Subgroups — C₂×C₇₃×#3199 #32970147

Order 18688.

2506 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#535×C₇₃	C₂	1	2	yes	maximal, complemented
2	C₇₃×#3199	C₂	1	16	yes	maximal, direct product factor
3	C₂×#482×C₇₃	C₂	1	4	yes	maximal, complemented
4	C₂×#469×C₇₃	C₂	1	2	yes	maximal, complemented
5	C₂×#466×C₇₃	C₂	1	2	yes	maximal, complemented
6	C₂×#447×C₇₃	C₂	1	4	yes	maximal, complemented
7	C₂×#408×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₇₃	C₂²	1	2	yes	complemented
10	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
11	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
12	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
13	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
14	#535×C₇₃	—	2	8	no	—
15	#535×C₇₃	C₂²	1	16	yes	complemented
16	C₂×#127×C₇₃	—	2	2	no	—
17	C₂×#124×C₇₃	—	2	2	no	—
18	C₂×#121×C₇₃	C₂²	1	4	yes	—
19	C₂×#121×C₇₃	C₂²	1	4	yes	complemented
20	C₂×#120×C₇₃	—	2	2	no	—
21	C₂×#120×C₇₃	—	2	2	no	—
22	C₂×#117×C₇₃	C₂²	1	2	yes	complemented
23	#482×C₇₃	C₂²	1	32	yes	complemented
24	#469×C₇₃	C₂²	1	16	yes	complemented
25	#466×C₇₃	C₂²	1	16	yes	complemented
26	#447×C₇₃	C₂²	1	32	yes	complemented
27	C₂×#107×C₇₃	C₂²	1	2	yes	complemented
28	C₂×#106×C₇₃	C₂²	1	2	yes	complemented
29	C₂×#102×C₇₃	C₂²	1	4	yes	complemented
30	C₂×#102×C₇₃	C₂²	1	4	yes	complemented
31	#408×C₇₃	C₂²	1	8	yes	complemented
32	C₂×C₂²⋊C₈×C₇₃	C₂²	1	4	yes	complemented
33	C₂⁵×C₇₃	—	2	2	no	—
34	C₂×#41×C₇₃	—	4	2	no	—
35	C₂×#41×C₇₃	—	4	2	no	—
36	C₂×#41×C₇₃	D₄	1	4	yes	—
37	C₂×#41×C₇₃	C₂³	1	4	yes	—
38	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
39	C₂²×D₄×C₇₃	—	2	4	no	—
40	C₂²×D₄×C₇₃	—	2	4	no	—
41	C₂²×D₄×C₇₃	—	2	2	no	—
42	C₂²×D₄×C₇₃	—	2	4	no	—
43	C₂²×D₄×C₇₃	—	4	4	no	—
44	C₂²×D₄×C₇₃	—	4	4	no	—
45	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₇₃	D₄	1	2	yes	—
47	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
48	C₂²×D₄×C₇₃	C₂³	1	8	yes	complemented
49	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
51	C₂×D₈×C₇₃	—	4	4	no	—
52	C₂×D₈×C₇₃	—	4	4	no	—
53	C₂×D₈×C₇₃	C₂³	1	8	yes	—
54	C₂×D₈×C₇₃	C₂³	1	8	yes	—
55	C₂×M₁₆×C₇₃	—	4	2	no	—
56	C₂×M₁₆×C₇₃	C₂³	1	4	yes	complemented
57	C₂²×C₈×C₇₃	—	4	2	no	—
58	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
59	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
60	C₂²×C₈×C₇₃	C₂³	1	4	yes	complemented
61	#127×C₇₃	—	2	16	no	—
62	#124×C₇₃	—	2	16	no	—
63	#121×C₇₃	—	2	8	no	—
64	#121×C₇₃	—	2	8	no	—
65	#121×C₇₃	C₂³	1	16	yes	—
66	#121×C₇₃	C₂³	1	16	yes	complemented
