Subgroups — C₆₇×#61679 #30740930

Order 17152.

2224 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3549	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3325	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3319	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3303	C₂	1	2	yes	maximal, complemented
6	D₄×D₈×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3272	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3264	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3214	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3207	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3198	C₂	1	4	yes	maximal, complemented
12	C₆₇×#3109	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3100	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3008	C₂	1	4	yes	maximal, complemented
15	C₆₇×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	complemented
17	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
18	C₂²×D₈×C₆₇	C₂²	1	4	yes	complemented
19	H(3,𝔽₄)×C₆₇	—	2	2	no	—
20	#555×C₆₇	—	2	1	no	—
21	#555×C₆₇	C₂²	1	2	yes	complemented
22	#555×C₆₇	C₂²	1	2	yes	complemented
23	#547×C₆₇	—	2	1	no	—
24	#547×C₆₇	C₂²	1	2	yes	complemented
25	#546×C₆₇	—	2	2	no	—
26	#546×C₆₇	C₂²	1	4	yes	complemented
27	D₄²×C₆₇	—	2	1	no	—
28	D₄²×C₆₇	—	2	1	no	—
29	D₄²×C₆₇	C₂²	1	2	yes	complemented
30	D₄²×C₆₇	C₂²	1	2	yes	complemented
31	D₄²×C₆₇	C₂²	1	2	yes	complemented
32	#537×C₆₇	C₂²	1	2	yes	complemented
33	#535×C₆₇	—	2	2	no	—
34	#535×C₆₇	—	2	2	no	—
35	#535×C₆₇	C₂²	1	4	yes	complemented
36	#534×C₆₇	—	2	2	no	—
37	#532×C₆₇	C₂²	1	1	yes	characteristic
38	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	C₂×#121×C₆₇	—	2	2	no	—
42	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	#496×C₆₇	C₂²	1	2	yes	complemented
44	#493×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	#492×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#489×C₆₇	C₂²	1	2	yes	complemented
47	#487×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#485×C₆₇	C₂²	1	4	yes	complemented
50	#482×C₆₇	C₂²	1	4	yes	complemented
51	#481×C₆₇	C₂²	1	2	yes	complemented
52	#480×C₆₇	C₂²	1	2	yes	complemented
53	#476×C₆₇	C₂²	1	2	yes	complemented
54	#474×C₆₇	C₂²	1	2	yes	complemented
55	#469×C₆₇	C₂²	1	4	yes	complemented
56	#468×C₆₇	C₂²	1	4	yes	complemented
57	#466×C₆₇	C₂²	1	4	yes	complemented
58	#465×C₆₇	C₂²	1	4	yes	complemented
59	#463×C₆₇	C₂²	1	4	yes	complemented
60	#461×C₆₇	C₂²	1	2	yes	complemented
61	#459×C₆₇	C₂²	1	2	yes	complemented
62	#459×C₆₇	C₂²	1	2	yes	complemented
63	#459×C₆₇	C₂²	1	2	yes	complemented
64	#450×C₆₇	C₂²	1	4	yes	complemented
65	#449×C₆₇	C₂²	1	4	yes	complemented
66	#449×C₆₇	C₂²	1	4	yes	complemented
67	#449×C₆₇	C₂²	1	4	yes	complemented
68	#449×C₆₇	C₂²	1	4	yes	complemented
69	#447×C₆₇	C₂²	1	4	yes	complemented
70	#447×C₆₇	C₂²	1	4	yes	complemented
71	#447×C₆₇	C₂²	1	4	yes	complemented
72	#447×C₆₇	C₂²	1	2	yes	complemented
73	#447×C₆₇	C₂²	1	2	yes	complemented
74	#442×C₆₇	C₂²	1	4	yes	complemented
75	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
76	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
77	#436×C₆₇	C₂²	1	2	yes	complemented
78	#435×C₆₇	C₂²	1	4	yes	complemented
79	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
80	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
82	#418×C₆₇	C₂²	1	4	yes	complemented
83	#416×C₆₇	C₂²	1	4	yes	complemented
84	#408×C₆₇	C₂²	1	4	yes	complemented
85	H(5,𝔽₂)×C₆₇	—	4	8	no	—
86	C₂×#41×C₆₇	—	2	2	no	—
87	C₂×#41×C₆₇	—	2	1	no	—
88	C₂×#41×C₆₇	—	2	1	no	—
89	C₂×#41×C₆₇	C₂³	1	4	yes	—
90	C₂×#41×C₆₇	C₂³	1	2	yes	—
91	C₂×#41×C₆₇	C₂³	1	2	yes	—
92	C₂²×D₄×C₆₇	—	2	4	no	—
93	C₂²×D₄×C₆₇	—	2	2	no	—
94	C₂²×D₄×C₆₇	—	2	2	no	—
95	C₂²×D₄×C₆₇	—	2	2	no	—
