Subgroups — C₇₃×#25777 #32935181

Order 18688.

1638 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#495×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#493×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#466×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#449×C₇₃	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2431	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2014	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2012	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1969	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₂²⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₇₃	C₂²	1	2	yes	—
13	C₂×#135×C₇₃	—	2	4	no	—
14	C₂×#135×C₇₃	—	2	4	no	—
15	C₂×#135×C₇₃	—	2	4	no	—
16	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
18	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
19	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
21	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×#127×C₇₃	C₂²	1	2	yes	—
24	C₂×#124×C₇₃	C₂²	1	2	yes	—
25	C₂×#121×C₇₃	C₂²	1	2	yes	—
26	#495×C₇₃	—	2	4	no	—
27	#493×C₇₃	—	2	4	no	—
28	#466×C₇₃	—	2	4	no	—
29	#449×C₇₃	—	2	8	no	—
30	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×#103×C₇₃	C₂²	1	2	yes	—
32	C₂×#102×C₇₃	C₂²	1	2	yes	—
33	C₂×#102×C₇₃	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
37	#392×C₇₃	—	2	4	no	—
38	#391×C₇₃	C₂²	1	2	yes	—
39	#390×C₇₃	C₂²	1	2	yes	—
40	#386×C₇₃	—	2	4	no	—
41	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
42	#336×C₇₃	C₂²	1	1	yes	characteristic
43	#336×C₇₃	C₂²	1	1	yes	characteristic
44	C₂×#41×C₇₃	—	2	4	no	—
45	C₂×#41×C₇₃	—	2	4	no	—
46	C₂×#41×C₇₃	—	2	4	no	—
47	C₂×#41×C₇₃	—	2	4	no	—
48	C₂×#41×C₇₃	—	4	2	no	—
49	C₂×#41×C₇₃	—	4	2	no	—
50	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
51	C₂²×D₄×C₇₃	—	2	2	no	—
52	C₂²×D₄×C₇₃	—	2	2	no	—
53	C₂²×D₄×C₇₃	—	2	4	no	—
54	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
55	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₇₃	—	2	2	no	—
57	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
58	#135×C₇₃	—	2	32	no	—
59	C₂×Q₁₆×C₇₃	—	2	2	no	—
60	C₂×Q₁₆×C₇₃	—	2	2	no	—
61	C₂×Q₁₆×C₇₃	D₄	1	4	yes	complemented
62	C₂×SD₁₆×C₇₃	—	2	4	no	—
63	C₂×SD₁₆×C₇₃	—	2	4	no	—
64	C₂×SD₁₆×C₇₃	—	2	4	no	—
65	C₂×SD₁₆×C₇₃	—	2	4	no	—
66	C₂×SD₁₆×C₇₃	—	2	4	no	—
67	C₂×SD₁₆×C₇₃	—	4	2	no	—
68	C₂×D₈×C₇₃	—	2	4	no	—
69	C₂×D₈×C₇₃	—	2	2	no	—
70	C₂×D₈×C₇₃	—	2	2	no	—
71	C₂×D₈×C₇₃	—	2	4	no	—
72	C₂×D₈×C₇₃	—	2	2	no	—
73	C₂×D₈×C₇₃	—	2	2	no	—
74	C₂×D₈×C₇₃	—	2	2	no	—
75	C₂×D₈×C₇₃	—	4	2	no	—
76	C₂×D₈×C₇₃	D₄	1	4	yes	complemented
77	C₂²×C₈×C₇₃	—	2	2	no	—
78	C₂²×C₈×C₇₃	—	2	2	no	—
79	C₂²×C₈×C₇₃	D₄	1	4	yes	complemented
80	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
84	#127×C₇₃	—	2	4	no	—
85	#127×C₇₃	—	4	2	no	—
86	#124×C₇₃	—	2	4	no	—
87	#124×C₇₃	—	4	2	no	—
88	#121×C₇₃	—	2	4	no	—