67	#120×C₇₃	—	2	16	no	—
68	#120×C₇₃	—	2	16	no	—
69	#117×C₇₃	—	2	4	no	—
70	#117×C₇₃	C₂³	1	8	yes	complemented
71	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
72	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
74	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
75	C₂×C₄²×C₇₃	—	2	2	no	—
76	#107×C₇₃	C₂³	1	8	yes	complemented
77	#106×C₇₃	C₂³	1	8	yes	complemented
78	#102×C₇₃	C₂³	1	16	yes	complemented
79	#102×C₇₃	C₂³	1	16	yes	complemented
80	C₂²⋊C₈×C₇₃	C₂³	1	16	yes	complemented
81	C₂⁴×C₇₃	—	2	4	no	—
82	C₂⁴×C₇₃	—	2	8	no	—
83	C₂⁴×C₇₃	—	4	8	no	—
84	C₂⁴×C₇₃	—	8	8	no	—
85	C₂⁴×C₇₃	C₂×D₄	1	2	yes	—
86	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
87	#41×C₇₃	—	4	8	no	—
88	#41×C₇₃	—	4	4	no	—
89	#41×C₇₃	—	4	4	no	—
90	C₂×Q₈×C₇₃	—	4	2	no	—
91	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
92	C₂×D₄×C₇₃	—	2	16	no	—
93	C₂×D₄×C₇₃	—	2	16	no	—
94	C₂×D₄×C₇₃	—	2	4	no	—
95	C₂×D₄×C₇₃	—	2	8	no	—
96	C₂×D₄×C₇₃	—	2	8	no	—
97	C₂×D₄×C₇₃	—	2	8	no	—
98	C₂×D₄×C₇₃	—	4	8	no	—
99	C₂×D₄×C₇₃	—	4	8	no	—
100	C₂×D₄×C₇₃	—	4	4	no	—
101	C₂×D₄×C₇₃	—	4	2	no	—
102	C₂×D₄×C₇₃	—	4	8	no	—
103	C₂×D₄×C₇₃	—	4	16	no	—
104	C₂×D₄×C₇₃	—	8	8	no	—
105	C₂×D₄×C₇₃	—	8	8	no	—
106	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
107	C₂×D₄×C₇₃	C₂×D₄	1	8	yes	—
108	C₂×D₄×C₇₃	C₂⁴	1	8	yes	—
109	C₂²×C₄×C₇₃	—	2	2	no	—
110	C₂²×C₄×C₇₃	—	2	2	no	—
111	C₂²×C₄×C₇₃	—	2	4	no	—
112	C₂²×C₄×C₇₃	—	2	4	no	—
113	C₂²×C₄×C₇₃	—	2	4	no	—
114	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
119	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
120	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
121	D₈×C₇₃	—	4	8	no	—
122	D₈×C₇₃	—	4	8	no	—
123	M₁₆×C₇₃	—	4	4	no	—
124	C₂×C₈×C₇₃	—	2	4	no	—
125	C₂×C₈×C₇₃	—	2	4	no	—
126	C₂×C₈×C₇₃	—	4	4	no	—
127	C₂×C₈×C₇₃	C₂⁴	1	4	yes	—
128	C₂×C₈×C₇₃	C₂⁴	1	4	yes	—
129	C₄⋊C₄×C₇₃	—	2	4	no	—
130	C₄⋊C₄×C₇₃	C₂⁴	1	8	yes	—
131	C₂²⋊C₄×C₇₃	—	2	8	no	—
132	C₂²⋊C₄×C₇₃	—	2	16	no	—
133	C₂²⋊C₄×C₇₃	—	2	16	no	—
134	C₄²×C₇₃	—	2	8	no	—
135	C₂³×C₇₃	—	2	4	no	—
136	C₂³×C₇₃	—	2	2	no	—
137	C₂³×C₇₃	—	2	4	no	—
138	C₂³×C₇₃	—	2	8	no	—
139	C₂³×C₇₃	—	2	8	no	—
140	C₂³×C₇₃	—	4	16	no	—
141	C₂³×C₇₃	—	4	8	no	—
142	C₂³×C₇₃	—	4	8	no	—
143	C₂³×C₇₃	—	4	8	no	—
144	C₂³×C₇₃	—	8	16	no	—
145	C₂³×C₇₃	—	8	32	no	—
146	C₂³×C₇₃	C₂²×D₄	1	4	yes	—
147	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
148	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
149	Q₈×C₇₃	—	4	4	no	—
150	D₄×C₇₃	—	2	8	no	—
151	D₄×C₇₃	—	2	8	no	—
152	D₄×C₇₃	—	4	8	no	—
153	D₄×C₇₃	—	4	4	no	—
154	D₄×C₇₃	—	4	16	no	—
