈×C₇₃	—	4	4	no	—
86	C₄×Q₈×C₇₃	—	2	8	no	—
87	C₄×Q₈×C₇₃	—	4	2	no	—
88	C₄×D₄×C₇₃	—	4	2	no	—
89	C₂×C₄⋊C₄×C₇₃	—	2	8	no	—
90	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
107	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
110	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
111	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
112	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
114	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
115	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
117	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
119	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
121	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
122	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
123	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
124	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
126	#95×C₇₃	C₂³	1	4	yes	—
127	#95×C₇₃	C₂³	1	2	yes	—
128	#95×C₇₃	C₂³	1	2	yes	—
129	#95×C₇₃	C₂³	1	2	yes	—
130	#95×C₇₃	C₂³	1	4	yes	—
131	#95×C₇₃	C₂³	1	2	yes	—
132	#95×C₇₃	C₂³	1	4	yes	—
133	#95×C₇₃	C₂³	1	2	yes	—
134	#95×C₇₃	C₂³	1	4	yes	—
135	#95×C₇₃	C₂³	1	4	yes	—
136	#95×C₇₃	C₂³	1	2	yes	—
137	#95×C₇₃	C₂³	1	4	yes	—
138	#95×C₇₃	C₂³	1	4	yes	—
139	#95×C₇₃	C₂³	1	4	yes	—
140	#95×C₇₃	C₂³	1	4	yes	—
141	#95×C₇₃	C₂³	1	4	yes	—
142	#95×C₇₃	C₂³	1	4	yes	—
143	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
144	C₂×Q₈×C₇₃	—	2	4	no	—
145	C₂×Q₈×C₇₃	—	2	4	no	—
146	C₂×Q₈×C₇₃	—	2	4	no	—
147	C₂×Q₈×C₇₃	—	4	1	no	—
148	C₂×Q₈×C₇₃	—	4	1	no	—
149	C₂×Q₈×C₇₃	—	4	2	no	—
150	C₂×Q₈×C₇₃	—	4	4	no	—
151	C₂×Q₈×C₇₃	C₂×Q₈	1	4	yes	—
152	C₂×D₄×C₇₃	—	4	1	no	—
153	C₂×D₄×C₇₃	—	4	1	no	—
154	C₂×D₄×C₇₃	C₂×Q₈	1	4	yes	—
155	C₂²×C₄×C₇₃	—	2	4	no	—
156	C₂²×C₄×C₇₃	—	2	4	no	—
157	C₂²×C₄×C₇₃	—	2	4	no	—
158	C₂²×C₄×C₇₃	—	2	8	no	—
159	C₂²×C₄×C₇₃	—	4	4	no	—
160	C₂²×C₄×C₇₃	—	4	4	no	—
161	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
163	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
168	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
169	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
175	C₄⋊C₄×C₇₃	—	2	8	no	—
176	C₄⋊C₄×C₇₃	—	2	4	no	—
177	C₄⋊C₄×C₇₃	—	2	8	no	—
178	C₄⋊C₄×C₇₃	—	2	8	no	—
179	C₄⋊C₄×C₇₃	—	2	4	no	—
180	C₄⋊C₄×C₇₃	—	4	4	no	—
181	C₄⋊C₄×C₇₃	—	4	4	no	—
182	C₄⋊C₄×C₇₃	—	4	4	no	—
183	C₄⋊C₄×C₇₃	—	4	1	no	—
184	C₄⋊C₄×C₇₃	—	4	1	no	—
185	C₄⋊C₄×C₇₃	—	4	1	no	—
186	C₄⋊C₄×C₇₃	—	4	1	no	—
187	C₄⋊C₄×C₇₃	—	4	4	no	—
188	C₄⋊C₄×C₇₃	—	4	2	no	—
189	C₄⋊C₄×C₇₃	—	4	2	no	—
190	C₄⋊C₄×C₇₃	—	4	2	no	—
191	C₄⋊C₄×C₇₃	#41	1	8	yes	—
192	C₂²⋊C₄×C₇₃	—	2	8	no	—
193	C₂²⋊C₄×C₇₃	—	4	2	no	—
194	C₂²⋊C₄×C₇₃	—	4	2	no	—
195	C₂²⋊C₄×C₇₃	—	4	4	no	—
196	C₂²⋊C₄×C₇₃	—	4	2	no	—
197	C₂²⋊C₄×C₇₃	—	4	4	no	—
198	C₂²⋊C₄×C₇₃	C₂×Q₈	1	8	yes	—
199	C₂²⋊C₄×C₇₃	C₂×Q₈	1	8	yes	—
200	C₄²×C₇₃	—	2	4	no	—
201	C₄²×C₇₃	—	2	8	no	—
202	C₄²×C₇₃	—	2	2	no	—
203	C₄²×C₇₃	—	2	2	no	—
204	C₄²×C₇₃	—	2	2	no	—
205	C₄²×C₇₃	—	4	2	no	—
206	C₄²×C₇₃	—	4	4	no	—
207	C₄²×C₇₃	—	4	2	no	—
208	C₄²×C₇₃	—	4	2	no	—
209	C₄²×C₇₃	—	4	1	no	—
210	C₄²×C₇₃	C₂×Q₈	1	4	yes	—
211	C₂³×C₇₃	—	2	2	no	—
212	C₂³×C₇₃	—	2	2	no	—
213	C₂³×C₇₃	—	2	2	no	—
214	C₂³×C₇₃	—	2	2	no	—