89	#121×C₇₃	—	2	4	no	—
90	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
91	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
93	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
94	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
95	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
97	#107×C₇₃	—	2	2	no	—
98	#103×C₇₃	—	2	4	no	—
99	#102×C₇₃	—	2	4	no	—
100	#102×C₇₃	—	2	4	no	—
101	C₂²⋊C₈×C₇₃	D₄	1	4	yes	complemented
102	C₄×C₈×C₇₃	—	2	2	no	—
103	C₄×C₈×C₇₃	—	2	2	no	—
104	#95×C₇₃	—	2	4	no	—
105	#95×C₇₃	D₄	1	2	yes	—
106	C₂⁴×C₇₃	—	2	2	no	—
107	C₂⁴×C₇₃	—	2	2	no	—
108	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
109	#41×C₇₃	—	2	16	no	—
110	#41×C₇₃	—	4	8	no	—
111	#41×C₇₃	—	4	8	no	—
112	#41×C₇₃	—	4	8	no	—
113	C₂×Q₈×C₇₃	—	2	2	no	—
114	C₂×Q₈×C₇₃	—	2	2	no	—
115	C₂×Q₈×C₇₃	—	2	2	no	—
116	C₂×Q₈×C₇₃	—	2	2	no	—
117	C₂×Q₈×C₇₃	—	2	2	no	—
118	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
119	C₂×D₄×C₇₃	—	2	2	no	—
120	C₂×D₄×C₇₃	—	2	2	no	—
121	C₂×D₄×C₇₃	—	2	2	no	—
122	C₂×D₄×C₇₃	—	2	2	no	—
123	C₂×D₄×C₇₃	—	2	2	no	—
124	C₂×D₄×C₇₃	—	2	2	no	—
125	C₂×D₄×C₇₃	—	2	2	no	—
126	C₂×D₄×C₇₃	—	2	2	no	—
127	C₂×D₄×C₇₃	—	2	2	no	—
128	C₂×D₄×C₇₃	—	2	2	no	—
129	C₂×D₄×C₇₃	—	2	2	no	—
130	C₂×D₄×C₇₃	—	4	4	no	—
131	C₂×D₄×C₇₃	—	4	8	no	—
132	C₂×D₄×C₇₃	—	4	4	no	—
133	C₂×D₄×C₇₃	—	4	4	no	—
134	C₂×D₄×C₇₃	—	4	4	no	—
135	C₂×D₄×C₇₃	—	4	8	no	—
136	C₂×D₄×C₇₃	—	8	4	no	—
137	C₂×D₄×C₇₃	—	8	4	no	—
138	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
139	C₂²×C₄×C₇₃	—	2	1	no	—
140	C₂²×C₄×C₇₃	—	2	1	no	—
141	C₂²×C₄×C₇₃	—	2	1	no	—
142	C₂²×C₄×C₇₃	—	2	1	no	—
143	C₂²×C₄×C₇₃	—	2	2	no	—
144	C₂²×C₄×C₇₃	—	2	2	no	—
145	C₂²×C₄×C₇₃	—	4	4	no	—
146	C₂²×C₄×C₇₃	—	4	4	no	—
147	C₂²×C₄×C₇₃	—	4	4	no	—
148	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
154	Q₁₆×C₇₃	—	2	8	no	—
155	SD₁₆×C₇₃	—	2	16	no	—
156	SD₁₆×C₇₃	—	4	8	no	—
157	D₈×C₇₃	—	2	8	no	—
158	D₈×C₇₃	—	4	8	no	—
159	D₈×C₇₃	—	4	4	no	—
160	C₂×C₈×C₇₃	—	2	1	no	—
161	C₂×C₈×C₇₃	—	2	1	no	—
162	C₂×C₈×C₇₃	—	2	1	no	—
163	C₂×C₈×C₇₃	—	2	1	no	—
164	C₂×C₈×C₇₃	—	2	1	no	—
165	C₂×C₈×C₇₃	—	2	1	no	—
166	C₂×C₈×C₇₃	—	2	8	no	—
167	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
168	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
169	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
170	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
171	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
172	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
173	C₄⋊C₄×C₇₃	—	2	2	no	—
174	C₄⋊C₄×C₇₃	—	2	2	no	—
175	C₂²⋊C₄×C₇₃	—	2	4	no	—
176	C₂²⋊C₄×C₇₃	—	4	8	no	—
177	C₂²⋊C₄×C₇₃	—	4	4	no	—
178	C₂²⋊C₄×C₇₃	—	8	4	no	—
179	C₄²×C₇₃	—	2	1	no	—
180	C₄²×C₇₃	—	2	1	no	—
181	C₄²×C₇₃	—	2	1	no	—
182	C₄²×C₇₃	—	2	1	no	—
183	C₂³×C₇₃	—	2	1	no	—
184	C₂³×C₇₃	—	2	1	no	—
185	C₂³×C₇₃	—	2	2	no	—
186	C₂³×C₇₃	—	2	2	no	—