155	D₄×C₇₃	—	4	8	no	—
156	D₄×C₇₃	—	8	16	no	—
157	D₄×C₇₃	—	8	16	no	—
158	C₂×C₄×C₇₃	—	2	4	no	—
159	C₂×C₄×C₇₃	—	2	2	no	—
160	C₂×C₄×C₇₃	—	2	8	no	—
161	C₂×C₄×C₇₃	—	2	4	no	—
162	C₂×C₄×C₇₃	—	2	2	no	—
163	C₂×C₄×C₇₃	—	2	2	no	—
164	C₂×C₄×C₇₃	—	2	4	no	—
165	C₂×C₄×C₇₃	—	2	4	no	—
166	C₂×C₄×C₇₃	—	2	8	no	—
167	C₂×C₄×C₇₃	—	4	8	no	—
168	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
169	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
172	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
173	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
174	C₈×C₇₃	—	2	4	no	—
175	C₈×C₇₃	—	2	4	no	—
176	C₂²×C₇₃	—	2	4	no	—
177	C₂²×C₇₃	—	2	2	no	—
178	C₂²×C₇₃	—	2	4	no	—
179	C₂²×C₇₃	—	2	8	no	—
180	C₂²×C₇₃	—	4	4	no	—
181	C₂²×C₇₃	—	4	8	no	—
182	C₂²×C₇₃	—	4	8	no	—
183	C₂²×C₇₃	—	4	8	no	—
184	C₂²×C₇₃	—	4	8	no	—
185	C₂²×C₇₃	—	8	32	no	—
186	C₂²×C₇₃	—	8	16	no	—
187	C₂²×C₇₃	#534	1	2	yes	—
188	C₂²×C₇₃	#576	1	4	yes	—
189	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
190	C₄×C₇₃	—	2	4	no	—
191	C₄×C₇₃	—	2	2	no	—
192	C₄×C₇₃	—	4	8	no	—
193	C₄×C₇₃	#534	1	2	yes	—
194	C₄×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
195	C₄×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
196	C₂×#3199	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂×C₇₃	—	4	2	no	—
198	C₂×C₇₃	—	4	4	no	—
199	C₂×C₇₃	—	8	8	no	—
200	C₂×C₇₃	#3199	1	4	yes	direct product factor
201	C₂×C₇₃	C₂×#534	1	1	yes	characteristic
202	C₂×C₇₃	C₂×#576	1	2	yes	—
203	C₂×#535	C₂×C₇₃	1	2	yes	complemented
204	#3199	C₂×C₇₃	1	16	yes	direct product factor
205	C₂×#482	C₂×C₇₃	1	4	yes	complemented
206	C₂×#469	C₂×C₇₃	1	2	yes	complemented
207	C₂×#466	C₂×C₇₃	1	2	yes	complemented
208	C₂×#447	C₂×C₇₃	1	4	yes	complemented
209	C₂×#408	C₂×C₇₃	1	1	yes	characteristic, complemented
210	C₇₃	C₂×#3199	1	1	yes	characteristic, direct product factor, Sylow
211	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
212	C₂³×D₄	C₂²×C₇₃	1	2	yes	complemented
213	C₂²×D₈	C₂²×C₇₃	1	2	yes	—
214	C₂²×D₈	C₂²×C₇₃	1	2	yes	—
215	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
216	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
217	#535	—	2	8	no	—
218	#535	C₂²×C₇₃	1	16	yes	complemented
219	C₂×#127	—	2	2	no	—
220	C₂×#124	—	2	2	no	—
221	C₂×#121	C₂²×C₇₃	1	4	yes	—
222	C₂×#121	C₂²×C₇₃	1	4	yes	complemented
223	C₂×#120	—	2	2	no	—
224	C₂×#120	—	2	2	no	—
225	C₂×#117	C₂²×C₇₃	1	2	yes	complemented
226	#482	C₂²×C₇₃	1	32	yes	complemented
227	#469	C₂²×C₇₃	1	16	yes	complemented
228	#466	C₂²×C₇₃	1	16	yes	complemented