96	C₂²×D₄×C₆₇	—	2	2	no	—
97	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
99	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
100	C₂³×C₄×C₆₇	—	2	1	no	—
101	AGL(1,ℤ/8)×C₆₇	—	4	8	no	—
102	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
104	C₂×D₈×C₆₇	—	4	8	no	—
105	C₂×D₈×C₆₇	C₂³	1	2	yes	—
106	C₂×D₈×C₆₇	C₂³	1	4	yes	—
107	C₂×D₈×C₆₇	C₂³	1	2	yes	—
108	C₂×D₈×C₆₇	C₂³	1	4	yes	—
109	C₂×D₈×C₆₇	C₂³	1	4	yes	—
110	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
111	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
112	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
113	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
116	#127×C₆₇	—	2	4	no	—
117	#127×C₆₇	D₄	1	1	yes	characteristic
118	#127×C₆₇	C₂³	1	1	yes	characteristic
119	#127×C₆₇	C₂³	1	1	yes	characteristic
120	#127×C₆₇	C₂³	1	1	yes	characteristic
121	#124×C₆₇	—	2	4	no	—
122	#124×C₆₇	—	2	4	no	—
123	#124×C₆₇	—	2	4	no	—
124	#124×C₆₇	—	2	1	no	—
125	#124×C₆₇	—	2	1	no	—
126	#124×C₆₇	D₄	1	2	yes	—
127	#124×C₆₇	C₂³	1	2	yes	—
128	#123×C₆₇	—	2	4	no	—
129	#123×C₆₇	—	2	4	no	—
130	C₂²⋊Q₈×C₆₇	—	2	2	no	—
131	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
132	#121×C₆₇	—	2	4	no	—
133	#121×C₆₇	—	2	2	no	—
134	#121×C₆₇	—	2	2	no	—
135	#121×C₆₇	—	2	2	no	—
136	#121×C₆₇	—	2	2	no	—
137	#121×C₆₇	—	2	1	no	—
138	#121×C₆₇	—	2	1	no	—
139	#121×C₆₇	—	2	1	no	—
140	#121×C₆₇	—	2	1	no	—
141	#121×C₆₇	—	2	2	no	—
142	#121×C₆₇	—	2	2	no	—
143	#121×C₆₇	—	2	2	no	—
144	#121×C₆₇	—	2	4	no	—
145	#121×C₆₇	D₄	1	2	yes	—
146	#121×C₆₇	D₄	1	2	yes	—
147	#121×C₆₇	C₂³	1	2	yes	—
148	#121×C₆₇	C₂³	1	2	yes	—
149	#121×C₆₇	C₂³	1	4	yes	—
150	#121×C₆₇	C₂³	1	4	yes	—
151	#121×C₆₇	C₂³	1	4	yes	—
152	#120×C₆₇	—	2	4	no	—
153	#120×C₆₇	—	2	4	no	—
154	#120×C₆₇	—	2	4	no	—
155	#120×C₆₇	—	2	4	no	—
156	#120×C₆₇	—	2	4	no	—
157	#120×C₆₇	—	2	4	no	—
158	C₄×D₄×C₆₇	—	2	1	no	—
159	C₄×D₄×C₆₇	—	2	1	no	—
160	C₄×D₄×C₆₇	—	2	1	no	—
161	C₄×D₄×C₆₇	—	2	1	no	—
162	C₄×D₄×C₆₇	—	2	1	no	—
163	C₄×D₄×C₆₇	—	2	1	no	—
164	C₄×D₄×C₆₇	C₂³	1	2	yes	—
165	C₄×D₄×C₆₇	C₂³	1	2	yes	—
166	C₄×D₄×C₆₇	C₂³	1	2	yes	—
167	C₄×D₄×C₆₇	C₂³	1	2	yes	—
168	C₄×D₄×C₆₇	C₂³	1	2	yes	—
169	C₄×D₄×C₆₇	C₂³	1	2	yes	—
170	#117×C₆₇	—	2	2	no	—
171	#117×C₆₇	—	2	2	no	—
172	#117×C₆₇	C₂³	1	4	yes	—
173	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
176	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
177	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
178	#107×C₆₇	C₂³	1	2	yes	—
179	#107×C₆₇	C₂³	1	2	yes	—
180	#106×C₆₇	C₂³	1	4	yes	—
181	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
182	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
183	#103×C₆₇	C₂³	1	4	yes	—
184	#103×C₆₇	C₂³	1	4	yes	—
185	#102×C₆₇	C₂³	1	2	yes	—
186	#102×C₆₇	C₂³	1	4	yes	—
187	#102×C₆₇	C₂³	1	4	yes	—
188	#102×C₆₇	C₂³	1	4	yes	—
189	#102×C₆₇	C₂³	1	2	yes	—
190	#102×C₆₇	C₂³	1	4	yes	—
191	#102×C₆₇	C₂³	1	2	yes	—
192	#102×C₆₇	C₂³	1	2	yes	—
193	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
194	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
195	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
196	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
197	#97×C₆₇	C₂³	1	2	yes	—
198	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
199	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
200	C₂⁴×C₆₇	—	2	1	no	—
201	C₂⁴×C₆₇	—	2	4	no	—
202	C₂⁴×C₆₇	—	2	4	no	—
203	#41×C₆₇	—	2	8	no	—
204	#41×C₆₇	—	4	4	no	—
205	#41×C₆₇	—	4	4	no	—
206	#41×C₆₇	—	4	4	no	—
207	#41×C₆₇	—	4	8	no	—
208	#41×C₆₇	—	8	2	no	—
209	#41×C₆₇	—	8	2	no	—
210	C₂×Q₈×C₆₇	—	2	1	no	—
211	C₂×Q₈×C₆₇	—	2	1	no	—
212	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
213	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
214	C₂×D₄×C₆₇	—	2	4	no	—