187	C₂³×C₇₃	—	2	4	no	—
188	C₂³×C₇₃	—	4	2	no	—
189	C₂³×C₇₃	—	4	2	no	—
190	C₂³×C₇₃	—	4	4	no	—
191	C₂³×C₇₃	—	4	4	no	—
192	C₂³×C₇₃	—	4	2	no	—
193	C₂³×C₇₃	—	4	2	no	—
194	C₂³×C₇₃	—	4	2	no	—
195	C₂³×C₇₃	—	4	4	no	—
196	C₂³×C₇₃	—	4	4	no	—
197	C₂³×C₇₃	#127	1	2	yes	—
198	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
199	Q₈×C₇₃	—	2	4	no	—
200	Q₈×C₇₃	—	2	4	no	—
201	Q₈×C₇₃	—	4	2	no	—
202	Q₈×C₇₃	—	4	2	no	—
203	D₄×C₇₃	—	2	4	no	—
204	D₄×C₇₃	—	2	4	no	—
205	D₄×C₇₃	—	4	16	no	—
206	D₄×C₇₃	—	4	2	no	—
207	D₄×C₇₃	—	4	2	no	—
208	D₄×C₇₃	—	4	2	no	—
209	D₄×C₇₃	—	4	2	no	—
210	D₄×C₇₃	—	4	2	no	—
211	D₄×C₇₃	—	4	2	no	—
212	D₄×C₇₃	—	8	16	no	—
213	D₄×C₇₃	—	8	8	no	—
214	C₂×C₄×C₇₃	—	2	2	no	—
215	C₂×C₄×C₇₃	—	2	1	no	—
216	C₂×C₄×C₇₃	—	2	1	no	—
217	C₂×C₄×C₇₃	—	2	2	no	—
218	C₂×C₄×C₇₃	—	2	2	no	—
219	C₂×C₄×C₇₃	—	2	2	no	—
220	C₂×C₄×C₇₃	—	2	2	no	—
221	C₂×C₄×C₇₃	—	2	2	no	—
222	C₂×C₄×C₇₃	—	2	2	no	—
223	C₂×C₄×C₇₃	—	2	4	no	—
224	C₂×C₄×C₇₃	—	2	2	no	—
225	C₂×C₄×C₇₃	—	2	2	no	—
226	C₂×C₄×C₇₃	—	4	16	no	—
227	C₂×C₄×C₇₃	—	4	2	no	—
228	C₂×C₄×C₇₃	—	4	2	no	—
229	C₂×C₄×C₇₃	—	4	2	no	—
230	C₂×C₄×C₇₃	—	4	4	no	—
231	C₂×C₄×C₇₃	#127	1	2	yes	—
232	C₂×C₄×C₇₃	#135	1	4	yes	complemented
233	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
239	C₈×C₇₃	—	2	2	no	—
240	C₈×C₇₃	—	2	2	no	—
241	C₈×C₇₃	—	2	2	no	—
242	C₈×C₇₃	#120	1	4	yes	—
243	C₂²×C₇₃	—	2	2	no	—
244	C₂²×C₇₃	—	2	2	no	—
245	C₂²×C₇₃	—	2	2	no	—
246	C₂²×C₇₃	—	4	2	no	—
247	C₂²×C₇₃	—	4	2	no	—
248	C₂²×C₇₃	—	4	4	no	—
249	C₂²×C₇₃	—	4	8	no	—
250	C₂²×C₇₃	—	8	2	no	—
251	C₂²×C₇₃	—	8	2	no	—
252	C₂²×C₇₃	—	8	4	no	—
253	C₂²×C₇₃	—	8	2	no	—
254	C₂²×C₇₃	—	8	2	no	—
255	C₂²×C₇₃	—	8	2	no	—
256	C₂²×C₇₃	—	8	4	no	—
257	C₂²×C₇₃	—	8	4	no	—
258	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
259	C₂²×C₇₃	D₄²	1	1	yes	characteristic
260	C₂²×C₇₃	D₄²	1	1	yes	characteristic
261	C₂²×C₇₃	C₂×#135	1	2	yes	—
262	C₂²×C₇₃	#576	1	2	yes	—
263	C₄×C₇₃	—	2	2	no	—
264	C₄×C₇₃	—	2	4	no	—
265	C₄×C₇₃	—	4	4	no	—
266	C₄×C₇₃	—	4	2	no	—
267	C₄×C₇₃	—	8	2	no	—
268	C₄×C₇₃	C₂×#120	1	1	yes	characteristic
269	C₄×C₇₃	#535	1	1	yes	characteristic
270	C₄×C₇₃	D₄²	1	1	yes	characteristic
271	C₄×C₇₃	D₄²	1	1	yes	characteristic
272	#25777	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
273	C₂×C₇₃	—	4	2	no	—
274	C₂×C₇₃	—	8	4	no	—
275	C₂×C₇₃	—	16	2	no	—
276	C₂×C₇₃	#2433	1	1	yes	characteristic
277	C₂×C₇₃	#3147	1	1	yes	characteristic
278	C₂×C₇₃	#3155	1	1	yes	characteristic
279	C₂×C₇₃	#3280	1	2	yes	—
280	C₂×C₇₃	#3287	1	2	yes	—
281	C₂²×#135	C₂×C₇₃	1	1	yes	characteristic, complemented
282	C₂×#495	C₂×C₇₃	1	1	yes	characteristic, complemented
283	C₂×#493	C₂×C₇₃	1	1	yes	characteristic, complemented
284	C₂×#466	C₂×C₇₃	1	1	yes	characteristic, complemented
285	C₂×#449	C₂×C₇₃	1	2	yes	complemented
286	#2431	C₂×C₇₃	1	2	yes	complemented
287	#2014	C₂×C₇₃	1	2	yes	complemented