229	#447	C₂²×C₇₃	1	32	yes	complemented
230	C₂×#107	C₂²×C₇₃	1	2	yes	complemented
231	C₂×#106	C₂²×C₇₃	1	2	yes	complemented
232	C₂×#102	C₂²×C₇₃	1	4	yes	complemented
233	C₂×#102	C₂²×C₇₃	1	4	yes	complemented
234	#408	C₂²×C₇₃	1	8	yes	complemented
235	C₂×C₂²⋊C₈	C₂²×C₇₃	1	4	yes	complemented
236	C₂⁵	—	2	2	no	—
237	C₂×#41	—	4	2	no	—
238	C₂×#41	—	4	2	no	—
239	C₂×#41	D₄×C₇₃	1	4	yes	—
240	C₂×#41	C₂³×C₇₃	1	4	yes	—
241	C₂²×Q₈	D₄×C₇₃	1	1	yes	characteristic
242	C₂²×D₄	—	2	4	no	—
243	C₂²×D₄	—	2	4	no	—
244	C₂²×D₄	—	2	2	no	—
245	C₂²×D₄	—	2	4	no	—
246	C₂²×D₄	—	4	4	no	—
247	C₂²×D₄	—	4	4	no	—
248	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
249	C₂²×D₄	D₄×C₇₃	1	2	yes	—
250	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
251	C₂²×D₄	C₂³×C₇₃	1	8	yes	complemented
252	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
253	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
254	C₂×D₈	—	4	4	no	—
255	C₂×D₈	—	4	4	no	—
256	C₂×D₈	C₂³×C₇₃	1	8	yes	—
257	C₂×D₈	C₂³×C₇₃	1	8	yes	—
258	C₂×M₁₆	—	4	2	no	—
259	C₂×M₁₆	C₂³×C₇₃	1	4	yes	complemented
260	C₂²×C₈	—	4	2	no	—
261	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
262	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
263	C₂²×C₈	C₂³×C₇₃	1	4	yes	complemented
264	#127	—	2	16	no	—
265	#124	—	2	16	no	—
266	#121	—	2	8	no	—
267	#121	—	2	8	no	—
268	#121	C₂³×C₇₃	1	16	yes	—
269	#121	C₂³×C₇₃	1	16	yes	complemented
270	#120	—	2	16	no	—
271	#120	—	2	16	no	—
272	#117	—	2	4	no	—
273	#117	C₂³×C₇₃	1	8	yes	complemented
274	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	4	no	—
277	C₂×C₂²⋊C₄	—	2	4	no	—
278	C₂×C₄²	—	2	2	no	—
279	#107	C₂³×C₇₃	1	8	yes	complemented
280	#106	C₂³×C₇₃	1	8	yes	complemented
281	#102	C₂³×C₇₃	1	16	yes	complemented
282	#102	C₂³×C₇₃	1	16	yes	complemented
283	C₂²⋊C₈	C₂³×C₇₃	1	16	yes	complemented
284	C₂⁴	—	2	4	no	—
285	C₂⁴	—	2	8	no	—
286	C₂⁴	—	4	8	no	—
287	C₂⁴	—	8	8	no	—
288	C₂⁴	C₂×D₄×C₇₃	1	2	yes	—
289	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
290	#41	—	4	8	no	—
291	#41	—	4	4	no	—
292	#41	—	4	4	no	—
293	C₂×Q₈	—	4	2	no	—
294	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
295	C₂×D₄	—	2	16	no	—
296	C₂×D₄	—	2	16	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	8	no	—
299	C₂×D₄	—	2	8	no	—
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	4	8	no	—
302	C₂×D₄	—	4	8	no	—
303	C₂×D₄	—	4	4	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	8	no	—
306	C₂×D₄	—	4	16	no	—
307	C₂×D₄	—	8	8	no	—
308	C₂×D₄	—	8	8	no	—
