Subgroups — C₇₃×#25685 #32935089

Order 18688.

1096 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#540×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#501×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#486×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2628	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2034	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2033	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1991	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1961	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1864	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1862	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1750	C₂	1	1	yes	maximal, characteristic, complemented
12	#540×C₇₃	—	2	4	no	—
13	#540×C₇₃	—	2	4	no	—
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×#123×C₇₃	—	2	1	no	—
18	C₂×#123×C₇₃	—	2	1	no	—
19	C₂×#121×C₇₃	—	2	1	no	—
20	C₂×#121×C₇₃	—	2	1	no	—
21	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
26	#501×C₇₃	—	2	4	no	—
27	#486×C₇₃	—	2	4	no	—
28	C₂×#107×C₇₃	C₂²	1	2	yes	—
29	C₂×#106×C₇₃	C₂²	1	2	yes	—
30	C₂×#102×C₇₃	C₂²	1	2	yes	—
31	C₂×#102×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	2	yes	—
35	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
37	#400×C₇₃	—	2	1	no	—
38	#399×C₇₃	—	2	1	no	—
39	#395×C₇₃	—	2	1	no	—
40	#393×C₇₃	—	2	1	no	—
41	#389×C₇₃	C₂²	1	2	yes	—
42	#382×C₇₃	C₂²	1	1	yes	characteristic
43	#380×C₇₃	C₂²	1	2	yes	—
44	#340×C₇₃	C₂²	1	2	yes	—
45	#340×C₇₃	C₂²	1	2	yes	—
46	#336×C₇₃	C₂²	1	2	yes	—
47	C₂²×Q₈×C₇₃	—	2	1	no	—
48	C₂²×D₄×C₇₃	—	2	1	no	—
49	C₂²×D₄×C₇₃	—	2	1	no	—
50	C₂²×D₄×C₇₃	—	2	1	no	—
51	C₂²×D₄×C₇₃	—	2	1	no	—
52	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₇₃	—	2	1	no	—
55	C₂³×C₄×C₇₃	—	2	1	no	—
56	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
58	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
59	C₄⋊Q₈×C₇₃	—	2	2	no	—
60	C₄⋊Q₈×C₇₃	—	2	2	no	—
61	#127×C₇₃	—	2	2	no	—
62	#127×C₇₃	D₄	1	4	yes	—
63	#125×C₇₃	—	2	2	no	—
64	#125×C₇₃	D₄	1	4	yes	—
65	#123×C₇₃	—	2	8	no	—
66	#123×C₇₃	—	2	8	no	—
67	#121×C₇₃	—	2	8	no	—
68	#121×C₇₃	—	2	8	no	—
69	#121×C₇₃	—	2	2	no	—
70	#121×C₇₃	—	2	2	no	—
71	#121×C₇₃	—	2	2	no	—
72	#121×C₇₃	—	2	2	no	—
73	C₄×D₄×C₇₃	—	2	2	no	—
74	C₄×D₄×C₇₃	—	2	2	no	—
75	C₄×D₄×C₇₃	—	2	2	no	—
76	C₄×D₄×C₇₃	—	2	2	no	—
77	#117×C₇₃	—	2	2	no	—
78	#117×C₇₃	—	2	2	no	—
79	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
81	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
83	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
98	#107×C₇₃	—	2	4	no	—
99	#106×C₇₃	—	2	4	no	—
100	#102×C₇₃	—	2	4	no	—
101	#102×C₇₃	—	2	4	no	—
102	#102×C₇₃	—	2	4	no	—
103	#102×C₇₃	—	2	4	no	—
104	C₂²⋊C₈×C₇₃	—	2	4	no	—
105	#97×C₇₃	—	2	2	no	—
106	C₄×C₈×C₇₃	—	2	2	no	—
107	#95×C₇₃	—	2	2	no	—
108	#95×C₇₃	—	2	1	no	—
109	#95×C₇₃	—	2	1	no	—
110	#95×C₇₃	—	2	2	no	—