288	#2012	C₂×C₇₃	1	2	yes	complemented
289	#1970	C₂×C₇₃	1	1	yes	characteristic, complemented
290	#1969	C₂×C₇₃	1	1	yes	characteristic, complemented
291	C₈×C₂²⋊C₄	C₂×C₇₃	1	1	yes	characteristic, complemented
292	C₇₃	#25777	1	1	yes	characteristic, direct product factor, Sylow
293	C₂²×#41	C₂²×C₇₃	1	2	yes	—
294	C₂×#135	—	2	4	no	—
295	C₂×#135	—	2	4	no	—
296	C₂×#135	—	2	4	no	—
297	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
298	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
299	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
300	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
301	C₂²×D₈	C₂²×C₇₃	1	2	yes	—
302	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
303	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
304	C₂×#127	C₂²×C₇₃	1	2	yes	—
305	C₂×#124	C₂²×C₇₃	1	2	yes	—
306	C₂×#121	C₂²×C₇₃	1	2	yes	—
307	#495	—	2	4	no	—
308	#493	—	2	4	no	—
309	#466	—	2	4	no	—
310	#449	—	2	8	no	—
311	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic
312	C₂×#103	C₂²×C₇₃	1	2	yes	—
313	C₂×#102	C₂²×C₇₃	1	2	yes	—
314	C₂×#102	C₂²×C₇₃	1	2	yes	—
315	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
316	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
317	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
318	#392	—	2	4	no	—
319	#391	C₂²×C₇₃	1	2	yes	—
320	#390	C₂²×C₇₃	1	2	yes	—
321	#386	—	2	4	no	—
322	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
323	#336	C₂²×C₇₃	1	1	yes	characteristic
324	#336	C₂²×C₇₃	1	1	yes	characteristic
325	C₂×#41	—	2	4	no	—
326	C₂×#41	—	2	4	no	—
327	C₂×#41	—	2	4	no	—
328	C₂×#41	—	2	4	no	—
329	C₂×#41	—	4	2	no	—
330	C₂×#41	—	4	2	no	—
331	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
332	C₂²×D₄	—	2	2	no	—
333	C₂²×D₄	—	2	2	no	—
334	C₂²×D₄	—	2	4	no	—
335	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
336	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
337	C₂³×C₄	—	2	2	no	—
338	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
339	#135	—	2	32	no	—
340	C₂×Q₁₆	—	2	2	no	—
341	C₂×Q₁₆	—	2	2	no	—
342	C₂×Q₁₆	D₄×C₇₃	1	4	yes	complemented
343	C₂×SD₁₆	—	2	4	no	—
344	C₂×SD₁₆	—	2	4	no	—
345	C₂×SD₁₆	—	2	4	no	—
346	C₂×SD₁₆	—	2	4	no	—
347	C₂×SD₁₆	—	2	4	no	—
348	C₂×SD₁₆	—	4	2	no	—
349	C₂×D₈	—	2	4	no	—
350	C₂×D₈	—	2	2	no	—
351	C₂×D₈	—	2	2	no	—
352	C₂×D₈	—	2	4	no	—
353	C₂×D₈	—	2	2	no	—
354	C₂×D₈	—	2	2	no	—
355	C₂×D₈	—	2	2	no	—
356	C₂×D₈	—	4	2	no	—
357	C₂×D₈	D₄×C₇₃	1	4	yes	complemented
358	C₂²×C₈	—	2	2	no	—
359	C₂²×C₈	—	2	2	no	—
360	C₂²×C₈	D₄×C₇₃	1	4	yes	complemented
361	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
362	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
363	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
365	#127	—	2	4	no	—
366	#127	—	4	2	no	—
367	#124	—	2	4	no	—
368	#124	—	4	2	no	—
369	#121	—	2	4	no	—
370	#121	—	2	4	no	—