215	C₂³×C₇₃	—	2	2	no	—
216	C₂³×C₇₃	—	2	2	no	—
217	C₂³×C₇₃	C₂²×Q₈	1	4	yes	—
218	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
219	Q₈×C₇₃	—	4	4	no	—
220	Q₈×C₇₃	—	4	8	no	—
221	Q₈×C₇₃	—	8	4	no	—
222	D₄×C₇₃	—	4	4	no	—
223	C₂×C₄×C₇₃	—	2	2	no	—
224	C₂×C₄×C₇₃	—	2	1	no	—
225	C₂×C₄×C₇₃	—	2	1	no	—
226	C₂×C₄×C₇₃	—	2	1	no	—
227	C₂×C₄×C₇₃	—	2	2	no	—
228	C₂×C₄×C₇₃	—	2	1	no	—
229	C₂×C₄×C₇₃	—	2	1	no	—
230	C₂×C₄×C₇₃	—	2	4	no	—
231	C₂×C₄×C₇₃	—	2	1	no	—
232	C₂×C₄×C₇₃	—	2	4	no	—
233	C₂×C₄×C₇₃	—	2	2	no	—
234	C₂×C₄×C₇₃	—	2	4	no	—
235	C₂×C₄×C₇₃	—	2	4	no	—
236	C₂×C₄×C₇₃	—	2	2	no	—
237	C₂×C₄×C₇₃	—	2	2	no	—
238	C₂×C₄×C₇₃	—	2	4	no	—
239	C₂×C₄×C₇₃	—	2	1	no	—
240	C₂×C₄×C₇₃	—	2	1	no	—
241	C₂×C₄×C₇₃	—	2	1	no	—
242	C₂×C₄×C₇₃	—	2	4	no	—
243	C₂×C₄×C₇₃	—	2	2	no	—
244	C₂×C₄×C₇₃	—	2	4	no	—
245	C₂×C₄×C₇₃	—	2	2	no	—
246	C₂×C₄×C₇₃	—	2	4	no	—
247	C₂×C₄×C₇₃	—	2	2	no	—
248	C₂×C₄×C₇₃	—	2	2	no	—
249	C₂×C₄×C₇₃	—	2	4	no	—
250	C₂×C₄×C₇₃	—	2	4	no	—
251	C₂×C₄×C₇₃	—	2	2	no	—
252	C₂×C₄×C₇₃	—	2	4	no	—
253	C₂×C₄×C₇₃	—	2	2	no	—
254	C₂×C₄×C₇₃	—	4	8	no	—
255	C₂×C₄×C₇₃	—	8	8	no	—
256	C₂×C₄×C₇₃	C₂²×Q₈	1	4	yes	—
257	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
258	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
259	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
260	C₂×C₄×C₇₃	C₂×#41	1	8	yes	—
261	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
262	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
263	C₂²×C₇₃	—	2	4	no	—
264	C₂²×C₇₃	—	2	4	no	—
265	C₂²×C₇₃	—	2	4	no	—
266	C₂²×C₇₃	—	4	2	no	—
267	C₂²×C₇₃	—	4	2	no	—
268	C₂²×C₇₃	—	4	2	no	—
269	C₂²×C₇₃	—	4	2	no	—
270	C₂²×C₇₃	C₂³×Q₈	1	1	yes	characteristic
271	C₂²×C₇₃	C₂²×#41	1	2	yes	—
272	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
273	C₂²×C₇₃	#585	1	2	yes	—
274	C₂²×C₇₃	#585	1	1	yes	characteristic
275	C₄×C₇₃	—	2	4	no	—
276	C₄×C₇₃	—	2	2	no	—
277	C₄×C₇₃	—	2	2	no	—
278	C₄×C₇₃	—	2	2	no	—
279	C₄×C₇₃	—	2	8	no	—
280	C₄×C₇₃	—	4	2	no	—
281	C₄×C₇₃	—	4	4	no	—
282	C₄×C₇₃	—	4	2	no	—
283	C₄×C₇₃	—	4	4	no	—
284	C₄×C₇₃	—	4	1	no	—
285	C₄×C₇₃	—	4	1	no	—
286	C₄×C₇₃	—	4	4	no	—
287	C₄×C₇₃	—	4	1	no	—
288	C₄×C₇₃	#555	1	4	yes	—
289	#59935	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
290	C₂×C₇₃	—	4	4	no	—
291	C₂×C₇₃	C₂×#555	1	1	yes	characteristic
292	C₂×C₇₃	Q₈×#41	1	2	yes	—
293	C₂×C₇₃	#3501	1	1	yes	characteristic
294	C₂×C₇₃	#3521	1	2	yes	—
295	C₂×C₇₃	#3551	1	1	yes	characteristic
296	#2809	C₂×C₇₃	1	2	yes	complemented
297	#2784	C₂×C₇₃	1	2	yes	—
298	#2612	C₂×C₇₃	1	2	yes	complemented
299	#2574	C₂×C₇₃	1	4	yes	complemented
300	#2568	C₂×C₇₃	1	1	yes	characteristic, complemented
301	#2567	C₂×C₇₃	1	1	yes	characteristic, complemented
302	#2497	C₂×C₇₃	1	4	yes	complemented
303	#2492	C₂×C₇₃	1	2	yes	complemented
304	#2429	C₂×C₇₃	1	2	yes	complemented
305	#2417	C₂×C₇₃	1	2	yes	—
306	#2372	C₂×C₇₃	1	2	yes	—
307	#2360	C₂×C₇₃	1	2	yes	complemented
308	#2345	C₂×C₇₃	1	2	yes	complemented
309	C₄×#124	C₂×C₇₃	1	1	yes	characteristic
310	#2295	C₂×C₇₃	1	2	yes	complemented
311	C₇₃	#59935	1	1	yes	characteristic, direct product factor, Sylow
312	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
