Subgroups — C₆₇×#61080 #30740331

Order 17152.

2742 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#577×C₆₇	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3496	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3269	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3268	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3266	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3265	C₂	1	4	yes	maximal, complemented
8	C₆₇×#3150	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3061	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3036	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3013	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3012	C₂	1	2	yes	maximal, complemented
14	C₂×#440×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2932	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	2	yes	complemented
17	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	—
18	#577×C₆₇	—	2	16	no	—
19	C₂×#137×C₆₇	C₂²	1	4	yes	complemented
20	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
21	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
22	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
23	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
24	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
25	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
27	C₂²×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
28	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
29	#550×C₆₇	—	2	1	no	—
30	#550×C₆₇	C₂²	1	2	yes	complemented
31	D₄×Q₈×C₆₇	—	2	1	no	—
32	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
33	#548×C₆₇	—	2	2	no	—
34	#548×C₆₇	C₂²	1	4	yes	complemented
35	#547×C₆₇	—	2	1	no	—
36	#547×C₆₇	C₂²	1	2	yes	—
37	#546×C₆₇	—	2	2	no	—
38	#546×C₆₇	C₂²	1	4	yes	—
39	D₄²×C₆₇	—	2	1	no	—
40	D₄²×C₆₇	C₂²	1	2	yes	—
41	#537×C₆₇	—	2	2	no	—
42	#537×C₆₇	C₂²	1	2	yes	—
43	#537×C₆₇	C₂²	1	2	yes	complemented
44	#534×C₆₇	—	2	2	no	—
45	#532×C₆₇	—	2	2	no	—
46	#532×C₆₇	C₂²	1	1	yes	characteristic
47	#532×C₆₇	C₂²	1	1	yes	characteristic
48	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	C₂×#121×C₆₇	—	2	2	no	—
50	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
52	#497×C₆₇	C₂²	1	2	yes	complemented
53	#497×C₆₇	C₂²	1	2	yes	complemented
54	#496×C₆₇	C₂²	1	2	yes	complemented
55	#496×C₆₇	C₂²	1	2	yes	complemented
56	#468×C₆₇	C₂²	1	4	yes	complemented
57	#468×C₆₇	C₂²	1	4	yes	complemented
58	#467×C₆₇	C₂²	1	4	yes	complemented
59	#466×C₆₇	C₂²	1	4	yes	complemented
60	#464×C₆₇	C₂²	1	4	yes	complemented
61	#463×C₆₇	C₂²	1	4	yes	complemented
62	#462×C₆₇	C₂²	1	2	yes	complemented
63	#461×C₆₇	C₂²	1	2	yes	complemented
64	#460×C₆₇	C₂²	1	2	yes	complemented
65	#459×C₆₇	C₂²	1	2	yes	complemented
66	#452×C₆₇	C₂²	1	4	yes	complemented
67	#452×C₆₇	C₂²	1	4	yes	complemented
68	#451×C₆₇	C₂²	1	4	yes	complemented
69	#450×C₆₇	C₂²	1	4	yes	complemented
70	#449×C₆₇	C₂²	1	4	yes	complemented
71	#449×C₆₇	C₂²	1	4	yes	complemented
72	#448×C₆₇	C₂²	1	4	yes	complemented
73	#447×C₆₇	C₂²	1	4	yes	complemented
74	#440×C₆₇	C₂²	1	4	yes	complemented
75	#440×C₆₇	C₂²	1	4	yes	complemented
76	#435×C₆₇	C₂²	1	4	yes	complemented
77	#435×C₆₇	C₂²	1	4	yes	complemented
78	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
79	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
80	#417×C₆₇	C₂²	1	2	yes	complemented
81	#417×C₆₇	C₂²	1	2	yes	complemented
82	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
83	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
84	#408×C₆₇	C₂²	1	2	yes	complemented
85	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic, complemented
86	2₋¹⁺⁴×C₆₇	—	2	8	no	—
87	2₋¹⁺⁴×C₆₇	—	4	4	no	—
88	H(5,𝔽₂)×C₆₇	—	2	8	no	—
89	H(5,𝔽₂)×C₆₇	—	4	4	no	—
90	C₂×#41×C₆₇	—	2	2	no	—
91	C₂×#41×C₆₇	—	2	4	no	—
92	C₂×#41×C₆₇	—	2	2	no	—
93	C₂×#41×C₆₇	C₂³	1	2	yes	—
94	C₂×#41×C₆₇	C₂³	1	2	yes	—
95	C₂×#41×C₆₇	C₂³	1	4	yes	—
96	C₂×#41×C₆₇	C₂³	1	4	yes	—
97	C₂×#41×C₆₇	C₂³	1	2	yes	—
98	C₂²×Q₈×C₆₇	—	2	2	no	—
99	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
100	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