215	C₂×D₄×C₆₇	—	2	8	no	—
216	C₂×D₄×C₆₇	—	2	4	no	—
217	C₂×D₄×C₆₇	—	2	2	no	—
218	C₂×D₄×C₆₇	—	2	4	no	—
219	C₂×D₄×C₆₇	—	2	4	no	—
220	C₂×D₄×C₆₇	—	2	4	no	—
221	C₂×D₄×C₆₇	—	2	2	no	—
222	C₂×D₄×C₆₇	—	2	2	no	—
223	C₂×D₄×C₆₇	—	2	1	no	—
224	C₂×D₄×C₆₇	—	2	1	no	—
225	C₂×D₄×C₆₇	—	2	1	no	—
226	C₂×D₄×C₆₇	—	2	1	no	—
227	C₂×D₄×C₆₇	—	2	4	no	—
228	C₂×D₄×C₆₇	—	2	1	no	—
229	C₂×D₄×C₆₇	—	2	1	no	—
230	C₂×D₄×C₆₇	—	2	1	no	—
231	C₂×D₄×C₆₇	—	2	4	no	—
232	C₂×D₄×C₆₇	—	4	4	no	—
233	C₂×D₄×C₆₇	—	4	4	no	—
234	C₂×D₄×C₆₇	—	4	4	no	—
235	C₂×D₄×C₆₇	—	4	8	no	—
236	C₂×D₄×C₆₇	—	4	16	no	—
237	C₂×D₄×C₆₇	—	8	4	no	—
238	C₂×D₄×C₆₇	—	8	4	no	—
239	C₂×D₄×C₆₇	—	8	4	no	—
240	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
241	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
242	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
243	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
244	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
245	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
246	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
247	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₆₇	—	2	1	no	—
249	C₂²×C₄×C₆₇	—	2	4	no	—
250	C₂²×C₄×C₆₇	—	2	2	no	—
251	C₂²×C₄×C₆₇	—	2	2	no	—
252	C₂²×C₄×C₆₇	—	2	2	no	—
253	C₂²×C₄×C₆₇	—	2	2	no	—
254	C₂²×C₄×C₆₇	—	2	2	no	—
255	C₂²×C₄×C₆₇	—	8	2	no	—
256	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
260	SD₁₆×C₆₇	—	4	4	no	—
261	SD₁₆×C₆₇	—	4	4	no	—
262	D₈×C₆₇	—	2	4	no	—
263	D₈×C₆₇	—	2	8	no	—
264	D₈×C₆₇	—	2	4	no	—
265	D₈×C₆₇	—	4	4	no	—
266	D₈×C₆₇	—	4	4	no	—
267	M₁₆×C₆₇	—	4	4	no	—
268	C₂×C₈×C₆₇	—	4	4	no	—
269	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
270	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
271	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
272	C₄⋊C₄×C₆₇	—	2	1	no	—
273	C₄⋊C₄×C₆₇	—	2	4	no	—
274	C₄⋊C₄×C₆₇	—	2	1	no	—
275	C₄⋊C₄×C₆₇	—	2	1	no	—
276	C₄⋊C₄×C₆₇	—	2	1	no	—
277	C₄⋊C₄×C₆₇	—	2	1	no	—
278	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
283	C₂²⋊C₄×C₆₇	—	2	4	no	—
284	C₂²⋊C₄×C₆₇	—	2	4	no	—
285	C₂²⋊C₄×C₆₇	—	2	2	no	—
286	C₂²⋊C₄×C₆₇	—	2	2	no	—
287	C₂²⋊C₄×C₆₇	—	2	2	no	—
288	C₂²⋊C₄×C₆₇	—	2	4	no	—
289	C₂²⋊C₄×C₆₇	—	2	4	no	—
290	C₂²⋊C₄×C₆₇	—	2	4	no	—
291	C₂²⋊C₄×C₆₇	—	2	2	no	—
292	C₂²⋊C₄×C₆₇	—	2	2	no	—
293	C₂²⋊C₄×C₆₇	—	2	2	no	—
294	C₂²⋊C₄×C₆₇	—	2	2	no	—
295	C₂²⋊C₄×C₆₇	—	2	2	no	—
296	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
297	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
298	C₄²×C₆₇	—	2	4	no	—
299	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
302	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
303	C₂³×C₆₇	—	2	4	no	—
304	C₂³×C₆₇	—	2	2	no	—
305	C₂³×C₆₇	—	2	2	no	—
306	C₂³×C₆₇	—	2	2	no	—
307	C₂³×C₆₇	—	2	2	no	—
308	C₂³×C₆₇	—	4	8	no	—
309	C₂³×C₆₇	—	8	1	no	—
310	C₂³×C₆₇	—	8	1	no	—
311	C₂³×C₆₇	—	8	4	no	—
312	C₂³×C₆₇	—	8	4	no	—
313	C₂³×C₆₇	—	8	4	no	—
314	C₂³×C₆₇	—	8	4	no	—
315	C₂³×C₆₇	—	8	4	no	—
316	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
317	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
318	Q₈×C₆₇	—	2	4	no	—
319	Q₈×C₆₇	—	4	2	no	—
320	Q₈×C₆₇	—	8	1	no	—
321	Q₈×C₆₇	—	8	1	no	—
322	D₄×C₆₇	—	2	4	no	—
323	D₄×C₆₇	—	2	4	no	—
324	D₄×C₆₇	—	2	2	no	—
325	D₄×C₆₇	—	2	2	no	—
326	D₄×C₆₇	—	2	4	no	—
327	D₄×C₆₇	—	2	2	no	—
328	D₄×C₆₇	—	2	4	no	—
329	D₄×C₆₇	—	4	2	no	—
330	D₄×C₆₇	—	4	4	no	—
331	D₄×C₆₇	—	4	2	no	—
332	D₄×C₆₇	—	4	8	no	—
333	D₄×C₆₇	—	4	2	no	—
334	D₄×C₆₇	—	4	8	no	—
335	D₄×C₆₇	—	4	4	no	—
336	D₄×C₆₇	—	4	2	no	—
337	D₄×C₆₇	—	4	2	no	—
338	D₄×C₆₇	—	8	1	no	—
339	D₄×C₆₇	—	8	4	no	—
340	D₄×C₆₇	—	8	1	no	—
341	D₄×C₆₇	—	8	1	no	—
342	D₄×C₆₇	—	8	4	no	—
343	D₄×C₆₇	—	8	4	no	—
344	D₄×C₆₇	—	8	4	no	—
345	D₄×C₆₇	—	8	2	no	—
346	D₄×C₆₇	—	8	2	no	—
347	D₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