111	C₂⁴×C₇₃	—	2	1	no	—
112	C₂⁴×C₇₃	—	2	1	no	—
113	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
114	C₂×Q₈×C₇₃	—	4	2	no	—
115	C₂×Q₈×C₇₃	—	8	2	no	—
116	C₂×D₄×C₇₃	—	2	4	no	—
117	C₂×D₄×C₇₃	—	2	4	no	—
118	C₂×D₄×C₇₃	—	2	4	no	—
119	C₂×D₄×C₇₃	—	2	4	no	—
120	C₂×D₄×C₇₃	—	2	1	no	—
121	C₂×D₄×C₇₃	—	2	1	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	—	8	2	no	—
127	C₂×D₄×C₇₃	—	8	2	no	—
128	C₂×D₄×C₇₃	—	8	2	no	—
129	C₂×D₄×C₇₃	—	8	2	no	—
130	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
131	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₇₃	—	2	1	no	—
133	C₂²×C₄×C₇₃	—	2	1	no	—
134	C₂²×C₄×C₇₃	—	2	4	no	—
135	C₂²×C₄×C₇₃	—	2	4	no	—
136	C₂²×C₄×C₇₃	—	2	1	no	—
137	C₂²×C₄×C₇₃	—	2	1	no	—
138	C₂²×C₄×C₇₃	—	2	2	no	—
139	C₂²×C₄×C₇₃	—	2	2	no	—
140	C₂²×C₄×C₇₃	—	2	2	no	—
141	C₂²×C₄×C₇₃	—	2	2	no	—
142	C₂²×C₄×C₇₃	—	8	2	no	—
143	C₂²×C₄×C₇₃	—	8	2	no	—
144	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
150	C₂×C₈×C₇₃	—	2	2	no	—
151	C₂×C₈×C₇₃	—	2	2	no	—
152	C₂×C₈×C₇₃	—	2	2	no	—
153	C₂×C₈×C₇₃	—	2	2	no	—
154	C₂×C₈×C₇₃	—	2	2	no	—
155	C₂×C₈×C₇₃	#41	1	4	yes	—
156	C₄⋊C₄×C₇₃	—	2	4	no	—
157	C₄⋊C₄×C₇₃	—	2	4	no	—
158	C₄⋊C₄×C₇₃	—	2	2	no	—
159	C₄⋊C₄×C₇₃	—	2	2	no	—
160	C₄⋊C₄×C₇₃	—	2	1	no	—
161	C₄⋊C₄×C₇₃	—	2	1	no	—
162	C₄⋊C₄×C₇₃	—	2	2	no	—
163	C₄⋊C₄×C₇₃	—	2	2	no	—
164	C₄⋊C₄×C₇₃	—	2	2	no	—
165	C₄⋊C₄×C₇₃	—	2	2	no	—
166	C₄⋊C₄×C₇₃	—	4	2	no	—
167	C₄⋊C₄×C₇₃	—	8	2	no	—
168	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
169	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
170	C₂²⋊C₄×C₇₃	—	2	4	no	—
171	C₂²⋊C₄×C₇₃	—	2	4	no	—
172	C₂²⋊C₄×C₇₃	—	2	4	no	—
173	C₂²⋊C₄×C₇₃	—	2	4	no	—
174	C₂²⋊C₄×C₇₃	—	2	2	no	—
175	C₂²⋊C₄×C₇₃	—	2	2	no	—
176	C₂²⋊C₄×C₇₃	—	8	2	no	—
177	C₄²×C₇₃	—	2	1	no	—
178	C₄²×C₇₃	—	2	1	no	—
179	C₄²×C₇₃	C₂×D₄	1	2	yes	—
180	C₄²×C₇₃	C₂×D₄	1	2	yes	—
181	C₂³×C₇₃	—	2	1	no	—
182	C₂³×C₇₃	—	2	2	no	—
183	C₂³×C₇₃	—	2	2	no	—
184	C₂³×C₇₃	—	2	1	no	—
185	C₂³×C₇₃	—	2	1	no	—
186	C₂³×C₇₃	—	2	2	no	—
187	C₂³×C₇₃	—	2	2	no	—
188	C₂³×C₇₃	—	4	1	no	—
189	C₂³×C₇₃	—	4	1	no	—
190	C₂³×C₇₃	—	4	1	no	—
191	C₂³×C₇₃	—	4	1	no	—
192	C₂³×C₇₃	—	4	2	no	—
193	C₂³×C₇₃	—	4	2	no	—
194	C₂³×C₇₃	—	4	2	no	—
195	C₂³×C₇₃	—	4	2	no	—
196	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
197	Q₈×C₇₃	—	8	4	no	—
198	D₄×C₇₃	—	2	4	no	—
199	D₄×C₇₃	—	2	4	no	—
200	D₄×C₇₃	—	4	2	no	—
201	D₄×C₇₃	—	4	2	no	—
202	D₄×C₇₃	—	8	4	no	—
203	D₄×C₇₃	—	8	4	no	—
204	D₄×C₇₃	—	8	4	no	—
205	D₄×C₇₃	—	8	4	no	—
206	C₂×C₄×C₇₃	—	2	2	no	—
207	C₂×C₄×C₇₃	—	2	2	no	—
208	C₂×C₄×C₇₃	—	2	1	no	—
209	C₂×C₄×C₇₃	—	2	1	no	—
210	C₂×C₄×C₇₃	—	2	1	no	—
211	C₂×C₄×C₇₃	—	2	2	no	—
212	C₂×C₄×C₇₃	—	2	2	no	—
213	C₂×C₄×C₇₃	—	2	1	no	—
214	C₂×C₄×C₇₃	—	2	1	no	—
215	C₂×C₄×C₇₃	—	2	2	no	—
216	C₂×C₄×C₇₃	—	2	2	no	—
217	C₂×C₄×C₇₃	—	4	2	no	—
218	C₂×C₄×C₇₃	—	4	2	no	—
219	C₂×C₄×C₇₃	—	4	2	no	—
220	C₂×C₄×C₇₃	—	4	2	no	—
221	C₂×C₄×C₇₃	—	4	2	no	—
222	C₂×C₄×C₇₃	—	4	2	no	—