101	C₂²×D₄×C₆₇	—	2	4	no	—
102	C₂²×D₄×C₆₇	—	2	2	no	—
103	C₂²×D₄×C₆₇	—	2	2	no	—
104	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
105	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₆₇	—	2	1	no	—
107	#137×C₆₇	—	2	8	no	—
108	#137×C₆₇	—	2	16	no	—
109	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
110	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
111	#135×C₆₇	—	2	16	no	—
112	#135×C₆₇	—	2	8	no	—
113	#135×C₆₇	—	4	4	no	—
114	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
115	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
116	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
117	C₂×SD₁₆×C₆₇	—	2	16	no	—
118	C₂×SD₁₆×C₆₇	D₄	1	8	yes	complemented
119	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
120	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
121	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
122	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
126	C₂×D₈×C₆₇	C₂³	1	4	yes	—
127	C₂×D₈×C₆₇	C₂³	1	2	yes	—
128	C₂×D₈×C₆₇	C₂³	1	2	yes	—
129	#131×C₆₇	—	2	8	no	—
130	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
131	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
132	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
133	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
135	C₄⋊Q₈×C₆₇	—	2	2	no	—
136	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
137	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
138	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
139	#127×C₆₇	—	2	2	no	—
140	#127×C₆₇	D₄	1	1	yes	characteristic
141	#127×C₆₇	C₂³	1	1	yes	characteristic
142	#127×C₆₇	C₂³	1	1	yes	characteristic
143	#124×C₆₇	—	2	4	no	—
144	#124×C₆₇	D₄	1	2	yes	—
145	#124×C₆₇	C₂³	1	2	yes	—
146	#124×C₆₇	C₂³	1	2	yes	—
147	#123×C₆₇	—	2	4	no	—
148	#123×C₆₇	—	2	4	no	—
149	C₂²⋊Q₈×C₆₇	—	2	2	no	—
150	C₂²⋊Q₈×C₆₇	—	2	2	no	—
151	C₂²⋊Q₈×C₆₇	—	2	4	no	—
152	C₂²⋊Q₈×C₆₇	—	2	4	no	—
153	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
154	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
155	#121×C₆₇	—	2	4	no	—
156	#121×C₆₇	—	2	2	no	—
157	#121×C₆₇	—	2	4	no	—
158	#121×C₆₇	—	2	4	no	—
159	#121×C₆₇	—	2	2	no	—
160	#121×C₆₇	—	2	2	no	—
161	#121×C₆₇	—	2	1	no	—
162	#121×C₆₇	—	2	1	no	—
163	#121×C₆₇	—	2	1	no	—
164	#121×C₆₇	—	2	1	no	—
165	#121×C₆₇	—	2	2	no	—
166	#121×C₆₇	—	2	4	no	—
167	#121×C₆₇	—	2	4	no	—
168	#121×C₆₇	D₄	1	2	yes	—
169	#121×C₆₇	D₄	1	2	yes	—
170	#121×C₆₇	C₂³	1	4	yes	—
171	#121×C₆₇	C₂³	1	4	yes	—
172	#120×C₆₇	—	2	4	no	—
173	#120×C₆₇	—	2	4	no	—
174	C₄×Q₈×C₆₇	—	2	1	no	—
175	C₄×Q₈×C₆₇	—	2	1	no	—
176	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
177	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
178	C₄×D₄×C₆₇	—	2	2	no	—
179	C₄×D₄×C₆₇	—	2	2	no	—
180	C₄×D₄×C₆₇	—	2	4	no	—
181	C₄×D₄×C₆₇	—	2	1	no	—
182	C₄×D₄×C₆₇	—	2	1	no	—
183	C₄×D₄×C₆₇	—	2	1	no	—
184	C₄×D₄×C₆₇	—	2	1	no	—
185	C₄×D₄×C₆₇	—	2	1	no	—
186	C₄×D₄×C₆₇	—	2	1	no	—
187	C₄×D₄×C₆₇	C₂³	1	2	yes	—
188	C₄×D₄×C₆₇	C₂³	1	2	yes	—
189	C₄×D₄×C₆₇	C₂³	1	2	yes	—
190	C₄×D₄×C₆₇	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
192	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
193	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
196	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
197	C₂×C₄²×C₆₇	—	2	1	no	—
198	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
199	#107×C₆₇	C₂³	1	4	yes	—
200	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
201	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
202	#103×C₆₇	C₂³	1	4	yes	—
203	#103×C₆₇	C₂³	1	4	yes	—
204	#103×C₆₇	C₂³	1	4	yes	—
205	#102×C₆₇	C₂³	1	4	yes	—
206	#102×C₆₇	C₂³	1	4	yes	—
207	#102×C₆₇	C₂³	1	4	yes	—
208	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
209	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
210	#97×C₆₇	C₂³	1	2	yes	—
211	#97×C₆₇	C₂³	1	2	yes	—
212	C₂⁴×C₆₇	—	2	1	no	—
213	C₂⁴×C₆₇	—	2	4	no	—
214	#41×C₆₇	—	2	4	no	—
215	#41×C₆₇	—	2	4	no	—
216	#41×C₆₇	—	2	8	no	—
217	#41×C₆₇	—	2	8	no	—
218	#41×C₆₇	—	2	4	no	—
219	#41×C₆₇	—	2	4	no	—
220	#41×C₆₇	—	2	4	no	—