348	C₂×C₄×C₆₇	—	2	2	no	—
349	C₂×C₄×C₆₇	—	2	4	no	—
350	C₂×C₄×C₆₇	—	2	4	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	2	no	—
353	C₂×C₄×C₆₇	—	2	2	no	—
354	C₂×C₄×C₆₇	—	2	2	no	—
355	C₂×C₄×C₆₇	—	2	2	no	—
356	C₂×C₄×C₆₇	—	4	1	no	—
357	C₂×C₄×C₆₇	—	4	8	no	—
358	C₂×C₄×C₆₇	—	4	4	no	—
359	C₂×C₄×C₆₇	—	4	4	no	—
360	C₂×C₄×C₆₇	—	4	4	no	—
361	C₂×C₄×C₆₇	—	4	4	no	—
362	C₂×C₄×C₆₇	—	8	2	no	—
363	C₂×C₄×C₆₇	—	8	1	no	—
364	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
365	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
371	C₈×C₆₇	—	2	2	no	—
372	C₈×C₆₇	—	2	4	no	—
373	C₈×C₆₇	—	2	2	no	—
374	C₂²×C₆₇	—	2	1	no	—
375	C₂²×C₆₇	—	2	4	no	—
376	C₂²×C₆₇	—	2	1	no	—
377	C₂²×C₆₇	—	2	4	no	—
378	C₂²×C₆₇	—	2	4	no	—
379	C₂²×C₆₇	—	2	1	no	—
380	C₂²×C₆₇	—	2	4	no	—
381	C₂²×C₆₇	—	4	2	no	—
382	C₂²×C₆₇	—	4	2	no	—
383	C₂²×C₆₇	—	4	2	no	—
384	C₂²×C₆₇	—	4	2	no	—
385	C₂²×C₆₇	—	4	2	no	—
386	C₂²×C₆₇	—	4	2	no	—
387	C₂²×C₆₇	—	4	2	no	—
388	C₂²×C₆₇	—	4	2	no	—
389	C₂²×C₆₇	—	4	2	no	—
390	C₂²×C₆₇	—	4	2	no	—
391	C₂²×C₆₇	—	4	2	no	—
392	C₂²×C₆₇	—	8	4	no	—
393	C₂²×C₆₇	—	16	8	no	—
394	C₂²×C₆₇	—	16	8	no	—
395	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
396	C₄×C₆₇	—	2	1	no	—
397	C₄×C₆₇	—	2	1	no	—
398	C₄×C₆₇	—	2	1	no	—
399	C₄×C₆₇	—	2	4	no	—
400	C₄×C₆₇	—	2	1	no	—
401	C₄×C₆₇	—	4	2	no	—
402	C₄×C₆₇	—	4	2	no	—
403	C₄×C₆₇	—	4	2	no	—
404	C₄×C₆₇	—	4	2	no	—
405	C₄×C₆₇	#576	1	2	yes	—
406	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
407	#61679	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
408	C₂×C₆₇	—	4	1	no	—
409	C₂×C₆₇	—	4	4	no	—
410	C₂×C₆₇	—	4	4	no	—
411	C₂×C₆₇	—	8	2	no	—
412	C₂×C₆₇	—	8	2	no	—
413	C₂×C₆₇	—	8	2	no	—
414	C₂×C₆₇	#3484	1	1	yes	characteristic
415	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
416	C₂×C₆₇	#3585	1	1	yes	characteristic
417	#3549	C₂×C₆₇	1	1	yes	characteristic, complemented
418	#3496	C₂×C₆₇	1	1	yes	characteristic, complemented
419	#3325	C₂×C₆₇	1	2	yes	complemented
420	#3319	C₂×C₆₇	1	4	yes	complemented
421	#3303	C₂×C₆₇	1	2	yes	complemented
422	D₄×D₈	C₂×C₆₇	1	2	yes	complemented
423	#3272	C₂×C₆₇	1	2	yes	complemented
424	#3264	C₂×C₆₇	1	4	yes	complemented
425	#3214	C₂×C₆₇	1	1	yes	characteristic, complemented
426	#3207	C₂×C₆₇	1	1	yes	characteristic, complemented
427	#3198	C₂×C₆₇	1	4	yes	complemented
428	#3109	C₂×C₆₇	1	1	yes	characteristic, complemented
429	#3100	C₂×C₆₇	1	1	yes	characteristic, complemented
430	#3008	C₂×C₆₇	1	4	yes	complemented
431	#2981	C₂×C₆₇	1	1	yes	characteristic, complemented
432	C₆₇	#61679	1	1	yes	characteristic, direct product factor, Sylow
433	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	complemented
434	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
435	C₂²×D₈	C₂²×C₆₇	1	4	yes	complemented
436	H(3,𝔽₄)	—	2	2	no	—
437	#555	—	2	1	no	—
438	#555	C₂²×C₆₇	1	2	yes	complemented
439	#555	C₂²×C₆₇	1	2	yes	complemented
440	#547	—	2	1	no	—
441	#547	C₂²×C₆₇	1	2	yes	complemented
442	#546	—	2	2	no	—
443	#546	C₂²×C₆₇	1	4	yes	complemented
444	D₄²	—	2	1	no	—
445	D₄²	—	2	1	no	—
446	D₄²	C₂²×C₆₇	1	2	yes	complemented
447	D₄²	C₂²×C₆₇	1	2	yes	complemented
448	D₄²	C₂²×C₆₇	1	2	yes	complemented
449	#537	C₂²×C₆₇	1	2	yes	complemented
450	#535	—	2	2	no	—
451	#535	—	2	2	no	—
452	#535	C₂²×C₆₇	1	4	yes	complemented
453	#534	—	2	2	no	—
454	#532	C₂²×C₆₇	1	1	yes	characteristic
455	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
456	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
457	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
458	C₂×#121	—	2	2	no	—
459	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
460	#496	C₂²×C₆₇	1	2	yes	complemented
461	#493	C₂²×C₆₇	1	1	yes	characteristic, complemented