223	C₂×C₄×C₇₃	—	4	2	no	—
224	C₂×C₄×C₇₃	—	4	2	no	—
225	C₂×C₄×C₇₃	—	4	2	no	—
226	C₂×C₄×C₇₃	—	4	2	no	—
227	C₂×C₄×C₇₃	—	8	4	no	—
228	C₂×C₄×C₇₃	—	8	4	no	—
229	C₂×C₄×C₇₃	#120	1	2	yes	—
230	C₂×C₄×C₇₃	#120	1	2	yes	—
231	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
234	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
235	C₈×C₇₃	—	2	4	no	—
236	C₈×C₇₃	—	4	2	no	—
237	C₂²×C₇₃	—	4	2	no	—
238	C₂²×C₇₃	—	4	1	no	—
239	C₂²×C₇₃	—	4	2	no	—
240	C₂²×C₇₃	—	4	2	no	—
241	C₂²×C₇₃	—	4	2	no	—
242	C₂²×C₇₃	—	4	2	no	—
243	C₂²×C₇₃	—	4	1	no	—
244	C₂²×C₇₃	—	4	2	no	—
245	C₂²×C₇₃	—	4	2	no	—
246	C₂²×C₇₃	—	4	1	no	—
247	C₂²×C₇₃	—	4	2	no	—
248	C₂²×C₇₃	—	8	2	no	—
249	C₂²×C₇₃	—	8	2	no	—
250	C₂²×C₇₃	—	8	2	no	—
251	C₂²×C₇₃	—	8	2	no	—
252	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
253	C₂²×C₇₃	#532	1	1	yes	characteristic
254	C₂²×C₇₃	#536	1	1	yes	characteristic
255	C₂²×C₇₃	#576	1	2	yes	—
256	C₂²×C₇₃	#577	1	2	yes	—
257	C₄×C₇₃	—	2	2	no	—
258	C₄×C₇₃	—	2	2	no	—
259	C₄×C₇₃	—	4	1	no	—
260	C₄×C₇₃	—	4	1	no	—
261	C₄×C₇₃	—	4	2	no	—
262	C₄×C₇₃	—	4	1	no	—
263	C₄×C₇₃	—	4	2	no	—
264	C₄×C₇₃	—	8	2	no	—
265	C₄×C₇₃	—	8	2	no	—
266	C₄×C₇₃	#547	1	2	yes	—
267	C₄×C₇₃	#548	1	2	yes	—
268	#25685	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
269	C₂×C₇₃	—	8	1	no	—
270	C₂×C₇₃	—	8	2	no	—
271	C₂×C₇₃	—	8	2	no	—
272	C₂×C₇₃	#2432	1	1	yes	characteristic
273	C₂×C₇₃	#3008	1	1	yes	characteristic
274	C₂×C₇₃	#3009	1	1	yes	characteristic
275	C₂×C₇₃	#3179	1	2	yes	—
276	C₂×C₇₃	#3241	1	2	yes	—
277	C₂×#540	C₂×C₇₃	1	1	yes	characteristic
278	C₂×#501	C₂×C₇₃	1	1	yes	characteristic, complemented
279	C₂×#486	C₂×C₇₃	1	1	yes	characteristic, complemented
280	#2628	C₂×C₇₃	1	1	yes	characteristic, complemented
281	#2034	C₂×C₇₃	1	2	yes	complemented
282	#2033	C₂×C₇₃	1	2	yes	complemented
283	#1991	C₂×C₇₃	1	1	yes	characteristic, complemented
284	#1961	C₂×C₇₃	1	1	yes	characteristic, complemented
285	#1864	C₂×C₇₃	1	2	yes	complemented
286	#1862	C₂×C₇₃	1	2	yes	complemented
287	#1750	C₂×C₇₃	1	1	yes	characteristic, complemented
288	C₇₃	#25685	1	1	yes	characteristic, direct product factor, Sylow
289	#540	—	2	4	no	—
290	#540	—	2	4	no	—
291	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
292	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
293	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
294	C₂×#123	—	2	1	no	—
295	C₂×#123	—	2	1	no	—
296	C₂×#121	—	2	1	no	—
297	C₂×#121	—	2	1	no	—
298	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
299	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
300	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
301	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
302	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
303	#501	—	2	4	no	—
304	#486	—	2	4	no	—
305	C₂×#107	C₂²×C₇₃	1	2	yes	—
306	C₂×#106	C₂²×C₇₃	1	2	yes	—
307	C₂×#102	C₂²×C₇₃	1	2	yes	—
308	C₂×#102	C₂²×C₇₃	1	2	yes	—