221	#41×C₆₇	—	2	4	no	—
222	#41×C₆₇	—	4	4	no	—
223	#41×C₆₇	—	4	4	no	—
224	#41×C₆₇	—	4	16	no	—
225	#41×C₆₇	—	4	8	no	—
226	#41×C₆₇	—	4	8	no	—
227	C₂×Q₈×C₆₇	—	2	1	no	—
228	C₂×Q₈×C₆₇	—	2	4	no	—
229	C₂×Q₈×C₆₇	—	2	2	no	—
230	C₂×Q₈×C₆₇	—	2	8	no	—
231	C₂×Q₈×C₆₇	—	4	4	no	—
232	C₂×Q₈×C₆₇	—	4	8	no	—
233	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
234	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	complemented
235	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
236	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
237	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
238	C₂×D₄×C₆₇	—	2	8	no	—
239	C₂×D₄×C₆₇	—	2	4	no	—
240	C₂×D₄×C₆₇	—	2	2	no	—
241	C₂×D₄×C₆₇	—	2	2	no	—
242	C₂×D₄×C₆₇	—	2	4	no	—
243	C₂×D₄×C₆₇	—	2	4	no	—
244	C₂×D₄×C₆₇	—	2	4	no	—
245	C₂×D₄×C₆₇	—	2	1	no	—
246	C₂×D₄×C₆₇	—	2	1	no	—
247	C₂×D₄×C₆₇	—	2	1	no	—
248	C₂×D₄×C₆₇	—	2	4	no	—
249	C₂×D₄×C₆₇	—	2	1	no	—
250	C₂×D₄×C₆₇	—	2	1	no	—
251	C₂×D₄×C₆₇	—	2	2	no	—
252	C₂×D₄×C₆₇	—	4	4	no	—
253	C₂×D₄×C₆₇	—	4	8	no	—
254	C₂×D₄×C₆₇	—	4	16	no	—
255	C₂×D₄×C₆₇	—	8	4	no	—
256	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
257	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
258	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
259	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
260	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
261	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
262	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
263	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₆₇	—	2	1	no	—
265	C₂²×C₄×C₆₇	—	2	4	no	—
266	C₂²×C₄×C₆₇	—	2	1	no	—
267	C₂²×C₄×C₆₇	—	2	1	no	—
268	C₂²×C₄×C₆₇	—	2	4	no	—
269	C₂²×C₄×C₆₇	—	2	2	no	—
270	C₂²×C₄×C₆₇	—	2	2	no	—
271	C₂²×C₄×C₆₇	—	2	4	no	—
272	C₂²×C₄×C₆₇	—	2	2	no	—
273	C₂²×C₄×C₆₇	—	2	2	no	—
274	C₂²×C₄×C₆₇	—	8	2	no	—
275	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
278	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
279	Q₁₆×C₆₇	—	2	8	no	—
280	Q₁₆×C₆₇	—	2	4	no	—
281	Q₁₆×C₆₇	—	4	2	no	—
282	SD₁₆×C₆₇	—	2	8	no	—
283	SD₁₆×C₆₇	—	2	8	no	—
284	SD₁₆×C₆₇	—	2	4	no	—
285	SD₁₆×C₆₇	—	2	4	no	—
286	SD₁₆×C₆₇	—	4	2	no	—
287	SD₁₆×C₆₇	—	4	2	no	—
288	SD₁₆×C₆₇	C₂×D₄	1	16	yes	complemented
289	D₈×C₆₇	—	2	8	no	—
290	D₈×C₆₇	—	2	4	no	—
291	D₈×C₆₇	—	4	2	no	—
292	M₁₆×C₆₇	—	2	4	no	—
293	M₁₆×C₆₇	—	2	8	no	—
294	C₂×C₈×C₆₇	—	2	2	no	—
295	C₂×C₈×C₆₇	—	2	8	no	—
296	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	complemented
297	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
298	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
299	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
300	C₄⋊C₄×C₆₇	—	2	1	no	—
301	C₄⋊C₄×C₆₇	—	2	2	no	—
302	C₄⋊C₄×C₆₇	—	2	2	no	—
303	C₄⋊C₄×C₆₇	—	2	4	no	—
304	C₄⋊C₄×C₆₇	—	2	1	no	—
305	C₄⋊C₄×C₆₇	—	2	1	no	—
306	C₄⋊C₄×C₆₇	—	2	1	no	—
307	C₄⋊C₄×C₆₇	—	2	1	no	—
308	C₄⋊C₄×C₆₇	—	2	4	no	—
309	C₄⋊C₄×C₆₇	—	2	1	no	—
310	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
312	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
314	C₂²⋊C₄×C₆₇	—	2	4	no	—
315	C₂²⋊C₄×C₆₇	—	2	4	no	—
316	C₂²⋊C₄×C₆₇	—	2	2	no	—
317	C₂²⋊C₄×C₆₇	—	2	2	no	—
318	C₂²⋊C₄×C₆₇	—	2	2	no	—
319	C₂²⋊C₄×C₆₇	—	2	4	no	—
320	C₂²⋊C₄×C₆₇	—	2	2	no	—
321	C₂²⋊C₄×C₆₇	—	2	2	no	—
322	C₂²⋊C₄×C₆₇	—	2	2	no	—
323	C₂²⋊C₄×C₆₇	—	2	4	no	—
324	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
325	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
326	C₄²×C₆₇	—	2	2	no	—
327	C₄²×C₆₇	—	2	2	no	—
328	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
331	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
332	C₂³×C₆₇	—	2	2	no	—
333	C₂³×C₆₇	—	2	4	no	—
334	C₂³×C₆₇	—	2	2	no	—
335	C₂³×C₆₇	—	2	2	no	—
336	C₂³×C₆₇	—	4	8	no	—
337	C₂³×C₆₇	—	8	1	no	—
338	C₂³×C₆₇	—	8	1	no	—
339	C₂³×C₆₇	—	8	4	no	—
340	C₂³×C₆₇	—	8	4	no	—
341	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
342	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
343	Q₈×C₆₇	—	2	4	no	—
344	Q₈×C₆₇	—	2	4	no	—
345	Q₈×C₆₇	—	2	2	no	—
346	Q₈×C₆₇	—	2	2	no	—
347	Q₈×C₆₇	—	2	2	no	—
348	Q₈×C₆₇	—	2	2	no	—
349	Q₈×C₆₇	—	2	2	no	—
350	Q₈×C₆₇	—	4	8	no	—