462	#492	C₂²×C₆₇	1	1	yes	characteristic, complemented
463	#489	C₂²×C₆₇	1	2	yes	complemented
464	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
465	#486	C₂²×C₆₇	1	1	yes	characteristic, complemented
466	#485	C₂²×C₆₇	1	4	yes	complemented
467	#482	C₂²×C₆₇	1	4	yes	complemented
468	#481	C₂²×C₆₇	1	2	yes	complemented
469	#480	C₂²×C₆₇	1	2	yes	complemented
470	#476	C₂²×C₆₇	1	2	yes	complemented
471	#474	C₂²×C₆₇	1	2	yes	complemented
472	#469	C₂²×C₆₇	1	4	yes	complemented
473	#468	C₂²×C₆₇	1	4	yes	complemented
474	#466	C₂²×C₆₇	1	4	yes	complemented
475	#465	C₂²×C₆₇	1	4	yes	complemented
476	#463	C₂²×C₆₇	1	4	yes	complemented
477	#461	C₂²×C₆₇	1	2	yes	complemented
478	#459	C₂²×C₆₇	1	2	yes	complemented
479	#459	C₂²×C₆₇	1	2	yes	complemented
480	#459	C₂²×C₆₇	1	2	yes	complemented
481	#450	C₂²×C₆₇	1	4	yes	complemented
482	#449	C₂²×C₆₇	1	4	yes	complemented
483	#449	C₂²×C₆₇	1	4	yes	complemented
484	#449	C₂²×C₆₇	1	4	yes	complemented
485	#449	C₂²×C₆₇	1	4	yes	complemented
486	#447	C₂²×C₆₇	1	2	yes	complemented
487	#447	C₂²×C₆₇	1	2	yes	complemented
488	#447	C₂²×C₆₇	1	4	yes	complemented
489	#447	C₂²×C₆₇	1	4	yes	complemented
490	#447	C₂²×C₆₇	1	4	yes	complemented
491	#442	C₂²×C₆₇	1	4	yes	complemented
492	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
493	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
494	#436	C₂²×C₆₇	1	2	yes	complemented
495	#435	C₂²×C₆₇	1	4	yes	complemented
496	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
497	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
498	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
499	#418	C₂²×C₆₇	1	4	yes	complemented
500	#416	C₂²×C₆₇	1	4	yes	complemented
501	#408	C₂²×C₆₇	1	4	yes	complemented
502	H(5,𝔽₂)	—	4	8	no	—
503	C₂×#41	—	2	2	no	—
504	C₂×#41	—	2	1	no	—
505	C₂×#41	—	2	1	no	—
506	C₂×#41	C₂³×C₆₇	1	4	yes	—
507	C₂×#41	C₂³×C₆₇	1	2	yes	—
508	C₂×#41	C₂³×C₆₇	1	2	yes	—
509	C₂²×D₄	—	2	4	no	—
510	C₂²×D₄	—	2	2	no	—
511	C₂²×D₄	—	2	2	no	—
512	C₂²×D₄	—	2	2	no	—
513	C₂²×D₄	—	2	2	no	—
514	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
515	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
516	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
517	C₂³×C₄	—	2	1	no	—
518	AGL(1,ℤ/8)	—	4	8	no	—
519	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
520	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
521	C₂×D₈	—	4	8	no	—
522	C₂×D₈	C₂³×C₆₇	1	2	yes	—
523	C₂×D₈	C₂³×C₆₇	1	4	yes	—
524	C₂×D₈	C₂³×C₆₇	1	2	yes	—
525	C₂×D₈	C₂³×C₆₇	1	4	yes	—
526	C₂×D₈	C₂³×C₆₇	1	4	yes	—
527	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
528	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
529	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
530	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
531	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
532	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
533	#127	—	2	4	no	—
534	#127	D₄×C₆₇	1	1	yes	characteristic
535	#127	C₂³×C₆₇	1	1	yes	characteristic
536	#127	C₂³×C₆₇	1	1	yes	characteristic
537	#127	C₂³×C₆₇	1	1	yes	characteristic
538	#124	—	2	4	no	—
539	#124	—	2	4	no	—
540	#124	—	2	4	no	—
541	#124	—	2	1	no	—
542	#124	—	2	1	no	—
543	#124	D₄×C₆₇	1	2	yes	—
544	#124	C₂³×C₆₇	1	2	yes	—
545	#123	—	2	4	no	—
546	#123	—	2	4	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
549	#121	—	2	4	no	—
550	#121	—	2	2	no	—
551	#121	—	2	2	no	—
552	#121	—	2	2	no	—
553	#121	—	2	2	no	—
554	#121	—	2	1	no	—
555	#121	—	2	1	no	—
556	#121	—	2	1	no	—
557	#121	—	2	1	no	—
558	#121	—	2	2	no	—
559	#121	—	2	2	no	—
560	#121	—	2	2	no	—
561	#121	—	2	4	no	—
562	#121	D₄×C₆₇	1	2	yes	—
563	#121	D₄×C₆₇	1	2	yes	—
564	#121	C₂³×C₆₇	1	2	yes	—
565	#121	C₂³×C₆₇	1	2	yes	—
566	#121	C₂³×C₆₇	1	4	yes	—
567	#121	C₂³×C₆₇	1	4	yes	—