313	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
314	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
315	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
316	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
317	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
318	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
319	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
320	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
321	#400	C₂²×C₇₃	1	2	yes	—
322	#400	C₂²×C₇₃	1	2	yes	—
323	#400	C₂²×C₇₃	1	4	yes	—
324	#398	C₂²×C₇₃	1	4	yes	—
325	#398	C₂²×C₇₃	1	4	yes	—
326	#396	C₂²×C₇₃	1	4	yes	—
327	#396	C₂²×C₇₃	1	4	yes	—
328	#395	C₂²×C₇₃	1	2	yes	—
329	#395	C₂²×C₇₃	1	2	yes	—
330	#393	C₂²×C₇₃	1	4	yes	—
331	#391	C₂²×C₇₃	1	2	yes	—
332	#391	C₂²×C₇₃	1	2	yes	—
333	#391	C₂²×C₇₃	1	2	yes	—
334	#391	C₂²×C₇₃	1	2	yes	—
335	#391	C₂²×C₇₃	1	4	yes	—
336	#391	C₂²×C₇₃	1	2	yes	—
337	#391	C₂²×C₇₃	1	1	yes	characteristic
338	#390	C₂²×C₇₃	1	1	yes	characteristic
339	#389	C₂²×C₇₃	1	2	yes	—
340	#389	C₂²×C₇₃	1	2	yes	—
341	#389	C₂²×C₇₃	1	2	yes	—
342	#389	C₂²×C₇₃	1	4	yes	—
343	#389	C₂²×C₇₃	1	4	yes	—
344	#388	C₂²×C₇₃	1	2	yes	—
345	#388	C₂²×C₇₃	1	4	yes	—
346	#388	C₂²×C₇₃	1	4	yes	—
347	#388	C₂²×C₇₃	1	2	yes	—
348	#387	C₂²×C₇₃	1	4	yes	—
349	#387	C₂²×C₇₃	1	4	yes	—
350	#387	C₂²×C₇₃	1	4	yes	—
351	#387	C₂²×C₇₃	1	4	yes	—
352	#387	C₂²×C₇₃	1	4	yes	—
353	#386	C₂²×C₇₃	1	4	yes	—
354	#385	C₂²×C₇₃	1	4	yes	—
355	#384	C₂²×C₇₃	1	2	yes	—
356	#382	C₂²×C₇₃	1	2	yes	—
357	#382	C₂²×C₇₃	1	1	yes	characteristic
358	#380	C₂²×C₇₃	1	4	yes	—
359	#380	C₂²×C₇₃	1	2	yes	—
360	#380	C₂²×C₇₃	1	4	yes	—
361	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
362	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
363	C₄×C₄⋊C₄	C₂²×C₇₃	1	4	yes	—
364	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
365	C₄×C₂²⋊C₄	C₂²×C₇₃	1	4	yes	—
366	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
367	C₄×C₂²⋊C₄	C₂²×C₇₃	1	4	yes	—
368	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
369	#376	C₂²×C₇₃	1	4	yes	—
370	C₄³	C₂²×C₇₃	1	1	yes	characteristic
371	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
372	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
373	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
374	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
375	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
376	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
377	C₄⋊Q₈	—	4	2	no	—
378	C₄⋊Q₈	—	4	2	no	—
379	#124	Q₈×C₇₃	1	8	yes	complemented
380	C₂²⋊Q₈	—	2	8	no	—
381	C₂²⋊Q₈	—	4	4	no	—
382	C₄×Q₈	—	2	8	no	—
383	C₄×Q₈	—	4	2	no	—
384	C₄×D₄	—	4	2	no	—
385	C₂×C₄⋊C₄	—	2	8	no	—
386	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
387	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
388	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
389	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
390	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
391	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
396	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
397	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