309	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
310	C₂×D₄	C₂×D₄×C₇₃	1	8	yes	—
311	C₂×D₄	C₂⁴×C₇₃	1	8	yes	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
320	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
321	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
322	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
323	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
324	D₈	—	4	8	no	—
325	D₈	—	4	8	no	—
326	M₁₆	—	4	4	no	—
327	C₂×C₈	—	2	4	no	—
328	C₂×C₈	—	2	4	no	—
329	C₂×C₈	—	4	4	no	—
330	C₂×C₈	C₂⁴×C₇₃	1	4	yes	—
331	C₂×C₈	C₂⁴×C₇₃	1	4	yes	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	C₂⁴×C₇₃	1	8	yes	—
334	C₂²⋊C₄	—	2	8	no	—
335	C₂²⋊C₄	—	2	16	no	—
336	C₂²⋊C₄	—	2	16	no	—
337	C₄²	—	2	8	no	—
338	C₂³	—	2	4	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	4	no	—
341	C₂³	—	2	8	no	—
342	C₂³	—	2	8	no	—
343	C₂³	—	4	16	no	—
344	C₂³	—	4	8	no	—
345	C₂³	—	4	8	no	—
346	C₂³	—	4	8	no	—
347	C₂³	—	8	16	no	—
348	C₂³	—	8	32	no	—
349	C₂³	C₂²×D₄×C₇₃	1	4	yes	—
350	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
351	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
352	Q₈	—	4	4	no	—
353	D₄	—	2	8	no	—
354	D₄	—	2	8	no	—
355	D₄	—	4	8	no	—
356	D₄	—	4	4	no	—
357	D₄	—	4	16	no	—
358	D₄	—	4	8	no	—
359	D₄	—	8	16	no	—
360	D₄	—	8	16	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	8	no	—
370	C₂×C₄	—	4	8	no	—
371	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
372	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
373	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
374	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
375	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
376	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
377	C₈	—	2	4	no	—
378	C₈	—	2	4	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	8	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	4	8	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	8	no	—
386	C₂²	—	4	8	no	—
387	C₂²	—	4	8	no	—
388	C₂²	—	8	32	no	—
389	C₂²	—	8	16	no	—
390	C₂²	#534×C₇₃	1	2	yes	—
391	C₂²	#576×C₇₃	1	4	yes	—
392	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
393	C₄	—	2	4	no	—
394	C₄	—	2	2	no	—
395	C₄	—	4	8	no	—
396	C₄	#534×C₇₃	1	2	yes	—
397	C₄	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
398	C₄	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
399	C₂	—	4	4	no	—
400	C₂	—	4	2	no	—
401	C₂	—	8	8	no	—
402	C₂	C₇₃×#3199	1	4	yes	direct product factor
403	C₂	C₂×#534×C₇₃	1	1	yes	characteristic