351	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
352	D₄×C₆₇	—	2	8	no	—
353	D₄×C₆₇	—	2	4	no	—
354	D₄×C₆₇	—	2	4	no	—
355	D₄×C₆₇	—	2	2	no	—
356	D₄×C₆₇	—	2	2	no	—
357	D₄×C₆₇	—	2	2	no	—
358	D₄×C₆₇	—	2	2	no	—
359	D₄×C₆₇	—	2	2	no	—
360	D₄×C₆₇	—	4	2	no	—
361	D₄×C₆₇	—	4	2	no	—
362	D₄×C₆₇	—	4	8	no	—
363	D₄×C₆₇	—	4	8	no	—
364	D₄×C₆₇	—	4	2	no	—
365	D₄×C₆₇	—	4	2	no	—
366	D₄×C₆₇	—	4	8	no	—
367	D₄×C₆₇	—	4	4	no	—
368	D₄×C₆₇	—	4	4	no	—
369	D₄×C₆₇	—	8	1	no	—
370	D₄×C₆₇	—	8	1	no	—
371	D₄×C₆₇	—	8	4	no	—
372	D₄×C₆₇	—	8	4	no	—
373	D₄×C₆₇	C₂²×D₄	1	4	yes	—
374	C₂×C₄×C₆₇	—	2	4	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	2	4	no	—
377	C₂×C₄×C₆₇	—	2	4	no	—
378	C₂×C₄×C₆₇	—	2	2	no	—
379	C₂×C₄×C₆₇	—	2	2	no	—
380	C₂×C₄×C₆₇	—	2	2	no	—
381	C₂×C₄×C₆₇	—	2	2	no	—
382	C₂×C₄×C₆₇	—	4	1	no	—
383	C₂×C₄×C₆₇	—	4	1	no	—
384	C₂×C₄×C₆₇	—	4	8	no	—
385	C₂×C₄×C₆₇	—	4	8	no	—
386	C₂×C₄×C₆₇	—	4	8	no	—
387	C₂×C₄×C₆₇	—	4	4	no	—
388	C₂×C₄×C₆₇	—	4	4	no	—
389	C₂×C₄×C₆₇	—	4	4	no	—
390	C₂×C₄×C₆₇	—	8	2	no	—
391	C₂×C₄×C₆₇	—	8	1	no	—
392	C₂×C₄×C₆₇	—	8	1	no	—
393	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
398	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
401	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
402	C₈×C₆₇	—	2	4	no	—
403	C₈×C₆₇	—	2	2	no	—
404	C₈×C₆₇	C₂²×D₄	1	4	yes	—
405	C₂²×C₆₇	—	2	1	no	—
406	C₂²×C₆₇	—	2	1	no	—
407	C₂²×C₆₇	—	2	4	no	—
408	C₂²×C₆₇	—	2	4	no	—
409	C₂²×C₆₇	—	2	4	no	—
410	C₂²×C₆₇	—	2	4	no	—
411	C₂²×C₆₇	—	4	2	no	—
412	C₂²×C₆₇	—	4	2	no	—
413	C₂²×C₆₇	—	4	2	no	—
414	C₂²×C₆₇	—	4	2	no	—
415	C₂²×C₆₇	—	4	2	no	—
416	C₂²×C₆₇	—	4	2	no	—
417	C₂²×C₆₇	—	4	2	no	—
418	C₂²×C₆₇	—	4	2	no	—
419	C₂²×C₆₇	—	8	4	no	—
420	C₂²×C₆₇	—	16	8	no	—
421	C₂²×C₆₇	D₄²	1	2	yes	—
422	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
423	C₄×C₆₇	—	2	1	no	—
424	C₄×C₆₇	—	2	1	no	—
425	C₄×C₆₇	—	2	1	no	—
426	C₄×C₆₇	—	2	1	no	—
427	C₄×C₆₇	—	2	4	no	—
428	C₄×C₆₇	—	2	4	no	—
429	C₄×C₆₇	—	4	2	no	—
430	C₄×C₆₇	—	4	2	no	—
431	C₄×C₆₇	—	4	2	no	—
432	C₄×C₆₇	—	4	2	no	—
433	C₄×C₆₇	D₄²	1	2	yes	—
434	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
435	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
436	#61080	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
437	C₂×C₆₇	—	2	2	no	—
438	C₂×C₆₇	—	4	4	no	—
439	C₂×C₆₇	—	4	4	no	—
440	C₂×C₆₇	—	8	2	no	—
441	C₂×C₆₇	—	8	2	no	—
442	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
443	C₂×C₆₇	#3585	1	1	yes	characteristic
444	C₂×C₆₇	#3586	1	1	yes	characteristic
445	C₂×#577	C₂×C₆₇	1	2	yes	complemented
446	#3497	C₂×C₆₇	1	1	yes	characteristic, complemented
447	#3496	C₂×C₆₇	1	1	yes	characteristic, complemented
448	#3269	C₂×C₆₇	1	4	yes	complemented
449	#3268	C₂×C₆₇	1	4	yes	complemented
450	#3266	C₂×C₆₇	1	4	yes	complemented
451	#3265	C₂×C₆₇	1	4	yes	complemented
452	#3150	C₂×C₆₇	1	1	yes	characteristic, complemented
453	#3061	C₂×C₆₇	1	2	yes	complemented
454	#3037	C₂×C₆₇	1	1	yes	characteristic, complemented
455	#3036	C₂×C₆₇	1	1	yes	characteristic, complemented
456	#3013	C₂×C₆₇	1	2	yes	complemented
457	#3012	C₂×C₆₇	1	2	yes	complemented
458	C₂×#440	C₂×C₆₇	1	1	yes	characteristic, complemented
459	#2932	C₂×C₆₇	1	1	yes	characteristic, complemented
460	C₆₇	#61080	1	1	yes	characteristic, direct product factor, Sylow
461	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	2	yes	complemented
462	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
463	#577	—	2	16	no	—
464	C₂×#137	C₂²×C₆₇	1	4	yes	complemented
465	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
466	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
467	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
468	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
469	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
470	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
471	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
472	C₂²×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
473	C₂×#131	C₂²×C₆₇	1	2	yes	complemented
474	#550	—	2	1	no	—
475	#550	C₂²×C₆₇	1	2	yes	complemented
476	D₄×Q₈	—	2	1	no	—