398	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
400	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
401	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
402	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
404	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
405	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
406	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
411	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
412	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
413	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
414	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
415	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
416	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
417	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
418	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
419	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
420	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
421	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
422	#95	C₂³×C₇₃	1	4	yes	—
423	#95	C₂³×C₇₃	1	4	yes	—
424	#95	C₂³×C₇₃	1	4	yes	—
425	#95	C₂³×C₇₃	1	4	yes	—
426	#95	C₂³×C₇₃	1	2	yes	—
427	#95	C₂³×C₇₃	1	2	yes	—
428	#95	C₂³×C₇₃	1	2	yes	—
429	#95	C₂³×C₇₃	1	4	yes	—
430	#95	C₂³×C₇₃	1	2	yes	—
431	#95	C₂³×C₇₃	1	4	yes	—
432	#95	C₂³×C₇₃	1	2	yes	—
433	#95	C₂³×C₇₃	1	4	yes	—
434	#95	C₂³×C₇₃	1	4	yes	—
435	#95	C₂³×C₇₃	1	2	yes	—
436	#95	C₂³×C₇₃	1	4	yes	—
437	#95	C₂³×C₇₃	1	4	yes	—
438	#95	C₂³×C₇₃	1	4	yes	—
439	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
440	C₂×Q₈	—	2	4	no	—
441	C₂×Q₈	—	2	4	no	—
442	C₂×Q₈	—	2	4	no	—
443	C₂×Q₈	—	4	1	no	—
444	C₂×Q₈	—	4	1	no	—
445	C₂×Q₈	—	4	2	no	—
446	C₂×Q₈	—	4	4	no	—
447	C₂×Q₈	C₂×Q₈×C₇₃	1	4	yes	—
448	C₂×D₄	—	4	1	no	—
449	C₂×D₄	—	4	1	no	—
450	C₂×D₄	C₂×Q₈×C₇₃	1	4	yes	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	8	no	—
455	C₂²×C₄	—	4	4	no	—
456	C₂²×C₄	—	4	4	no	—
457	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
458	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
459	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
460	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
461	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
462	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
463	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
464	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
465	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
466	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
467	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
468	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
469	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
470	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
471	C₄⋊C₄	—	2	8	no	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	8	no	—
474	C₄⋊C₄	—	2	8	no	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	4	4	no	—
477	C₄⋊C₄	—	4	4	no	—
478	C₄⋊C₄	—	4	4	no	—
479	C₄⋊C₄	—	4	1	no	—
480	C₄⋊C₄	—	4	1	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₄⋊C₄	—	4	1	no	—
483	C₄⋊C₄	—	4	4	no	—
484	C₄⋊C₄	—	4	2	no	—