309	C₂×#102	C₂²×C₇₃	1	2	yes	—
310	C₂×#102	C₂²×C₇₃	1	2	yes	—
311	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
312	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
313	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
314	#400	—	2	1	no	—
315	#399	—	2	1	no	—
316	#395	—	2	1	no	—
317	#393	—	2	1	no	—
318	#389	C₂²×C₇₃	1	2	yes	—
319	#382	C₂²×C₇₃	1	1	yes	characteristic
320	#380	C₂²×C₇₃	1	2	yes	—
321	#340	C₂²×C₇₃	1	2	yes	—
322	#340	C₂²×C₇₃	1	2	yes	—
323	#336	C₂²×C₇₃	1	2	yes	—
324	C₂²×Q₈	—	2	1	no	—
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	—	2	1	no	—
329	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
330	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
331	C₂³×C₄	—	2	1	no	—
332	C₂³×C₄	—	2	1	no	—
333	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
334	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
335	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
336	C₄⋊Q₈	—	2	2	no	—
337	C₄⋊Q₈	—	2	2	no	—
338	#127	—	2	2	no	—
339	#127	D₄×C₇₃	1	4	yes	—
340	#125	—	2	2	no	—
341	#125	D₄×C₇₃	1	4	yes	—
342	#123	—	2	8	no	—
343	#123	—	2	8	no	—
344	#121	—	2	8	no	—
345	#121	—	2	8	no	—
346	#121	—	2	2	no	—
347	#121	—	2	2	no	—
348	#121	—	2	2	no	—
349	#121	—	2	2	no	—
350	C₄×D₄	—	2	2	no	—
351	C₄×D₄	—	2	2	no	—
352	C₄×D₄	—	2	2	no	—
353	C₄×D₄	—	2	2	no	—
354	#117	—	2	2	no	—
355	#117	—	2	2	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
361	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₂²⋊C₄	—	2	2	no	—
371	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
372	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
373	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
374	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
375	#107	—	2	4	no	—
376	#106	—	2	4	no	—
377	#102	—	2	4	no	—
378	#102	—	2	4	no	—
379	#102	—	2	4	no	—
380	#102	—	2	4	no	—
381	C₂²⋊C₈	—	2	4	no	—
382	#97	—	2	2	no	—
383	C₄×C₈	—	2	2	no	—
384	#95	—	2	2	no	—
385	#95	—	2	1	no	—
386	#95	—	2	1	no	—
387	#95	—	2	2	no	—
388	C₂⁴	—	2	1	no	—
389	C₂⁴	—	2	1	no	—
390	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
391	C₂×Q₈	—	4	2	no	—
392	C₂×Q₈	—	8	2	no	—
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	8	2	no	—
404	C₂×D₄	—	8	2	no	—
405	C₂×D₄	—	8	2	no	—
406	C₂×D₄	—	8	2	no	—
407	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
408	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	8	2	no	—
420	C₂²×C₄	—	8	2	no	—
421	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
423	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
426	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	#41×C₇₃	1	4	yes	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	4	2	no	—
444	C₄⋊C₄	—	8	2	no	—
445	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
446	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	8	2	no	—
454	C₄²	—	2	1	no	—
455	C₄²	—	2	1	no	—