477	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
478	#548	—	2	2	no	—
479	#548	C₂²×C₆₇	1	4	yes	complemented
480	#547	—	2	1	no	—
481	#547	C₂²×C₆₇	1	2	yes	—
482	#546	—	2	2	no	—
483	#546	C₂²×C₆₇	1	4	yes	—
484	D₄²	—	2	1	no	—
485	D₄²	C₂²×C₆₇	1	2	yes	—
486	#537	—	2	2	no	—
487	#537	C₂²×C₆₇	1	2	yes	—
488	#537	C₂²×C₆₇	1	2	yes	complemented
489	#534	—	2	2	no	—
490	#532	—	2	2	no	—
491	#532	C₂²×C₆₇	1	1	yes	characteristic
492	#532	C₂²×C₆₇	1	1	yes	characteristic
493	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
494	C₂×#121	—	2	2	no	—
495	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
496	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
497	#497	C₂²×C₆₇	1	2	yes	complemented
498	#497	C₂²×C₆₇	1	2	yes	complemented
499	#496	C₂²×C₆₇	1	2	yes	complemented
500	#496	C₂²×C₆₇	1	2	yes	complemented
501	#468	C₂²×C₆₇	1	4	yes	complemented
502	#468	C₂²×C₆₇	1	4	yes	complemented
503	#467	C₂²×C₆₇	1	4	yes	complemented
504	#466	C₂²×C₆₇	1	4	yes	complemented
505	#464	C₂²×C₆₇	1	4	yes	complemented
506	#463	C₂²×C₆₇	1	4	yes	complemented
507	#462	C₂²×C₆₇	1	2	yes	complemented
508	#461	C₂²×C₆₇	1	2	yes	complemented
509	#460	C₂²×C₆₇	1	2	yes	complemented
510	#459	C₂²×C₆₇	1	2	yes	complemented
511	#452	C₂²×C₆₇	1	4	yes	complemented
512	#452	C₂²×C₆₇	1	4	yes	complemented
513	#451	C₂²×C₆₇	1	4	yes	complemented
514	#450	C₂²×C₆₇	1	4	yes	complemented
515	#449	C₂²×C₆₇	1	4	yes	complemented
516	#449	C₂²×C₆₇	1	4	yes	complemented
517	#448	C₂²×C₆₇	1	4	yes	complemented
518	#447	C₂²×C₆₇	1	4	yes	complemented
519	#440	C₂²×C₆₇	1	4	yes	complemented
520	#440	C₂²×C₆₇	1	4	yes	complemented
521	#435	C₂²×C₆₇	1	4	yes	complemented
522	#435	C₂²×C₆₇	1	4	yes	complemented
523	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
524	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
525	#417	C₂²×C₆₇	1	2	yes	complemented
526	#417	C₂²×C₆₇	1	2	yes	complemented
527	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
528	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
529	#408	C₂²×C₆₇	1	2	yes	complemented
530	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic, complemented
531	2₋¹⁺⁴	—	2	8	no	—
532	2₋¹⁺⁴	—	4	4	no	—
533	H(5,𝔽₂)	—	2	8	no	—
534	H(5,𝔽₂)	—	4	4	no	—
535	C₂×#41	—	2	2	no	—
536	C₂×#41	—	2	4	no	—
537	C₂×#41	—	2	2	no	—
538	C₂×#41	C₂³×C₆₇	1	2	yes	—
539	C₂×#41	C₂³×C₆₇	1	2	yes	—
540	C₂×#41	C₂³×C₆₇	1	4	yes	—
541	C₂×#41	C₂³×C₆₇	1	4	yes	—
542	C₂×#41	C₂³×C₆₇	1	2	yes	—
543	C₂²×Q₈	—	2	2	no	—
544	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
545	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
546	C₂²×D₄	—	2	4	no	—
547	C₂²×D₄	—	2	2	no	—
548	C₂²×D₄	—	2	2	no	—
549	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
550	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
551	C₂³×C₄	—	2	1	no	—
552	#137	—	2	8	no	—
553	#137	—	2	16	no	—
554	AGL(1,ℤ/8)	—	2	8	no	—
555	AGL(1,ℤ/8)	—	2	16	no	—
556	#135	—	2	16	no	—
557	#135	—	2	8	no	—
558	#135	—	4	4	no	—
559	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
560	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
561	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
562	C₂×SD₁₆	—	2	16	no	—
563	C₂×SD₁₆	D₄×C₆₇	1	8	yes	complemented
564	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
565	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
566	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
567	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
568	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
569	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
570	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
571	C₂×D₈	C₂³×C₆₇	1	4	yes	—
572	C₂×D₈	C₂³×C₆₇	1	2	yes	—
573	C₂×D₈	C₂³×C₆₇	1	2	yes	—
574	#131	—	2	8	no	—
575	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
576	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
577	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
578	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
579	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
580	C₄⋊Q₈	—	2	2	no	—