568	#121	C₂³×C₆₇	1	4	yes	—
569	#120	—	2	4	no	—
570	#120	—	2	4	no	—
571	#120	—	2	4	no	—
572	#120	—	2	4	no	—
573	#120	—	2	4	no	—
574	#120	—	2	4	no	—
575	C₄×D₄	—	2	1	no	—
576	C₄×D₄	—	2	1	no	—
577	C₄×D₄	—	2	1	no	—
578	C₄×D₄	—	2	1	no	—
579	C₄×D₄	—	2	1	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	C₂³×C₆₇	1	2	yes	—
582	C₄×D₄	C₂³×C₆₇	1	2	yes	—
583	C₄×D₄	C₂³×C₆₇	1	2	yes	—
584	C₄×D₄	C₂³×C₆₇	1	2	yes	—
585	C₄×D₄	C₂³×C₆₇	1	2	yes	—
586	C₄×D₄	C₂³×C₆₇	1	2	yes	—
587	#117	—	2	2	no	—
588	#117	—	2	2	no	—
589	#117	C₂³×C₆₇	1	4	yes	—
590	C₂×C₄⋊C₄	—	2	2	no	—
591	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
592	C₂×C₂²⋊C₄	—	2	1	no	—
593	C₂×C₂²⋊C₄	—	2	4	no	—
594	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
595	#107	C₂³×C₆₇	1	2	yes	—
596	#107	C₂³×C₆₇	1	2	yes	—
597	#106	C₂³×C₆₇	1	4	yes	—
598	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
599	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
600	#103	C₂³×C₆₇	1	4	yes	—
601	#103	C₂³×C₆₇	1	4	yes	—
602	#102	C₂³×C₆₇	1	2	yes	—
603	#102	C₂³×C₆₇	1	4	yes	—
604	#102	C₂³×C₆₇	1	2	yes	—
605	#102	C₂³×C₆₇	1	4	yes	—
606	#102	C₂³×C₆₇	1	4	yes	—
607	#102	C₂³×C₆₇	1	2	yes	—
608	#102	C₂³×C₆₇	1	2	yes	—
609	#102	C₂³×C₆₇	1	4	yes	—
610	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
611	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
612	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
613	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
614	#97	C₂³×C₆₇	1	2	yes	—
615	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
616	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
617	C₂⁴	—	2	1	no	—
618	C₂⁴	—	2	4	no	—
619	C₂⁴	—	2	4	no	—
620	#41	—	2	8	no	—
621	#41	—	4	4	no	—
622	#41	—	4	4	no	—
623	#41	—	4	4	no	—
624	#41	—	4	8	no	—
625	#41	—	8	2	no	—
626	#41	—	8	2	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
630	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	8	no	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	2	no	—
639	C₂×D₄	—	2	2	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	1	no	—
647	C₂×D₄	—	2	1	no	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	4	4	no	—
650	C₂×D₄	—	4	4	no	—
651	C₂×D₄	—	4	4	no	—
652	C₂×D₄	—	4	8	no	—
653	C₂×D₄	—	4	16	no	—
654	C₂×D₄	—	8	4	no	—
655	C₂×D₄	—	8	4	no	—
656	C₂×D₄	—	8	4	no	—
657	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
658	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
659	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
660	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
661	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
662	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
663	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
664	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	8	2	no	—
673	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
674	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
677	SD₁₆	—	4	4	no	—
678	SD₁₆	—	4	4	no	—
679	D₈	—	2	4	no	—
680	D₈	—	2	8	no	—
681	D₈	—	2	4	no	—
682	D₈	—	4	4	no	—
683	D₈	—	4	4	no	—
684	M₁₆	—	4	4	no	—
685	C₂×C₈	—	4	4	no	—
686	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
687	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
688	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
696	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
697	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
698	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
699	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	2	no	—
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	—	2	2	no	—
711	C₂²⋊C₄	—	2	2	no	—
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
714	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