371	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	—	2	4	no	—
374	C₂×C₂²⋊C₄	—	2	4	no	—
375	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
376	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
377	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
378	#107	—	2	2	no	—
379	#103	—	2	4	no	—
380	#102	—	2	4	no	—
381	#102	—	2	4	no	—
382	C₂²⋊C₈	D₄×C₇₃	1	4	yes	complemented
383	C₄×C₈	—	2	2	no	—
384	C₄×C₈	—	2	2	no	—
385	#95	—	2	4	no	—
386	#95	D₄×C₇₃	1	2	yes	—
387	C₂⁴	—	2	2	no	—
388	C₂⁴	—	2	2	no	—
389	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
390	#41	—	2	16	no	—
391	#41	—	4	8	no	—
392	#41	—	4	8	no	—
393	#41	—	4	8	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	4	4	no	—
412	C₂×D₄	—	4	8	no	—
413	C₂×D₄	—	4	4	no	—
414	C₂×D₄	—	4	4	no	—
415	C₂×D₄	—	4	4	no	—
416	C₂×D₄	—	4	8	no	—
417	C₂×D₄	—	8	4	no	—
418	C₂×D₄	—	8	4	no	—
419	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	4	4	no	—
427	C₂²×C₄	—	4	4	no	—
428	C₂²×C₄	—	4	4	no	—
429	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
430	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
432	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
433	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
434	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
435	Q₁₆	—	2	8	no	—
436	SD₁₆	—	2	16	no	—
437	SD₁₆	—	4	8	no	—
438	D₈	—	2	8	no	—
439	D₈	—	4	8	no	—
440	D₈	—	4	4	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	8	no	—
448	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
449	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
450	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
451	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
452	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
453	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	4	8	no	—
458	C₂²⋊C₄	—	4	4	no	—
459	C₂²⋊C₄	—	8	4	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	1	no	—
462	C₄²	—	2	1	no	—
463	C₄²	—	2	1	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	1	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	4	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	4	2	no	—
471	C₂³	—	4	4	no	—
472	C₂³	—	4	4	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	4	2	no	—
475	C₂³	—	4	2	no	—
476	C₂³	—	4	4	no	—
477	C₂³	—	4	4	no	—
478	C₂³	#127×C₇₃	1	2	yes	—
479	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
480	Q₈	—	2	4	no	—
481	Q₈	—	2	4	no	—
482	Q₈	—	4	2	no	—
483	Q₈	—	4	2	no	—
484	D₄	—	2	4	no	—
485	D₄	—	2	4	no	—
486	D₄	—	4	16	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	2	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	2	no	—
491	D₄	—	4	2	no	—
492	D₄	—	4	2	no	—
493	D₄	—	8	16	no	—
494	D₄	—	8	8	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	4	16	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	4	no	—