485	C₄⋊C₄	—	4	2	no	—
486	C₄⋊C₄	—	4	2	no	—
487	C₄⋊C₄	#41×C₇₃	1	8	yes	—
488	C₂²⋊C₄	—	2	8	no	—
489	C₂²⋊C₄	—	4	2	no	—
490	C₂²⋊C₄	—	4	2	no	—
491	C₂²⋊C₄	—	4	4	no	—
492	C₂²⋊C₄	—	4	2	no	—
493	C₂²⋊C₄	—	4	4	no	—
494	C₂²⋊C₄	C₂×Q₈×C₇₃	1	8	yes	—
495	C₂²⋊C₄	C₂×Q₈×C₇₃	1	8	yes	—
496	C₄²	—	2	4	no	—
497	C₄²	—	2	8	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	2	2	no	—
501	C₄²	—	4	2	no	—
502	C₄²	—	4	4	no	—
503	C₄²	—	4	2	no	—
504	C₄²	—	4	2	no	—
505	C₄²	—	4	1	no	—
506	C₄²	C₂×Q₈×C₇₃	1	4	yes	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	2	2	no	—
513	C₂³	C₂²×Q₈×C₇₃	1	4	yes	—
514	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
515	Q₈	—	4	4	no	—
516	Q₈	—	4	8	no	—
517	Q₈	—	8	4	no	—
518	D₄	—	4	4	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	4	8	no	—
551	C₂×C₄	—	8	8	no	—
552	C₂×C₄	C₂²×Q₈×C₇₃	1	4	yes	—
553	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
554	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
555	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
556	C₂×C₄	C₂×#41×C₇₃	1	8	yes	—
557	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
558	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
559	C₂²	—	2	4	no	—
560	C₂²	—	2	4	no	—
561	C₂²	—	2	4	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	2	no	—
566	C₂²	C₂³×Q₈×C₇₃	1	1	yes	characteristic
567	C₂²	C₂²×#41×C₇₃	1	2	yes	—
568	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
569	C₂²	#585×C₇₃	1	2	yes	—
570	C₂²	#585×C₇₃	1	1	yes	characteristic
571	C₄	—	2	4	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	8	no	—
576	C₄	—	4	2	no	—
577	C₄	—	4	4	no	—
578	C₄	—	4	4	no	—
579	C₄	—	4	2	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	4	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	#555×C₇₃	1	4	yes	—
585	C₂	—	4	4	no	—
586	C₂	C₂×#555×C₇₃	1	1	yes	characteristic
587	C₂	Q₈×#41×C₇₃	1	2	yes	—
588	C₂	C₇₃×#3501	1	1	yes	characteristic
589	C₂	C₇₃×#3521	1	2	yes	—
590	C₂	C₇₃×#3551	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₂²×D₄×C₇₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#2809	C₂	semidirect
3. C₇₃×#2612	C₂	semidirect
4. C₇₃×#2574	C₂	semidirect
5. C₇₃×#2568	C₂	semidirect
6. C₇₃×#2567	C₂	semidirect
7. C₇₃×#2497	C₂	semidirect
8. C₇₃×#2492	C₂	semidirect
9. C₇₃×#2429	C₂	semidirect
12. C₇₃×#2360	C₂	semidirect
13. C₇₃×#2345	C₂	semidirect
15. C₇₃×#2295	C₂	semidirect
83. #124×C₇₃	Q₈	semidirect
289. #59935	C₇₃	direct (N × H)
296. #2809	C₂×C₇₃	semidirect
298. #2612	C₂×C₇₃	semidirect
299. #2574	C₂×C₇₃	semidirect
300. #2568	C₂×C₇₃	semidirect
301. #2567	C₂×C₇₃	semidirect
302. #2497	C₂×C₇₃	semidirect
303. #2492	C₂×C₇₃	semidirect
304. #2429	C₂×C₇₃	semidirect
307. #2360	C₂×C₇₃	semidirect
308. #2345	C₂×C₇₃	semidirect
310. #2295	C₂×C₇₃	semidirect
311. C₇₃	#59935	direct (N × H)
379. #124	Q₈×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#2809	2
C₇₃×#2784	2
C₇₃×#2612	2
C₇₃×#2574	2
C₇₃×#2568	2
C₇₃×#2567	2
C₇₃×#2497	2
C₇₃×#2492	2
C₇₃×#2429	2
C₇₃×#2417	2
C₇₃×#2372	2
C₇₃×#2360	2
C₇₃×#2345	2
C₄×#124×C₇₃	2
C₇₃×#2295	2
#59935	73

Subgroups — C73×#59935 #32969339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59935 #32969339