581	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
582	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
583	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
584	#127	—	2	2	no	—
585	#127	D₄×C₆₇	1	1	yes	characteristic
586	#127	C₂³×C₆₇	1	1	yes	characteristic
587	#127	C₂³×C₆₇	1	1	yes	characteristic
588	#124	—	2	4	no	—
589	#124	D₄×C₆₇	1	2	yes	—
590	#124	C₂³×C₆₇	1	2	yes	—
591	#124	C₂³×C₆₇	1	2	yes	—
592	#123	—	2	4	no	—
593	#123	—	2	4	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	—	2	2	no	—
596	C₂²⋊Q₈	—	2	4	no	—
597	C₂²⋊Q₈	—	2	4	no	—
598	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
599	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
600	#121	—	2	4	no	—
601	#121	—	2	2	no	—
602	#121	—	2	4	no	—
603	#121	—	2	4	no	—
604	#121	—	2	2	no	—
605	#121	—	2	2	no	—
606	#121	—	2	1	no	—
607	#121	—	2	1	no	—
608	#121	—	2	1	no	—
609	#121	—	2	1	no	—
610	#121	—	2	2	no	—
611	#121	—	2	4	no	—
612	#121	—	2	4	no	—
613	#121	D₄×C₆₇	1	2	yes	—
614	#121	D₄×C₆₇	1	2	yes	—
615	#121	C₂³×C₆₇	1	4	yes	—
616	#121	C₂³×C₆₇	1	4	yes	—
617	#120	—	2	4	no	—
618	#120	—	2	4	no	—
619	C₄×Q₈	—	2	1	no	—
620	C₄×Q₈	—	2	1	no	—
621	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
622	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	—	2	4	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	1	no	—
628	C₄×D₄	—	2	1	no	—
629	C₄×D₄	—	2	1	no	—
630	C₄×D₄	—	2	1	no	—
631	C₄×D₄	—	2	1	no	—
632	C₄×D₄	C₂³×C₆₇	1	2	yes	—
633	C₄×D₄	C₂³×C₆₇	1	2	yes	—
634	C₄×D₄	C₂³×C₆₇	1	2	yes	—
635	C₄×D₄	C₂³×C₆₇	1	2	yes	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	—	2	2	no	—
638	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
640	C₂×C₂²⋊C₄	—	2	1	no	—
641	C₂×C₂²⋊C₄	—	2	4	no	—
642	C₂×C₄²	—	2	1	no	—
643	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
644	#107	C₂³×C₆₇	1	4	yes	—
645	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
646	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
647	#103	C₂³×C₆₇	1	4	yes	—
648	#103	C₂³×C₆₇	1	4	yes	—
649	#103	C₂³×C₆₇	1	4	yes	—
650	#102	C₂³×C₆₇	1	4	yes	—
651	#102	C₂³×C₆₇	1	4	yes	—
652	#102	C₂³×C₆₇	1	4	yes	—
653	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
654	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
655	#97	C₂³×C₆₇	1	2	yes	—
656	#97	C₂³×C₆₇	1	2	yes	—
657	C₂⁴	—	2	1	no	—
658	C₂⁴	—	2	4	no	—
659	#41	—	2	4	no	—
660	#41	—	2	4	no	—
661	#41	—	2	8	no	—
662	#41	—	2	8	no	—
663	#41	—	2	4	no	—
664	#41	—	2	4	no	—
665	#41	—	2	4	no	—
666	#41	—	2	4	no	—
667	#41	—	4	4	no	—
668	#41	—	4	4	no	—
669	#41	—	4	16	no	—
670	#41	—	4	8	no	—
671	#41	—	4	8	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	4	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	8	no	—
676	C₂×Q₈	—	4	4	no	—
677	C₂×Q₈	—	4	8	no	—
678	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
679	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	complemented
680	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
681	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
682	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
683	C₂×D₄	—	2	8	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	1	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	2	4	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	4	4	no	—
698	C₂×D₄	—	4	8	no	—
699	C₂×D₄	—	4	16	no	—
700	C₂×D₄	—	8	4	no	—
701	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
702	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
703	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
704	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
705	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
706	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
707	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
708	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	8	2	no	—
720	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
721	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
723	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
724	Q₁₆	—	2	8	no	—
725	Q₁₆	—	2	4	no	—
726	Q₁₆	—	4	2	no	—
727	SD₁₆	—	2	8	no	—
728	SD₁₆	—	2	8	no	—