404	C₂	C₂×#576×C₇₃	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂²×#41×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#535×C₇₃	C₂	semidirect
2. C₇₃×#3199	C₂	direct (N × H)
3. C₂×#482×C₇₃	C₂	semidirect
4. C₂×#469×C₇₃	C₂	semidirect
5. C₂×#466×C₇₃	C₂	semidirect
6. C₂×#447×C₇₃	C₂	semidirect
7. C₂×#408×C₇₃	C₂	semidirect
9. C₂³×D₄×C₇₃	C₂²	semidirect
12. C₂²×M₁₆×C₇₃	C₂²	semidirect
13. C₂³×C₈×C₇₃	C₂²	semidirect
15. #535×C₇₃	C₂²	semidirect
19. C₂×#121×C₇₃	C₂²	semidirect
22. C₂×#117×C₇₃	C₂²	semidirect
23. #482×C₇₃	C₂²	semidirect
24. #469×C₇₃	C₂²	semidirect
25. #466×C₇₃	C₂²	semidirect
26. #447×C₇₃	C₂²	semidirect
27. C₂×#107×C₇₃	C₂²	semidirect
28. C₂×#106×C₇₃	C₂²	semidirect
29. C₂×#102×C₇₃	C₂²	semidirect
30. C₂×#102×C₇₃	C₂²	semidirect
31. #408×C₇₃	C₂²	semidirect
32. C₂×C₂²⋊C₈×C₇₃	C₂²	semidirect
48. C₂²×D₄×C₇₃	C₂³	semidirect
56. C₂×M₁₆×C₇₃	C₂³	semidirect
60. C₂²×C₈×C₇₃	C₂³	semidirect
66. #121×C₇₃	C₂³	semidirect
70. #117×C₇₃	C₂³	semidirect
76. #107×C₇₃	C₂³	semidirect
77. #106×C₇₃	C₂³	semidirect
78. #102×C₇₃	C₂³	semidirect
79. #102×C₇₃	C₂³	semidirect
80. C₂²⋊C₈×C₇₃	C₂³	semidirect
196. C₂×#3199	C₇₃	direct (N × H)
200. C₂×C₇₃	#3199	direct (N × H)
203. C₂×#535	C₂×C₇₃	semidirect
204. #3199	C₂×C₇₃	direct (N × H)
205. C₂×#482	C₂×C₇₃	semidirect
206. C₂×#469	C₂×C₇₃	semidirect
207. C₂×#466	C₂×C₇₃	semidirect
208. C₂×#447	C₂×C₇₃	semidirect
209. C₂×#408	C₂×C₇₃	semidirect
210. C₇₃	C₂×#3199	direct (N × H)
212. C₂³×D₄	C₂²×C₇₃	semidirect
215. C₂²×M₁₆	C₂²×C₇₃	semidirect
216. C₂³×C₈	C₂²×C₇₃	semidirect
218. #535	C₂²×C₇₃	semidirect
222. C₂×#121	C₂²×C₇₃	semidirect
225. C₂×#117	C₂²×C₇₃	semidirect
226. #482	C₂²×C₇₃	semidirect
227. #469	C₂²×C₇₃	semidirect
228. #466	C₂²×C₇₃	semidirect
229. #447	C₂²×C₇₃	semidirect
230. C₂×#107	C₂²×C₇₃	semidirect
231. C₂×#106	C₂²×C₇₃	semidirect
232. C₂×#102	C₂²×C₇₃	semidirect
233. C₂×#102	C₂²×C₇₃	semidirect
234. #408	C₂²×C₇₃	semidirect
235. C₂×C₂²⋊C₈	C₂²×C₇₃	semidirect
251. C₂²×D₄	C₂³×C₇₃	semidirect
259. C₂×M₁₆	C₂³×C₇₃	semidirect
263. C₂²×C₈	C₂³×C₇₃	semidirect
269. #121	C₂³×C₇₃	semidirect
273. #117	C₂³×C₇₃	semidirect
279. #107	C₂³×C₇₃	semidirect
280. #106	C₂³×C₇₃	semidirect
281. #102	C₂³×C₇₃	semidirect
282. #102	C₂³×C₇₃	semidirect
283. C₂²⋊C₈	C₂³×C₇₃	semidirect
402. C₂	C₇₃×#3199	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×#535×C₇₃	2
C₇₃×#3199	2
C₂×#482×C₇₃	2
C₂×#469×C₇₃	2
C₂×#466×C₇₃	2
C₂×#447×C₇₃	2
C₂×#408×C₇₃	2
C₂×#3199	73

Subgroups — C2×C73×#3199 #32970147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₃×#3199 #32970147