715	C₄²	—	2	4	no	—
716	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
717	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
718	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
719	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
720	C₂³	—	2	4	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	4	8	no	—
726	C₂³	—	8	1	no	—
727	C₂³	—	8	1	no	—
728	C₂³	—	8	4	no	—
729	C₂³	—	8	4	no	—
730	C₂³	—	8	4	no	—
731	C₂³	—	8	4	no	—
732	C₂³	—	8	4	no	—
733	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
734	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
735	Q₈	—	2	4	no	—
736	Q₈	—	4	2	no	—
737	Q₈	—	8	1	no	—
738	Q₈	—	8	1	no	—
739	D₄	—	2	4	no	—
740	D₄	—	2	4	no	—
741	D₄	—	2	2	no	—
742	D₄	—	2	2	no	—
743	D₄	—	2	4	no	—
744	D₄	—	2	2	no	—
745	D₄	—	2	4	no	—
746	D₄	—	4	2	no	—
747	D₄	—	4	4	no	—
748	D₄	—	4	2	no	—
749	D₄	—	4	8	no	—
750	D₄	—	4	2	no	—
751	D₄	—	4	8	no	—
752	D₄	—	4	4	no	—
753	D₄	—	4	2	no	—
754	D₄	—	4	2	no	—
755	D₄	—	8	4	no	—
756	D₄	—	8	1	no	—
757	D₄	—	8	1	no	—
758	D₄	—	8	1	no	—
759	D₄	—	8	4	no	—
760	D₄	—	8	4	no	—
761	D₄	—	8	4	no	—
762	D₄	—	8	2	no	—
763	D₄	—	8	2	no	—
764	D₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	4	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	8	no	—
775	C₂×C₄	—	4	4	no	—
776	C₂×C₄	—	4	4	no	—
777	C₂×C₄	—	4	4	no	—
778	C₂×C₄	—	4	4	no	—
779	C₂×C₄	—	8	2	no	—
780	C₂×C₄	—	8	1	no	—
781	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
782	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
784	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
785	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
786	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
787	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
788	C₈	—	2	2	no	—
789	C₈	—	2	4	no	—
790	C₈	—	2	2	no	—
791	C₂²	—	2	1	no	—
792	C₂²	—	2	4	no	—
793	C₂²	—	2	1	no	—
794	C₂²	—	2	4	no	—
795	C₂²	—	2	1	no	—
796	C₂²	—	2	4	no	—
797	C₂²	—	2	4	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	8	4	no	—
810	C₂²	—	16	8	no	—
811	C₂²	—	16	8	no	—
812	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
813	C₄	—	2	1	no	—
814	C₄	—	2	1	no	—
815	C₄	—	2	1	no	—
816	C₄	—	2	1	no	—
817	C₄	—	2	4	no	—
818	C₄	—	4	2	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	2	no	—
822	C₄	#576×C₆₇	1	2	yes	—
823	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
824	C₂	—	4	1	no	—
825	C₂	—	4	4	no	—
826	C₂	—	4	4	no	—
827	C₂	—	8	2	no	—
828	C₂	—	8	2	no	—
829	C₂	—	8	2	no	—
830	C₂	C₆₇×#3484	1	1	yes	characteristic
831	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
832	C₂	C₆₇×#3585	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. C₆₇×#3549	C₂	semidirect
2. C₆₇×#3496	C₂	semidirect
3. C₆₇×#3325	C₂	semidirect
4. C₆₇×#3319	C₂	semidirect
5. C₆₇×#3303	C₂	semidirect
6. D₄×D₈×C₆₇	C₂	semidirect
7. C₆₇×#3272	C₂	semidirect
8. C₆₇×#3264	C₂	semidirect
9. C₆₇×#3214	C₂	semidirect
10. C₆₇×#3207	C₂	semidirect
11. C₆₇×#3198	C₂	semidirect
12. C₆₇×#3109	C₂	semidirect
13. C₆₇×#3100	C₂	semidirect
14. C₆₇×#3008	C₂	semidirect
15. C₆₇×#2981	C₂	semidirect
16. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
17. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
18. C₂²×D₈×C₆₇	C₂²	semidirect
21. #555×C₆₇	C₂²	semidirect
22. #555×C₆₇	C₂²	semidirect
24. #547×C₆₇	C₂²	semidirect
26. #546×C₆₇	C₂²	semidirect
29. D₄²×C₆₇	C₂²	semidirect
30. D₄²×C₆₇	C₂²	semidirect
31. D₄²×C₆₇	C₂²	semidirect
32. #537×C₆₇	C₂²	semidirect
35. #535×C₆₇	C₂²	semidirect
38. #532×C₆₇	C₂²	semidirect
39. #532×C₆₇	C₂²	semidirect
40. #532×C₆₇	C₂²	semidirect
42. C₂×C₄×D₄×C₆₇	C₂²	semidirect
43. #496×C₆₇	C₂²	semidirect
44. #493×C₆₇	C₂²	semidirect
45. #492×C₆₇	C₂²	semidirect
46. #489×C₆₇	C₂²	semidirect
47. #487×C₆₇	C₂²	semidirect