456	C₄²	C₂×D₄×C₇₃	1	2	yes	—
457	C₄²	C₂×D₄×C₇₃	1	2	yes	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	4	1	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	4	2	no	—
471	C₂³	—	4	2	no	—
472	C₂³	—	4	2	no	—
473	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
474	Q₈	—	8	4	no	—
475	D₄	—	2	4	no	—
476	D₄	—	2	4	no	—
477	D₄	—	4	2	no	—
478	D₄	—	4	2	no	—
479	D₄	—	8	4	no	—
480	D₄	—	8	4	no	—
481	D₄	—	8	4	no	—
482	D₄	—	8	4	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	8	4	no	—
505	C₂×C₄	—	8	4	no	—
506	C₂×C₄	#120×C₇₃	1	2	yes	—
507	C₂×C₄	#120×C₇₃	1	2	yes	—
508	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
509	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
510	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
511	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
512	C₈	—	2	4	no	—
513	C₈	—	4	2	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	1	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	1	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	8	2	no	—
526	C₂²	—	8	2	no	—
527	C₂²	—	8	2	no	—
528	C₂²	—	8	2	no	—
529	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
530	C₂²	#532×C₇₃	1	1	yes	characteristic
531	C₂²	#536×C₇₃	1	1	yes	characteristic
532	C₂²	#576×C₇₃	1	2	yes	—
533	C₂²	#577×C₇₃	1	2	yes	—
534	C₄	—	2	2	no	—
535	C₄	—	2	2	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	2	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	1	no	—
541	C₄	—	8	2	no	—
542	C₄	—	8	2	no	—
543	C₄	#547×C₇₃	1	2	yes	—
544	C₄	#548×C₇₃	1	2	yes	—
545	C₂	—	8	1	no	—
546	C₂	—	8	2	no	—
547	C₂	—	8	2	no	—
548	C₂	C₇₃×#2432	1	1	yes	characteristic
549	C₂	C₇₃×#3008	1	1	yes	characteristic
550	C₂	C₇₃×#3009	1	1	yes	characteristic
551	C₂	C₇₃×#3179	1	2	yes	—
552	C₂	C₇₃×#3241	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#540×C₇₃	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×#117×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#501×C₇₃	C₂	semidirect
3. C₂×#486×C₇₃	C₂	semidirect
4. C₇₃×#2628	C₂	semidirect
5. C₇₃×#2034	C₂	semidirect
6. C₇₃×#2033	C₂	semidirect
7. C₇₃×#1991	C₂	semidirect
8. C₇₃×#1961	C₂	semidirect
9. C₇₃×#1864	C₂	semidirect
10. C₇₃×#1862	C₂	semidirect
11. C₇₃×#1750	C₂	semidirect
268. #25685	C₇₃	direct (N × H)
278. C₂×#501	C₂×C₇₃	semidirect
279. C₂×#486	C₂×C₇₃	semidirect
280. #2628	C₂×C₇₃	semidirect
281. #2034	C₂×C₇₃	semidirect
282. #2033	C₂×C₇₃	semidirect
283. #1991	C₂×C₇₃	semidirect
284. #1961	C₂×C₇₃	semidirect
285. #1864	C₂×C₇₃	semidirect
286. #1862	C₂×C₇₃	semidirect
287. #1750	C₂×C₇₃	semidirect
288. C₇₃	#25685	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#540×C₇₃	2
C₂×#501×C₇₃	2
C₂×#486×C₇₃	2
C₇₃×#2628	2
C₇₃×#2034	2
C₇₃×#2033	2
C₇₃×#1991	2
C₇₃×#1961	2
C₇₃×#1864	2
C₇₃×#1862	2
C₇₃×#1750	2
#25685	73

Subgroups — C73×#25685 #32935089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25685 #32935089