512	C₂×C₄	#127×C₇₃	1	2	yes	—
513	C₂×C₄	#135×C₇₃	1	4	yes	complemented
514	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
516	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
518	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
519	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
520	C₈	—	2	2	no	—
521	C₈	—	2	2	no	—
522	C₈	—	2	2	no	—
523	C₈	#120×C₇₃	1	4	yes	—
524	C₂²	—	2	2	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	2	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	8	no	—
530	C₂²	—	4	4	no	—
531	C₂²	—	8	4	no	—
532	C₂²	—	8	2	no	—
533	C₂²	—	8	2	no	—
534	C₂²	—	8	4	no	—
535	C₂²	—	8	4	no	—
536	C₂²	—	8	2	no	—
537	C₂²	—	8	2	no	—
538	C₂²	—	8	2	no	—
539	C₂²	C₂×#127×C₇₃	1	1	yes	characteristic
540	C₂²	D₄²×C₇₃	1	1	yes	characteristic
541	C₂²	D₄²×C₇₃	1	1	yes	characteristic
542	C₂²	C₂×#135×C₇₃	1	2	yes	—
543	C₂²	#576×C₇₃	1	2	yes	—
544	C₄	—	2	4	no	—
545	C₄	—	2	2	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	4	no	—
548	C₄	—	8	2	no	—
549	C₄	C₂×#120×C₇₃	1	1	yes	characteristic
550	C₄	#535×C₇₃	1	1	yes	characteristic
551	C₄	D₄²×C₇₃	1	1	yes	characteristic
552	C₄	D₄²×C₇₃	1	1	yes	characteristic
553	C₂	—	4	2	no	—
554	C₂	—	8	4	no	—
555	C₂	—	16	2	no	—
556	C₂	C₇₃×#2433	1	1	yes	characteristic
557	C₂	C₇₃×#3147	1	1	yes	characteristic
558	C₂	C₇₃×#3155	1	1	yes	characteristic
559	C₂	C₇₃×#3280	1	2	yes	—
560	C₂	C₇₃×#3287	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₄×C₂²⋊C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#135×C₇₃	C₂	semidirect
2. C₂×#495×C₇₃	C₂	semidirect
3. C₂×#493×C₇₃	C₂	semidirect
4. C₂×#466×C₇₃	C₂	semidirect
5. C₂×#449×C₇₃	C₂	semidirect
6. C₇₃×#2431	C₂	semidirect
7. C₇₃×#2014	C₂	semidirect
8. C₇₃×#2012	C₂	semidirect
9. C₇₃×#1970	C₂	semidirect
10. C₇₃×#1969	C₂	semidirect
11. C₈×C₂²⋊C₄×C₇₃	C₂	semidirect
61. C₂×Q₁₆×C₇₃	D₄	semidirect
76. C₂×D₈×C₇₃	D₄	semidirect
79. C₂²×C₈×C₇₃	D₄	semidirect
101. C₂²⋊C₈×C₇₃	D₄	semidirect
232. C₂×C₄×C₇₃	#135	semidirect
272. #25777	C₇₃	direct (N × H)
281. C₂²×#135	C₂×C₇₃	semidirect
282. C₂×#495	C₂×C₇₃	semidirect
283. C₂×#493	C₂×C₇₃	semidirect
284. C₂×#466	C₂×C₇₃	semidirect
285. C₂×#449	C₂×C₇₃	semidirect
286. #2431	C₂×C₇₃	semidirect
287. #2014	C₂×C₇₃	semidirect
288. #2012	C₂×C₇₃	semidirect
289. #1970	C₂×C₇₃	semidirect
290. #1969	C₂×C₇₃	semidirect
291. C₈×C₂²⋊C₄	C₂×C₇₃	semidirect
292. C₇₃	#25777	direct (N × H)
342. C₂×Q₁₆	D₄×C₇₃	semidirect
357. C₂×D₈	D₄×C₇₃	semidirect
360. C₂²×C₈	D₄×C₇₃	semidirect
382. C₂²⋊C₈	D₄×C₇₃	semidirect
513. C₂×C₄	#135×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#135×C₇₃	2
C₂×#495×C₇₃	2
C₂×#493×C₇₃	2
C₂×#466×C₇₃	2
C₂×#449×C₇₃	2
C₇₃×#2431	2
C₇₃×#2014	2
C₇₃×#2012	2
C₇₃×#1970	2
C₇₃×#1969	2
C₈×C₂²⋊C₄×C₇₃	2
#25777	73

Subgroups — C73×#25777 #32935181

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25777 #32935181