48. #486×C₆₇	C₂²	semidirect
49. #485×C₆₇	C₂²	semidirect
50. #482×C₆₇	C₂²	semidirect
51. #481×C₆₇	C₂²	semidirect
52. #480×C₆₇	C₂²	semidirect
53. #476×C₆₇	C₂²	semidirect
54. #474×C₆₇	C₂²	semidirect
55. #469×C₆₇	C₂²	semidirect
56. #468×C₆₇	C₂²	semidirect
57. #466×C₆₇	C₂²	semidirect
58. #465×C₆₇	C₂²	semidirect
59. #463×C₆₇	C₂²	semidirect
60. #461×C₆₇	C₂²	semidirect
61. #459×C₆₇	C₂²	semidirect
62. #459×C₆₇	C₂²	semidirect
63. #459×C₆₇	C₂²	semidirect
64. #450×C₆₇	C₂²	semidirect
65. #449×C₆₇	C₂²	semidirect
66. #449×C₆₇	C₂²	semidirect
67. #449×C₆₇	C₂²	semidirect
68. #449×C₆₇	C₂²	semidirect
69. #447×C₆₇	C₂²	semidirect
70. #447×C₆₇	C₂²	semidirect
71. #447×C₆₇	C₂²	semidirect
72. #447×C₆₇	C₂²	semidirect
73. #447×C₆₇	C₂²	semidirect
74. #442×C₆₇	C₂²	semidirect
75. C₄×D₈×C₆₇	C₂²	semidirect
76. C₄×D₈×C₆₇	C₂²	semidirect
77. #436×C₆₇	C₂²	semidirect
78. #435×C₆₇	C₂²	semidirect
79. C₈×D₄×C₆₇	C₂²	semidirect
80. #432×C₆₇	C₂²	semidirect
81. #431×C₆₇	C₂²	semidirect
82. #418×C₆₇	C₂²	semidirect
83. #416×C₆₇	C₂²	semidirect
84. #408×C₆₇	C₂²	semidirect
407. #61679	C₆₇	direct (N × H)
417. #3549	C₂×C₆₇	semidirect
418. #3496	C₂×C₆₇	semidirect
419. #3325	C₂×C₆₇	semidirect
420. #3319	C₂×C₆₇	semidirect
421. #3303	C₂×C₆₇	semidirect
422. D₄×D₈	C₂×C₆₇	semidirect
423. #3272	C₂×C₆₇	semidirect
424. #3264	C₂×C₆₇	semidirect
425. #3214	C₂×C₆₇	semidirect
426. #3207	C₂×C₆₇	semidirect
427. #3198	C₂×C₆₇	semidirect
428. #3109	C₂×C₆₇	semidirect
429. #3100	C₂×C₆₇	semidirect
430. #3008	C₂×C₆₇	semidirect
431. #2981	C₂×C₆₇	semidirect
432. C₆₇	#61679	direct (N × H)
433. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
434. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
435. C₂²×D₈	C₂²×C₆₇	semidirect
438. #555	C₂²×C₆₇	semidirect
439. #555	C₂²×C₆₇	semidirect
441. #547	C₂²×C₆₇	semidirect
443. #546	C₂²×C₆₇	semidirect
446. D₄²	C₂²×C₆₇	semidirect
447. D₄²	C₂²×C₆₇	semidirect
448. D₄²	C₂²×C₆₇	semidirect
449. #537	C₂²×C₆₇	semidirect
452. #535	C₂²×C₆₇	semidirect
455. #532	C₂²×C₆₇	semidirect
456. #532	C₂²×C₆₇	semidirect
457. #532	C₂²×C₆₇	semidirect
459. C₂×C₄×D₄	C₂²×C₆₇	semidirect
460. #496	C₂²×C₆₇	semidirect
461. #493	C₂²×C₆₇	semidirect
462. #492	C₂²×C₆₇	semidirect
463. #489	C₂²×C₆₇	semidirect
464. #487	C₂²×C₆₇	semidirect
465. #486	C₂²×C₆₇	semidirect
466. #485	C₂²×C₆₇	semidirect
467. #482	C₂²×C₆₇	semidirect
468. #481	C₂²×C₆₇	semidirect
469. #480	C₂²×C₆₇	semidirect
470. #476	C₂²×C₆₇	semidirect
471. #474	C₂²×C₆₇	semidirect
472. #469	C₂²×C₆₇	semidirect
473. #468	C₂²×C₆₇	semidirect
474. #466	C₂²×C₆₇	semidirect
475. #465	C₂²×C₆₇	semidirect
476. #463	C₂²×C₆₇	semidirect
477. #461	C₂²×C₆₇	semidirect
478. #459	C₂²×C₆₇	semidirect
479. #459	C₂²×C₆₇	semidirect
480. #459	C₂²×C₆₇	semidirect
481. #450	C₂²×C₆₇	semidirect
482. #449	C₂²×C₆₇	semidirect
483. #449	C₂²×C₆₇	semidirect
484. #449	C₂²×C₆₇	semidirect
485. #449	C₂²×C₆₇	semidirect
486. #447	C₂²×C₆₇	semidirect
487. #447	C₂²×C₆₇	semidirect
488. #447	C₂²×C₆₇	semidirect
489. #447	C₂²×C₆₇	semidirect
490. #447	C₂²×C₆₇	semidirect
491. #442	C₂²×C₆₇	semidirect
492. C₄×D₈	C₂²×C₆₇	semidirect
493. C₄×D₈	C₂²×C₆₇	semidirect
494. #436	C₂²×C₆₇	semidirect
495. #435	C₂²×C₆₇	semidirect
496. C₈×D₄	C₂²×C₆₇	semidirect
497. #432	C₂²×C₆₇	semidirect
498. #431	C₂²×C₆₇	semidirect
499. #418	C₂²×C₆₇	semidirect
500. #416	C₂²×C₆₇	semidirect
501. #408	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3549	2
C₆₇×#3496	2
C₆₇×#3325	2
C₆₇×#3319	2
C₆₇×#3303	2
D₄×D₈×C₆₇	2
C₆₇×#3272	2
C₆₇×#3264	2
C₆₇×#3214	2
C₆₇×#3207	2
C₆₇×#3198	2
C₆₇×#3109	2
C₆₇×#3100	2
C₆₇×#3008	2
C₆₇×#2981	2
#61679	67

Subgroups — C67×#61679 #30740930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61679 #30740930