729	SD₁₆	—	2	4	no	—
730	SD₁₆	—	2	4	no	—
731	SD₁₆	—	4	2	no	—
732	SD₁₆	—	4	2	no	—
733	SD₁₆	C₂×D₄×C₆₇	1	16	yes	complemented
734	D₈	—	2	8	no	—
735	D₈	—	2	4	no	—
736	D₈	—	4	2	no	—
737	M₁₆	—	2	4	no	—
738	M₁₆	—	2	8	no	—
739	C₂×C₈	—	2	2	no	—
740	C₂×C₈	—	2	8	no	—
741	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	complemented
742	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
743	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
744	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	1	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
756	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
757	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
758	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
770	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	2	no	—
773	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
774	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
775	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
776	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
777	C₂³	—	2	2	no	—
778	C₂³	—	2	4	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	4	8	no	—
782	C₂³	—	8	1	no	—
783	C₂³	—	8	1	no	—
784	C₂³	—	8	4	no	—
785	C₂³	—	8	4	no	—
786	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
787	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
788	Q₈	—	2	4	no	—
789	Q₈	—	2	4	no	—
790	Q₈	—	2	2	no	—
791	Q₈	—	2	2	no	—
792	Q₈	—	2	2	no	—
793	Q₈	—	2	2	no	—
794	Q₈	—	2	2	no	—
795	Q₈	—	4	8	no	—
796	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
797	D₄	—	2	8	no	—
798	D₄	—	2	4	no	—
799	D₄	—	2	4	no	—
800	D₄	—	2	2	no	—
801	D₄	—	2	2	no	—
802	D₄	—	2	2	no	—
803	D₄	—	2	2	no	—
804	D₄	—	2	2	no	—
805	D₄	—	4	2	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	8	no	—
808	D₄	—	4	8	no	—
809	D₄	—	4	2	no	—
810	D₄	—	4	2	no	—
811	D₄	—	4	8	no	—
812	D₄	—	4	4	no	—
813	D₄	—	4	4	no	—
814	D₄	—	8	1	no	—
815	D₄	—	8	1	no	—
816	D₄	—	8	4	no	—
817	D₄	—	8	4	no	—
818	D₄	C₂²×D₄×C₆₇	1	4	yes	—
819	C₂×C₄	—	2	4	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	4	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	8	no	—
830	C₂×C₄	—	4	8	no	—
831	C₂×C₄	—	4	8	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	8	2	no	—
836	C₂×C₄	—	8	1	no	—
837	C₂×C₄	—	8	1	no	—
838	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
840	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
843	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
845	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
846	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
847	C₈	—	2	4	no	—
848	C₈	—	2	2	no	—
849	C₈	C₂²×D₄×C₆₇	1	4	yes	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	4	no	—
853	C₂²	—	2	4	no	—
854	C₂²	—	2	4	no	—
855	C₂²	—	2	4	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	8	4	no	—
865	C₂²	—	16	8	no	—
866	C₂²	D₄²×C₆₇	1	2	yes	—
867	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
868	C₄	—	2	1	no	—
869	C₄	—	2	1	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	1	no	—
872	C₄	—	2	4	no	—
873	C₄	—	2	4	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	2	no	—
878	C₄	D₄²×C₆₇	1	2	yes	—
879	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
880	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
881	C₂	—	2	2	no	—
882	C₂	—	4	4	no	—
883	C₂	—	4	4	no	—
884	C₂	—	8	2	no	—
885	C₂	—	8	2	no	—
886	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
887	C₂	C₆₇×#3585	1	1	yes	characteristic
888	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#577×C₆₇	C₂	semidirect
2. C₆₇×#3497	C₂	semidirect
3. C₆₇×#3496	C₂	semidirect
4. C₆₇×#3269	C₂	semidirect
5. C₆₇×#3268	C₂	semidirect
6. C₆₇×#3266	C₂	semidirect
7. C₆₇×#3265	C₂	semidirect
8. C₆₇×#3150	C₂	semidirect
9. C₆₇×#3061	C₂	semidirect
10. C₆₇×#3037	C₂	semidirect
11. C₆₇×#3036	C₂	semidirect
12. C₆₇×#3013	C₂	semidirect
13. C₆₇×#3012	C₂	semidirect
14. C₂×#440×C₆₇	C₂	semidirect
15. C₆₇×#2932	C₂	semidirect
16. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
19. C₂×#137×C₆₇	C₂²	semidirect
20. C₂×#137×C₆₇	C₂²	semidirect
22. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
23. C₂×#135×C₆₇	C₂²	semidirect
24. C₂×#135×C₆₇	C₂²	semidirect
25. C₂×#135×C₆₇	C₂²	semidirect
27. C₂²×SD₁₆×C₆₇	C₂²	semidirect
28. C₂×#131×C₆₇	C₂²	semidirect
30. #550×C₆₇	C₂²	semidirect
32. D₄×Q₈×C₆₇	C₂²	semidirect
34. #548×C₆₇	C₂²	semidirect
43. #537×C₆₇	C₂²	semidirect
48. #532×C₆₇	C₂²	semidirect
50. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
52. #497×C₆₇	C₂²	semidirect
53. #497×C₆₇	C₂²	semidirect
54. #496×C₆₇	C₂²	semidirect
55. #496×C₆₇	C₂²	semidirect
56. #468×C₆₇	C₂²	semidirect
57. #468×C₆₇	C₂²	semidirect
58. #467×C₆₇	C₂²	semidirect
59. #466×C₆₇	C₂²	semidirect
60. #464×C₆₇	C₂²	semidirect
61. #463×C₆₇	C₂²	semidirect
62. #462×C₆₇	C₂²	semidirect
63. #461×C₆₇	C₂²	semidirect
64. #460×C₆₇	C₂²	semidirect
65. #459×C₆₇	C₂²	semidirect
66. #452×C₆₇	C₂²	semidirect
67. #452×C₆₇	C₂²	semidirect
68. #451×C₆₇	C₂²	semidirect
69. #450×C₆₇	C₂²	semidirect
70. #449×C₆₇	C₂²	semidirect
71. #449×C₆₇	C₂²	semidirect
72. #448×C₆₇	C₂²	semidirect
73. #447×C₆₇	C₂²	semidirect
74. #440×C₆₇	C₂²	semidirect
75. #440×C₆₇	C₂²	semidirect
76. #435×C₆₇	C₂²	semidirect
77. #435×C₆₇	C₂²	semidirect
78. C₂×#107×C₆₇	C₂²	semidirect
79. #423×C₆₇	C₂²	semidirect
80. #417×C₆₇	C₂²	semidirect
81. #417×C₆₇	C₂²	semidirect
82. C₂×#103×C₆₇	C₂²	semidirect
84. #408×C₆₇	C₂²	semidirect
85. C₂×#97×C₆₇	C₂²	semidirect
118. C₂×SD₁₆×C₆₇	D₄	semidirect
234. C₂×Q₈×C₆₇	C₂×D₄	semidirect
288. SD₁₆×C₆₇	C₂×D₄	semidirect
296. C₂×C₈×C₆₇	C₂×D₄	semidirect
436. #61080	C₆₇	direct (N × H)
445. C₂×#577	C₂×C₆₇	semidirect
446. #3497	C₂×C₆₇	semidirect
447. #3496	C₂×C₆₇	semidirect
448. #3269	C₂×C₆₇	semidirect
449. #3268	C₂×C₆₇	semidirect
450. #3266	C₂×C₆₇	semidirect
451. #3265	C₂×C₆₇	semidirect
452. #3150	C₂×C₆₇	semidirect
453. #3061	C₂×C₆₇	semidirect
454. #3037	C₂×C₆₇	semidirect
455. #3036	C₂×C₆₇	semidirect
456. #3013	C₂×C₆₇	semidirect
457. #3012	C₂×C₆₇	semidirect
458. C₂×#440	C₂×C₆₇	semidirect
459. #2932	C₂×C₆₇	semidirect
460. C₆₇	#61080	direct (N × H)
461. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
464. C₂×#137	C₂²×C₆₇	semidirect
465. C₂×#137	C₂²×C₆₇	semidirect
467. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
468. C₂×#135	C₂²×C₆₇	semidirect
469. C₂×#135	C₂²×C₆₇	semidirect
470. C₂×#135	C₂²×C₆₇	semidirect
472. C₂²×SD₁₆	C₂²×C₆₇	semidirect
473. C₂×#131	C₂²×C₆₇	semidirect
475. #550	C₂²×C₆₇	semidirect
477. D₄×Q₈	C₂²×C₆₇	semidirect
479. #548	C₂²×C₆₇	semidirect
488. #537	C₂²×C₆₇	semidirect
493. #532	C₂²×C₆₇	semidirect
495. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
497. #497	C₂²×C₆₇	semidirect
498. #497	C₂²×C₆₇	semidirect
499. #496	C₂²×C₆₇	semidirect
500. #496	C₂²×C₆₇	semidirect
501. #468	C₂²×C₆₇	semidirect
502. #468	C₂²×C₆₇	semidirect
503. #467	C₂²×C₆₇	semidirect
504. #466	C₂²×C₆₇	semidirect
505. #464	C₂²×C₆₇	semidirect
506. #463	C₂²×C₆₇	semidirect
507. #462	C₂²×C₆₇	semidirect
508. #461	C₂²×C₆₇	semidirect
509. #460	C₂²×C₆₇	semidirect
510. #459	C₂²×C₆₇	semidirect
511. #452	C₂²×C₆₇	semidirect
512. #452	C₂²×C₆₇	semidirect
513. #451	C₂²×C₆₇	semidirect
514. #450	C₂²×C₆₇	semidirect
515. #449	C₂²×C₆₇	semidirect
516. #449	C₂²×C₆₇	semidirect
517. #448	C₂²×C₆₇	semidirect
518. #447	C₂²×C₆₇	semidirect
519. #440	C₂²×C₆₇	semidirect
520. #440	C₂²×C₆₇	semidirect
521. #435	C₂²×C₆₇	semidirect
522. #435	C₂²×C₆₇	semidirect
523. C₂×#107	C₂²×C₆₇	semidirect
524. #423	C₂²×C₆₇	semidirect
525. #417	C₂²×C₆₇	semidirect
526. #417	C₂²×C₆₇	semidirect
527. C₂×#103	C₂²×C₆₇	semidirect
529. #408	C₂²×C₆₇	semidirect
530. C₂×#97	C₂²×C₆₇	semidirect
563. C₂×SD₁₆	D₄×C₆₇	semidirect
679. C₂×Q₈	C₂×D₄×C₆₇	semidirect
733. SD₁₆	C₂×D₄×C₆₇	semidirect
741. C₂×C₈	C₂×D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#577×C₆₇	2
C₆₇×#3497	2
C₆₇×#3496	2
C₆₇×#3269	2
C₆₇×#3268	2
C₆₇×#3266	2
C₆₇×#3265	2
C₆₇×#3150	2
C₆₇×#3061	2
C₆₇×#3037	2
C₆₇×#3036	2
C₆₇×#3013	2
C₆₇×#3012	2
C₂×#440×C₆₇	2
C₆₇×#2932	2
#61080	67

Subgroups — C67×#61080 #30740331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61080 #30740331